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Electric field induced predissociation of molecular iodine Zhou, Xiang 1991

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E L E C T R I C FIELD I N D U C E D PREDISSOCIATION OF M O L E C U L A R IODINE By Xiang Zhou B. A . Sc. (Electrical Engineering) Tsinghua University, China A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES PHYSICS We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH C O L U M B I A Sept. 1991 © Xiang Zhou, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia Vancouver, Canada Date: Abstract Electric field induced predissociation of the B 3I10+ electronic state of molecular iodine has been investigated. The flourescence spectra of I2 , corresponding to the upper vibra-tional quantum mumber v'= 4 to v'= 10 have been recorded with and without a high electric field applied. Because these levels have a large natural predissociation, a specially designed high voltage cell has been built and electric fields up to 140kV/cm have been applied in order to observe the induced predissociation. By combining our results with the previous work by Dalby et a/.[10] (from v'— 10 to v'= 22), we have the most complete predissociation data for I2 . Both numerical and semiclassical treatments have been used to analyse the data. The form of the interacting repulsive potential curve, 3 I I i 9 , has been revised. i i Table of Contents Abstract ii List of Tables vi List of Figures viii Acknowledgement x 1 Introduction 1 1.1 What is electric field induced predissociation 1 1.2 The Franck-Condon principle in predissociation 3 1.3 Literature review 4 2 Theory of Predissociation 9 2.1 Stark Hamiltonian and its nature 9 2.2 The Selection rules for predissociation 10 2.3 The expression of the predissociation rate 11 3 Semi-classical Approach of Predissociation Rate 13 3.1 Derivation of predissociation rate 13 3.2 The method to calculate C curve directly 17 4 Experiment Apparatus and Spectrum 19 4.1 Preparation of the experiment 19 4.1.1 Preparation of the high voltage cell 19 ii i 4.1.2 Measurement of the separation of the plates 19 4.1.3 Calibrat ion of the high voltage supply 23 4.1.4 Design of the pumping system 25 4.1.5 Getting clean I 2 27 4.2 Experimental apparatus 28 4.3 Experimental procedure 30 5 Spectrum and Data Analysis 33 5.1 Sample spectrum 33 5.2 Impurities 33 5.3 Data analysis 36 5.3.1 Assignment of the spectrum 36 5.3.2 Calculations 36 5.4 Rotational quantum number dependence 38 5.5 Vibra t ional quantum number dependence 38 6 Numerical Solution 50 6.1 Formulas and constants 50 6.2 Numerical result 54 6.3 F i t t i ng for higher J value 56 6.4 Conclusion 59 Appendices 61 A Experimental Data 61 B Calculated predissociation rate from experiment data 68 iv C The wave function solution of a straight line potential 81 Bibliography 82 v List of Tables 4.1 Table to explain the labels used in the drawing of high voltage cell design 21 4.2 Confirming the correction of the microscope measurement 23 4.3 The measurement of the distance between the electrodes 23 4.4 Measurement of the conversion factor of the test circuit 24 4.5 Calibration of the power supply 25 5.6 Predissociation rates for v = 4 vibronic band 39 5.7 Predissociation rates for v = 5 vibronic band 40 5.8 Predissociation rates for v = 6 vibronic band 41 5.9 Predissociation rates for v = 7 vibronic band 42 5.10 Predissociation rates for v = 8 vibronic band 43 5.11 Predissociation rates for v = 9 vibronic band 44 5.12 v dependence of the predissociation rate 45 5.13 v dependence of the predissociation rate from Dalby's paper 45 5.14 The phase of the electric field induced predissociation rate constant as a function of energy for J = 0 48 6.15 Calculated predissociation rate constants by quantum mechanic method for J = 0 54 6.16 Calculated predissociation rate constants for J = 0(lsd = 0.76, K = 3.149). 56 6.17 Classical turning points for J = 0, 50, 100 effective potential curves. . . 58 6.18 Calculated predissociation rate constants for J = 50(lsd = 0.68, K = 3.755) 59 vi 6.19 Calculated predissociation rate constants for J = 100(lsd = 0.64, K = 5.586) A.20 Constants C%, al and TR used in the calculation of predissociation rate constants /? vii List of Figures 1.1 Potential curves of the X ,B and repulsive C states of molecular iodine. . 2 1.2 Potential curves explaining the action of the Franck-Condon principle in predissociation. The broken-line curves represent the eigenfunctions. . . 4 1.3 Natural predissociation constant al given by Vigue et al 5 1.4 Natural predissociation constant C% given by Vigue et al 6 1.5 Electric field-induced predissociation rate constants given by Sullivan and Dow et al 6 1.6 Electric field-induced predissociation rate constants given by Dalby et al. 7 1.7 The B 3LT0+ state and the deduced 3LT.i9 state potential curves given by Dalby et al 8 3.8 Potential curves showing symbols used in the text 14 4.9 The sketch of the high voltage cell 20 4.10 The simple test circuit 24 4.11 The calibration curve of the power supply. 26 4.12 The design of the pumping and filling system 27 4.13 The performance of the oil diffusion pump at different temperature. . . 28 4.14 Experimental arrangement 29 5.15 The spectrum showing the electric field induced predissociation effect. . 34 5.16 The spectrum showing the direct measurement of the difference signal. . 34 5.17 Fluorescence intensities change due to the impurities in the cell 35 vm 5.18 J dependence for v = 4 vibronic band 39 5.19 J dependence for v = 5 vibronic band 40 5.20 J dependence for v = 6 vibronic band 41 5.21 J dependence for v = 7 vibronic band 42 5.22 J dependence for v = 8 vibronic band 43 5.23 J dependence for v = 9 vibronic band 44 5.24 The measured predissociation rate constants /? for J = 0 as a function of vibrational quantum number of the B state of molecular iodine 46 5.25 The measured predissociation rate constants /3 for J = 50 as a function of vibrational quantum number of the B state of molecular iodine 46 5.26 The measured predissociation rate constants /? for J = 100 as a function of vibrational quantum number of the B state of molecular iodine. . . . 47 5.27 The phase (defined in Section 3.2) of the electric field induced predissoci-ation rate constant as a function of energy for J = 0 49 6.28 B state wave function for v' = 5, E' = 667.88cm - 1 and C state wave-function for slope = 9.77 x 1 0 4 c m - 1 / A , intercept = 3.064 A and E' = 667.88cm"1 55 6.29 Revised 3 I I i g state potential curve 57 ix Acknowledgement It gives me great pleasure to express my heartfelt thanks to my supervisor, Dr. F. W. Dalby, for his support, guidance and encouragement during the course of the project. I am very grateful to Dr. I. Ozier for his valuable instructions and suggestions. My sincere thanks are also due to Jim Booth and Alak Chanda. Their constant help and valuable sugges-tions were very important for the success of the project. P. Haas and J . Spencer gave many suggestions on improving the design of the high voltage cell; E . Williams did the glassblowing job. I would like to express my thanks to all of them. Thanks also goes to Dr. W. Ho for the useful conversations. x Chapter 1 Introduction 1.1 What is electric field induced predissociation Iodine (I2 ), a diatomic molecule with many desirable properties for spectroscopy study, such as convenient vapor pressure at room temperature, strong absorption spectrum and bright fluorescence spectrum in the visible region, has been intensively researched for about a century[1]. The research on the predissociation has been played an important role on the understanding of the electronic states of I2 . The visible fluorescence spectrum of iodine is due to a transition in the electronic structure of the molecule from the excited state B3LT0+ to the ground state X X E + . Fig. 1.1 shows a sketch of the potential energy curves of the molecule versus the internuclear distance r, for the X and B states. Each state has a set of quantum numbers, v', J' for the B state and v", J" for the X state, to label the vibrational and the rotational levels respectively. Also shown in the graph is the estimated energy of the dissociative 3Hig state by Mulliken[21]; here we call it C state for convenience. If the molecule is excited optically to the upper electronic level, say (B, v', J') state, it may return to the (X, v", J") state by radiative decay, giving rise to a fluorescence spectrum. In addition, in the presence of a dissociating potential curve like C in Fig. 1.1, the excited molecule can be transferred from the (B, v', J') state to C state by some internal or externally induced mechanism. As the result, the molecule does not emit any light, but breaks apart into two atoms[2]. The latter process is called predissociation. 1 Chapter 1. Introduction 2 3 4 5 Internuclear distance r/A Figure 1.1: Potential curves of the X ,B and repulsive C states of molecular iodine. When predissociation occurs, the fluorescence lines from the corresponding energy levels are broadened due to the decrease in the lifetime of the excited state, and the emission from these levels is weakened. The predissociation may be induced by the vibration of the molecule, the coupling of the spin of the electrons with their orbital angular momentum, the rotation of the molecule, etc. This kind of predissociation is known as natural predissociation. A mag-netic field or a electric field can also induce predissociation. In this work, we will mainly discuss electric field induced predissociation. Using the experimentally measured predissociation rate constants, one can deduce information about the upper energy level B, and about the dissociative potential curve C. The latter is the main concern of this thesis. In chapter 2, we will first discuss the usual predissociation theory. Chapter3 is about a semiclassical approach developed by Landau[3] and Child[4,5,6,7,8,9] as to obtain the Chapter 1. Introduction 3 C potential curve from the predissociation data. But some of their approximations might not be appropriate for this work. We will describe our experiment apparatus in Chapter 4. Chapter 5 is devoted to experiment data and data analysis. We will discuss our numerical method and the derived C potential curve in Chapter 6. The previous work of Dalby et al. [10] implies that the C potential curve is almost vertical. Assuming the C state potential curve is a straight line, the wave function of the C state for a given energy should be an as Airy function according to the solution of the Schrodinger equation for the C state(see appendix 3). The wavefunctions for the lower vibrational levels of the B potential curve can also be obtained by semiclassical expressions. With the data of the above two wavefunctions, the predissociation rate was calculated numerically. 1.2 The Franck-Condon principle in predissociation The well-known Franck-Condon principle[2] is: The electron jump in a molecule takes place so rapidly in comparison to the vibrational motion that immediately afterwards the nuclei still have very nearly the same relative position and velocity as before the "jump". The Fig. 1.2 explains the action of the Franck-Condon Principle in predissociation. When the molecule in the state B is in the neighborhood of the point of intersection / with internuclear separation r = R, a transition to the C state is possible without an appreciable alteration of position and momentum, and thus a decomposition of the molecule may take place with a significant probability. The molecule will in general carry out a number of vibrations in the stable state B before it jumps over to the unstable state C while traversing the point of intersection of the two potential curves. If the coupling Hamiltonian is W, the predissociation rate, Tp, is given by the Fermi Chapter 1. Introduction 4 u B r Figure 1.2: Potential curves explaining the action of the Franck-Condon principle in predissociation. The broken-line curves represent the eigenfunctions. Golden rule: where %l>m is the wavefunction of the level m of the stable state B and the ipn is the wavefunction of the level n of the continuum C having the same energy as the level m. So, if xj)m and tpn are known, the predissociation rate can be calculated. 1.3 Literature review The natural predissociation of I 2 has been very well studied[16,17,18]. In order to cal-culate the natural predissociation rate Tyv using Eq. 1.1, the vibrational Hamiltonian Hy, the rotational Hamiltonian HR and the hyperfine Hamiltonian HHFS have to be considered. Beside the HHFS, all the other terms which gives non-diagonal contribution form a group called gyroscopic Hamiltonian HQ- By substituting the HHFS and the Ha (1.1) Chapter 1. Introduction Figure 1.3: Natural predissociation constant a\ given by Vigue eta/.. into Eq. 1.1, a complicated expression for the natural predissociation rate-IV has been derived[16]. Vigue gave an approximation as[22]: TN = C2vJ(J+l) + A.7a2v for even J (1.2) TN = C2VJ(J + 1) + 6.Sa2v for odd J (1.3) where Cv comes from the term HQ, and av from HHFS- The constants 4.7 and 6.8 are obtained numerically. Fig. 1.3 and Fig. 1.4 give the natural predissociation constants a\ and Ci as function of vibrational quantum number v according to Vigue et al. [18]. As early as in 1933, Zener[20] predicted the effect of electric field induced predissoci-ation. The Hamiltonian which causes this effect is called Stark Hamiltonian. This effect was first observed in molecular I2 by Sullivan and Dow[19] in 1979. Fig. 1.5 shows their results. In 1983, Dalby et al.[10] measured the electric field induced predissociation rate con-stant /3 as a function of vibrational quantum number v' from v'= 10 to v'= 22 in electric Chapter 1. Introduction 6 Figure 1.5: Electric field-induced predissociation rate constants given by Sullivan and Dow et ai. Chapter 1. Introduction 7 tO 12 14 16 18 20 22 VIBRATIONAL QUANTUM NUMBER v' Figure 1.6: Electric field-induced predissociation rate constants given by Dalby et al. fields as high as %kV/cm. The electric field induced predissociation. rate constant is defined as: TE = f3E2 (1.4) Where E is electric field strength and YE is electric field induced predissociation rate. Dr. Dalby etc. had determined that the predissociation was caused by coupling to the 3H.i 9 state which is called C state in this paper. Fig. 1.6 shows their experimental data. Using the semiclassical method suggested by Landau[3] and Child[4], they found that the curve of phases of data points against energy is close to a straight line(the word "phase" used here will be explained in detail in Section 3.2). They assumed this linear functional behavior was valid for the electric field induced predissociations of the low lying vibrational levels and derived the 3 IT l 9 state potential curve. Fig. 1.7 shows their assignment of 3 n l s state. Due to the strong natural predissociation of the low lying vibrational levels, a high Chapter 1. Introduction 8 Figure 1.7: The B 3TI 0+ state and the deduced 3 I I i s state potential curves given by Dalby et al. electric field is needed to measure the induced predissociation rate accurately. The task of this work is to measure the electric field induced predissociation of the B state's low lying vibrational levels and revise the 3 I I i 9 potential curve. Chapter 2 Theory of Predissociation There are a few different kinds of predissociations. Here we will only discuss Case I predissociation[2] which is defined to arise from the overlapping of a certain electronic state (that is, of its vibrational or rotational levels) by the dissociation continuum be-longing to another electronic state. In the case of diatomic molecule, we assume that the wave function of the molecule falls into the product of an electron wave function (depending on the distance between the nuclei as a parameter) and a wave function for the motion of the nuclei. According to Landau[3], Eq. 1.1 then becomes: 2TT ZTT r Tp OC — |y X*nuc,l(r)V(r)Xnuc,2(r)dl (2.5) where Xnuc = ri\)nuc (Vw being the wave function of the radial motion of the nuclei) and V(r) is the perturbing energy. 2.1 Stark Hamiltonian and its nature When an electric field E is applied to a molecule, a coupling happens between the electric dipole of the molecule fl and the electric field strength E. The corresponding energy operator is called the Stark Hamiltonian, which is given by Hs = -p-E (2.6) 9 Chapter 2. Theory of Predissociation 10 Substitute this into Eq. 2.5 and taking into account the average of the square of the direction cosine, we have: In the case of a homonuclear diatomic molecule, the molecule has a center of sym-metry. In consequence of this symmetry the electronic eigenfunctions remain either unchanged or only change sign when reflected at the center. In the first case the state to which the eigengunction belongs is called an even state(denoted by g) and in the second case an odd state(denoted by u). 2.2 The Selection rules for predissociation Predissociation is a special case of perturbation. According to perturbation theory, the effect of a perturbation depends on the matrix element of the perturbation function V ; that is it depends on the eigenfunctions tpi and ip2 of the two states involved. The conditions for non-vanishing V 1 2 are called the selection rules. From Eq: 2.7, one can derive the selection rules for electric field induced predissocia-tion. Here the perturbing energy is fiE. The selection rules are[16]: 1. The orbital angular momentum about the internuclear axis A of the two states may differ only by 0 or ± 1; that is, A A = 0, ± 1 . 2. Both states must have the same multiplicity; that is, A S = 0. 3. Both states must have the same component of the spin vector on the internuclear axis E; that is: A E = 0. (2.7) (2.8) Chapter 2. Theory of Predissociation 11 4. The total electronic angular momentum about the internuclear axis, denoted by 0, may differ only by 0 or ± 1; ACl — 0, ± 1 . 5. The total angular momentum J o f the two states may differ only by 0 or ± 1; that is, A J = 0, ± 1 . 6. The two eigenfunctions involved must have different g - u parities; that is, electronic field only couple a g state and a u state, g<-m. 7. The two eigenfunctions involved must have different total parities; that is, +<->-. where selection rules 1, 2 and 3 are only approximatly true. 2.3 The expression of the predissociation rate We use n and n* to denote the populations of the lower and upper energy levels involved in a electronic transition respectively. The equation for the upper level population is: where A: is a constant, I is laser intensity, TR is the radiative decay rate, TN is the natural predissociation rate, Tc is the collision induced predissociation rate, and TE is the electric field induced predissociation rate. dn* = kin - (TR + TN + Tc + TE)n* (2.9) dt = 0, and we can get the upper (2-10) where Tr = TR + TN + Tc- (2-11) Chapter 2. Theory of Predissociation 12 We use EE to denote the fluorescence intensity of the molecules in the presence of a electric field; then we have: and obviously we have EN = TRn* where EN is the fluorescence intensity with the absence of the electric field. From the above two equations, one can easily deduce the expression for the electric field induced predissociation rate as: TE = TT{^T)- (2-14) EN and EE can be measured experimentally. So if Ty is known, TE can be calculated from the experimental data. (2.12) kInTR (2.13) Chapter 3 Semi-classical Approach of Predissociation Rate 3.1 Derivation of predissociation rate Fig. 3.8 shows effective potential energy curves of two electron states of iodine molecule. Uf(r) is a bounded state and Uj(r) is a dissociating potential curve. We use X s ( r ) to represent the wavefunction of the bounded state B for a given energy, and X c ( r ) the wavefunction for the dissociating C state. From equation 2.7, we have the predissociation rate: TE = -j-\J XB(r)»EXc(r)dr (3.15) Because of the large masses of the nuclei their motion is quasi-classical. In general, the "transition point" / at which the transition of the system from one state to the other occurs is determined by classical conservation laws[3]. Since the total energy of the system is conserved in the transition, the condition for it to be "classically possible" is that the potential energies should be equal: UB(r) = Uc{r) (3.16) If the potential energy curves intersect in the classically accessible region (as shown in Fig. 3.8), transition will occur with an appreciable probability (proportional to the F-C overlap integral). Eq. 3.16 can be written in another form: fB = rc, PB = PC (3-17) where p is the momentum of the relative radial motion of the nuclei. When a transition 13 Chapter 3. Semi-classical Approach of Predissociation Rate 14 INTERNUCLEAR SEPARATION r Figure 3.8: Potential curves showing symbols used in the text. occurs, the distance between the nuclei and their relative momentum remain unchanged. The Franck-Condon principle is satisfied. In the semiclassical approximation, we have wave functions[5j: X f l ( r ) = vw° 5 ( l L M r ' ) d r ' -1)' (3-18) x c ( r ) = v ^ ~ccos ( I L p c { r ' ) d r ' ~ i ) ' ( 3 - 1 9 ) XB(^) is normalized to unity. Xc(r) is normalized by the delta function of momentum as: jxlXv'dr = 27rh8(p-p') (3.20) VB and the vc are the velocities of the relative radial motion of the nuclei. By substituting these functions into Eq. 3.15 and following Landau[3], we get 4u; I f°° [ fl f , , 1 fr , ,\ T e = ItflJo icos \ h L M r ) d r + n L P c { r ) d r ) + Chapter 3. Semi-classical Approach of Predissociation Rate 15 cos T I PB(r')dr - \ I pc(r')dr tl J an tl J an \xEdr (3.21) y/VBVc In the neighborhood of the crossing point, pB « pc- The second term in Eq: 3.21, IaBPB(r')dr' — pc{r')dr , remains almost constant while the first term, faBPB(r')dr + Jac Pc(r')dr', keeps increasing. The second term makes main contri-bution to the integral due to the slow varying phase while the first term makes little contribution to the integral due to the fast varying phase. Only the second cosine term which has a slow varying phase is important, so that 2 (3.22) 4u JO C°S\~hJa P B ^ ) ~ * ' PC\r)dr % Jac r^ V ' J y/VBVc When r is away from the crossing point, both cosine terms have rapidly changing phases and the integral converges rapidly. So the argument of the cosine can be expanded in powers of £ = r — R. Since at the point of intersection, PB — Pc = 0, we have \ [ PB{r')dr> - \ f Pc(r')dr' « * B - d>c + \ fe - , ) ? (3.23) hJaB n Jac 2 \dr \r'=R dr \r'=Rj where $B = T I PB{r')dr tl J as $c = r / Pc(r')dr Ti Jac In semiclassical theory, we have E 2m + V (3.24) (3.25) (3.26) where E is the total energy of the system, V is the potential energy, m is the reduced mass. So the above two equations can be written as 1 rR 1 fR *B = \ l R j2m(E-VB(r))dr tl Jag $ c = i [R j2m(E - Vc(r))dr fl J an (3.27) (3.28) Chapter 3. Semi-classical Approach of Predissociation Rate 16 We can replace the slowly varying coefficient of the cosine by its value at r = R. The derivative of the momentum can be expressed in terms of the force Differentiating the equation we have dr Ek + yB = EL + Vc 2m 2m dpB dpc „ „ VB—, vc—r~ — rB- rc Thus l_ r h Jag dr \ pB(r )dr - - pc(r )dr « $ B - $c + — £ Jan a Jac JnVR dr FB — Fc (3.29) (3.30) (3.31) (3.32) where VR is the common value of the VB and the vc at the point of intersection. FB and Fc are the negative derivative of the B state and C state potential curves evaluated at the crossing point r = R. Then the transition rate becomes (3.33) where 8 = ($B - ®c) and e - (FB - FC)/2VR1I. This integral is well known[ll]: f00 I 2 \ 7 V71" 7 7 / coslax )dx - —i=cos— a > 0 Jo V ' 2^/E 4 I stnlax )ax = —T=sin Jo y ' 2ja 4 a > 0 (3.34) (3.35) In the case shown in fig 3.8, one can see that FB — Fc < 0 regardless of whether the intersection is to the left of the minimum or to the right. We change from +e to — e: /oo cos(8 + e £ 2 K -oo /•oo = 2 / cos(-8-ee)dt Jo roo poo i(-S) / cos(-et2)d( - sin(-8) / sini-c^W Jo Jo = 2 cos[ Chapter 3. Semi-classical Approach of Predissociation Rate 17 (3.36) Then Eq. 3.33 becomes: AupPE2 $B - $C + T (3.37) hvR(Fc - FB) This is a little bit different with Landau's result[3] due to the different shape of the continuum potential curves concerned. If the B and C potential curves are known, the predissociation rate of different vibrational levels can be calculated accordingly. On the other hand, if we have the predissociation rates of the different vibrational levels from the experiment, and the potential of the stable state B is known, one can find the continuum C potential curve by varying its form until a set of predissociation rates agreeing with experimental data is obtained. 3.2 The method to calculate C curve directly Using the semiclassical approximation, by means of an R K R form of integral, Child[5] has developed a way to get the continuum potential curve directly. It is as follows. If one can get the predissociation rate for the different vibrational levels, a curve of TE(V) versus the vibrational energy e can be plotted. From Eq. 3.37 one can see that this will be a sine squared curve with slow varying amplitude. Fitting the experimental data into Eq. 3.37, one can get the phase, $ = ($B — $ c ) , as a function of energy. From the knowledge of this curve the distance between left turning points of Vjg(r) and Vc(r) at each vibrational level can be calculated as: (3.38) Chapter 3. Semi-classical Approach of Predissociation Rate 18 where SR is the energy at the crossing point as shown in Fig. 3.8. Since the values of the turning points CLR on the bound-state curve UB(r) are known[12], this completes the determination of the repulsive curve Uc(r). Chapter 4 Experiment Apparatus and Spectrum 4.1 Preparation of the experiment 4.1.1 Preparation of the high voltage cell An original design from MIT has been modified to be suitable for our purpose. Fig. 4.9 shows the sketch of the high voltage cell. The cell has two stainless-steel parallel plates electrodes surrounded by grounded electrodes. The separation of plates can be varied. This make it possible to choose the best separation of the plates experimentally, so that we can get higher electric field without discharge. The two pyrex long arms of the cell allow us to directly compare the fluorescence from the high field region and from field free region. The ceramic rods hold the electrodes and keep them parallel to each other. The ceramic rods also separate the high voltage from the cell, so that the chance of current leakage and discharges was reduced. 4.1.2 Measurement of the separation of the plates Referring to Eq. 3.37, one can see that for a given vibronic level, the predissociation rate TE is proportional to the square of the electric field strength E, as: = j3E2 (4.39) where (1 is called predissociation rate constant. This relation had been proven by Dalby et al. [10]. If the potential difference between the two electrodes is V and the separation 19 Figure 4.9: The sketch of the high voltage cell. Chapter 4. Experiment Apparatus and Spectrum 21 1: High voltage electrodes (x2, stainless steel with nickel) 2: Stycast seals (x2) 3: Insulator tubes (x2, ceramic ) 4: Shields (x2, stainless steel ) 5: Spacer posts (x4, stainless steel) 6: Ground electrodes (x2, stainless steel) 7: 4-40 x | alien head screw (x8, stainless steel) 8: 4-40 rods (x4, stainless steel) 9: Pyrex glass cylinder with two arms and two windows 10: 2\ x 2 | x i Viton O-rings (x2) 11: end covers (x2, stainless steel) 12: 10-32 screw rods (x4, stainless steel) 13: seal covers (x2, brass) 14: | x | x i Viton O-ring (x4) 15: Ring spacers (x4, stainless steel) 16: fittings (x2, stainless steel) 17: 4-40 x | set screw (x2, stainless steel) 18: |-nuts (x2, brass) 19: 4-40x^ alien head screws (x8, stainless steel) 20: Ring protectors (x2, teflon) 21: High voltage wires (x2) 22: Pyrex glass windows (x2) Table 4.1: Table to explain the labels used in the drawing of high voltage cell design Chapter 4. Experiment Apparatus and Spectrum 22 of the two electrodes is D, then we have: E = V_ D (4.40) So accurately measuring the separation of electrodes is important for getting the correct predissociation rate. Since the separation of the electrodes is small and electrodes are surrounded by shields (refer to Fig. 4.9), direct measurement is difficult. During the assembling of the cell, a T-shape spacer has been used to keep electrodes at roughly desired separation and at the right relative position. Then a microscope accurate to 0.001mm ( W H I T T A M 2573, U B C 21-5410 No.9) was employed to measure the separation. The microscope was first focused on the surface of one electrode and the reading was taken. Then the microscope was moved and focused to another surface and another reading was taken. The difference of the two readings gives the separation of the electrodes. In this way, we could measure the separation from somewhere away from the elec-trodes. To confirm that the measurement is correct, we put a caliper ( M I T U T O Y O DIGIMATIC Caliper series No.500-115 460506) at approximate same distance and set the reading to 2.69±0.01 mm. Table 4.2 gives the result of the measurement of this sepa-ration. The result is 2.746±0.004mm. The errors do not cover each other, the measured value is about 2% bigger than the reading of the caliper. This accuracy is enough for our purpose. Table 4.3 gives the result of the measure-ment of distance between the plates. We choose four different spots to do the measure-ment. The first three lines in the table give the data taken when microscope was moved from left to right, and the last three lines from right to left. The distance measured is 1.28±0.03mm. Within 2.3%, the two plates are parallel. Chapter 4. Experiment Apparatus and Spectrum 23 1 left—»right 2 right->left 3 left-bright 4 right—>left left reading(mm) 2.257 4.512 1.854 4.602 right reading(mm) 5.006 1.770 4.604 1.858 difference(mm) 2.749 2.742 2.750 2.744 Table 4.2: Confirming the correction of the microscope measurement. first spot second spot at one end the other end left reading(mm) 4.926 4.564 3.235 3.968 right reading(mm) 6.215 5.845 4.496 5.284 difference(mm) 1.289 1.281 1.261 1.316 right reading(mm) 6.139 5.915 4.404 5.364 left reading(mm) 4.850 4.636 3.149 4.062 difference(mm) 1.289 1.279 1.255 1.302 Table 4.3: The measurement of the distance between the electrodes. 4.1.3 Calibration of the high voltage supply From Eq. 3.37 one can see that calibration of the high voltage supply has the same importance as measurement of the separation of the electrodes. We used a Brandenburg regulated high voltage power supply Model 907, serial No. 36H, which gives up to 60 k V DC high voltage. To calibrate it, we built a simple test circuit as in Fig. 4.10. Since the B E C K M A N digital multimeter used has lOMfi internal resistance for all the scales, if the reading of the multimeter is x volts, then the voltage supply should be: H , x l + f l 3 x x volts (4.41) Substituting the values of three resistances, we get a conversion factor of 121. However because of the uncertainty of the values of the resistances, this result can only be used as a rough guide. The real conversion factor was measured experimentally. A n F33 Chapter 4. Experiment Apparatus and Spectrum 24 6 voltage source R2= 50MC1 Rl=1000Mfl 6 multimeter R3=10Mfl Figure 4.10: The simple test circuit. inputvolts measured by multimeter(V) outputvolts measured by testcircuit(V) ratio 10.080±0.001 0.0896±0.0001 112.50 6.207±0.001 0.0550±0.0002 112.85 4.212±0.001 0.0374±0.0002 112.62 Table 4.4: Measurement of the conversion factor of the test circuit. Function Generator (ser. No. 0557) was used as DC voltage source. The output was first measured directly by the digital multimeter, then the multimeter was connected as in Fig. 4.10, and another reading was taken. The ratio gives the conversion factor. Table 4.4 gives the data. The ratio measured was 112.6±0.2. Then the voltage source was replaced by the high voltage supply. Table 4.5 shows the calibration result. The procedure for the calibration was: the power supply was first set to l k V visually and the reading from test circuit was taken, then to 2kV, 3kV, • • •, until 20kV. The power supply was set randomly to a few previously measured values to test the repeatability of visually setting.(This is the biggest error source.) The data are shown in the Table 4.5. When 20kV was applied to the test circuit, the current that flowed Chapter 4. Experiment Apparatus and Spectrum 25 panel reading first meas. second meas. third meas. calibrated (±0.1kV) (±0.01) (±0.01) (±0.01) (kV) 1 9.11 1.02 2 18.80 19.17 18.82 2.13±0.02 3 27.80 28.00 3.14±0.02 4 36.92 4.16 5 45.40 45.88 45.53 5.14±0.03 6 54.64 6.15 7 64.10 7.22 8 73.30 73.45 73.15 8.25±0.02 9 82.51 9.29 10 91.70 91.80 91.62 10.33±0.01 11 101.30 11.41 12 110.42 110.78 111.17 12.48±0.04 13 119.69 120.48 13.52±0.06 14 129.20 128.49 14.51±0.06 18 167.80 168.40 18.93±0.05 19 177.70 177.78 20.01±0.01 20 188.00 21.17 Table 4.5: Calibration of the power supply. through the circuit was about 0.02mA, which produced about 0.4W heat, (negligible). Fig 4.11 fits the data to a straight line, so we get the calibration formula V= 1.052VP -0.110 (4.42) where Vp is the front panel reading of the voltage supply and V is the calibrated value. 4.1.4 Design of the pumping system Fig. 4.12 shows the sketch of the pumping and the filling system including an oil diffusion pump, a mechanical pump as fore pump, air cooling fan, a cold trap with O-ring seal, an ion gauge with controller (Varian 843), an iodine cell and an opening to connect the high voltage cell. Chapter 4. Experiment Apparatus and Spectrum 26 25.00 -, 20.00 -> 15.00 -V •*-> £ 10.00 .o o u 5.00 -0.00 0.00 1 ' 1 I ' ' ' ' ' ' 1 1 ' 1 ' 1 I ' I ' ' ' I I I ' I 11 ' I I I I I I I I I I 1 1 1 1 5.00 10.00 15.00 20.00 25.00 p a n e l r e a d i n g (kV) Figure 4.11: The calibration curve of the power supply. There are a few important points to keep in mind when using the pump to get a good vacuum inside the cell. • The temperature of the oil has to be right to get good performance of the pump. We have measured the pumping speed at different temperatures, Fig. 4.13 shows the result. For the N E O Y A C S Y oil used, the best voltage applied to the heater is about 85 volts. • During the experiment, the cold trap has to be kept at liquid nitrogen temperature all the times to prevent oil vapor from feeding back to sample cell. At night, valves sci and sc5(Fig: 4.12) were closed to keep the cell at low pressure. • There should not be any blind holes inside the cell. Otherwise they might slowly degas for a long time. • The cell has to be thoroughly pumped out and baked at 100° C for 2 days before Chapter 4. Experiment Apparatus and Spectrum 27 Figure 4.12: The design of the pumping and filling system. use. • Since I 2 might attack vacuum grease, we made the cell grease free. 4.1.5 Getting clean I 2 The I 2 cell was first baked and pumped out at 150°C for 8 hours. Then an I 2 crystal was placed inside it. Since I 2 crystal had absorbed water vapor when it was exposed to air, it is necessary to clean the I 2 . Since the vapof'pressure of I 2 at 0°C is 0.03 torr while for water it is 4.6 torr[13], this difference, a factor of 150, makes it possible to separate I 2 and water. While the I 2 cell was kept at 0°C, the valve sc3(refer to Fig. 4.12) was time(min.) Figure 4.13: The performance of the oil diffusion pump at different temperature. slowly opened, the water vapor and some I2 vapor was pumped out. Then the valve sc3 was closed. Since the cold trap was at liquid nitrogen temperature, most of the I 2 vapor was trapped there so it did not harm the pump. Then the I 2 cell was heated up until all the I2 molecules were redistributed. This was to release any water trapped inside the I 2 crystal. The cell was then pumped out again at 0°C. The same procedure was repeated 3 or 4 times, to prepare the I2 for use in the experiment. 4.2 Experimental apparatus A block diagram of the experimental arrangement used for measuring the electric field induced predissociation in the B 3II0+ state of molecular iodine is shown in Fig. 4.14. A Coherent CR-15 SG argon ion laser was tuned to the 5145 A line, and an output power of 6.5W was used to pump a Coherent CR-699-21 scanning ring dye laser. D C M dye was used which allowed the laser to cover from 14500 c m - 1 to 16200 c m - 1 with Chapter 4. Experiment Apparatus and Spectrum 29 To scope PD: Photodiode, L : Lenses, A: Aperture, F: Filters, E: High Field Region. A— — F n PM2 PM1 To PSD To PSD P l , P2: Polarizers, P M : Photomultipliers, PSD: Phase Sensitive Detecters, M : Mirrors. Figure 4.14: Experimental arrangement. Chapter 4. Experiment Apparatus and Spectrum 30 a peak power of 400 mW. A chopper working at 1.8 kHz chopped the laser beam and sent a reference signal to the lock-in amplifiers. With two polarizer PI and P2 we could decrease the laser intensity to any level we needed and the laser light was polarized parallel to the applied electric field to minimize the Hanle effect [22, pages 70 - 71]. A 31 cm focal length lens focused the beam down to one-third of the electrodes separation and ensured that laser beam did not hit the electrodes. Photomultipliers PMT1 (EMI 9558 B) and P M T 2 (EMI 9558 QB), both with Corning CS2-64 red pass filters and 100 kH loads, were used to detect the fluorescence from high field region Ee or En and field free region Ne or Nn respectively. Here subscript n means that the high field is off and e means that it is on. To ensure that PMT1 only saw the signal from between the plates, a lens with 3.5 cm focal length was placed 4.6 cm away from the center of the plates. A 3 times magnified image was obtained at the back focal area where a 2x2 cm aperture was employed to let only center j of the total fluorescence pass. The outputs from two PMTs were sent to two P A R model 121 lock-in amplifiers and were recorded by a double line recorder(PM8252A). A third lock-in amplifier(PAR model 128) and another PM8252A double line recorder were used to record the difference signal Nn — En or Ne — Ee electronically. A photodiode was placed behind the iodine cell so that we could monitor the laser intensity on an oscilloscope. 4.3 Experimental procedure During the experiment, the high voltage cell was connected to a pumping station shown in Fig. 4.12. The cell was first thoroughly pumped out and baked at 100°C for 2 days. The pressure measured by the ion gauge was as low as 1.2 x 1 0 - 5 torr. Then valve sc5 was closed and the I 2 in the iodine cell was given a final clean up. It was pumped out at room temperature for 5 sec; then valve sc2 was closed and valve sc5 was open; the high Chapter 4. Experiment Apparatus and Spectrum 31 voltage cell was filled at room temperature for 30 sec. Then both valve sc3 and valve sc5 were closed and the filling was completed. Since stainless steel absorbs a lot of I 2 , we had to fill the high voltage cell at a pressure a lot higher than needed; otherwise there wouldn't be enough I 2 inside the high voltage cell. The chopped laser beam was sent in, the laser was turned to a fluorescence line so the trace of laser beam inside the cell could be observed. The beam was visually set to between the plates and the reflected beam from the far end window was also arranged to go back between the plates. Scanning the laser frequency, without the electric field, the spectrum from field-free region labeled Nn, and that from between the plates En were recorded, the difference signal Dn = Nn — En was also recorded. A conversion factor, Con, was also measured to reflect the gain difference between model 121 and model 128 lock-in amplifiers. Then a high voltage was applied to electrodes so that an electric field was established between the plates. We recorded another set of the spectra: Ne,Ee and De. We have two slightly different ways to calculate predissociation rate. Refer to Eq. 2.14. Experimentally we cannot measure En and Ee at the same time. Unfortunately during two different scans, laser intensity and I 2 concentration may change slightly. To correct this we had to multiply the ratio jjf- to En. Eq. 2.14 becomes: n PE2 = r T x En X Ee (4.43) Denoting n Ee (4.44) (4.45) we get x In h (4.46) Chapter 4. Experiment Apparatus and Spectrum 32 E is the electric field strength which equal to voltage applied to electrodes V over sepa-ration of the plates D. We call this RATIO method. When the predissociation rate is small, ie. In « Ie, the term /„ — Ie may induce a large error, but if we can measure the In — Ie electronically, this error might be reduced. The other method called D I F F E R E N C E method was an attempt to reduce this error. We adjusted the gain difference of the two photo multiplier tubes until En = Nn, the Eq. 4.43 becomes: (4.47) Since De ='Ne — Ee, we have: E2 Ee x Con (4.48) The conversion factor, Con, was obtained by taking the ratio of the outputs of the two lock-in amplifiers when their inputs were exactly same. Chapter 5 Spectrum and Data Analysis 5.1 Sample spectrum Fig. 5.15 is the spectrum showing an electric field induced predissociation effect. The number in the bracket is the rotational quantum number; v is the upper level vibrational quantum number; and v" is the lower level vibrational quantum number. When an electric field of the order of 140 k V / c m was applied to the I 2 molecules, the fluorescence dimmed. Fig. 5.16 illustrates the D I F F E R E N C E method. When spectrum dimmed, the difference signal, / J e , increased. There is a 3 mm offset between the horizontal scales in the upper and lower drawings. 5.2 Impurities Although the high voltage cell had been baked before use, due to the complicated struc-ture of the cell, there are a few reasons that there may be impurities in the cell. • When there is a discharge, foreign gas can be knocked out of the electrodes. • The cell contains different materials, making it impossible to bake it to a very high temperature, so that there might be still some outgasing going on in the cell. • There might be some very small leaks which we didn't find. The effect of impurities in the cell is that, for the different vibrational and rotational levels, the relative intensities of the fluorescence signal are changed and the over all 33 Chapter 5. Spectrum and Data Analysis 34 a: ZERO FIELD b: 140 k V / c m Figure 5.16: The spectrum showing the direct measurement of the difference signal. Chapter 5. Spectrum and Data. Analysis 35 7 j / M L R1 Fluorescence from a clean h cell. b: That when there are imoutitles in the cell. Figure 5.17: Fluorescence intensities change due to the impurities in the cell. intensities are reduced. Booth et al. [14] have given a theoretical explanation of this effect. Since the high voltage cell was connected to the pumping system all the times, we could pump out the impurities by keeping the cell at low temperature and opening the valve sc5. Comparing the spectrum before and after the pumping, we could easily observe this effect. Fig. 5.17 shows this effect. If valve sc5 (refer to Fig. 4.12) had been closed for about an hour, what we observed is the spectrum (b) in Fig. 5.17. Then keeping the cell at -21°C, we opened the sc5 for 10 sec, pumping out the impurities and some I 2 molecules, the spectrum changed to (a) in Fig. 5.17. We can see that the 14—1 decreased more than 1 6 - 2 lines did. The relative intensities of the lines changed. So if there is a significant amount of impurities in the cell, the predissociation rate we get would be a combination of the two effects -r Chapter 5. Spectrum and Data Analysis 36 the electric field induced predissociation and the collision effect. This was taken care of in the experiment by pumping out the cell at about -21° C regularly until no change in relative intensities could be observed. 5.3 Data analysis 5.3.1 Assignment of the spectrum Frequencies and relative intensities of the fluorescence spectrum of different vibronic bands were calculated using the computer program provided by A . Chanda. During the experiment, a monbchrometer was used to monitor the frequency of the laser beam. The pattern and the frequency of the spectrum were compared with the absorption measure-ments of Gerstenkorn and Luc[15]. The relative intensities and the frequencies were also compared with the calculation. The frequencies agreed usually to within 0.05cm _ 1 and a systematical difference of 0.005cm - 1 was found. The intensities of the different lines also agreed with the calculation very well, making the line assignment quite straightforward. 5.3.2 Calculations We have measured electric field induced predissociation for low, medium and high rota-tional quantum numbers j ' , from v'= 4 to v'= 9 vibrational bands. A few measurements for v'= 12 and v'= 16 bands have been carried on for comparing with the previous results taken by Dalby et al. [10]. The predissociation rate constants we got is about 30% higher than the previous value. We do not know the reason for this, but this should has little impact to the assignment of the C potential curve because that only the phases (defined in Section 3.2) of the data points determine the shape of the repulsive potential curve. Appendix A gives the raw data of these measurements. Appendix B gives all the predissociation rates calculated from the experimental data. For some of them, the Chapter 5. Spectrum and Data Analysis 37 calculated value from the RATIO method and from D I F F E R E N C E method do not quite agree to each other. There are several reasons for this: • In the RATIO method, one need not worry about different gains in the different channels. Both In and Ie are expressed in a ratio form; it's a very straight forward method. In the D I F F E R E N C E method, the model 121 and the model 128 lock-in amplifiers may have different gains, and even the model 128 itself may have differ-ent gains when it's in D I F F E R E N C E mode and when it's in S I N G L E - C H A N N E L mode. The differences between the photo multipliers may also give the contribution to the final result. A l l these made it difficult to get correct results through this ; . method. • Eq. 4.47 is equivalent to Eq. 2.14 only when Nn = En. For some reasons, it happened that Dn was not zero at some frequencies. In this case, we could not make Eq. 4.47 equivalent to Eq. 2.14. • Difference signal is always noisier, so it is harder to locate the correct baseline of the spectrum. • Since the scans of Ne,Ee always followed the scans of Nn,En, they have the same baseline. Even if the baseline is in error by a small amount, this will not have very big influence on the ratio especially when the predissociation is small. However in the difference method, any error on the baseline would go directly into the calculation of predissociation rate, and the errors are add up. This could possibly change the results a lot. So we believe the RATIO method is more reliable. We will use the results calculated by this method. Chapter 5. Spectrum and Data Analysis 38 5.4 Rotational quantum number dependence Table. 5.6 to Table. 5.11 give the predissociation rates constants p calculated by the ratio method as a function of rotational quantum number J'. They are the average of the two j3 values for the different voltage in the Appendix B . Errors were calculated using the error of Nn, Ne, En, Ee listed in Appendix A and follow the E q . 4.44 to E q . 4.46. However if this error is smaller than the corresponding error in Appendix B which is obtained by taking the difference of the three calculated /3s, the latter is chosen. F i g . 5.18 to F i g . 5.23 are the drawing of the J dependance. The least squared fitting suggested that there is a J(J + 1) dependence of the P values from v' = 4 to v' = 9, where J is the rotational quantum number. From the least squared fitting of /? values from the Table. 5.6 to Table. 5.11, we got their J dependence as: 0 = 0.027(±0.004) J ( J + 1) + 102(±9) x2 = 5.3 for v = 4 (5.49) p = - 0 . 0 0 0 8 ( ± 0 . 0 0 0 5 ) J(J + 1) + 4 3 ( ± 1 ) x2-= 10. for v = = 5 (5.50) p = 0.0154(±0.0007) J ( J + 1) + 186(±3) x2-= 4.9 for v = = 6 (5.51) P = 0.0090(±0.0001)J(J + 1) - 8 .1(±0.4) x2-= 30. for v = 7 (5.52) P = - 0 . 0 0 4 6 ( ± 0 . 0 0 0 2 ) J ( J + 1) + 121.2(±1.2) x2 = 18. for v = 8 (5.53) P = 0.00554(±0.00006) J ( J + 1) + 84.7(±0.6) x2 = 25. for v = = 9 (5.54) where x2 1S defined as: Y (err.o//??) 2 5.5 Vibrational quantum number dependence From the fitting of F i g . 5.18 to F i g . 5.23, one can get the predissociation rate constant (3 as a function of vibrational quantum number v for a given J. Tab. 5.12 gives this Chapter 5. Spectrum and Data Analysis 39 • • i n • V - V p or r J' P{cm2kV-2s-x) 4-4 P 26 99 ± 15 4-4 P 27 100 ± 51 4-4 r 33 125 ± 31 4-4 r 34 142 ± 21 4-4 P 45 175 ± 26 4-4 r 51 158 ± 23 4-4 r 52 215 ± 36 4-4 P 72 267 ± 41 4-4 P 89 286 ± 42 Table 5.6: Predissociation rates for v = 4 vibronic band. Figure 5.18: J dependence for v = 4 vibronic band. Chapter 5. Spectrum and Data Analysis 40 7 Tl V - V p or r J' P(cm2kV-2s-1) 5-3 P 24 63 ± 9 5-3 P 25 41 ± 6 5-3 r 31 43 ± 7 5-3 P 50 34 ± 8 5-3 r 56 48 ± 7 5-2 P 64 34 ± 5 5-2 r 70 48 ± 7 5-2 P 86 31 ± 5 5-3 P 93 26 ± 13 Table 5.7: Predissociation rates for v = 5 vibronic band. 3 5 0 - | 2 5 0 -_Q 1 5 0 5 0 i • 5 0 - f - i — i — i — i — i — i — i — r — i — | — i -0 2 0 0 0 - I — I — I — | I I—I—I—I—I—I—1—I—|—I—I T I— I — I — I — I — I — J — I —I— I — I — 1 8 0 0 0 4 0 0 0 6 0 0 0 J(J+1 ) Figure 5.19: J dependence for v = 5 vibronic band. Chapter 5. Spectrum and Data Analysis 41 1 — IT— V - V p or r J' ^(cmW- 2 ^- 1 ) 6-3 P 33 209 ± 14 6-3 r 39 221 ± 15 6-3 P 51 209 ± 15 6-3 r 57 234 ± 16 6-5 r 65 253 ± 51 6-5 r 75 242 ± 29 6-2 P 84 301 ± 21 6-3 P 87 299 ± 23 6-3 r 93 276 ± 17 Table 5.8: Predissociation rates for v = 6 vibronic band. 3 5 0 - , 5 0 -— 50 | i i i i—i i i > i i i i—n—| i i i i i i i i i | i i i i i i i i i | i i i i i 0 2000 4000 6000 8000 J ( J + 1 ) Figure 5.20: J dependence for v = 6 vibronic band. Chapter 5. Spectrum and Data Analysis 42 —r rr— V - V p or r J' P(cm2kV-2s-1) 7-3 P 28 11 ± 2 7-3 P 29 4 ± 2 7-3 r 32 6 ± 2 7-3 r 33 9 ± 3 7-3 P 46 10 ± 2 7-3 r 52 17 ± 3 7-4 P 68 26 ± 8 7-4 r 74 26 ± 3 7-3 P 78 36 ± 4 7-3 r 84 50 ± 5 7-3 P 93 82 ± 8 Table 5.9: Predissociation rates for v = 7 vibronic band. 350 250 !50-50--50' _ i i i i i | i i i i i i i i i i i i i i i i 0 2000 4000 6000 8000 J ( J + 1 ) Figure 5.21: J dependence for v = 7 vibronic band. Chapter 5. Spectrum and Data Analysis 43 • / V - V p or r J ' P(cm2W-2s-1) 8-5 P 27 122 ± 11 8-3 P 31 114 ± 9 8-5 r 32 93 ± 7 8-5 r 33 118 ± 9 8-3 r 37 112 ± 9 8-4 P 66 106 ± 8 8-4 r 72 97 ± 7 8-3 P 93 75 ± 6 8-4 P 96 88 ± 7 8-3 r 99 70 ± 5 8-4 r 102 79 ± 5 8-3 P 103 63 ± 5 Table 5.10: Predissociation rates for v = 8 vibronic band. 350-i 250-O % 150: I 1 1 1 1 1 1 1 1 1 I 1 I I I I I I I I I I I I I I I I I , 1 I , 0 2000 4000 6000 8000 10000 12000 J ( J+1) Figure 5.22: J dependence for v = 8 vibronic band. Chapter 5. Spectrum and Data Analysis 44 V - V p or r J' P(cm2kV-2s-1) 9-4 P 25 88 ± 4 9-4 r 30 82 ± 3 9-4 r 31 95 ± 4 9-4 P 46 103 ± 4 9-4 r 52 106 ± 4 9-4 P 59 119 ± 5 9-4 r 65 122 ± 5 9-4 P 86 132 ± 5 9-4 r 92 145 ± 13 9-4 P 103 144 ± 6 9-3 P 110 155 ± 15 9-4 P 119 166 ± 7 Table 5.11: Predissociation rates for v = 9 vibronic band. Figure 5.23: J dependence for v = 9 vibronic band. Chapter 5. Spectrum and Data Analysis 45 V 4 5 6 7 8 9 J = 0 108 ± 15 43 ± 4 186 ± 5 -8 ± 1 121 ± 2 85 ± 2 J = 50 180 ± 25 41 ± 5 225 ± 8 15 ± 2 109 ± 3 99 ± 3 J = 100 380 ± 45 35 ± 7 341 ± 15 83 ± 6 75 ± 6 141 ± 5 Table 5.12: v dependence of the predissociation rate. V 10 11 12 13 14 15 16 J = 0 -2 46 74 17 -4 54 63 J = 50 -2 43 74 21 -4 37 55 J = 100 -2 3 74 50 -4 19 47 V 17 18 19 20 21 22 J = 0 8 -3 19 35 10 -3 J = 50 27 -3 4 34 48 26 J = 100 58 23 -3 22 44 52 Table 5.13: v dependence of the predissociation rate from Dalby's paper. dependence for low, medium and high J respectively. Combined with the data from Dalby's paper[10] shown in Tab. 5.13, we have the predissociation rates constants from v = 4 to v = 22. Fig. 5.24, Fig. 5.25 and Fig. 5.24 are the drawings of the predissociation rate constants for J = 0, J = 50 and J = 100 respectively. In these drawings the smooth curves connecting the points are intended as a visual guide only. From Eq. 3.37 one can see that the curve /? against energy should be a sine squared form with the amplitude modulation. Taking out the amplitude modulation from Fig. 5.24 etc., one can get a sine square curve out of which one can get the phase for each data point. This phase $ can be expressed as a function of energy e. Tab. 5.14 and Fig. 5.27 gives this relationship. The least square fitting gives the expression of this as: $ = -9.689 x 10~V + 0.01152e + 1.989 (5.56) This $(e) then can be used to calculate the C potential curve as described in Eq. 3.38, Chapter 5. Spectrum and Data Analysis 46 390 -i VIBRATIONAL QUANTUM NUMBER v Figure 5.24: The measured predissociation rate constants /? for J = 0 as a function of vibrational quantum number of the B state of molecular iodine. 390-1 1 1 1 1 ' ' ' < ' j. • • ' ' i i ' ' i i i i i i i I I I I I I i i i ^ 7 12 17 22 VIBRATIONAL QUANTUM NUMBER v Figure 5.25: The measured predissociation rate constants fi for J = 50 as a function of vibrational quantum number of the B state of molecular iodine. Chapter 5. Spectrum and Data Analysis 390-1 47 V I B R A T I O N A L Q U A N T U M N U M B E R v Figure 5.26: The measured predissociation rate constants for J = 100 as a function of vibrational quantum number of the B state of molecular iodine. but this method failed in our case because a potential curve which is not a single-valued function of internuclear distance r was derived. In the curve as the energy decreases the internuclear distance increases then decreases. The possibility that the C potential curve-might have huge slope has caused concern about the validity of some approximation made in semiclassical theory. To avoid these, we tried to use numerical method to solve the problem. Chapter 5. Spectrum and Data Analysis 48 1 V e cm 1 phase $ 4 549.97 7.77 5 667.88 9.14 6 784.18 10.37 7 898.83 11.78 8 1011.82 12.86 9 1123.17 13.97 10 1232.80 14.92 11 1340.72 15.77 12 1446.90 16.50 13 1551.33 17.61 14 1653.97 18.06 15 1754.80 19.17 16 1853.81 19.88 17 1950.96 20.81 18 2046.22 21.21 19 2139.61 22.02 20 2231.06 22.78 21 2320.58 23.78 22 2408.13 24.34 Table 5.14: The phase of the electric field induced predissociation rate constant as a function of energy for J = 0. Chapter 5. Spectrum and Data Analysis 49 Figure 5.27: The phase (defined in Section 3.2) of the electric field induced predissociation rate constant as a function of energy for J = 0. Chapter 6 Numerical Solution 6.1 Formulas and constants We want to locate where the crossing of the two potential curves is and to determine the slope of the C curve. So for the small vibrational quantum numbers, we suppose the C curve is a straight line. By quantum mechanics theory, the wave function of a straight line potential curve has the form(See Appendix C): T(?7) is called the Airy function; A is the normalization factor; r is the internuclear distance; e is the energy; F is the absolute value of the slope of the potential straight line; B equals to F x b, while b is the intercept of the potential straight line on the r axis. Normalize the wavefunction to Delta function of energy by the equation: X(v) = AT(-ri) (6.57) where n is defined as: (6.58) (6.59) We can find the normalization coefficient is[3, page 75] A = (2m) 1/ 3 (6.60) 7T 1/2^1/6^2/3 where m is the reduced mass of iodine molecule. 50 Chapter 6. Numerical Solution 51 Take m equal to 1.0545 x 10~ 2 5 Kg . Then we get , , 1.9695 x 10lf> X(r) = - i T -1 .5563F3( r -6+- | ) (6.61) where F is in e is in cm x ; r and b are in A . The unit of x is ^ i / f m 3 / a • The Airy function can be numerically calculated by an ascending series: T( , ) = 0.35503 £ 3* ^ + 0.25882 £ 3* (j) »7 3fc+l *(3fc + l)! (6.62) where 3/ o = 1 ( a + ^ ) = (3a + l)(3a + 4)- . . (3a + 3fc-2) (a arbitrary; fc = 1,2,3,...) When ?; is large, we can simply use the semiclassical expression[3, page 345]: ' '1 r X(r) = irhvC0S Y% r \ • j p(r')dr' — — 7r (6.63) This is also normalized by delta function of momentum. A factor of has to be added to Eq. 6.63 to be consistent with Eq. 6.61. (The Eq. 24.6 and the Eq. 24.4 in page 75 of reference [3] also differ by factor of y/ir.) With p — mv = \j2m(e — U(r)), Eq: 6.63 becomes X(r) 9.94814 x 10 1 5 cos 1.9408 JT sjE - U(r')dr' - j {E-U(r))* where E and U are in c m - 1 ; r is in A . The B state wavefunction can be calculated using semiclassical expression: (6.64) (6.65) 2u> r l r 7ri (6.66) Chapter 6. Numerical Solution 52 x ( r ) = V 2 ^ G X P I" p(r')dr' J a for E < U(r) (6.67) These are normalized by / |x|2dr = 1. (6.68) Ja Since the wavefunction in the classical unacceptable region would give very little contri-bution to the integral, the integral limitation was taken from a to b instead of from 0 to oo, where a and b are left and right turning points. The unit of x 1S l/y/rn. The classical oscillation frequency u> can be calculated according to Ey — EV-1 . . uv = , (6.69) where v is vibrational quantum number. Working out all the constants for the Eq: 6.66, we have X(r) = 78600.5 x yJEv - Ev.x x (Ev - U(r))~* cos [l.9408 x f ^JEV - U(r')dr' - j . (6.70) The constants for Eq: 6.67 are similar. The semiclassical expression is only good when the atoms are far from turning points. Eq: 6.66 and Eq: 6.67 should joint smoothly at the turning points, but they both tend to infinity at the turning points. In these small neighborhoods of turning points, we have to change empirically the calculated data to join the two curves. To test this change, we did the integral according the Eq: 6.68 and got 1.03 ± 0.01 for all the vibrational levels involved. This means the change is reasonable within 3% error. To correct this 3% error, we used these data to re-normalize the wavefunction. The actual constants used are: 1.0467, 1.0395, 1.0405, 1.0377, 1.0292 and 1.0325 for vibrational level 4, 5, 6, 7, 8, and 9 respectively. Now we have got both B state and the C state wave functions numerically. We generated a computer program to multiply the two wavefunction and do the integral Chapter 6. Numerical Solution 53 from — oo to +00 according to the definition Eq. 3.15. We give a rough estimation of the amplitude of the dipole moment fi as: fi = ez = 1.6 x 1 ( T 1 9(C) x i r r n ( m ) = 1.6 x 10~ 2 1(c7m). (6.71) After the constants are put into Eq. 3.15, it becomes: /+ CO XBXcdr -00 (6.72) Where dr is in the unit of A. There are two parameters varied during the numerical calculation. One is the location of crossing point, the other is the slope of the C potential curve. We scanned the intersection from left turning point to the right turning point of v — 4 vibrational state by every 0.002 A. The slope of the C potential curve was changed from 1 0 3 c m - 1 / ^ t o 10 4 c m - 1 / A by every 0.5 x 10 3 cm _ 1 /A , then from 104 cm-1/A to 1 0 5 c m - 1 /A by every 0.5 x 10 4 cm _ 1 /A , and finally from 10 5 c m _ 1 / A to 10 6 c m _ 1 / A by every 0.5 x 10 5 c m - 1 / A . We calculated f3 value for many possible positions of the C potential curve. Since Eq: 6.71 only gives a rough estimate of dipole moment fi, a constant factor is left out in the expression 6.72. In order to evaluate the calculation, a constant K has to be worked out to get the smallest least — squared — difference value. The Isd value is defined as M - EU-rr. of fit)2 ' ^ where [3e are experimental results and f3c are calculated data. A good fit should give Isd value as about 1. The denominator is denoted as ERR which is a constant. It is 450 for j = 0. Differentiate Eq: 6.73, we can get the expression of K as Chapter 6. Numerical Solution 54 slope(xl(T 4 c m " 1 / A ) lsd 5.00 41. 31. 25. 20. 10. 4.1 3.3 6.00 29. 17. 12. 7.7 2.1 2.1 8.9 7.00 21. 11. 6.6 3.7 1.6 5.7 16. 8.00 16. 7.1 4.0 2.0 2.4 9.7 24. 9.00 9.3 3.0 1.4 1.0 4.3 13. 29. 10.00 8.1 2.0 0.8 1.3 7.0 19. 36. 15.00 3.8 3.0 4.5 7.7 19. 37. 58. 20.00 3.0 5.0 7.8 12. 24. 42. 62. 25.00 3.0 6.9 11. 17. 32. 50. 71. 30.00 3.6 8.1 13. 19. 35. 53. 73. 35.00 4.3 10. 15. 21. 36. 55. 77. 40.00 3.9 10. 14. 20. 36. 57. 78. 45.00 5.2 12. 16. 23. 40. 60. 80. 50.00 5.3 13. 18. 25. 43. 63. 82. intercept(A) 3.061 3.063 3.064 3.065 3.067 3.069 3.071 Table 6.15: Calculated predissociation rate constants by quantum mechanic method for J = 0. 6.2 Numerical result Tab. 6.15 gives calculated lsd value in the near neighborhood of the crossing point(where lsd value are among the smallest). The global minimum lsd value is 0.76. It happens when the slope of the C potential curve is 9.77 x 104cm'1/A and the crossing point with r axis is R = 3.064A. A l l the local minimums which are not shown in the Table 6.15 are bigger than 3. Fig. 6.28 gives the B state wavefunction for v' — 5 vibrational state and the C state wavefunction at above slope and intersection. The calculated predissociation rate constant at the above slope and intercept is shown in Table 6.16. In the third column of the Table 6.16 are the calculated rc values of the C potencial curve (for J = 0) at which energy (second column) applied. Also shown Chapter 6. Numerical Solution 55 Figure 6.28: B state wave function for v' = 5, E' = 667.88cm 1 and C state wavefunction for slope = 9.77 x 104cm-7A, intercept = 3.064 A and E' = 667.88cm"1. Chapter 6. Numerical Solution 56 V e rc Pe Pc ( cm- 1 ) (A) 4 549.97 3.0585 102±20 122 5 667.88 3.0573 43±4 47.5 6 784.18 3.0562 186±5 177 7 898.83 3.0550 -8±1 3.3 8 1011.82 3.0534 121±2 117 9 1123.17 3.0528 85±2 86.3 Table 6.16: Calculated predissociation rate constants for J = 0(lsd = 0.76, K = 3.149). in the table is the experimental data for the same vibrational and rotational quantum numbers for comparison. The errors of the /3e in Table 6.16 are estimated from the Fig. 5.18 to Fig. 5.23. They are not same with computer calculated errors shown in Eq.5.48 to Eq.5.53. 6.3 Fitting for higher J value For the B state of molecular iodine, the effective potential curve for a given rotational quantum number J is related to the potential curve of J = 0 by[3, pages 314-316]: t/ J(r)(cm" 1) = f / J = 0 ( r ) (cm- 1 ) + - ^ ( I W ) ^ ^ 1 (6.75) Taking m = 1.0545 x 10_25/<"<jr as before, we got the effective potential curves for both J = 50 and J = 100 of the vibrational levels 4 to 9. The energy corresponding to a given rotational level can also be written as: Ej = EJ=0 + BVJ(J + 1) - DVJ\J + l ) 2 (6.76) Where Bv is called rotational constant in the vibrational state v, which is actually the average of the term B(R) = -^-^ over r in this vibrational state. Dv is the quadratic centrifugal distortion constant. Using the Bv and Dv values given by Gerstenkorn and Figure 6.29: Revised 3 I I l 9 state potential curve. Chapter 6. Numerical Solution 58 V turning points of J=0 turning points of J=50 turning points of J=100 R • A R A R • A 1 Lmin R A •'•'•max R • A R A 4 2.85696 3.25645 2.85842 3.25862 2.86226 3.26548 5 2.84203 3.28614 2.84348 3.28839 2.84735 3.29599 6 2.82880 3.31436 2.83024 3.31696 2.83414 3.32453 7 2.81690 3.34153 2.81838 3.34394 2.82225 3.35183 8 2.80606 3.36794 2.80749 3.37044 2.81150 3.37863 9 2.79616 3.39350 2.79759 3.39609 2.80177 3.40426 Table 6.17: Classical turning points for J — 0, 50, 100 effective potential curves. Luc[23], the energy of J = 50 and J = 100 levels of v — 4 to 9 were also calculated. With these energy values and the effective potential curves calculated by Eq: 6.75, we calculated classical turning points of these potential curves for the different vibrational levels. Table 6.17 shows the result. The turning points of J = 0 potential curve shown in this table comes from Barrow and Yee's paper[12]. Using the same procedure we used to J = 0 potential curve, we calculated B state wavefunctions for J = 50 and J = 100 of v — 4 to 9 and then the slope and the intercept of the C state potential curve. The results agree with J = 0's result very well except for the data of J = 100, v — 9 which is ignored in the table 6.19. Table 6.18 and Table 6.19 show the results. For J = 0, The calculated values agree with experimental values very well for all the vibrational level (refer to Table 6.16). For J = 50 (6.18), we got good agreement only for low v. And we have to ignore calculated fi for v = 9 for J = 100 in order to get reasonable small Isd value. This suggestes that C potencial curve has a bigger curvature for higher J . Since we suppose that C potencial curve is a straight line, this method is less appliable for higher J . If we take the region with Isd < 1.0 as acceptable, we can work out the error of the Chapter 6. Numerical Solution 59 V e rc Pc (cm" 1) (A) 4 622.10 3.0594 180±25 171 5 739.60 3.0582 41±5 37.8 6 855.47 3.0570 225±8 219 7 969.69 3.0558 15±2 11.0 8 1082.25 3.0547 109±3 119 9 1193.15 3.0535 99±3 115 Table 6.18: Calculated predissociation rate constants for J = 50(/sd = 0.68, K = 3.755). V £ rc Pe Pc (cm" 1) (A) 4 835.15 3.0576 380±45 373 5 951.40 3.0563 35±7 4.47 6 1066.02 3.0550 341±15 342 7 1233.05 3.0531 83±6 86.4 8 1290.21 3.0525 75±6 96.9 9 1399.78 3.0513 141±5 Table 6.19: Calculated predissociation rate constants for J = 100(lsd = 0.64, K = 5.586). result(refer to Table 6.15). The 3H\g state potential curves of J = 0, J = 50 and J = 100 all intersect the corresponding B 3 II 0 + state potential curves at R = 3.064 ± 0.001 A with the slope 9.8(±0.3) x 104,cm-VA, 9.8(±0.3) x 104,cm-VA and 8.9(±0.4) x 104,cm-VA respectively. 6.4 Conclusion In this paper, we have presented a detailed research on the electric field induced predisso-ciation of molecular I 2 . The induced predissociation rate constant of v = 4 to v = 9 was Chapter 6. Numerical Solution' 60 measured in a electric field as high as 133 kV/cm. Combining with the previous work by Dalby et al., we have obtained the most completed data of induced predissociation of I2 • A detailed table and a drawing (Fig. 6.29) about the revised 3 ITi 9 potential curve has be given. Compare to the result previously given by Dalby et a/.[10], the slope of the C potential obtained through this work is about factor of 5 smaller and the interception shifted to right by 0.08A. Appendix A Experimental Data Tab. A.20 give the parameters used to calculate the natural predissociation rate; these data are from Vigue's paper[16]. According to Eq: 2.11, Eq: 1.2 and Eq: 1.3, the total radiative decay rate T? is calculated by TT = TR + C2VJ(J + 1) + 4.7a2 for even J (A.77) IV = TR + C2VJ{J + 1) + 6.8a2 for odd J (A.78) where Tc is taken as zero due to the low pressure in the cell. The calculated TT for all the transitions is given in appendix B . Starting from page 63 in this appendix lists all the raw data from our experiment. In the lists v', v" is the upper and lower vibrational quantum number respectively; PR means P or R branch; J is rotational quantum number; E is electric field strength in the unit of kV/cm; NO and E0 are the peak fluorescence intensity of given rotational transitions in the field free region and field region respectively when electric field is not applied. DO is the difference of the above two transitions measured electronically. Con is the converting factor defined in Eq. 4.48 and only be used in D I F F E R E N C E method. Ni and Ei (i = 1, 2, 3) are the peak fluorescence intensity of given rotational transitions in the field free region and field region respectively when electric field is applied. Di (i = 1, 2, 3) is the difference of the above two transitions measured electronically. The numbers in the brackets are the errors. These data were used in the program data.c to calculate the predissociation rate constants. Here we give one example of calculation. 61 V < (i) r* (}) 4 292. 339000. 908000. 5 314. 363000. 897000. 6 303. 350000. 884000. 7 287. 324000. 872000. 8 187. 232000. 860000. 9 141. 146000. 847000. 10 95. 110000. 833000. 11 51. 40000. 819000. 12 21. 16000. 806000. Table A.20: Constants C 2 , a 2 and T,R used in the calculation of predissociation rate constants /3. For the first group of data in the list, the transition is 10' — 4" r51, taking constants from Tab. A.20 and using Eq. A.78 we have T T = 833000. + 95 x 51 x (51 + 1) + 6.8 x 110000 = 1.83 x 106 (A.79) For RATIO method, using Eq: 4.47 we have TT 1.83 x 1 0 s ft, — — * N 0 E o ^ EO 1382 x 102  97 112 110 112 ^ = 3.2 (A.80) /?2 is calculated similarly using N2, E2, NO, E0. In total 5 (3 can be obtained using 5 sets of data for a given transition. The average of these 5 (3 was used as the electric field induced predissociation rate constant. For D I F F E R E N C E method, /3 was calculated by DI P l E2 X El x Con 1.83 x 106 22 x 1.24 x ——— - 11. (A.81) 1382 " 112 x 2.024 Where constant 1.24 corrects the gain difference of the two lock-in amplifiers and is same for all data. The constant 2.024, read from data listed below, corrects the gain difference due to different setting related to two lock-in amplifiers and will change among different group of data. We also have 5 different f3 for a given transition, but these data were not used and the reason was discussed in Chapter 5. 62 v' V " J E NO EO DO NI E l (kV/cm) (1.) (2.) (3.) (1.) (2.) 10 4 r51 138. 97. 110. 0. 101.5 111.5 9 3 p l l O 138. 38.5 44. 0. 39.5 24.5 8 3 r37 138. 128. 159. 5 29. 135. 94. 8 3 p31 138. 109.5 138. 29. 116. 80. 10 4 p45 138. 93.5 106. 0. 101. 109. 10 4 r51 96. 9 97. 110. 0. 95. 102.5 9 3 p l l O 96.9 38.5 44. 0. 37. 30. 8 3 r37 96.9 128. 159. 5 29. 131. 115. 8 3 p31 96. 9 109.5 138. 29. 109.5 94.5 10 4 p45 96.9 93.5 106. 0. 100. 107. v' V " J E NO EO DO NI E l (kV) (1.) (1.) (3.) (1.) (1.) 8 3 r99 138. 121. 133. 0. I l l . 95. 10 4 p98 138. 93. 87. 42. 91. 68. 8 3 p93 138. 162.5 178. 5 0. 165.5 133 6 2 p84 138. 62.5 65. 15. 70. 34. 8 3 r99 96. 9 121. 133. 0. 121.5 114. 10 4 p98 96.9 93. 87. 42. 90. 76.5 8 3 p93 96.9 162.5 178. 5 0. 152. 143. 6 2 p84 96.9 62.5 65. 15. 63.5 40. v' v" J E NO EO DO NI E l (kV) (1.) (1.) (1. ) (1.) (1.) 8 3 pl03 138. 98. 120. -11. 92. 88. 9 4 r 31 138. 211. 220. 5 15. 197. 108. 9 4 p 25 138. 186. 193. 15. 174. 97. 10 4 pl07 138. 105. 114 . 4. 102. 75. 9 4 r 30 138. 199. 203. 20. 189.5 101. 8 3 pl03 96.9 98. 120. -11. 101. 108.5 9 4 r 31 96.9 211. 220. 5 15. 219.5 155. 9 4 p 25 96.9 186. 193. 15. 189.5 136. 10 4 pl07- 96.9 105. 114. 4. 107. 91.5 9 4 r 30 96.9 199. 203. 20. 200. 138. 7 3 p 29 138. 91.5 111. -9. 96. 112. DI N2 E2 D2 N3 E3 D3 Cov. (3.) (1.) (2.) (3.) (1.) (2.) (3.) (0.003) 21.5 101.5 109. 23. 96. 102. 25. 2.024 41. 38. 22. 44. 38. 23.5 41. 2.024 119.5 136. 96. 115. 132. 94. 112. 2.024 104. 116. 79.5 106. 114. 78.5 102. 2.024 20. 104. 112.5 20. 99. 106. 26. 2.024 11. 89. 97. 9. 2.024 23. 35.5 27. 24.5 2.024 64. 123. 108. 59. 2.024 58. 94. 84.5 50. 2.024 10. 90. 97. 9. 2.024 DI N2 E2 D2 N3 E3 D3 Cov. (3.) (1.) (1.) (3.) (1.) (1.) (3.) (0.003) 73. 125.5 107.5 83. 106. 88. 77. 4.048 87. 99.5 74. 92. 77.5 60. 70. 4.048 128.5 167.5 135. 129. 130.5 104. 104. 4.048 108. 61.5 30. 97. 52.5 25.5 82. 4.048 56. 121. 115. 48. 4 . 048 61. 91. 73.5 69. 4 . 048 68. 141.5 132.5 61. 4.048 76. 59. 37.5 68.5 4.048 DI N2 E2 D2 N3 E3 D3 Cov. (1.) (1.) (1.) (1.) (1.) (1.) (1.) (0.004) 15. 85.5 82. 14. 100. 97.5 16. 1.007 114. 177. 96.5 103. 218. 120. 126. 1.007 102. 153.5 86. 87.5 187. 105. 107. 1.007 40. 81. 60. 31. 105. 80. 41. 1.007 114.5 157. 83.5 95.5 197. 106. 118. 1.007 5. 99.5 107. 4. 1.007 92. 216. 153.5 89.5 1.007 78. 189.5 134. 78. 1.007 29. 107. 92. 27. 1.007 88. 198. 137. 85. 1.007 11. 95. 111. 13. 85. 101. -11. 1.007 7 3 r 33 138. 105. 5 130. -11. 114. 130.5 12. 9 4 r 52 138. 130. 138. 7. 140. 74.5 81. 9 4 P 46 138. 132. 140. 7. 141.5 73. 83. 7 3 P 28 138. 93. 112. -8.5 99. 111. 13. 7 3 r 32 138. 104. 125. 5 -10. 108. 126.5 7. 7 3 P 29 96.9 91.5 111. -9. 93.5 113.5 -10 7 3 r 3" :. 9 105. 5 130. -11. 107.5 130.5 -10 9 4 r 5^ .6.9 130. 138. 7. 133. 91.5 59. 9 4 P 46 96.9 132. 140. 7. 130. 90. 57. 7 3 P 28 96.9 93. 112. -8.5 91. 106. -9. 7 3 r 32 96. 9 104. 125. 5 -10. 97. 116. -7. v' V " J E NO EO DO NI El DI (kV) (1.) (1.) (1.5) (1.) (1.) (1.5) 7 3 P 46 138. 141. 5 163. 5 -12. 145. 158.5 15. 7 3 r 52 138. 122. 5 145. -14. 144.5 154. 17. 9 4 r 65 138. 167. 173. 5 9. 184. 97.5 106. 9 4 P 59 138. 184. 5 194. 8. 186.5 103.5 103. 7 3 P 46 96.9 141. 5 163. 5 -12. 149.5 167. 4. 7 3 r 52 96.9 122. 5 145. -14. 143.5 161. 5. 9 4 r 65 96.9 167. 173. 5 9. 180. 124.5 73. 9 4 P 59 96.9 184. 5 194. 8. 192.5 133.5 78. v' v" J E NO EO DO NI El DI (kV) (1.) (1.) (1.5) (1.) (1.) (1.5) 5 2 P 64 138. 58. 65. 0. 56. 53. 9.5 7 3 P 78 138. 142. 163. -11. 138. 137.5 22. 7 3 r 84 138. 123. 5 140. 5 -7. 120. 112. 20. 9 4 r 92 138 . 130. 135. 7. 124. 68. 68. 5 2 r 70 138. 55. 63. 0. 56. 52.5 10. 9 4 P 86 138. 152. 155. 11. 156. 82. 90. 5 2 P 64 96.9 58. 65. 0. 57. 58.5 6. 7 3 P 78 96.9 142. 163. -11. 142.5 150. 7. 7 3 r 84 96. 9 123. 5 140. 5 -7. 123. 125. 9. 9 4 r 92 96.9 130. 135. 7. 130. 90. 51. 5 2 r 70 96.9 55. 63. 0. 57. 58. 3. 9 4 P 86 96.9 152. 155. 11. 154. 104.5 65. 5 2 P 86 138. 46. 52. 0. 47.5 46. 6. 110.5 129. 12. 100. 118. -11. 1.007 136.5 71. 77. 127. 69. 75. 1.007 139. 73. 83. 129. 68.5 78. 1.007 99. 110.5 13. 90. 101. -10. 1.007 107. 123. 6. 100. 116. 5 -6. 1.007 93. 112. -11. 1.007 110. 132. -12. 1.007 131.5 90. 57. 1.007 142.5 97. 63. 1.007 100. 115. -10. 1.007 112. 131. -7. 1.007 N2 E2 D2 N3 E3 D3 Cov. (1.) (1.) (1.5) (1.) (1.) (1 .5) (0.002) 161. 175. 17. 163.5 177. 17. 1.007 146. 157. 15. 147. 161. 5 15. 1.007 180. 95. 103. 188.5 102. 107. 1.007 191. 102. 109. 210.5 115. 5 119. 1.007 145.5 162.5 5. 1.007 131. 147. 4. 1.007 171. 121. 67. 1.007 190. 132. 78. 1.007 N2 E2 D2 N3 E3 D3 Cov. (1.) (1.) (1.5) (1.) (1.) (1.5) (0.01) 53. 50. 9. 57. 55. 9. 1.04 138. 136.5 21. 144 . 143 23. 1.04 116.5 110.5 21. 123.5 118 20. 1.04 122. 60. 69. 139. 76. 77. 1.04 53.5 50.5 9.5 57. 54. 10. 1.04 146. 76. 89. 164. 86. 96. 1.04 56. 59. 3. 1.04 141.5 150. 7. 1.04 122. 125.5 9. 1.04 130. 88. 54. 1.04 54.5 57. 3. 1.04 153. 105. 63. 1.04 49. 50. 8. 1.04 9 4 pl03 138. 130. 138. 0. 130. 5 77. 66. 129. 76. 65. 1.04 5 2 p 86 96. 9 46. 52. 0. 5. 48.5 1.5 1.04 9 4 pl03 96. 9 130. 138. 0. 130. 97. 45.5 1.04 7 3 p 93 138. 203. 230. -8. 210. 188. 48. 210. 186. 51. 1.04 12 6 r 40 138 . 34. 39.5 0. 37. 18. 23. 37.5 17.5 24. 1.04 10 5 r 29 138 . 66. 72. 0. 70. 73.5 7. 70. 76.5 6. 1.04 10 5 p 23 138. 55. 59. 0. 55. 59.5 5. 57.5 63. 6. 1.04 7 3 p 93 96. 9 203. 230. -8. 212. 209.5 26.5 209.5 207.5 25. 1.04 12 6 r 40 96.9 34. 39.5 0. 32. 21. 15. 36. 23.5 17. 1.04 10 5 r 29 96.9 66. 72. 0. 70.5 77.5 3. 68. 75. 2. 1.04 10 5 p 23 96.9 55. 59. 0. 58. 63. 3. 56.5 61.5 3. 1.04 6 3 p 33 138 . 108.5 120.5 0. 106. 54. 65. 103. 54.5 59. 5 1.04 6 3 r 39 138 . 126.5 141.5 0. 117. 5 62. 69.5 113.5 59. 68. 1.04 9 4 p l l 9 138. 41. 47. 0. 40. 25. 20. 38.5 25. 17. 1.04 6 3 p 33 96.9 154.5 169. 0. 128. 90. 53. 147.5 103. 60. 5 1.04 6 3 r 39 96.9 169.5 187. 0. 149. 103. 64. 153. 107. 64. 1.04 9 4 p l l 9 96.9 55.5 61.5 0. 49. 38. 16.5 55. 43. 18. 1.04 v' v' " J E NO EO DO Nl E l DI N2 E2 D2 N3 E3 D3 Cov. (kV) (1.) (1.5) (2.5) (1.) (1.5) (2.5) (1.) (1.5) (2.5) (1.) (1.5) (2.5) (0.01) 6 3 p 51 138 . 128. 126.5 0. 125. 5 64. 85.5 125. 65. 81. 5 1.34 6 3 r 57 138 . 138. 138. 0. 136. 70. 91.5 138.5 66.5 98. 1.34 8 4 r 72 138 . 136. 142. 5. 131. 84. 63.5 134.5 86. 66. 5 1.34 8 4 p 66 138. 149.5 157.5 5. 158. 5 99. 82. 160. 102.5 82. 1.34 6 3 p 51 96.9 128. 126.5 0. 129. 5 8.3. 62.5 116.5 75. 56. 1.34 6 3 r 57 96.9 138. 138. 0. 140. 90. 66. 127 . 81.5 61. 1.34 8 4 r 72 96.9 136. 142. 5. 135. 107.5 36.5 122. 97. 34. 1.34 8 4 p 66 96.9 149.5 157.5 5. 167. 127. 54. 154. 116. 51. 1.34 6 3 p 87 138. 123. 121.5 0. 120. 59. 83. 119. 59.5 82. 127 .5 66. 86. 1.34 4 2 P 72 138 . 33.5 40. 0. 33. 19.5 20. 33. 16. 25. 33. 5 18. 5 22. 1.34 6 3 r 93 138. 101. 103. 0. 101. 50.5 68. 95. 50. 62. 5 101 .5 55. 64. 1.34 8 4 rl02 138 . 90.5 100. -4. 89. 74.5 22. 87. 73.5 24. 95. 78. 5 30. 1.34 8 4 p 96 138. 123. 131. -5. 119. 5 91. 39. 115.5 89.5 38. 125 .5 98. 5 38. 1.34 6 3 p 87 96.9 123. 121.5 0. 121. 5 80. 58. 125. 77. 65. 1.34 4 2 p 72 96.9 33.5 40. 0. 33. 24. 13. 29. 21. 12. 1.34 6 3 r 93 96.9 101. 103. 0. 102. 5 74. 42. 101.5 72. 43. 1.34 8 4 rl02 96.9 90.5 100. -4. 96. 86. 16. 93. 85. 17. 1.34 8 4 p 96 96.9 123. 131. -5. 126. 5 104. 31. 124.5 108. 25. 1.34 5 3 P 25 138. 130.5 133. 0. 126. 102. 5 41. 124. 101. 38. 131. 100. 44. 1. 34 5 3 r 31 138. 138. 146. 0. 140. 119. 41. 136. 115.5 39. 143. 119. 42. 1.34 8 4 rl 2 6 138. 35. 35. 0. 34. 35. 6. 38. 29.5 5. 38. 33. 7. 1. 34 5 3 P 24 138. 109. 120. 0. 110.5 91. 36. 109. 85.5 42. 116. 92. 40. 1.34 8 4 pl20 138. 51.5 53.5 0. 45. 47. 12. 45. 43. 6. 49. 45. 10. 1. 34 5 3 P 25 96.9 130.5 133. 0. 126.5 116. 20. 124 . 119.5 17. 1. 34 5 3 r 31 96. 9 138. 146. 0. 139. 130. 16. 135. 133. 19. 1. 34 8 4 rl 2 6 96. 9 35. 35. 0. 34.5 35. 3. 30.5 35. 3. 1.34 5 3 P 24 96.9 109. 120. 0. 112. 99. 23. 114.5 102.5 24. 1.34 8 4 pl20 96.9 51.5 53.5 0. 49.5 52.5 5. 51. 49. 5. 1.34 5 3 P 50 138. 153.5 153. 0. 149. 126. 49. 150. 132. 45. 153. 5 126. 47. 1. 34 5 3 r 56 138. 154.5 163. 0. 154 .5 133. 37. 150.5 135. 43. 5 159. 138. 42. 1.34 7 4 P 68 138. 215. 224. 0. 205. 195. 5 45. 212. 189.5 51. 5 214. 5 202. 46. 1.34 7 4 r 74 138. 199. 206. 0. 193. 172. 47. 192.5 178. 48. 197. 5 179. 42. 1.34 5 3 P 50 96.9 153.5 153. 0. 154.5 136. 5 34. 154. 142.5 30. 1.34 5 3 r 56 96.9 154.5 163. 0. 156. 143. 23. 157. 144. 32. 1.34 7 4 P 68 96.9 215. 224. 0. 215. 213. 19. 222. 212.5 20. 1.34 7 4 r 74 96.9 199. 206. 0. 194. 191. 5 21. 196.5 193. 19. 1.34 5 3 P 93 138. 94.5 102.5 0. 93.5 93. 16. 95. 94. 18. 97. 97.5 15. 1.34 8 5 P 27 138. 133. 146.5 0. 131.5 74.5 81. 135. 76. 82. 133. 5 83.5 80. 1.34 8 5 r 33 138. 160. 171. 0. 158. 92.5 95. 159.5 92. 98. 162. 92.5 102. 5 1.34 5 3 r 99 138. 97. 98.5 0. 93. 92.5 20. 94. 98. 17. 98. 93.5 17. 1.34 8 5 P 26 138. 133. 131. 0. 128.5 71.5 80. 129.5 73. 83. 132. 75.5 81.5 1. 34 8 5 r 32 138. 158.5 161.5 0. 153. 82.5 103 151. 82. I l l .5 159. 5 91. 101. 1. 34 5 3 P 93 96.9 94.5 102.5 0. 96. 97. 13. 5 94 . 102. 20. 1.34 8 5 P 27 96.9 133. 146.5 0. 136. 103. 57. 5 138.5 102. 62. 1. 34 8 5 r 33 96.9 160. 171. 0. 158. 116. 5 65. 162. 121. 63. 5 1. 34 5 3 r 99 96.9 97. 98.5 0. 96. 98. 12. 92. 96. 13. 1. 34 8 5 P 26 96.9 133. 131. 0. 130. 98. 52. 128.5 88. 59. 5 1.34 8 5 r 32 96.9 158.5 161.5 0. 154. 112. 61. 5 151. 111. 63. 1. 34 v' v" J E NO EO DO Nl E l DI N2 E2 D2 N3 E3 D3 Cov. (kV) (2.) (3.) (4.) (2.) (3.) (4.) (2.) (3.) (4.) (2.) (3.) (4.) (0.02) 4 4 r 34 138. 72.5 75.5 0. 70.5 44. 52. 74.5 41. 58. 73. 44. 47. 1.33 6 5 r 65 138. 132. 145.5 0. 126. 69. 87. 128.5 79. 77. 126. 70. 84. 1.33 4 4 P 27 138. 73.5 68.5 0. 75.5 43. 50. 5 72.5 50. 50. 67. 36. 48. 1.33 4 4 r 33 138. 87. 83. 0. 92.5 50. 72. 5 83. 51. 73. 82. 54.5 70. 1.33 4 4 P 26 138. 66. 68. 0. 62.5 35.5 53. 62. 38. 61. 62.5 40. 43. 1. 33 4 4 r 34 96. 9 72.5 75.5 0. 80. 51. 38. 77. 54. 41. 1.33 o o o o o o o o o o o o o o o o o o o o o o o o c o o o L O p- r H o r~ t> C T i C O oo r-CN r H CM 0 0 r -T r- y> p L O LO LO LO • • • • • V O CM 0 0 vo >=r cn r H CM o C T l r H r H r H r H LO v o p o i H o n i o ^ ^ o v o n v o m P ' C f L O f O v O C O C O C r i t O L O V O V O P V O C M r ^ r o c r i o o c T i c o c r i o r - ~ ' T ^ T r - r ~ c o ^ r i O ' 5 , ' = r r - L O L O L O L O c y i r - r - v o L O L O L O • L O m O • • • - O O T C M O • CN C N T V O C O O O C N C N C N r O O C N O r ~ r O O C N O r H r ^ O O V O o O r H r H r H r H C O r H r H r H r H C O O O M n H ^ C S v O r l O n O ^ C N t N L O r o c ^ r o r-c3~ i c r i o o c o L o r ^ L o r ~ - v o LO v o L O c o c n ^ r > O M o v o ( N [ ^ v o H r -O O L O L O ' 3 , ' 5 , r ~ - L O V O L O ^ D c r > r ~ O O V O LO LO LO •^ r • . • • o cn r H oo ' r i v o o o r -r H L O O L O r - ^ r o C N O O O ^ O C N O r H V O 0 0 V O C O i — t r — t r H r H 0 0 r H r H r H r H o o o o o o o o o o o o o o LO • LO L O • • • • c r i ' 3 , r > r H • o i T r - T—i T o o r o o o r ~ c M r H C M o r ~ C M r H C M O r H V O O O V O C T l r H r H r H r H C T l r H r H r H r H LO LO • L O LO • • • • LO • • • • CM • • • • O O C T l CM C O • C O C T i CM 0 0 r o r o r - - v o r - - c M o o o r H r - - C M o r o r H i - H r - O O V O 0 0 r H r H r H r H 0 0 r H r H r H r H C T i c T i c r i c r i cn cn CTI cn CTI • • • 0 0 CO OO OO 0 0 vo vo vo vo m n i o r o vo vo vo vo vo c r i o i o ^ c j N H H H H H c r i c n c n a ^ c r t LO l""- CO V O CM C T l LO LO r H CM C T l LO LO r H v o c M o o c M L O v o ^ r - L O L O v o ^ r - L O L O v ^ r ^ r ^ r L O ' ^ L O T T L O ^ L O v o ^ ^ r ^ ' ^ v o ^ v o ' ^ ' ^ r v o ^ r v D ^ r • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > C M C M C M C M C \ | C M C M C M C M C M C M o o ^ U • r H r H r H r H r H r H r H r H r H r H O • o • r- • ro .— • vo co vo L O CM Q • VO rH L O rH VO VO • L O • • • LO • L O CO •—* CM L O O CO rH W • 0 0 0 0 rH 0 0 rH W L O " • LO rH O CM co • oo vo CM r~- r o "Z Cn CO rH rH rH rH CM • o a r-" OO T • rH ^ ' o o o o r - - o o r o o o c M C M W ^ c O O O C ^ h C T i O O H H O O H • • • « • O 0 0 rH • LO • vo • C N C M O C M rH C M V O rH rH rH r-H rH t -CM 2 0 0 L O L O L O r H O O O O O r- i - H 0 0 L O C M O V O r H L O r H 0 0 L O ^ r H r H r H r H r H C T l r H r H r H r H • O • r H • • • • LO CM CM 0 0 LO 0 0 o CM V O r H r- r H ro 0 0 r H V O • - C M • T • <r> «3* - C M 2 , w r - o v o o ( N O O W H ^ r - C T l r H V O r H C T l r H r H r - r H LO LO LO . " T r - L O L O o c T i • r H r- co ro Z r o O L O o o L n c M r - L O o O L O O o —• r H r H i - H i - H i — I C T l i — I r H r H r H o * " Q . O C O L O O O O O O O O L O O O O O v o o o r ^ L O L O v o o o r - L O L O v o o . v o r - r - r H . v o r - r - r H M • r - ' = r O C M r H r - ' * O C M r H f O O H H H H O O H H H H LO LO LO LO LO LO o • c o r - C M ^ r i o o o r ~ C N j ^ T L O ^ O O O V O C M L O O O O V O C M L O O O ^ r - i r - l r - l i - i t - l t - t r - i t - i r - l r - l •—• C T i C T l C T i C T i C T i > 0 0 0 0 0 0 0 0 0 0 H^oororororovovovovovo '' r H r H r H r H r H C T l C T i C T l C T i C T t V O r O L O C T l r H V O r O L O C T l r H C M O C M O O r O C M O C M O O O O *- } r H r H > v o L n v o ^ v o v o i n v o ^ v o > r ^ v o [ ^ ^ < r - r - v o r ^ ' 3 , r -67 Appendix B Calculated predissociation rate from experiment data The electric field induced predissociation rate constants calculated from the data in appendix A are listed here. In the column Gamma are calculated total decay rate TT in the unit of K The unit of electric field strength is k V / c m . The unit of /?2 and /?3 are c m 2 k V _ 2 s _ 1 . For each given transition, the first two lines of data give those /?s calculated by RATIO method; the last two lines of data are those calculated by D I F F E R E N C E method and are not used in analysis of data. 1 J Gamma (1/s) E (kV/cm) betal beta2 beta3 ave, err 4-4 p 26 2.71e+06 138. 115 96 86 99 +- 16 from RATIO method 96.9 106 91 98 +- 8 138. 197 212 142 184 +- 42 from DIFFERENCE method 96.9 192 173 182 +- 10 4-4 p 27 3.33e+06 138. 111 61 128 100 +- 39 96.9 36 162 99 +- 63 138. 191 162 217 190 +- 27 96.9 229 331 280 +- 51 4-4 r 33 3.44e+06 138. 138 99 78 105 +- 32 96.9 116 174 145 +- 29 138. 243 240 215 233 +- 17 68 4-4 r 34 2.85e+06 4 -4 p 45 3.72e+06 4 -4 r 51 3.89e+06 4 -4 r 52 3.31e+06 4 -2 p 72 4.04e+06 4 -4 p 89 5.45e+06 5-3 p 24 2.79e+06 96.9 218 380 299 +- 81 138. 100 133 108 114 +- 19 96.9 192 147 170 +- 23 138. 164 196 148 170 +- 27 96.9 211 215 213 +- 2 138. 181 170 171 174 +- 7 96.9 179 172 176 +- 3 138. 283 269 237 263 +- 26 96.9 262 314 288 +- 26 138. 131 160 136 142 +- 18 96.9 177 171 174 +- 3 138. 274 318 256 283 +- 36 96.9 357 363 360 +- 3 138. 206 155 258 206 +- 52 96.9 202 244 223 +- 21 138. 260 201 288 250 +- 48 96.9 281 288 284 +- 4 138. 215 309 245 256 +- 52 96.9 276 279 278 +- 2 138. 201 306 233 246 +- 59 96.9 216 228 222 +- 6 138. 247 227 192 222 +- 30 96.9 377 322 349 +- 28 138. 305 355 327 329 +- 26 96.9 612 467 540 +- 73 138. 49 59 57 55 +- 6 69 5-3 p 25 3.46e+06 5-3 r 31 3.57e+06 5-3 p 50 3.40e+06 5-3 r 56 3.61e+06 5-2 p 64 3.91e+06 5-2 r 70 4.16e+06 96.9 73 68 71 +- 2 138. 54 66 59 60 +- 7 96.9 64 65 64 +- 0 138. 46 45 61 51 +- 10 96.9 41 21 31 +- 10 138. 67 63 74 68 +- 6 96.9 59 49 54 +- 5 138. 46 46 51 47 +- 3 96.9 50 28 39 +- 11 138. 60 58 61 60 +- 1 96.9 43 50 47 +- 3 138. 32 24 38 31 +- 8 96.9 46 ' 28 37 +- 9 138. 64 56 62 61 +- 4 96.9 84 71 77 +- 6 138. 43 33 41 39 +- 6 96.9 58 58 58 +- 0 138. 49 56 53 53 +- 4 96.9 57 79 68 +- 11 138. 38 38 33 36 +- 3 96.9 38 27 32 +- 6 138. 44 44 40 42 +- 3 96.9 51 25 38 +- 13 138. 48 46 46 47 +- 2 96.9 56 42 49 +- 7 138. 49 49 48 49 +- 1 70 96.9 5-2 p 86 4.95e+06 138. 96.9 138. 96.9 5-3 p 93 6.00e+06 138. 96.9 138. 96.9 5- 3 r 99 6.37e+06 138. 96.9 138. 96.9 6- 3 p 33 3.50e+06 138. 96.9 138. 96.9 6-3 r 39 3.63e+06 138. 96.9 138. 96.9 6-3 p 51 3.96e+06 138. 96.9 138. 96.9 6-3 r 57 4.16e+06 138. 71 27 28 28 +- 0 43 28 36 +- 8 26 26 +- 0 40 49 45 +- 5 19 19 +- 0 28 30 25 28 +- 3 47 -0 23 +- 24 50 56 45 50 +- 6 82 116 99 +- 17 7 -9 21 7 +- 15 -4 -18 -11 +- 7 67 54 56 59 +- 8 77 85 81 +- 4 216 201 209 +- 7 207 211 209 +- 2 262 238 250 +- 12 261 260 261 +- 0 213 219 216 +- 3 231 223 227 +- 4 253 260 257 +- 4 286 275 281 +- 5 194 187 190 +- 4 229 226 227 +- 1 257 241 249 +- 8 295 292 293 +- 1 205 236 220 +- 15 6-5 p 6-2 p 96.9 246 248 247 +- 1 138. 264 297 280 +- 17 96.9 301 308 304 +- 3 65 4. ,46e+06 138. 236 185 229 217 +- 32 96.9 218 358 288 +- 70 138. 274 212 261 249 +- 37 96.9 297 411 354 +- 57 69 4, ,62e+06 138. 201 168 227 199 +- 30 96.9 232 205 218 +- 14 138. 275 237 308 273 +- 36 96.9 331 322 327 +- 4 75 4. ,89e+06 138. 202 253 159 205 +- 48 96.9 271 289 280 +- 9 138. 315 380 261 319 +- 61 96.9 431 479 455 +- 24 84 4. . 69e+06 138. 280 278 280 279 +- 2 96.9 326 318 322 +- 4 138. 206 205 198 203 +- 5 96.9 234 219 226 +- 8 87 5, ,48e+06 138. 289 280 260 276 +- 16 96.9 292 352 322 +- 30 138. 374 366 346 362 +- 16 96.9 392 457 424 +- 32 93 5 .81e+06 138. 316 285 268 289 +- 26 96.9 255 271 263 +- 8 138. 379 352 328 353 +- 26 72 96.9 326 343 334 +- 9 6-5 pl03 6. ,40e+06 138. 133 206 234 191 +- 58 96.9 142 305 223 +- 82 138. 157 173 218 183 +- 35 96.9 42 270 156 +-114 7-6 p 25 3. ,16e+06 138. 27 -0 2 9 +- 17 96.9 54 57 55 +- 1 138. 27 28 2 19 +- 17 96.9 60 69 64 +- 5 7-6 p 26 2. ,60e+06 138. 12 -3 -18 -3 +- 15 96.9 -42 -31 -36 +- 5 138. 58 63 58 60 +- 4 96.9 23 39 31 +- 8 7-3 p 28 2, ,63e+06 138. 10 11 10 10 +- 0 96.9 9 13 11 +- 2 138. 33 33 -3 21 +- 24 96.9 -2 -4 -3 +- 1 7-3 p 29 3, ,23e+06 138. 7 6 4 6 +- 2 96.9 -0 3 1 +- 1 138. 37 41 -4 25 +- 29 96.9 -4 -8 -6 +- 2 7-6 r 31 3 .26e+06 138. 3 58 -10 17 +- 41 96.9 -9 -13 -11 +- 2 138. 11 61 -9 21 +- 40 96.9 -18 22 2 +- 20 7-3 r 32 2 .70e+06 138. 4 7 5 5 +- 2 7-3 r 33 3.30e+06 7-3 p 46 3.02e+06 7-3 r 52 3.19e+06 7-4 p 68 3.74e+06 7-4 r 74 3.99e+06 7-3 p 78 4.16e+06 96.9 3 9 6 +- 3 138. 23 23 6 17 +- 11 96.9 9 8 9 +- 1 138. 13 10 8 10 +- 3 96.9 5 9 7 +- 2 138. 37 38 0 25 +- 25 96.9 3 -3 0 +- 3 138. 9 10 11 10 +- 1 96.9 11 11 . 11 +- 0 138. 33 32 32 32 +- 1 96.9 38 41 40 +- 2 138. 18 17 13 16 +- 3 96.9 19 19 19 +- 0 138. 41 38 37 39 +- 3 96.9 49 51 50 +- 1 138. 18 32 21 24 +- 9 96.9 21 35 28 +- 7 138. 42 49 41 44 +- 5 96.9 33 35 34 +- 1 138. 34 25 30 29 +- 4 96.9 21 23 22 +- 1 138. 53 52 45 50 +- 5 96.9 43 39 41 +- 2 138. 33 35 34 34 +- 1 96.9 40 37 38 +- 2 138. 61 60 61 61 +- 1 74 7-3 r 84 4.44e+06 7-3 p 93 5.49e+06 8-5 p 26 2.08e+06 8-5 p 27 2.51e+06 8-3 p 31 2.55e+06 8-5 r 32 2.15e+06 8-5 r 33 2.58e+06 96.9 62 62 62 +- -0 138. 51 46 44 47 +- 4 96.9 57 50 53 +- 3 138. 67 70 63 67 +- 3 96.9 72 72 72 +- 0 138. 76 80 78 +- 2 96.9 86 84 85 +- 1 138. 102 108 105 +- 3 96.9 114 111 113 +- 2 138. 84 81 79 81 +- 3 96.9 68 97 83 +- 15 138. 113 115 109 112 +- 3 96.9 109 139 124 +- 15 138. 124 126 100 116 +- 17 96.9 122 133 127 +- 6 138. 132 131 117 127 +- 10 96.9 138 151 144 +- 6 138. 110 112 111 111 +- 1 96.9 125 109 117 +- 8 138. 77 79 76 77 +- 2 96.9 51 41 46 +- 5 138. 100 98 88 96 +- 7 96.9 92 88 90 +- 2 138. 130 142 116 129 +- 13 96.9 116 120 118 +- 2 138. 111 115 118 115 +- 3 75 96.9 123 118 121 +- 3 138. 128 133 138 133 +- 5 96.9 142 134 138 +- 4 8-3 r 37 2. 63e+06 138. 109 105 103 106 +- 3 96.9 118 118 118 +- 0 138. 81 76 74 77 +- 4 96.9 52 48 50 +- 2 8-4 P 66 2. 78e+06 138. 100 94 97 +- 3 96.9 114 118 116 +- 2 138. 105 101 103 +- 2 96.9 106 109 107 +- 1 8-4 r 72 2. , 93e+06 138. 96 97 97 +- 0 96.9 97 98 98 +- 0 138. 99 102 100 +- 1 96.9 85 87 86 +- 1 8-3 P 93 4. ,00e+06 138. 77 76 79 77 +- 2 96.9 71 74 73 +- 1 138. 62 61 64 62 +- 2 96.9 62 60 61 +- 1 8-4 P 96 3 ,69e+06 138. 77 72 69 73 +- 4 96.9 116 90 103 +- 13 138. 87 86 78 84 +- 5 96.9 126 101 114 +- 12 8-3 r 99 4 .22e+06 138. 63 62 71 66 +- 6 96.9 77 70 74 +- 3 138. 52 52 59 54 +- 5 76 96.9 68 57 63 +- 5 8-4 rl02 3. ,92e+06 138. 66 63 69 66 +- 3 96.9 97 87 92 +- 5 138. 66 72 82 74 +- 9 96.9 90 96 93 +- 3 8-3 pl03 4. ,37e+06 138. 64 63 58 62 +- 3 96.9 65 65 65 +- 0 138. 83 86 78 82 +- 4 96.9 85 80 82 +- 2 8-4 pl20 4. ,67e+06 138. -1 21 32 17 +- 19 96.9 -10 40 15 +- 25 138. 58 32 50 47 +- 15 96.9 44 47 45 +- 2 8-4 rl26 4. ,94e+06 138. -7 74 39 35 +- 43 96.9 -8 -68 -38 +- 30 138. 41 41 51 44 +- 7 96.9 42 42 42 +- -0 9-4 p 25 1, ,89e+06 138. 85 84 84 84 +- 1 96.9 90 94 92 +- 2 138. 109 102 107 106 +- 4 96.9 115 116 116 +- 1 9-4 r 30 1. ,66e+06 138. 80 80 78 79 +- 1 96.9 85 84 84 +- 0 138. 100 97 99 99 +- 2 96.9 108 104 106 +- 2 9-4 r 31 1 .94e+06 138. 92 93 91 92 +- 1 77 96.9 99 97 98 +- 1 138. 114 114 115 114 +- 1 96.9 126 123 125 +- 1 9-4 P 46 1. 84e+06 138. 101 98 96 98 +- 3 96.9 104 109 107 +- 3 138. 123 123 123 123 +- 0 96.9 134 139 137 +- 3 9-4 r 52 1. ,92e+06 138. 10 105 96 100 +- 4 96.9 111 113 112 +- 1 138. 123 122 122 122 +- 1 96.9 143 140 142 +- 2 9-4 P 59 2. ,30e+06 138. 107 116 110 111 +- 5 96.9 126 126 126 +- 0 138. 136 146 142 141 +- 6 96.9 158 160 159 +- 1 9-4 r 65 2 ,40e+06 138. 121 122 116 119 +- 4 96.9 128 120 124 +- 4 138. 154 153 149 152 +- 3 96.9 162 151 156 +- 5 9-4 P 86 2 . 59e+06 138. 127 130 128 128 +- 2 96.9 139 134 136 +- 2 138. 155 165 159 160 +- 5 96.9 169 162 166 +- 4 9-4 r 92 2 .74e+06 138. 128 159 129 139 +- 21 96.9 146 156 151 +- 5 138. 153 176 157 162 +- 14 96.9 170 185 178 +- 8 9-4 pl03 3. 31e+06 138. 138 139 138 +- 0 96.9 149 149 +- 0 138. 176 176 176 +- 0 96.9 196 196 +- 0 9-3 pllO 3. 25e+06 138. 143 166 144 151 +- 15 96.9 142 174 158 +- 16 138. 175 209 182 188 +- 20 96.9 163 193 178 +- 15 9-4 pl l 9 3. ,81e+06 138. 166 152 159 +- 7 96.9 174 169 172 +- 2 138. 189 161 175 +- 14 96.9 210 202 206 +- 4 10-5 p 23 1 .60e+06 138. -1 -2 -1 +- 1 96.9 -2 -2 -2 +- 0 138. 8 9 9 +- 1 96.9 1 1 1 +- 0 10-5 r 29 1 .63e+06 138. 3 -0 2 +- 2 96.9 -1 -2 -2 +- 0 138. 1 8 9 +- 1 96.9 8 6 7 +- 1 10-4 p 45 1 .74e+06 138. 5 4 5 5 +- 0 96.9 11 1 10 +- 1 138. 10 1 14 11 +- 2 96.9 11 11 11 +- 0 10-4 r 51 1 .80e+06 138. 3 5 6 5 +- 2 96.9 10 8 9 +- 1 138. 11 12 14 12 +- 2 96.9 13 11 12 +- 1 10-4 p 98 2. ,27e+06 138. 30 31 25 28 +- 4 96.9 24 38 31 +- 7 138. 24 25 17 22 +- 5 96.9 18 27 23 +- 4 10-4 pl07 2, ,65e+06 138. 66 64 59 63 +- 4 96.9 76 74 75 +- 1 138. 82 77 79 79 +- 3 96.9 95 87 91 +- 4 12-6 r 40 9, ,16e+05 138. 66 71 69 +- 2 96.9 75 76 76 +- 0 138. 73 78 75 +- 3 96.9 83 84 83 +- 1 80 Appendix C The wave function solution of a straight line potential Assume C potential curve is a straight line and pass the two points: x = b U = e x = R U = 0 Then the line equation is: U = -Fx + B where F = and B = FR. The schrodinger equation is: h2 d2^ + [E-U)y = 0 (C.82) (C.83) 2fi dx2 where \i is reduced mass, E is the total energy, U is the potential energy. Substitute into the Eq. C.82 we get: d2^ dx2 " The solution for Eq: C.84 is[3]: x + E-B F v%) = AT(-y) where x + E-B F T(-y) = Airy(-y) The above equations should be equivalent to semiclassical theory when y is large (C.84) (C.85) (C.86) (C.87) 81 Bibliography [1] J . C. Lehmann, Iodine, a test molecule in modern spectroscopy, Contemp. Phys. 19, No. 5, 449-468, (1978) [2] G. Herzberg, Molecular spectra and molecular structure, second edition, (1950) [3] L. D. Landau and E . M . Lifshitz Quantum mechanics, third edition, (Pergamon press, Oxford, 1977) [4] M . S. Child, Semi-classical analysis of weakly inelastic molecular collisiona, Mol. Phys. 8, 517-531, (1964) [5] M . S. Child, Repulsive potential curves from predisociation data, J. Mol. Phys. 33, 487-493, (1970) [6] D. S. Ramsay and M . S. Child, Analytical theory of fluctuations in the predissociation linewidth, Mol. Phys. 22, 263-271, (1971) [7] M . S. Child, Direct inversion of magnetic flourescence quenching data for the B3ILQ+ state of iodine, J. Mol. Spectrosc. 45, 293-297, (1973) [8] M . S. Child, Predissociation and photodissociation of IBr: A case of intermediate coupling strength, Mol. Phys. 32, No. 6, 1495-1510, (1976) [9] M . S. Child, Analytical interpretation of predisociation rates: the B 3 I I 0 + state of Br2, J. Phys. B: Atom. Molec. Phys., 13, 2557-2563, (1980) [10] F. W. Dalby, C. D. P. Levy and J . Vanderlinde, Vibrational and rotational depen-dence of electric field induced predissociation of I2 , Chem. Phys 85, No. 1, (1984) 82 [11] I. S. Gradshteyn and I. M . Ryzhik, Table of integrals, series, and products, corrected and enlarged edition, P399. [12] R. F . Barrow and K . K . Yee, B3U0+ - system of127I2: rotational analysis and long range potential in the B 3II0+ state, J. Chem. Soc. Faraday Trans. II 69, P684, (1973) [13] C. D. Hodgman et al. Handbook of chemistry and physics, 39th edition, (Chemical Rubber Publishing Co., Ohio 1957-1958) [14] J . L. Booth, F. W. Dalby, S. Parmar and J. Vanderlinde, Ortho-para iodine separa-tion revisited, Chem. Phys. 132, P209-217, (1989) [15] S. Gerstenkorn and P. Luc, Atlas du spectre d'Absorption de la molecule d'iode (C. N . R. S., Paris,1977) [16] J . Vigue, M . Broyer and J . C. Lehmann, Natural haperfine and magnetic predisso-ciation of the I2 B state, I., J. Physique 42, P937-947, (1981) [17] J . Vigue, M . Broyer and J . C. Lehmann, Natural haperfine and magnetic predisso-ciation of the h B state, II., J. Physique 42, P949-959, (1981) [18] J . Vigue, M . Broyer and J . C. Lehmann, Natural haperfine and magnetic predisso-ciation of the h B state, HI, J. Physique 42, P960-978, (1981) [19] B . J . Sullivan and D. A . Dows, Electric field-induced predissociation of I2 (B3H0+ ) Chem. Phys. 46, P231-236, (1980) [20] C. Zener, Proc. Roy. Soc. A140, 660, (1933) [21] R. S. Mulliken, Iodine Revisitd, J. Chem. Phys. 55, P289, (1971) 83 [22] J. Vigue, THESIS DE DOCTORAT D'ETAT, UNIVERSITE DE PARIS. P222. (1978) [23] S. Gerstenkorn and P. Luc, Discription of the absorption spectrum of iodine recorded by means of Fourier Transform Spectroscopy: the (B-X) system J. Physique 46, P867-881, (1985) 84 

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