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Radiative lifetime of the B³[Pi]₀₊u̳ state of Br₂ Deng, Qing 1989

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R A D I A T I V E L I F E T I M E OF T H E £3n o + u S T A T E OF Br2 By Qing Deng B. Sc. (Physics) Shandong University, China A THESIS S U B M I T T E D IN PART IAL 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 OF S C I E N C E in T H E F A C U L T Y OF G R A D U A T E STUDIES PHYSICS We accept this thesis as conforming to the required standard T H E UN IVERS ITY O F BRITISH C O L U M B I A September 1988 © Qing Deng, 1989 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 p H Y5 I CS The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract The absorption and fluorescence spectra of the molecule bromine corresponding to the transition between the ground state, X1E 04 5, and excited state, B3U0+U, have been measured from approximately 17464 cm-1 to 17480 cm'1. This region of the spectra covered the 14' — l " , 15' — l " , 17' — 2", 18' — 2", and 19' — 2" vibrational bands. The frequency of each absorption line was calculated and the integrated absorption coefficient under each absorption line was measured. At room temperature, the number of molecules per cm3 for (79,79)£?r2, (79,81).Br2 and (81,81)Br2 have been calculated. By using both theory and experiment the radiative lifetime rrad, from B state to X state of (79,79).Br2, (79,81)JBr2 and (81,81)i?r2 for v' = 14,15,17,18,19 have been obtained. The predissociation of Br2 in the B3U0+U state is discussed. ii Table of Contents Abstract i i List of Tables vi List of Figures vi i i Acknowledgements ix 1 Introduction 1 2 Theory 4 2.1 Internal motion of a diatomic molecule 4 2.2 Born-Oppenheimer method 5 2.2.1 The vibration and rotation of diatomic molecules 8 2.3 Electronic states of a diatomic molecule 11 2.4 Coupling of electronic motion and rotation 12 2.5 The symmetry properties of a diatomic molecule 12 2.5.1 The symmetry of the electronic wavefunction 12 2.5.2 g and u symmetry of electronic states 13 2.5.3 + , - parity of rotational states 13 2.5.4 s and a symmetry of rotational states 13 2.6 The selection rules of molecular bromine for transitions 13 2.6.1 For the electronic transitions 13 2.6.2 For the vibrational transitions 14 iii 2.6.3 For the rotational transitions . . 14 2.7 The distribution of the number of molecules 15 2.8 The effect of nuclear spin 16 2.9 Absorption of light by a diatomic molecule 19 2.9.1 Definition of the absorption coefficient 19 2.9.2 The relations between the Einstein coefficients and the integrated absoption coefficient 20 2.9.3 The relation between the Einstein coefficient and transition prob-abilities 22 2.9.4 The radiative lifetime of B3U.0+U state of Br2 . . 23 2.9.5 The predissociation of Br2 in the J53II0+ustate 25 3 Experimental apparatus and spectrum 27 3.1 Preparation of the sample cell 27 3.2 Experimental set-up 28 3.3 Absorption spectrum of molecular bromine . . 29 4 Data Analysis 31 4.1 Assignment of Br2 lines 31 4.2 Calculating the Br2 transition energies 32 4.3 The absorption band strengths 33 4.4 Calculating the integrated absorption coefficient 35 5 The Results and Discussions 39 Appendices 49 A The derivation of the transition probabilities 49 iv B The vibrational and rotational transition probabilities 51 B.l Vibrational transition probability 51 B.2 Calculation of the rotational transition probabilty 51 C The density of molecular bromine in a particular rovibronic state 54 D Identified and unused lines of Band 14' — l " 55 E Identified and unused lines of Band 17' — 2" 58 F Identified and unused lines of Band 18' — 2" 62 G Identified and unused lines of Band 19' — 2" 64 H Identified and unused lines of Band 15' — l " 65 Bibliography 71 v List of Tables 2.1 The degeneracy introduced by nuclear spin 17 4.2 Obtaining the band 15' - l " of (79-81)£r2 . 32 4.3 Molecular constants (cm-1) for the 1E0+U state 34 4.4 A part of the particle densities (in cm~3) on v" = 1, (79,79).Br2 34 5.5 | Re |2 values for 14' - l " of (79-79)#r2 41 5.6 | Re |2 value for overlapped lines 42 5.7 Mean | Re |2 for all identified bands . 43 5.8 rr a ii. for the excited state v . 43 5.9 The Trad. of <79^Br2 obtained by Clyen 44 5.10 The values of £?„v, vz 45 5.11 TTad, for the excited state v 47 D.12 Band 14' - l " bromine (79,81) 55 D. 13 Band 14' - l " bromine (79,79) 56 D.14 The unused lines from band 14' — l " bromine (79,79) . . 57 D. 15 The unused lines from band 14 - 1 bromine (79,81) 57 E. 16 Band 17' - 2" bromine (81,81) 58 E.17 Band 17' - 2" bromine (79,79) 59 E.18 Band 17' - 2" bromine (79,81) 60 E.19 The unused lines from band 17' — 2" bromine (79,79) 61 E.20 The unused lines from band 17' - 2" bromine (79,81) 61 vi E. 21 The unused lines from band 17' - 2" bromine (81,81) 61 F. 22 Band 18' - 2" bromine (79,79) 62 F.23 Band 18'- 2" bromine (79,81) 62 F.24 Band 18' - 2" bromine (81,81) 63 F.25 The unused lines from band 18' - 2" bromine (79,79) . . . . . . . . . . . 63 F.26 The unused lines from band 18' - 2" bromine (79,81) 63 F. 27 The unused lines from band 18' - 2" bromine (81,81) 63 G. 28 Band 19'- 2" bromine (79,79) . . . 64 G. 29 Band 19' - 2" bromine (79,81) < . . . . . 64 H. 30 Band 15' - l " bromine (79,79) 65 H.31 Band 15' - l " bromine (79,81) 65 H.32 Band 15' - l " bromine (81,81) 66 H.33 The unused lines from band 15' - l " bromine (79,79) 66 H.34 The unused lines from band 15' - l " bromine (81,81) 66 H.35 The F.C.F.used for calculating | Re |2 67 H.36 The F.C.F.((79'79)-Br2) used for calculating rrad 67 H.37 The F.C.F. used for calculating rrad 68 H.38 The F.C.F.((81-81)/5r2) used for calculating rTad 68 H.39 The F.C.F.((79-81)£r2) used for calculating Trad 69 H.40 The F.C.F. used for calculating Trad 70 vii List of Figures 1.1 Potential energy curves for Br2 2 2.2 The Cartesian and Molecule Coordinate Systems o -xyz is the molecule coordinate systems o-(n( is the space coordinate systems 5 2.3 The absorption of radiation 19 2.4 The typical shape of a spectral line 20 3.5 Experimental arrangment. Mi, M2: total reflectional mirror; S: splitter; Fu F2, F3, FA, F5: filter; PM: photomultiplier; PD: photodiode; MC: monochrameter; PC: photo counter; TLR1,TLR2: two line recorder . 28 3.6 Part of the Absorption Spectroscopy 30 4.7 Digitizing an absorption line 36 4.8 Overlapped absorption lines 37 5.9 + and A represent P and R branches 46 5.10 v = 16, £3n0+ustate of <79'79)£r2 47 5.11 v = 14, £3n0+ustate of (79-79)Br2 48 viii Acknowledgements I would like to express my heartfelt thanks to my supervisor, Dr. F.W.William Dalby, for his support, guidance and encouragement during the course of the project. I would also to thank Dr. Alan Bree for his suggestions and helps. Special thanks are extanded to Jim Booth for his valuble suggestions and constant helps. Many thanks to Alak Chandn for' his helps and helpful conversations. I would also to thank Patrick Tang for all his helps in analying part of the spectrum. ix Chapter 1 Introduction For a number of years the spectroscopy of halogen molecules, especially I2 , has attracted considerable interest. The spectrum of the B - X system of I2 has been studied successfully and extensively by various research groups. Bromine, being on the same column (VIIA) of the periodic table as iodine, has prop-erties that closely resemble those of iodine. Of special spectroscopic interest is the B -X system of Br2 which is very similar to the B - X system of I2, the absorption and fluoresence spectra of both lying in the visible region. The B - X system of Br2 has also been extensively investigated [5,9,10,19]. The bromine atom with atomic number 35 and international atomic weight of 79.909 a.m.u. has 35 electrons, 5 of which lie in the outermost, or valence, shell. The electronic configuration is expressed as Br(35): l.s2 2s2 2pe 3s2 3p6 3d10 4s2 4p5 or K L M 4s2 Ap5 Bromine occurs natually in two isotopes, yielding three types of Br2 which are 79'79£r2, 7g'slBr2, and 81<8lBr2 in a relative abundance of 1.0216 : 2.0 : 0.9784. The combination of two bromine atoms to form a molecule gives rise to a XXE0+U ground state and the first excited state B3H0+U (see Figure 1.1) [24]. A few other states lying above the ground states are also shown in Figure 1.1. Chapter II describes the theoretical work of dealing with the internal motion of a diatomic molecule. We consider molecular bromine as a non-translating rigid rotator 1 Chapter 1. Introduction 2 I I 1 ! ! ! 1 LS 2£> 2.5 3.0 3.5 4.0 4.3 INTCRNUCLEAR OlSTANCE (I) Figure 1.1: Potential energy curves for Br2 Chapter 1. Introduction 3 and this rigid rotator moves around the center of mass which are the origins of both space and molecular coordinate system. We also consider the vibration as a simple harmonic motion. From the Born-Oppenheimer approximation, the wave function of the system can be separated to a good approximation into an electronic part ij)e and a vibrational part i\)n so that the coupled Schrodinger equation of the system be separated. From solving the two Schrodinger equations we can obtain the electronic and nuclear (vibrational and rotational) energies. In fact, the vibration1 of molecule is a non-simple harmonic motion and the rotation of molecular bromine is not a rigid rotator. Therefore we have to amend the results obtained from the approximation to obtain finally the total energy of the system. In Chapter III we describe the apparatus used to study the radiative lifetime of B3n0+U state of Br2 and the construction of bromine sample cell. We also report the absorption spectum in this chapter. Chapter IV describes the procedure of analysing the data. We use the iodine atlas obtained by another research group [21] to calibrate the bromine spectrum. By checking the dispersion of each scan region we found the frequency of each absorption line. We used a digitizer to get two sets of data and then to calculate the area under each absorption line by using those data. In order to make sure the lines are not overlapped we assume the line is a Gaussian distrubution and then compare the two values of / kvdv between the Gaussian distrubution and the real / kvdv. We also calculate the half width of each absorption spectral line to check whether the line is overlapped or not. In order to obtain the radiative lifetime we also calaulate the density of Br2 in the different vibrational and rotational energy levels. Chapter V provides a discussion of the results; we compare our results of radiative lifetime with the results obtained by other authors. The predissociation rate of molecular bromine in the B3H0+U state is also discussed in this chapter. Chapter 2 Theory 2.1 Internal motion of a diatomic molecule An atom has only one nucleus and some electrons moving around it. Because the nucleus has much greater mass than the electrons, one can assume that all the electrons move approximately in a central potential produced by the nucleus and so estimate the energy levels. The simplest molecule consists of two atoms; for example, molecular bromine consists of two bromine atoms. The electrons in this kind of molecule move in the potential produced by the two nuclei, and nuclei will vibrate about their equinbrium positions (where the potential energy is at a minimum), and rotate around its center of mass. Therefore, both the electron and nuclear motions should be taken into account at the same time in the study of molecular internal motions. Because it has been found that there is a certain structure for every kind of molecule and this structure is determined by the equilibrium positions of nuclei, one can divide the molecular internal motion into three kinds: electronic motion, and rotational, vibrational motion of the nuclei. Before we start to look these three kinds of motions, two kinds of coordinate systems should be introduced. One is the normal Cartesian system which will be fixed in space and will not move with molecule; another one is called the molecular coordinate system which will be fixed on the molecule (actually nuclei's equilibrium positions) and will rotate with the molecule (Fig.2.2). Both of the two systems will take the center of mass of the molecule as their origins. The relation between the two systems can be described 4 Chapter 2. Theory 5 1 Figure 2.2: The Cartesian and Molecule Coordinate Systems o -xyz is the molecule coordinate systems o-£r]C, is the space coordinate systems by the Eulerian angles (<f>, 6, 6) [6]. For the molecular rotations, we can assume that each nucleus is fixed at its equilibrium position, the two nuclei can be recognized as a rigid rotor like a dumbell fixed on the z axis of the molecular coordinate system (Fig.2.2). This "dumbell" can rotate freely around the original point (center of mass). The vibrations can be described in the molecular coordinate system. 2.2 Born-Oppenheimer method In quantum mechanics, the quantum states of a physical system are charaterized by a wave function, \t, which contain all the information about the physical system. The Chapter 2. Theory 6 probability of finding the system in such a state ^  is | |2= J V*VdT (2.1) The dynamical evolution of the state vector \P is governed by the Schrodinger equa-tion: ih— = H* (2.2) where H is the Hamiltonian, an observable associated with the total energy of the system. That is, H = T + U (2.3) where T and U are the kinetic and potential energy of this dynamical system. The Hamiltonian of the Br2 molecule can be expressed, to the first order, as [26] 2 p2 Z!+Z2 2 Zi+Z2 7 „2 Zi+Z2 7 2 7 7 p2 „2 * = E ^ + E E T ^ - E f ^ + ^  + E ^ (2.4) ,=1 j=i Z m « j=i r i j j=i r2j -^12 j>j rtj where Zi, Z2: atomic numbers of atom one and atom two Pi: the linear momentum of nucleus i PJ: the linear momentum of electron j Mt: the mass of nucleus i mi%. the mass of electron i nJ: the distance between nucleus 1 and electron j r2f. the distance between nucleus 2 and electron j R\2: the intemuclear distance Chapter 2. Theory 7 r,-j-: the distance between electrons i and j In the above equation, the first term describes the kinetic energy of the two bromine nuclei; the second term the electron kinetic energy; the third and the fourth are the coulomb potential energy between electrons and the nucleus one and nucleus two, re-spectively; the fifth term is the coulomb potential energy between the two nuclei; and the last term is the coulomb potential energy between all electrons. In general, it is impossible to solve this Schrodinger equation exactly for such a system. Since the mass of electrons is much smaller than the mass of nucleus, the velocity of electron is much greater than that of nucleus. Whenever the nucleus moves a little bit, the electron has already moved through many orbits around it. Accordingly, Born and Oppenheimer introduced an approximation in which they separated the electronic and nuclear motions by supposing that the nuclei are fixed at their equilibrium positions and electrons move in a stable potential produced by the two nuclei, the distance between the two nuclei being regarded as a parameter. From solving the Schrodinger equation for the electrons, they could get the electron eigenenergy with the coordinate of nuclei as a parameter. Then, they solved the Schrodinger equation for the nuclear motions (i.e. vibrations and rotations) by substituting the electronic eigenenergy in. In order to realize that, they wrote the wavef unction as, *=Ve^n (2.5) where ipe is electronic eigenfunction and ipn is the nuclear eigenfunction. Substituting this eigenfuntion $ into the Eqn.(2.2), we can get two equations: t 2 Z1+Z2 y 2 Z1+Z2 7 2 „ 2 l - ^ - E v ? - E t 1 - E f + E f l ^ ^ ^ N W (2.6) Z m i j = l r l j j = l r 2 j i > j r « ? Chapter 2. Theory l 8 [- E 2 ^ V? +Ee(Rl2) + ^ g ^ n = (2.7) When solving Eqn.(2.6), one can recognize R\2 as a parameter in the electronic eigen-values and eigenfunctions. The third term of Eqn.(2.7) can be removed by supposing that it has be included in this parameter. Therefore the Eqn.(2.7) can be written as j - E | ; v j + £ ; ( m = % (2.8) So, one can solve the Eqn.(2.6) to get a set of eigenvalues E£: EZ = EZ(rij,R12) (2.9) and eigenfunctions tl>%: ^ = ^(rij,R12) (2.10) where _E£(r,j, .ft12) and (r,j, i?12) should be the sum of electronic kinetic and po-tential energy, and the electronic eigenfunctions for a certain molecular state. It is quite obvious that in the Eqn.(2.8), the E'e(Ri2) actually takes the role of potential energy in the Schrodinger equation. It is well known that whenever the E'e(Ri2) has a minimum, there should be a stable structure corresponding to it. So, theoretically speaking, once one obtained V'^( rtj, R12) and an electronic energy Ej?(r{j, i?i2), i.e. a stable molecular structure, from solving Eqn.(2.6) , one can in principle determine the nuclear motion: vibrations and rotations, from Eqn.(2.8). 2.2.1 The vibration and rotation of diatomic molecules In order to seperate the molecular vibrations and rotations, one can write down the Schrodinger Eqn.(2.3) in terms of a set of polar coordinates: r,0, and cf> [6] Chapter 2. Theory 9 [Te + Tv + Tr + U{R, x3,2/3, z3, ...xNl yN, zN) - Erve]$rve(R, 0, <f>,x3, ...zN) = 0 (2.11) where Te is the electron kinetic energy operator, *2 N +2 N where M/v is the total nuclear mass, i.e. MN = mx + m2 (2.13) Tv is the nuclear vibrational kinetic energy operator, where = _m1m^ ma + m2 while the Tr is the nuclear rotational kinetic energy operator, Tr = - ^ [ - ^ ( - I r + ^ m f l - ^ c o s ^ (2.16) where Lx, Ly and Lz are the electron angular momentum operators in the molecular coordinate system. From Eqn.(2.16), one can see that it is impossible to separate the electron and molec-ular coordinates except for neglecting Lx, Ly and Lz. People usually neglect these angular momenta first, solve the simplified equations to get the electron, vibration and rotation energy, and then to discuss the coupling between these motions. Chapter 2. Theory 10 From Herzberg, for the first approximation (small rotation) the wavefunction of the system can be written as [17] %ve = ^e~MRl2-Re)-A (2.17) itl2 where Re is the distance between two nuclei at the equilibrium position, tf r v e in the above equation is called the rovibronic wavefunction. The total energy of the system is Etot. = Ee + Ev + Er (2.18) Eqn.(2.17) holds to a good approximation expect for the high vibrational and rota-tional energy levels of the molecule. When the vibrational quantum number, v, increases, the amplitude of the vibration will increase, while when the rotational quantum number, J, increases, the distance between the two nulei will increase. Therefore, we have to use the model of the anharmonic oscillator and consider the molecule as a non-rigid rotator. After adding the potential of the anharmonic oscillator and the non-rigid rotator to the potential in Eqn.(2.8), we can ultimately obtain the rovibronic energy, E = hc{Te + [ue(v + l)-uexe(v + ±)2 + ...] + [Be _ a e ( u + I)]J(J+i) + [D. - {3e(v + I)] J2( J + l)2 + ...} (2.19) All the constants ue, ujexe, cte, (3e Te, Be, De can be obtain from [2,20] An important property is Be < ue < Te That means Chapter 2. Theory 11 AEe > AEV > AEr From the above equation, it can be seen that the rotational energy levels are added to the vibrational energy levels, while the vibrational energy levels are added to the electronic energy levels. 2.3 Electronic states of a diatomic molecule There is only an axial symmetry about the internuclear axis in a diatomic molecule. The constant of the motion is only the component of the electronic orbital angular momentum, L, along internuclear axis. That component M L of L is called A and A =| Mi | [13]. The value of A corresponding to each electronic state of molecule are shown in following table The A value: 0 1 2 3 ... The molecular state: E IT A $ ... All the states except for A = 0 are doubly degenerate because Ml can have the two values + A and —A. The spin of an electron is not affected by the electronic field. There is a magneitic field along the internuclear axis. For states A ^  0, the magneitic field causes a precession of S about the internuclear axis with a constant component E, Z = S,S -1,...,-S. (2.20) For each state A the spin degeneracy is 2S+1. The total electronic angular momentum (in units fi) along the internuclear axis is: ft =| A + E | (2.21) Chapter 2. Theory 12 where A: the projection of L along internucler axis S: the electron spin E: the projection of S along internucler axis Each electronic state finally is labelled by 2S+1A|A+E| 2.4 Coupling of electronic motion and rotation We consider the case where the interaction of nuclear and electronic motion is very weak and the electronic motion is coupled very strongly to the internuclear axis (Hund's case a), when the total angular momentum is: J = n + R (2.22) where R is the rotation of the nuclei. In this thesis we are interested in the cases in which 0 is equal to zero. Hence, J = R (2.23) 2.5 The symmetry properties of a diatomic molecule 2.5.1 The symmetry of the electronic wavefunction In a diatomic molecule, any plane through the internuclear axis is a plane of symmetry. So for a E state (A = 0), the electronic wavefunction eighter remains unchanged (for a E+ state), or changes sign (for a E~ state) upon reflection through such a plane of symmetry. Chapter 2. Theory 13 2.5.2 g and u symmetry of electronic states For homonuclear diatomic molecule the electronic wavefunction has a fixed parity. The wavefunction either remains unchanged (even or g (gerade)) upon inversion or change sign (odd or u (ungerade)). Because only homonuclear molecules have the inversion symmetry property, so the subscripts g and u are applicable to only homonuclear molecules. 2.5.3 + , - parity of rotational states Rotational levels have '+' or '-' parity depending on the symmetry of the total wavefunc-tion with respect to inversion at the origin of a space coordinate system. 2.5.4 s and a symmetry of rotational states s (symmetry) and a(antisymmetry) refer to the symmetry of the total wavefuction on exchanging the two identical nuclei (where the nuclear spin has been omitted). 2.6 The selection rules of molecular bromine for transitions The selection rules can be summerized as following [18]: 2.6.1 For the electronic transitions For electric dipole transitions between the electronic states, the selection rules are: AA 0,±1 (2.24) An 0,±1 (2.25) AS = 0 (2.26) (2.27) Chapter 2. Theory 14 £ - <—•• S " (2.28) g «—> u (2.29) For the bromine molecule, the third selection rule (2.26) cannot be used at all. Because Br<i is a heavy molecule, the interaction between L and S may be stronger than the interaction with the internuclear axis. S is not a good quantum number any more, so that AS = 0 is no longer true. 2.6.2 For the vibrational transitions For the transitions between the vibrational states, the selection rules are: But in the electronic transition the intensity of the vibrational spectrum band is proportional to the Franck-Condon Factor (F.C.F.). (See appendix B) 2.6.3 For the rotational transitions The selection rules for the transitions between the rotational states of a homonulear molecule are: Av = 0,±1,±2,... (2.30) AJ = ±1 (2.31) + <—• - (2.32) (2.33) (2.34) From Eqn (2.31) we can obtain Chapter 2. Theory 15 P branch: / = J" - 1 (2.35) and R branch: j = j + 1 (2.36.) where the single prime and double prime represent the excited state and initial state, respectively. 2.7 The distribution of the number of molecules Bromine molecules may exist in a variety of different states, each of which may be de-scribed by rotational, vibrational and electronic quantum numbers. When a molecular gas is at thermal equilibrium, the number of molecules in each state obeys the Boltzmann distribution: Ni = N0e~pEi (2.37) where Ni is the number of molecules in state i iVo is the total number of molecules k is the Boltzmann constant T is the temperature Chapter 2. Theory 16 If a state has degeneracy g,-, then the Boltzmann law becomes: Nt = Nogie-pEi (2.38) We can apply the Boltzmann law to rotation, vibrational and electronic energy levels in turn. Because the energy separations of electron levels is much bigger than the one of vibrational and rotational levels, we can think that molecules stay in the electronic ground state at room temperature. 2.8 The effect of nuclear spin There is a further symmetry property which must be considered, and which turns out to have very important implications for the population of different rotational levels. This symmetry property is the behaviour of the total wavefunction when equivalent nuclei are interchanged. As is known, nuclei with integer spin obey Bose-Einstein statistics, according to which the total wavefunction must be symmetric with respect to exchange of identical nuclei. Nuclei with half-integer spin obey Fermi-Dirac statistics, according to which the total wavefunction is antisymmetric with respect to exchange of nuclei. For Br2, exchange of nuclei leaves the electronic wavefunction unchanged. The vibrational wavefunction is also unchanged on nuclear exchange, because the vibrational wavefunc-tion only deponds on the magnitude of the bond length. But, the nuclear exchange influences the rotational wavefunction. Rotational wavefunctions are symmetric if J is even and are antisymmetric if J is odd. The bromine nucleus has spin I, the degeneracy introduced by nuclear spin is shown in table 2.1 The intensity of spectral lines are propotional to degeneracy. The neighbouring spec-tral lines in the same P branch and R branch will have symmetry and antisymmetry, respectively. When the nuclear spin I is equal to a integer, the ratio of the intensity of Chapter 2. Theory 17 Table 2.1: The degeneracy introduced by nuclear spin Nuclear spin Integer Half-integer tf • rue Degeneracy (I+1)(2I+1) a 1(21+1) (I+1)(2I+1) a 1(21+1) neighbour spectral lines is T T T T T ( 2'3 9 ) When I has a half-integral value, we have £ = ^  (2-40) Where the subscript s indicates a symmetric and a indicates an antisymmetric state. The nuclear spin, I, of each bromine atom is |. So, the total nuclear spin, I — I\ + 72, is 0,1,2,3. In the ground electronic state, X1Y,0+g, bromine molecules with odd J values are referred to as ortho-bromine and those with even J values as para-bromine. For odd J (ortho), we have I = 1 (21 + 1 = 3 states) and I = 3 (21 + 1 = 7 states), i.e. totally we have 10 antisymmetric states. For even J (para), we have 1 = 0 (23 + 1 = 1 state) and 7 = 2 (2J + 1=5 states), i.e. we totally have 6 symmetric states. Hence the hyperfine partition factor is ^§ = § for ortho states, and -j| = | for para states. Thus, at room temperature, we can get the number of moleculer per cm3 in a partic-ular vibrational and rotational states. The density of ortho state of (odd J) (79-79)£r2 and <81-81).Br2 satisfies Eqn.(2.41), and para state (even J) of (79'79)£?r2 and (81,81)jBr2 satisfies Eqn.(2.42). (For more details see appendix C) Chapter 2. Theory 18 N. n jii — No V x M e-pE*" 5 (2J" + l)e-"V x e -pEc (2.41) AT N° e-^ << 3 (2J" + l ) e - ^ " ^ ^ - x - — i ™ — x C-P£« (2.42) where the sum over j" is from 0 to infinit. There are no para and ortho states defined for (79'81)i?r2 where the two nuclei are inequivalent. The density of (79,81)J3r2, at room temperature, satisfies Eqn.(2.43) N0 e-PEv» ^ = T x M x E ^ z ^ 7 X (2J»+l)e-'**> 0 E , where j" includes odd J" and even j " . M is the fractional abundances of the type of molecule studied, where M is equal to 0.2554 for (79'79)£r2, 0.2446 for <81>81>Bra and 0.5 for (79-81>£r2. For the ground electronic state Ee is equal to zero. The partition function ^e „ is the probability of molecules in vibrational states. N P -j- = — = 2.08 x 1017(molecules/cm3) (2.44) V RT P : pressure in the cell R : molar gas constant T : room temperature Chapter 2. Theory 19 Figure 2.3: The absorption of radiation 2.9 Absorption of light by a diatomic molecule 2.9.1 Definition of the absorption coefficient When a beam of light is sent through a bromine gas cell the intensity of the transmitted light, IV, may show a frequency distribution similar to the one depicted in Figure 2.3.[23] where uq is the frequency at the centre of the line. In general, the absorption coefficient ku of the gas, is defined by the equation J„ = I0e-k"L that is, *„ = (l/L)ln(J0/J,) (2-46) where Iq is the intensity incident on the cell L is the length of the cell When L is meassured in cm, ku is expressed in cm-1, and v is the wavenumber of the radiation in cm'1. From Fig.2.3 and Eqn.(2.46), we have a curve in Figure 2.4 [23]. (2.45) Chapter 2. Theory 20 y, v, ^ »<tiK) Figure 2.4: The typical shape of a spectral line where Av is called the half-width of the absorption line. 2.9.2 The relations between the Einstein coefficients and the integrated ab-soption coefficient The intensity of an absorption line can be defined by equation [13] n is excited (higher energy) state Nm is the number of molecule per cm3 in the initial state m Bnm is the Einstein transition probability of absorption unm is the transition frequency The intensity of a spectral line in emission is written as = ISmNmBnmhvnmL (2.47) where m is initial(lower energy) state -nm (2.48) Chapter 2. Theory 21 where c is the speed of light and Anm is the Einstein transition probability of spon-taneous emission. From wave mechanics [13], we find for transitions between non-degenerate levels is Anm = | Rn m |2 (2.49) and B m n = W~c 1 | 2 ( 2 - 5 0 ) where Rn m is a transition dipole moment. Anm = 8irhv*mBmn (2.51) For the case of a transition between the two levels n and m of degeneracy dn and dm, respectively, we have Anm = £ | RnJ'mJ" |2 (2.52) Bmn = - £ L - £ | RnJ'mJ" |2 (2.53) on cam m^„ Anm = ^8nhc4mBmn (2.54) Because the absorption coefficient kv varies across an absorption line (or band), the light absorbed by the transition n — m for a small AL is given by [16] ITs. = J - h)dv = I°AL J kvdv (2.55) Chapter 2. Theory 22 where the incident intensity tf is assumed to be constant over the width of the line or band. Substituting Eqn.(2.47) into the above equation and taking JQ"1 as tf we obtain for the integrated absorption coefficient J kvdu = NmBmnhunm (2.56) 2.9.3 The relation between the Einstein coefficient and transition probabil-ities From Herzberg [15], the transition probability Bmnv»v> ff for absorption is given by 3 j ' j " 2 D 87T . N M | 2| T J V ' V " |2 E M ' M " 1 ^ TOt. 1 f0 r7\ Bmn,v"v',j"j' = I Ke II ^Vib. I 2 J » + 1 (2.57) where the total matrix element Rnm for the system is Rnm _ D U D I P V V ' D J ' J " fn — xt e ±Vyj b t^ot. \_Z.00) and the summation is over all values of the magnetic quantum numbers M' and M" of upper and lower states. The electronic transition probability is given by I R fn I2=l /VvMeVv'dre |2 (2.59) where Me is the electric moment which only depends on the electrons. The vibrational transition probability is given by I Rvib" I2=l / VvVV'dr | 2=|< v' |v" >|2 (2.60) The |< v'\v" >|2 is the well-known Franck-Condon Factor (F.C.F.) for the transition v — v" (see appendix B). Usually people use the symbol Chapter 2. Theory 23 W H < » V > P (2-61) The rotational transition probability For rotational transition probability we have to consider three directions, x, y, and z, in space coordinate system. For example, the transition probability in the z direction is I R?ot" I2=l / sin0cos0^.^r»d0<ty |2 (2.62) In appendix A, we have shown the derivation of these three equations in detail. The F.C.F. and rotational part are given in appendix B. We used both theory and experiment to obtain the electronic transition probability. | RE |2 is a more fundamental measure of the transition probability. From Eqn.(2.56) and (2.57), we can get | Re I = J „ J , - (2.63) s r ' N ^ h W v » j < r i R^ ;;v' i 2 M ' ^ ; ' > -where vnm is in wavenumber units. 2.9.4 The radiative lifetime of J?3n0+U state of f?r2 The radiative lifetime of an molecule in a definite excited electronic state n can be calculated theoretically. We have in general, W = — — (2.64) 2-im 'Vim The radiative lifetime of rovibronic levels in the -B3n0«< state of molecular bromine is: Chapter 2. Theory 24 W = = \ (2.65) > it ,n A i II ji jii where Av> „« is the Einstein coefficient for spontaneous emission from the state J' which is in the v state into the state j" of v" state. TTad. varies with v and this variation can be substantial over the whole vibrational energy range of an electronically-excited manifold. In order to compare the magnitudes of TTa^ obtained for different v levels in various investigations, it is desirable first to transform from TR values into the corresponding electronic transition probability | Re |2. In the Born-Oppenheimer approximation, | Re I2 *s a strictly electronic transition probability and the vibrational and rotational-energy dependences of rrad. are factored out by the transformation from T r a<f. to | Re |2. The expression of Tra^ is as follows [8], Trad. = ^ = — T , T » (2.66J From the absorption spectrum we can get the value of | Re |2 by using Eqn.(2.63). Also we know that ^  = 1 in our case and the rotation part of Eqn.(2.66) when the P and R branches are considered together is equal to 1 (see appendix B), so we finally can obtain the Eqn.(2.67), w = 64**111.1* E v - q v ' v " " 3 ( 2 ' 6 7 ) In our case, it is possible to calculate a Trad. value for v' = 14,15,17,18,19 by using the | Re |2 values obtained from theory and experiment. Chapter 2. Theory 25 2.9.5 The predissociation of Br2 in the 2?3II0+Ustate From Fig. 1.1 one can see that there is a crossing point between the excited state i?3II0+uand the unbound state 1 I I l u . The vibrational energy levels of the the J53no+unear the crossing point have a higher probability of producing a non-radiative transition to the 1 II i u state; then the atoms will separate, the entire process being called predissociation. The density of molecular bromine in the excited states, TV*, changing with time, can be written as [4] ^ = BNN. • IlaseT • (N - N*) - (TR + TP + Tc) • N' (2.68) Where Bnn» • haset'- the laser excitation rate N: the density of Br2 in the ground state r#: the radiative decay rate (Tr = •^—•) Tp: the predissociation rate Tc- the collisional decay rate Taking = 0, we can get N* = BNN'IlaserN ^ BNN'Ilaser + Tr + Tp + Tc For iodine, rP = kv.J'{J' + l) + al, (2.70) One can model bromine in the same way. The fluoresence intensity, If, is proportional to N*. So, one knows that i « J\J' + 1) Chapter 2. Theory One can draw a graph of vs. J'(J' -f 1) to measure the predissociation rate, Tp. Chapter 3 Experimental apparatus and spectrum In this chapter we describe the apparatus used to measure the radiative lifetime of the /33il0+u state of Br2 molecule. 3.1 Preparation of the sample cell A pyrex sample cell, of length 14.09 ± 0.05 cm, was continuously heated and evacuated to a background pressure of 3.8 x 10-6 torr. Part of the vacuum system was also cooled with liquid nitrogen. The sample cell was filled with dry Br2 vapour, and a mixed methanol and liquid nitrogen bath was used to cool the liquid bromine to a temperature of —(32.5 ± 0.2)°C. This environment was maintained for about ten mintues to allow bromine vapour to diffuse into the sample cell. The molecules were contained in T-shape pyrex sample cell, filled with isotopic bromine (79-79), (79-81), (81-81) whose relative abundances were 1.0216:2.0:0.9784, respectively. The sample cell was then sealed and removed from the vacuum system. Under these conditions the Br2 pressure inside the sample cell was 3.6 ± 0.2 torr, which was sufficient to obtain a peak absorption of about 30% for the rotational lines of bromine molecule under study. For stronger absorption, we could increase the pressure of the sample cell. Then, the collisions probability among bromine molecules will increase; this is a method of broadening the absorption line. Using the same techniques we can prepare an iodine sample cell. The spectrum of the B - X system of I2 has been studied successfully and extensively by various research groups. Therefore we can use a I2 sample cell to get the fluorescence spectrum of I2 and 27 Chapter 3. Experimental apparatus and spectrum 28 Argon Ion Loser Dye Loser Electronic Scanner TLR1 I P.M. — j — TLR2 P.M. P.C. I F4 P.M. M.C. h Cel F, E L D ^ - f l - " 1 Brc Cell [j-* — ^ F3 5 Mi M? Figure 3.5: Experimental arrangment. Mi,M2: total reflectional mirror; S: splitter; Fi, F2, F3, F4, F5: filter; PM: photomultiplier; PD: photodiode; MC: monochrameter; PC: photo counter; TLR1,TLR2: two line recorder then we can use the I2 fluorescence spectrum obtained by [21] to calibrate the spectrum of Br2. 3.2 Experimental set-up A block diagram of the experimental arrangement used for measuring the lifetime of the 53n0+u state of Br2 is shown in figure 3.5. A Coherent CR-15 SG argon ion laser tuned to the 5145 A line, and an output power of 6W was used to pump a Cohererent CR-699-21 scanning dye laser. The dye Chapter 3. Experimental apparatus and spectrum 29 laser, using Rhodamine 6G dye, gave a peak output power of 800mW. This dye laser was connected to an electronic scanning system capable of tuning the laser at different scan speeds. In our experiment we tuned the dye laser from approximately 17464 cm'1 to 17480 cm'1, with the electronic scanner set to scan a 30GHz (~ lcm-1) region per scan period of 5 minutes. This allowed us to excite the specific rovibrational levels (v',j') of Br2B3Il0+u state from the X1S0+S ground state. The dye laser beam was split into two by a beam splitter S. One of the beams was passed through the Br2 sample cell while the other was directed through an I2 sample cell. Less than 1 mW intensity of the beam was going into the Br2 sample cell. The beam area 3.14mm2. The spectrum of iodine, which has already been studied extensively by other research groups, served as a reference for calibration. Both, absorption and fluorescence spectra were recorded for Br2, whereas, only the fiuoresence spectrum was recorded for I2. A photodiode (HP PIN 5082-4220) and two photomultipliers (EMI 9558 B, EMI 9558 QB) were used as detectors for absorption and fluorescence, respectively. Several glass color filters were used in the path of the dye laser beam to reduce the intensity of the beam before it entered the sample cells and the detectors, in order to avoid saturation. Two double line recorders (PM 8252A) were used for recording purpose. One was used to record simultaneously the fluorescence spectra of Br2 and I2 with the other used to trace the absorption spectrum of Br2 and the fluorescence spectrum of I2. A monochrometer was used as an aid to obtain the accurate frequencies which were needed during the experiment. 3.3 Absorption spectrum of molecular bromine Chapter 3. Experimental apparatus and spectrum 30 1.00 P a r t o f t h e A b s o r p t i o n S p e c t r u m 1111111111 11 11 11111 111 1111111111111 ' ' ' ' i • ' i ' 17468.2 17468.6 17469.0 17469.4 17469.8 W a v e n u m b e r ( c m " ) Figure 3.6: Part of the Absorption Spectrum Chapter 4 Data Analysis 4.1 Assignment of Br2 lines An arbitrary zero on the horizontal axis of the spectrum was established. The distance to each I2 fluoresence peak was measured and the frequency vj2 in cm-1 was plotted against the distance d in cm. From this graph we can find the slope, a, and the intercept b on each scan of the laser. If v vs. d is linear then an average dispersion can be taken and we can use this dispersion a to find the frequency VBT2 on each Br2 line which is uBr2=ad' + b' (4.71) where d' is the distance from an arbitrary zero on the horizontal axis to each Br2 absorption line, and b' is the intercept for J3r2 lines on each scan of dye laser, that is 6'= 6 +0.428a (4.72) where the number 0.428 is the separation distance between I2 and Br2 lines. (Because the two line recorder (PM 8252A) has a fixed separation between the two pens) Using Eqn.(4.71) we obtained the frequencies of all the absorption lines from the experimental data. Then all these frequencies were compared with theoretical ones cal-culated using Eqns.(4.73) and (4.74). The difference between the two values should vary smoothly and in the same direction. Here we gave a example, (79,79)£?r2, band 15' - l " in table 4.2 31 Chapter 4. Data Analysis 32 Table 4.2: Obtaining the band 15' - l " of (79-81)#r2 line no. R(J),P(J) u(cm x) u(cm, 1) v — u 195 R(58) 17478.7155 17478.691 -0.025 153 R(59) 17475.1262 17475.099 -0.027 102 R(60) 17471.4733 17471.445 -0.028 50 R(61) 17467.7568 17467.732 -0.025 188 P(55) 17478.1605 17478.132 -0.029 149 P(56) 17474.5676 17474.530 -0.038 92 P(57) 17470.9113 17470.882 -0.029 42 P(58) 17467.1916 17467.161 -0.031 In the table 4.2 // and v are theoretical and experimental frequencies, respectively. 4.2 Calculating the Br2 transition energies The transition energies for 79,79.Br2 and 81'8lBr2 can be calculated by using the following formula: Ex-stau = I> + BV„(J"(J" + 1)) - DV„{J'\J" + I))2 + HV.,(J"(J" + l))3 (4.73) Es-state = TV, + BV,{J\J' + 1)) - DV,(J'(J' + I))2 + HV,(J'(J' + l))3 (4.74) Where TV = TVIJ-O is the vibrational term value relative to XxS0+fl state. The energy is measured in wave number (cm-1) units and the X —> B transitions for the P and R branches in (79,79)j3r2 and (81,81).Br2 were calculated. The constants, TV,BV,DV, and HV were obtained from [2]. For (79'81)j9r2, the transition energies were calculated by averaging the results of (79-79)f?r2 and (81,81)J9r2. Chapter 4. Data Analysis 33 4.3 The absorption band strengths From Eqn.(2.41),(2.42) and (2.43) we can obtain the number of bromine molecules in each rotational state of each vibrational state. (The probability of being in a vibrational state is estimated by summation from v = 0 to v = 10. The probability of being in a rotational state is integrated from J = 0 to J = oo for both R branch and P branch). At room temperature, the B-state levels are sparsely populated so only the X-state levels need te* -0E n be calculated. From calculating the partition function — - — „ , one can assume that E „ " e • most bromine molecules occupy the states v = 0,1 and 2 only. From Eqn.(2.38), the Boltzmann distribution law for rotational levels is now [22] Nj„ =• NQ(2J" + i)e-PB.J'V"+^) _ (4.75) The particle density will not be affected by nuclear spin. By differentiation Eqn.(4.75) it can be shown that the quantum number of the state with the greatest population is J m a x = \ / ^ L \ - \ (4.76) Taking the value of Bv = 0.08cm -1 [2], we can obtain Jmax = 35 (4.77) In the table 4.4 we gave the part of particle densities on para and ortho states of v" = 1. The constants used for calculating the particle density are shown in table 4.3 [2]-Franck-Condon factors gives an approximation to the relative intensities. A chart of F.C.F.'s for 0 < v < 48 to 0 < v" < 14 is given in [12]. From that chart we can see that er 4. Data Analysis Table 4.3: Molecular constants (cm 1) for the 1Eo+u state State Mol. Const. (79,79) 1 8 1 , 8 1 ) ^ (79,81 ) B r 2 So+u v" < 10 325.3213 321.29 323.3056 0JeXe 1.07742 1.064 1.0707 -2.29798 -2.2134 -2.2556 v" = l WBV 8.1627 7.9618 8.0622 108A, 2.108 2.005 2.011 -W6HV 2.89 0.0 1.445 v"=2 1&BV 8.1304 7.9306 8.0305 108/J>U 2.116 2.013 2.0645 -1013#v 2.88 0.0 1.44 Table 4.4: A part of the particle densities (in cm-3) on v" = 1, (79>79).Br2 • v -V P,R( J = even) Density P,R(J = odd) Density 1 0 1.4624 x 10™ 1 7.3060 x 10™ 1 2 7.2945 x1 012 3 1.6980 x 1013 1 4 1.3058 x 1013 5 2.6494 x 1013 1 6 1.8698 x 1013 7 3.5758 x 1013 1 8 2.4162 x 1013 9 4.4689 x 1013 1 10 2.9402 x 1013 11 5.3206 x 1013 1 12 3.4372 x 1013 13 6.1237 x 1013 1 14 3.9029 x 1013 15 6.8715 x 1013 1 16 4.3337 x 1013 17 7.5583 x 1013 1 18 4.7264 x 1013 19 8.1793 x 1013 1 20 5.0783 x 1013 21 8.7305 x 1013 1 22 5.3874 x 1013 23 9.2091 x 1013 1 24 5.6523 x 1013 25 9.6132 x 1013 1 26 5.8721 x 1013 27 9.9417 x 1013 1 28 6.0466 x 1013 29 1.0195 x 1014 1 30 6.1761 x 1013 31 1.0374 x 1014 1 32 6.2614 x 1013 33 1.0480 x 1014 1 34 6.3039 x 1013 35 1.0516 x 1014 1 36 6.3054 x 1013 37 1.0486 x 1014 1 38 6.2681 x 1013 39 1.0393 x 1014 1 40 6.1947 x 1013 41 1.0242 x 1014 Chapter 4. Data Analysis 35 transitions 17 — 2" should be very strong. Transitions 14' — l " , 23' — 3" will be strong but not as strong as the 17' — 2" transition. The Franck-Condon factors used for our calculation are listed in appendix B. The distribution of bromine isotopes also affects the transition intensity. Since the (78,8i)£?r2 aj-g twice as numerous as <79'79)l?r2 and ( 8 1 , 8 1 ) / 3 r 2 , ( 7 e , 8 1 ) £ ? r 2 transitions will have intensities twice as big as similar transitions in ( 7 9 , 7 9)2?r 2 and ( 8 1' 8 1)i?r 2. 4.4 Calculating the integrated absorption coefficient From Eqn (2.63) we knew that we have to obtain the integrated absorption coefficient / kvdv in order to obtain the experimental measure of the total strength of an electronic transition. We used several steps to obtain the integrated area , / kvdv. First, the coordinates of the lower left and upper right corners of each BT2 absorption line were calaulated and fixed. Then we used a digitizer to obtain a set of data, x and y coordinates. The abscissa x represented v in c m - 1 and the ordinate y represented the intensity / „ . The program VDIGIT (provided by the Computing Center at UBC) run from a VICTOR9000 terminal was used to create data files. Moving the cursor along the absorption line one can obtained a set of data, i.e. a set of v and lv values. Since the input intensity IQ varies with time, a line between A and B was choosen to represent an approximate I0 (see figure 4.7). If several absorption lines overlap each other (see figure 4.8), we digitized them to-gether. Second, one can obtain a series of k„ values by using Eqn.(2.46), and then one can obtain a set of v and kv values for each absorption line. By using those v and kv values one can obtain the values of / kvdv using a computer. Third, some apparently single fines were checked to see if they were, in fact, overlapped Chapter 4. Data Analysis 36 16.60 ? 16.40 { 5 16.20 c o -o 18-00 o i 15.80 : c p 15.60 : 15.40 B l ill I M i i | i i i i l l i 11 | i i i i i l l I I | l l l i i i i l u i 17469.61 17469.62 17469.63 17469.64 V7«9765\7469.66 17469.67 1 7469.68 Wavenumber (cm ) Figure 4.7: Digitizing an absorption line or not. We used two different methods to get two areas, using trapezoidal rule to get area A\ and assuming kv as a Gaussian distrubution to get area A 2 . Then we compared the two areas. If the area A2 was same as the area A\ (A2 may be somewhat larger than Ai because the Gaussian distrubution has long wings which may have been neglected by the first method), the line was not overlapped. If the area A2 was much larger than Ai, the line was overlapped. We also checked the half width, Av, for each absorption line. If the line is overlapped, the measured half width will be wider than the Gaussian width. At the half-height of the band, we have k • 1 i Jmin - 2 l l n l T (4.78) From Fig.2.4 we can find Chapter 4. Data Analysis 37 Figure 4.8: Overlapped absorption lines Chapter 4. Data Analysis 38 Av = v2-vi (4.79) Independently measurements of / kvdv agreed to within ±3.0% except for the weakest lines where the difference approached ±6.0%. / Chapter 5 The Results and Discussions After analysing the spectrum, we obtained data for the following bands: 14'- 1" (79,79) B r 2 1 < J" < 19 15'- 1" (79,79) 57 < J" < 63 17'- 2" (79,79) 0 < J" < 21 18'- 2" (79-79)£r2 53 < J" < 59 19'- 2" (79,79) 74 < J" < 78 14'- 1" 1 < J" < 11 15'- 1" (79,81)^ 55 < J" < 61 17'- 2" (79-81)£r2 0 < J" < 16 18'- 2" (79,8l) 5 r 2 51 < J" < 57 19'- 2" (79,81) 73 < J" < 78 15'- 1" (81.81)5^ 53 < J" < 60 17'-•2" (81,81) B r 2 0<J" < 8 18'- 2" (81,81)^ 50 < J" < 56 By using Eqn.(2.63) we estimated values for the electronic transition probability | Re |2 for each band. Here we give a detailed sample calculation that shows how one goes from / kvdv to | Re |2 with all factors explicitly given. From Eqn.(2.63), one can obtain Eqn.(5.80): 39 Chapter 5. The Results and Discussions \ 40 I Re \ 2 = ^ ^ -77^7 ( 5 - 8 ° ) w W ® I Rii I2 ^ ' ^ r For P(ll) of band 14' - l " of (79-79)£r2, the | Re |2 value is given by D l2 2.3694. x 10"4 e 1 5.3206 x 1013 • 17469.499 • (4.1623 x 1017) • 0.00509 • % = 2.52 x 10~37(er£ • cm3) (5.81) For the overlapped lines, a / kvdv over the total area has been used. For example, the overlap of the three lines, P(54): 18' - 2" of <79-79).Br2; R(8): 14' - l " of (79-79)£r2 and R(77): 19' - 2" of (79-79)5r2, Eqn.(5.80) can be written as: 1^1= c T T c 7 T c3 ( 5 > 8 2 ) where Ci,C2 and C3 are the denominators in Eqn.(5.80) for P(54), R(8) and R(77), respectively. The results of | Re |2 for the band 14' - l " of (79-79)Br2 is shown in table 5.5. The results for all other measured lines are showed in appendix D. Taking the average of all values of | Re |2 from table 5.5 we obtained Eqn.(5.83), the average value and standard diviation of the electronic transition probability. | Re | 2 = (2.54 ± 0.28) x 10 ' 3 7 (erg • cm 3 ) (5.83) Because we only obtained the small part of spectrum of molecular bromine from our experiment, some of the lines in the spectrum were overlapped with some other lines which cannot be identified. So, for those lines we cannot obtain better values of | R e | 2 in the band. Therefore when we calculate the values of | R e |2, we did not take into Chapter 5. The Results and Discussions 41 Table 5.5: | Re |2 values for 14' - l " of (™™Br2 P(J) v cm 1 ,"j / kvdv cm~ 1 Re - 2" cm 1 P(l) 17474.510 7.3066 X 10™ 2.3747 x 10" -4 2.82 X 10" 2.30 X lO"2 P(4) 17473.655 1.3058 X 1013 3.8263 x 10' 4 2.11 X 10" -37 2.07 X lO"2 P(6) 17472.770 1.8698 X 1013 0.7201 x 10" -4 2.25 X 10" -37 1.46 X io- 2 P(7) 17472.237 3.5758 X 1013 1.8767 x 10" -4 2.85 X io--37 2.01 X io- 2 P(8) 17471.645 2.4162 X 1013 1.0942 x 10" -4 2.60 X 10" -37 2.25 X io- 2 P(9) 17470.987 4.4689 X 1013 1.8651 x io--4 2.37 X io--37 2.27 X IO"2 P(ll) 17469.499 5.3206 X 1013 2.3694 x 10" -4 2.52 X io--37 2.12 X IO"2 P(12) 17468.656 3.4372 X 1013 1.5725 x io--4 2.58 X 10" -37 2.17 X IO-2 P(13) 17467.756 6.1237 X 1014 1.5741 x io--4 2.27 X 10" -37 2.07 X IO"2 P(14) 17466.796 3.9029 X 1013 3.0943 x 10" -4 2.89 X io--37 2.39 X IO"2 P(15) 17465.771 6.8715 X 1013 4.5367 x 10" -4 2.06 X io--37 2.47 X IO"2 P(16) 17464.684 4.3337 X 1013 1.9524 x 10" -4 2.51 X 10" -37 2.05 X io- 2 R(J) v cm'1 Nmv»jii / kvdv cm' 2 Au cm 1 R(4) 17474.546 1.3058 X 1013 10.4649 x IO"4 2.82 X 10" -37 2.78 X io- 2 R(5) 17474.359 2.6494 X 1013 1.5968 x 10" -4 2.98 X io--37 2.21 X IO"2 R(7) 17473.761 3.5758 X 1013 2.5813 x io--4 2.12 X io--37 1.94 X io- 2 R(8) 17473.368 2.4162 X 1013 1.5832 x 10" -4 3.00 X io--37 2.18 X IO"2 R(9) 17472.926 4.4689 X 1013 3.8333 x io--4 2.38 X io--37 2.17 X IO"2 R(ll) 17471.841 5.3206 X 1013 2.3285 x 10" -4 2.27 X 10" -37 1.94 X IO"2 R(12) 17471.199 3.4372 X 1013 1.6754 x 10" -4 2.53 X 10" -37 2.42 X IO"2 R(13) 17470.501 6.1237 X 1014 2.6743 x 10" -4 2J28 X 10" -37 1.96 X IO"2 R(14) 17469.749 3.9029 X 1013 1.4127 x 10" -4 2.22 X io--37 1.88 X io- 2 R(15) 17468.925 6.8715 X 1014 3.0055 x 10" -4 2.78 X 10" -37 2.03 X IO"2 R(16) 17468.042 4.3337 X 1013 2.7618 x 10" -4 2.65 X io--37 2.53 X IO"2 R(17) 17467.095 7.5583 X 1014 3.6602 x 10" -4 2.54 X io--37 2.09 X IO"2 R(18) 17466.096 4.7264 X 1013 7.0570 x 10" -4 2.65 X io--37 2.25 X IO"2 R(19) 17465.032 8.1793 X 1014 4.6456 x 10" -4 2.29 X 10" -37 2.46 X IO"2 I Chapter 5. The Results and Discussions 42 Table 5.6: j Re |2 value for overlapped lines P,R(J) v cm 1 Nmv»j» / kvdv cm 2 | R e •2 Av cm 1 P(2) 17474.273 7.2945 x 10" 1.0087 x 10" -A 9.34 x 10" -37 2.36 x 10" -2 P(3) 17473.990 1.6980 x 1013 1.0253 x 10--4 3.81 x 10" -37 2.58 x 10" -2 P(5) 17473.234 2.6494 x 1013 1.7751 x 10" -4 3.98 x 10" -37 2.80 x 10--2 P(10) 17470.271 2.9402 x 1013 2.9105 x 10" -4 5.62 x 10" -37 0.83 x 10" -2 R(6) 17474.090 1.8689 x 1014 1.2210 x 10 -4 3.28 x 10" -37 2.47 x 10" 72 R(10) 17472.412 2.9402 x 1013 2.4368 x 10 -4 4.27 x 10" -37 2.09 x 10" -2 account those lines, for instance, in band 14' — l " of ^ 79'79^Br2, the value of j R e j 2 of those lines overlapped with the line cannot be identified are showed in table 5.6. After calculating the electronic transition probability for all bands which we have analysed, we obtained the table 5.7. The mean value of | Re |2 is (2.52 ± 0.25) x 10"37(er5 • cm3) The average radiative lifetime, Trad> for each vibrational state v was obtained by using Eqn.(2.67) and the results are summarized in table 5.8 for the region 17464 cm-1 to 17480 cm'1. In the ground electronic state there are around 137 vibrational levels v". F.C.F. were only available to evaluate T,qv>v»v3 up tov =10 for v = 14,15,17,18,19 for (79>79)Br2 and <81-81).Br2; v" = 20 for v = 14,15,17; v" = 12 for v = 18,19 for (79-81)£r2 (see appendix E). The frequency of each observed line was used during the calculation of rTad. The results of radiative lifetime measurements obtained by Clyne [8] are showed in table 5.9 where the calculated T r a a \ values are based on Le Roy's work [24]. Le Roy used radial wavefunction to calculate diatomic molecule absorption coeffi-cients. In Clyne's work, 7YOA>. were obtained from measurements of collision-free lifetimes To of Br2 (B) excited molecules. The collision-free lifetime is given by Eqn.(5.84). Chapter 5. The Results and Discussions 43 Table 5.7: Mean | R e |2 for all identified bands Band Average Re |2 Standard diviation Error (14 - r ,79-79 2.54 x lO"37 0.28 x lO"37 11% (15' -1" ,79-79 2.43 x lO"37 0.18 x 10"37 7% (17' -2" ,79-79 2.58 x lO"37 0.24 x lO"37 9% (18' -2" ,79-79 2.62 x lO"37 0.25 x 10"37. 10% (19' -2" ,79-79 2.66 x lO"37 0.27 x 10"37 10% (14' -1" ,79-81 2.67 x lO"37 0.23 x 10"37 9% (15' -1" ,79-81 2.45 x lO"37 0.21 x 10"37 9% (17' -2" ,79-81 2.58 x 10"37 0.20 x lO"37 8% (18' -2" ,79-81 2.48 x lO"37 0.27 x lO"37 11% (19' -2" ,79-81 2.47 x lO"37 0.27 x 10"37 11% (15' -1" ,81-81 2.40 x 10"37 0.24 x 10"37 10% (17' -2" ,81-81 2.47 x 10"37 0.32 x lO"37 13% (18' -2" ,81-81 2.47 x 10"37 0.31 x 10"37 13% Table 5.8: rTad. for the excited state v Isotope Br2 Excited state v Average rraa\ Error Br2 (79-79) 14 17.1 fis 1.9 (is Br2 (79-81) 14 9.8 us 1.1 us Br2 (79-79) 17 22.2 us 2.4 fxs Br2 (79-81) 17 17.5 fis 1.9 ^ s Br2 (81-81) 17 23.6 fis 2.6 fis Br2 (79-79) 18 24.3 [is 2.7 (is Br2 (79,81) 18 22.0 /is 2.4 fis Br2 (81-81) 18 24.5 fis 2.7 fis Br2 (79-79) 19 24.5 fis 2.7 ^ s Br2 (79-81) 19 23.4 us 2.6 fis Br2 (79-79) 15 18.0 fxs 2.0 fis Br2 (79-81) 15 11.0 us 1.2 ^ s Br2 (81-81) 15 18.4 us 2.0 fis Chapter 5. The Results and Discussions 44 Table 5.9: The Trad. of (79-79)#r2 obtained by Clyen Mean | Re |2 2.04 x lO"37 Trad. Ms (cal.) Trad. fiB (obs.) Error 11 15.8 5.1 +1.5 -0.9 14 1.97 x 10"37 15.9 7,4 +1.5 -1.0 19 1.87 x 10"37 20.8 1.85 x 10"37 11.3 +2.0 -1.5 20 21.9 6.1 +2.5 •1.9 1_ T0 Trad + kv.f{j' + l) (5.84) where kv> is a constant dependent on v . For such a case, a plot of ^  vs. + 1) has been given and the intercept equal to From table 5.9 one can note that the calculated values are two to three times larger than the observed one, while our results (see table 5.8) are closer to Le Roy's estimates. The values of Trad. are very sensitive to the values of Hqvivi>v3 used in Eqn.(2.67). As more terms are added to the sum, the smaller rrad. becomes. Table 5.10 shows the difference among the values of E c 7 t / t » I / 3 a s more terms are added for the case of the 17' — 2" band of (79,81)jBr2. If we can obtain all the F.C.F. and sum over them, the value of E g ^ v ' shoud equal to 1 and then Eqn.(2.67) approximately can be written as Eqn.(5.85). 3/J Trad. — 647T4 | R e | 2 V Z the radiative lifetime Trad. has been given in table 5.11 by using Eqn.(5.85). (5.85) . Chapter 5. The Results and Discussions 45 Table 5.10: The values of Y,qv<v»vz Terms of F.C.F. Terms of F.C.F. 3 18.707 x IO 1 0 13 - 58.959 x 101U 4 32.259 x 101 0 14 62.480 x 101 0 5 36.552 x IO 1 0 15 62.625 x IO 1 0 6 36.873 x IO 1 0 16 64.518 x IO 1 0 7 43.126 x 101 0 17 67.299 x IO 1 0 8 48.417 x IO 1 0 18 67.395 x 101 0 9 48.466 x IO 1 0 19 68.991 x 101 0 10 51.961 x IO 1 0 20 71.198 x 101 0 11 56.377 x IO 1 0 21 71.248 x 101 0 12 56.519 x 101 0 However, now there is a difficulty in choosing a suitable value for v. We used the frequency of each observed line to calculate Y,qv>v»vz. One can chose the frequency which corresponds to the strongest F.C.F. Based on Le Roy's study, Clyne obtained the values of j Re [2 from Eqn.(5.86). | Re | 2= [0.3905 + 0.265(r - 2.3)]2 (5.86) the mean | Re | 2 were given in table 5.9. From table 5.8 one can also see that the electronic transition probability, | Re | 2 , are in close agreement with Clyne's work. In order to see the spontaneous predissociation rate, fj> , of Br2 7?3no+ustate one can draw a graph j- vs. J'(J' +1). The graphs shown in figure 5.9 does not follow Eqn.(2.70). From reference [25], we can obtain figure 5.10 (by using their data). In contract, one can obtain the firgure 5.11 from our data using the same method. Comparing figure 5.10 and figure 5.11 one can see that they both have very similar shape. Figure 5.11 suggests that there is probably a predissociation in v = 14 level near J'(f + 1). This method cannot be used for v = 15,17,18,19 levels because most of Chapter 5. The Results and Discussions 46 20.00 14'-1" Bromine (79,81) P R Branches -4—| '(/) 15.00 H C Q) -4-> C (D O C <D (/> a) o LL_ 10.00 H 5.00 PCI) + PU> + P(3) pl+) R*4) P(5J P ( 6 ) + * RCIO) A ROD 0.00 I i i i i i 11 i i | 11 i 11 111 111 i i 1111 i i i i 11 i 1111 i 11 i i i i 11 i 11 i i i 1111 i i | i i i i i i i i i 20 40 60 80 J ( J + 1 ) 100 120 140 Figure 5.9: + and A represent P and R branches Chapter 5. The Results and Discussions 47 Table 5.11: rrad, for the excited state v Isotope Excited state u' Average Trad. Error Br2 (79-79) 14 2.5 /xs 0.3 /xs Br2 (79-81) 14 2.7 /xs 0.2 /xs Br2 (79-79) 17 2.6 fxs 0.2 /xs Br2 (79-81) 17 2.6 /xs 0.2 /xs Br2 (81-81) 17 2.5 //s 0.3 /xs £r2 (79-79) 18 2.6 /xs 0.3 /xs £r2 (79,81) 18 2.5 /xs 0.3 /xs Br2 (81-81) 18 2.5 /xs 0.3 /xs £ r 2 (79-79) 19 2.7/xs 0.3 /xs £ r 2 (79-81) 19 2.5 /xs 0.3 /xs Br2 (79-79) 15 2.4 /xs 0.2 /xs 5r2 (79-81) 15 2.5 /xs 0.2 /xs Br2 (81-81) 15 2.4 /xs 0.2 lis 7.00 q O to o.OO 0.00 50.00 100.00 150.00 200.00 250.00 < J ' ( J'+1) Figure 5.10: v = 16, £3II0+Ustate of (79-79)£r2 Chapter 5. The Results and Discussions 48 0 . 6 0 -y in J D < 0 . 2 5 I i i i i i i ' i i i ' i i i i i i t i i i i i i i i i i i i i i i ' • i i i i i ' i i i i i ' ' ' 0 . 0 0 5 0 . 0 0 1 0 0 . 0 0 1 5 0 . 0 0 2 0 0 . 0 0 2 5 0 . 0 C J'(J'+1) Figure 5.11: v = 14, £3no+ustate of (79/79)£r2 lines from those v states are overlapped. Therefore it is hard to determine if there is a predissociation or not for those vibrational states. In this thesis, we have presented a detailed research of radiative lifetime, T r o a \ , of ( 7 9 , 7 9 ) £ r 2 j ( 7 9 , 8 i ) £ r 2 a n (j ( 8 i , 8 i ) £ r 2 > -p^ g apparatus and methods used to obtain the spectra and construction of the sample cells are described. The absorption and fluorescence spectra of the molecule bromine corresponding to the transitions between the ground state, X1E0+5, and excited state, B3Il0+u, have been measured from approximately 17464 cm"1 to 17480 cm"1. The radiative lifetimes rTad. for v = 14,15,17,18,19 of (79,79)£r2, (79,8i )_gf2 a nd (81>81)#r2 have been calculated from the spectra. However, there is a difficulty to determine the predissociations for some levels because of limited data. Appendix A The derivation of the transition probabilities From quantum mechanics, we have R = yy*M0"dr (A.87) where dr =drer2 sm6>drd6d<j> . (A.88) and M - Me + Mn (A.89) dre is the volume element in the configuration space of the electrons. M is the electronic momnent . Me and Mn depend on electrons and nuclei, respectrly. In the z direction, we have Mz = McosB = (Me + MN)cos6 (A.90) The complete eigenfunction of a molecule, to a first order approximation, is l/> = lj>e (A.91) r where 49 Appendix A. The derivation of the transition probabilities 50 V>e the electron eigenfunction. •0v the eigenfunction of a non simple harmonic vibration, t/v the eigenfunction of a rigid rotor. Thus, Rz = J ^.Me^^'dTe J ^l^dr J sin 0 cos 8il>*,if>Ti<d9d(p (A.92) Where we have used J xP*e,xJ>e»dTe = 0 (A.93) Considering three dimensions, we can obtain the total matrix element for the system The transition probability is proportional to | R n m | 2 . Appendix B The vibrational and rotational transition probabilities j B.l Vibrational transition probability From Eqn.(A.89) one know that in the electronic transition the intensity of the vibrational spectrum band is proportional to | / i[>l,ipviidr |2 (F.C.F.). Where ipvi and ^ V' belong to different electronic states, and they are not orthogonal. The integral / V£»VV' iS called overlap integral. The intensity of a vibrational band depends on the level of overlap between tj;vi and ?/V'- If we knew the electronic and vibrational wavefunctions, we can obtain the transition probability from.Eqn.(A.89). For the B3T10+U- X1'£0+g system of Br2, all the Franck-Condon factors in the B3H0+U state were obtained from several papers.[3,12] B.2 Calculation of the rotational transition probabilty First one can consider the z direction, (B.95) where tfM = N r p \ M \ ( c o s 9 y M v (B.96) 51 Appendix B. The vibrational and rotational transition probabilities 52 Thus J sin 6 cos 6[Nr.Nr» j e^M'-M"Uip]Ply '\cos 6) P1™"1 (cos 6) d6 = 2irNr.Nr» J** P]j?](x)xPl™\x)dx ( B . 9 7 ) where we have used Using the formulas ( B . 9 8 ) ( B . 9 9 ) ( B . 1 0 0 ) In this case, Nr = ( - 1 ) ' ( 2 J + 1 ) ( J - M ) ! 4TT(J + M ) ! ( B . 1 0 1 ) z = x V = /X = / = /' = m = M f J" M ( B . 1 0 2 ) ( B . 1 0 3 ) ( B . 1 0 4 ) ( B . 1 0 5 ) ( B . 1 0 6 ) ( B . 1 0 7 ) So, in z direction one can obtain the transition probability, Appendix B. The vibrational and rotational transition probabihties 53 £ I R rot J'J" I W'M" £ , M - i )2 m (2J' + 1)(J' — M)\ (2J" -f 1)(J" - Af)! T ^ , , 1 2J" + 1 ^ 47r ( J ' + M ) ! \ | 4TT(J" + M ) ! [ ( J " - M + 1)^| J»+ 1 + ( J " + M ) ^ ^ ] Finally, for the three dimensional system one obtains (B.108) M'M" (B.109) for the P branch, and for the R branch. Therefore, ^ IRj0{. | 2 = j " + l (B.110) j ' j " 2 2 J " + 1 - 1 Appendix C The density of molecular bromine in a particular rovibronic state The hyperfine partition factor is j§ = § for an ortho state (odd J), and yjj = § for a para state (even J). The density of a para state of (79,79)£r2, at room temperature, satisfies the following equation N0 e-W*" e~0E' Nv"jii = — x 0.2554 x — rrj?— x V ' E„»c-^«" Ene" 3(2J" + l)e-'*> • The equation above can be written as Nvnj„ = -77 x 0.2554 x V " E„«e-^." 3(2J- + l)e-^" . l3Ej»(2J" + l)e-^» + 2 x iEj»(2J" + l)e-^" J A ; Then we can obtain NvllJII = x 0.2554 x = ^ n r 3 (2J" + \)e-pEj" 4Ej''(2J" + l)e-^/' where i£ e is equal to zero for the ground electronic state. In the same way we can obtain Eqn.(2.41). (C.114) 54 Appendix D Identified and unused lines of Band 14' — l " Table D.12: Band 14' - l " bromine (79,81) P(J) v cm 1 mv J / kvdv cm 2 . 1 Re ? Ai> cm 1 P(3) 17466.705 2.6458 x 1013 0.7206 x 10" - 4 2.89 x 10" -3f 2.35 x IO"2 P(4) 17466.358 3.3911 x 1013 1.5938 x 10 - 4 2.88 x 10" -37 2.28 x IO"2 P(5) 17465.965 4.1285 x 1013 2.2497 x 10' - 4 2.65 x 10" -37 2.22 x IO"2 P(6) 17465.498 4.8563 x IO13 2.5790 x 10" - 4 2.42 x 10" -37 2.33 x IO"2 P(7) 17464.969 5.5729 x 1013 4.5523 x 10" - 4 2.89 x 10" -37 2.66 x IO"2 R(J) v cm-1 N a 7II mv J / kvdv cm~ 2 \Re V Au cm~l R(3) 17467.410 2.6458 x 1013 1.2148 x 10" - 4 2.29 x 10" -37 2.24 x IO"2 R(4) 17467.268 3.3911 x 1013 1.6490 x 10-- 4 2.50 x 10" -37 2.12 x 10~2 R(5) 17467.064 4.1285 x 1013 1.7696 x 10-- 4 2.24 x 10" -37 1.91 x 10~2 R(6) 17466.796 4.8653 x 1013 3.0943 x 10" - 4 2189 x 10" -37 2.54 x IO"2 R(7) 17466.477 5.5729 x 1013 2.9266 x 10-- 4 2.88 x 10" -37 2.16 x IO""2 •R(8) 17466.096 6.2766 x 1013 7.0570 x 10-- 4 2.79 x 10" -37 2.35 x IO"2 R(9) 17465.655 6.9659 x 1013 5.8730 x 10-- 4 2.70 x 10" -37 2.23 x IO"2 R(10) 17465.152 7.6392 x 1013 3.9626 x 10" - 4 2.89 x 10" -37 2.20 x IO"2 R(ll) 17464.591 8.2952 x 1013 3.7230 x 10-- 4 2.46 x 10--37 2.14 x IO"2 55 Appendix D. Identified and unused lines of Band 14' — l " Table D.13: Band 14' - l " bromine (79,79) P(J) u cm 1 j II / kvdu cm 2 \Re 2 Au cm 1 P(l) 17474.510 7.3060 X lO1^ 2.3747 X 10" -4 2.82 X 10" -'il 2.30 X 10" 2 P(4) 17473.655 1.3058 x 1013 3.8263 X io--4 2.11 X 10" -37 2.07 X 10" 2 P(6) 17472.770 1.8698 X 1013 0.7201 X 10" -4 2.25 X 10" -37 1.46 X 10" 2 P(7) 17472.237 3.5758 X 1013 1.8167 X 10" -4 2.85 X 10" -37 2.01 X 10" 2 P(8) 17471.645 2.4162 X 1013 1.0942 X 10" -4 2.60 X 10" -37 2.25 X 10" 2 P(9) 17470.987 4.4689 X 1013 1.8561 X io--4 2;37 X 10" -37 2.27 X i o - 2 P(ll) 17469.499 5.3206 X 1013 2.3694 X 10" -4 2.52 X 10" -37 2.12 X 10" 2 P(12) 17468.656 3.4372 X 1013 1.5725 X 10" -4 2.58 X 10" -37 2.17 X 10" 2 P(13) 17467.756 6.1237 X 1013 1.5741 X io--4 2.27 X io--37 2.07 X 10" 2 P(14) 17466.796 3.9029 X 1013 3.0943 X 10" -4 2.89 X 10" -37 2.39 X 10" 2 P(15) 17465.771 6.8715 X 1013 4.5367 X 10" -4 2.06 X io--37 2.47 X 10" 2 P(16) 17464.684 4.3337 X 1013 1.9524 X 10" -4 2.51 X io--37 2.05 X 10" 2 R(J) v cm~x ) J / kvdv cm 2 1 R< •I4 Au cm 1 R(4) 17474.546 1.3058 X 1013 10.465 X 10" -4 2.82 X 10" -37 2.78 X i o - 2 R(5) 17474.359 1.3058 X 1013 1.5958 X io-T4 2.65 X 10" -37 2.21 X 10" 2 R(7) 17473.761 2.5813 X 1013 2.5813 X io--4 2.12 X 10" -37 1.94 X 10" 2 R(8) 17473.368 1.5832 X 1013 1.5832 X 10--4 3.00 X 10" -37 2.18 X 10" •2 ••R(9) 17472.926 3.8333 X 1013 3.8333 X 10" -4 2.38 X 10" -37 2.17 X 10" •2 R(ll) 17471.841 2.3285 X 1013 2.3285 X 10" -4 2.23 X 10" -37 1.94 X i o --2 R(12) 17471.199 1.6754 X 1013 1.6754 X 10" -4 2.53 X 10" -37 2.42 X 10" •2 R(13) 17470.502 2.6743 X 1013 2.6743 X 10 -4 2.28 X 10" -37 1.96 X 10" •2 R(14) 17469.749 1.4127 X 1013 1.4127 X 10 -4 2.22 X 10" -37 1.88 X 10" -2 R(15) 17468.925 3.0055 X 1013 3.0055 X 10 -4 2.78 X 10" -37 2.03 X 10" •2 R(16) 17468.042 2.7618 X 1013 2.7618 X 10 -4 2.65 X 10" -37 2.53 X 10" -2 R(17) 17467.095 3.6602 X 1013 3.6602 X 10 -4 2.54 X 10" -37 2.09 X 10" -2 R(18) 17466.096 7.0570 X 1013 7.0570 X 10 -4 2.65 X 10--37 2.25 X 10" -2 R(19) 17465.032 4.6456 X 1013 4.6454 X 10 -4 2.89 X 10" -37 2.46 X 10" -2 endix D. Identified and unused lines of Band 14' — l " Table D.14: The unused lines from band 14' — l " bromine (79,79) P(J) • v cm 1 N //,// m o J / kudv cm 2 i Re r Av cm 1 P(2) P(3) P(5) P(10) 17474.273 17473.990 .17473.234 17470.271 7.4295 x 1012 1.6980 x 1013 2.6494 x 1013 2.9402 x 1013 1.0087 x 10"4 1.0253 x 10"4 1.7751 x lO"4 2.9105 x 10"4 9.34 x 10"37 3.81 x 10"37 3.98 x 10"37 5.62 x 10"37 2.36 x 10~2 2.58 x 10"2 2.80 x lO"2 0.83 x lO"2 R(J) v cm'1 N " 7 " 771U J [kudv cm~2 Re 2 Av cm'1 R(6) R(10) 17474.090 17472.412 1.2210 x 1013 2.4368 x 1013 1.2210 x 10"4 2.4368 x 10"4 3.28 x 10"37 4.27 x lO"37 1.94 x 10"2 2.09 x 10"2 Table D.15: The unused lines from band 14' — l " bromine (79,81) P(J) v cm 1 Nmv»j" / kudv cm 2 1 V Av cm 1 P(2) 17466.989 1.8943 x 1013 0.9814 x lO"4 3.70 x 10"37 2.86 x 10~2 R(J) v cm'1 JV // jii mv J / kudv cm'2 Re 2 Av cm'1 R(l) R(2) 17467.493 17467.493 1.1383 x 1013 1.8943 x 1013 2.7633 x 10"4 2.7633 x 10"4 0.65 x 10"37 0.65 x lO"37 2.94 x lO"'2 2.94 x 10"2 Appendix E Identified and unused lines of Band 17' — 2" Table E.16: Band 17' - 2" bromine (81,81) P(J) v cm 1 J mv J / kvdu cm 2 1 *e r A i / cm 1 P ( l ) 17465.821 1.5504 x 1012 1.3772 x IO' -4 2.06 x 10" -Al 2.27 x IO" 2 P(3) 17465.312 3.6068 x 1012 1.5765 x 10" -4 2.54 x 10" -37 1.92 x IO" 2 P(4) 17464.969 2.7715 x 1012 4.5523 x 10" -4 2.89 x 10" -37 2.59 x IO" 2 P(5) 17464.554 5.6241 x 1012 2.6528 x 10 -4 2.01 x 10" -37 2.19 x IO" 2 R(J) u cm'1 N a in / kvdu cm~ 1 Au cm~x R(l ) 17466.096 1.5504 x 1012 7.0570 x 10 -4 2.65 x 10" -37 2.25 x IO" 2 R(3) 17465.965 3.6038 x 1012 2.2497 x 10 -4 2.65 x 10" -37 2.19 x IO" 2 R(4) 17465.821 2.7715 x 1012 1.3772 x 10 -4 2.06 x 10" -37 2.27 x IO" 2 R(6) 17465.312 3.9696 x 1012 1.5765 x 10 -4 2.54 x 10" -37 1.92 x IO" 2 R(7) 17464.969 7.5930 x 1012 4.5523 x 10 -4 2.89 x 10--37 2.59 x 10~2 R(8) 17464.554 5.1316 x 1012 2.6528 x 10 -4 2.01 x 10" -37 2.19 x IO" 2 58 Appendix E. Identified and unused lines of Band 17' — 2" Table E.17: Band 17' - 2" bromine (79,79) P(J) ucm 1 " j It / kvdu cm I 1 Re la Au cm 1 P(l) 17478.173 1.5369 X 10™ 0.9337 X io-•4 2.62 X 10" 37 2.57 X io- '1 P(2) 17477.944 1.5345 x 1012 1.6993 X 10" •4 2.66 X 10" •37 2.25 X 10" 2 P(4) 17477.285 2.7469 X 1012 2.0088 X io--4 2.19 X 10" •37 2.89 X 10" 2 •P(5) 17476.860 5.5735 X 1012 2.4222 X 10" -4 2.65 X 10" •37 2.31 X 10" 2 P(6). 17476.377 3.9335 X 1012 2.9861 X io--4 2.52 X io--37 2.72 X 10" 2 P(7) 17475.815 7.5228 X 1012 1.5628 X io--4 2.06 X 10" -37 1.79 X 10" 2 P(8) 17475.190 5.0834 X 1012 4.0474 X io--4 2.74 X 10" -37 3.03 X io- 2 P(9) 17474.510 9.4022 X 1012 2.3747 X 10" -4 2.82 X 10" -37 2.30 X 10" 2 P(10) 17473.761 6.1862 X 1012 2.5813 X 10" -4 2.11 X 10" -37 1.94 X 10" 2 P(ll) 17472.956 1.1195 X IO13 2.5975 X io--4 2.77 X 10" -37 2.03 X 10" 2 P(14) 17470.118 8.2130 X IO12 1.3608 X io--4 2.34 X io--37 1.62 X 10" -2 P(15) 17469.035 1.4460 X IO13 3.0989 X 10" -4 2.78 X 10" -37 2.06 X 10" •2 P(17) 17466.680 1.5907 X IO13 3.5484 X io--4 2.89 X 10" -37 2.18 X 10" -2 P(18) 17465.402 9.9478 X IO12 4.2071 X io--4 2.42 X 10" -37 2.09 X 10" -2 R(J) u cm'1 // fit J / kudv cm 2 .• Re Is Au cm 1 R(0) 17478.438 3.0762 X IO11 0.5719 X 10" -4 2.66 X 10" -37 2.12 X 10" -2 R(2) 17478.438 1.5345 X 1012 0.5719 X io--4 2.66 X 10" -37 2.12 X 10" -2 R(4) 17478.173 2.7469 X IO12 0.9337 X 10" -4 2.62 X 10" -37 2.23 X 10" -2 R(5) 17477.944 5.5735 X 1012 1.6993 X io--4 2.66 X 10" -37 2.25 X 10" -2 R(7) 17477.285 7.5228 X 1012 2.0088 X 10" -4 2.19 X 10" -37 2.81 X 10" -2 R(8) 17476.860 5.0843 X 1012 2.4222 X io--4 2.65 X io--37 2.12 X 10" -2 R(9) 17476.377 9.4022 X IO12 2.9861 X io--4 2.52 X io--37 2.68 X 10" -2 R(10) 17475.815 6.1862 X 1012 .1.5628 X io--4 2.06 X io--37 1.79 X 10" -2 R(ll) 17475.190 1.1195 X IO13 4.0474 X 10" -4 2.74 X io--37 3.03 X 10" -2 R(12) 17474.510 7.2323 X 1012 2.3747 X io--4 2.82 X io--37 2.30 X 10" -2 R(14) 17472.926 8.2130 X IO12 3.8333 X 10" -4 2.38 X 10" -37 2.17 X io--2 R(15) 17472.050 1.4460 X IO13 5.6018 X 10" -4 2.62 X io--37 2.30 X 10" -2 R(16) 17471.094 9.1203 X 1012 2.4579 X io--4 2.99 X 10" -37 2.06 X io--2 R(17) 17470.089 1.5907 X IO13 3.3296 X 10 -4 2.34 X io--37 2.13 X 10" -2 R(18) 17469.002 9.9478 X 1012 3.1130 X 10 -4 2.78 X io--37 2.32 X io--2 R(19) 17467.860 1.721.6 X IO13 3.7253 X 10 -4 2.65 X io--37 2.03 X io--2 R(20) 17466.645 1.0690 X IO13 4.9965 X 10 -4 2.89 X 10 -37 2.02 X 10" -2 R(21) 17465.361 1.8379 X IO13 2.4221 X 10 -4 2.47 X 10 -37 2.11 X io--2 Appendix E. Identified and unused lines of Band 17' — 2" 60 Table E.18: Band 17' - 2" bromine (79,81) P(J) v cm 1 j II / kudv cm 2 \Re 2 Av cm 1 P(l) 17472.050 2.4178 X io1JJ 5.6018 x 10" -4 2.62 X io--'S7 2.30 X 10" !i P(2) 17471.819 4.0235 X 1012 2.7667 x 10" -4 2.50 X io--37 1.99 X 10" 2 P(3) 17471.522 5.6197 X 1012 3.5042 x 10" -4 2.54 X io--37 2.04 X io- 2 P(4) 17471.166 7.2029 X 1012 4.0899 x 10" -4 2.49 X io--37 2.12 X 10" 2 P(5) 17470.745 8.7694 X 1012 5.2775 x io--4 2.76 X io--37 2.14 X io- 2 P(7) 17469.724 1.1838 X 1013 5.6378 x 10" -4 2.22 X io--37 2.02 X io- 2 P(8) 17469.106 1.3333 X 1013 8.4040 x 10" -4 2.78 X io--37 2.61 X io- 2 P(9) 17468.438 1.4798 X 1013 7.3152 x 10" -4 2.51 X 10" -37 2.27 X io- 2 P(10) 17467.692 1.6229 X 1012 8.3822 x 10" -4 2.27 X 10" -37 2.49 X 10" 2 P(ll) 17466.880 1.7623 X 1013 8.2927 x 10" -4 2.45 X io--37 2.51 X io- 2 P(12) 17466.015 1.8977 X 1013 9.8095 x 10" -4 2.65 X 10" -37 2.74 X io- 2 P(13) 17465.080 2.0289 X 1013 11.5934 x 10"4 2.89 X io--37 2.90 X 10" 2 R(J) . v cm-1 // 1ll I J / kvdv cm -2 | Re Av cm 1 R(3) 17472.201 5.6197 X 1012 1.4712 x •10" -4 2.85 X io--37 1.83 X io- 2 R(4) 17472.050 7.2029 X. 1012 5.6018 x 10" -4 2.62 X io--37 2.30 X 10" 2 R(5) 17471.819 8.7694 X 1012 2.7667 x 10" -4 2.50 X io--37 1.97 X 10" 2 R(6) 17471.522 1.0316 X 1013 3.5042 x 10" -4 2.54 X io--37 2.04 X io--2 R(7) 17471.166 1.1838 X 1013 4.0899 x 10" -4 2.49 X io--37 2.12 X 10" -2 R(8) 17470.745 1.3333 X 1013 5.2775 x 10" -4 . 2.76 X io--37 2.14 X 10" -2 R(10) 17469.724 1.6229 X 1013 5.6378 x 10" -4 2.22 X io--37 2.02 X 10" •2 R(ll) 17469.106 1.7623 X 1013 8.4040 x 10" -4 2.78 X io--37 2.61 X 10" -2 R(12) 17468.438 1.8977 X 1013 7.3152 x io--4 2.51 X 10" -37 2.27 X 10" •2 R(13) 17467.692 2.0289 X 1013 8.3822 x io--4 2.27 X io--37 2.49 X 10" -2 R(14) 17466.880 2.1556 X 1013 8.2927 x io--4 2.45 X 10" -37 2.51 X 10" -2 R(15) 17466.015 2.2775 X 1013 9.8095 x io--4 2.65 X io--37 2.74 X 10" -2 R(16) 17465.080 2.3945 X 1013 11.593 x 10" -4 2.89 X io--37 2.90 X 10" -2 Appendix E. Identified and unused lines of Band 17' — 2' 61 Table E.19: The unused lines from band 17' - 2" bromine (79,79) P(J) u cm 1 N ",» m» J f k„du cm 2 Re 2 Au cm 1 P(3) P(13) 17477.652 17471.120 3.5720 x 1013 1.2886 x 1013 1.5972 x 10-4 3.5037 x IO"4 5.24 x IO"37 3.23 x IO"37 2.89 x IO-2 2.57 x IO"2 R(J) v cm'1 mv J / kudu cm-2 \Re 2 Au cm'1 R(l) R(3) 17478.461 17478.337 1.5369 x 10™ 3.5720.x 10™ 1.5994 x IO"4 1.1779 x IO"4 8.92 x IO"37 3.30 x IO"37 2.61 x IO"2 2.39 x IO-2 R(6) 17477.652 3.9335 x 1.0™ 1.5628 x IO"4 5.24 x IO"37 2.89 x IO"2 Table E.20: The unused lines from band 17' — 2" bromine (79,81) P(J) u cm 1 Nmv"j" / kvdu cm 2 Re 2 Au cm 1 P(6) 1747.271 1.0316 x 1013 2.9105 x IO"4 1.34 x IO"37 2.11 x IO"2 R(J) v cm'1 Nmv"j" / kudu cm'2 Re | 2 Au cm'1 R(O) R(l) R(2) R(9) 17472.276 17472.330 17472.276 17470.271 8.0657 x 10™ 2.4178 x 10™ 4.0235 x 10™ 1.4798 x 1013 11.584 x 10"4 I. 3005 x IO"4 II. 584 x IO"4 2.9105 x IO"4 20.8 x IO"37 4.51 x IO"37 20.8 x IO"37 1.34 x IO"37 2.07 x 10"2 2.16 x 10~2 2.07 x IO"2 2.11 x 10~2 Table E.21: The unused lines from band 17' — 2" bromine (81,81) P(J) u cm 1 ^mv"j" / k„dv cm 2 \Re \ z Au cm 1 P(2) 17465.597 1.5480 x 10™ 2.0183 x IO"4 3.09 x IO"37 2.11 x IO"2 R(J) v cm'1 Nmv"j" / kvdv cm'2 Re 2 Au cm'1 R(5) 17465.597 5.9624 x 10™ 2.0183 x IO"4 3.09 x 10"37 2.11 x IO"2 Appendix F Identified and unused lines of Band 18' — 2" Table F.22: Band 18' - 2" bromine (79,79) P(J) v cm'1 Xmv"j" / k„dv cm'2 Av cm 1 P(53) P(54) P(55) P(56) 17477.072 17473.334 17469.532 17465.655 1.7786 x 10" 1.0419 x 1013 1.6935 x 1013 9.8985 x 1012 4.7254 x 10"4 4.7261 x 10"4 3.6368 x 10"4 5.8730 x lO"4 2.96 x lO"37 3.00 x 10"37 2.40 x 10"37 2.70 x 10"37 2.45 x 10"2 2.41 x 10"2 1.99 x 10"2 2.25 x lO"2 R(J) v cm'1 / kvdv cm'2 l # e I2 Av cm'1 R(56) R(57) R(59) 17476.356 17472.602 17464.869 9.8985 x 1012 1.6054 x 1013 1.5152 x 1013 2.4532 x lO"4 3.4534 x 10"4 3.2013 x lO"4 2.72 x 10"37 2.36 x 10"37 2.32 x 10"37 2.09 x 10"2 2.09 x 10"2 1.88 x 10"2 Table F.23: Band 18' - 2" bromine (79,81) P(J) v cm'1 Mmv"j" / kvdv cm'2 •; 1 ^  V Av cm 1 P(51) P(52) P(54) P(55) 17479.440 17475.897 17468.593 17464.843 2.9630 x 1013 2.9010 x 1013 2.7713 x 1013 2.7041 x 1013 7.1115 x 10"4 6.2008 x 10"4 5.7247 x lO"4 5.7254 x lO"4 2.62 x lO"37 2.06 x lO"37 2.31 x lO"37 2.37 x 10"37 2.17 x 10~2 2.02 x 10~2 1.88 x 10~2 1.88 x 10~2 R(J) v cm'1 ^ m v " j " / kvdv cm'2 \Re 2 Av cm'1 R(54) R(55) R(56) R(57) 17478.826 17475.257 17471.616 17467.919 2.7713 x 1013 2.7041 x 1013 2.6356 x 1013 2.5661 x 1013 5.5294 x 10"4 10.7176 x lO"4 6.9485 x lO"4 6.5901 x 10"4 2.19 x 10"37 2.74 x lO"37 2.89 x lO"37 2.65 x lO"37 2.06 x lO"2 2.51-x lO"2 2.37 xlO-2 2.21 x 10~2 62 Appendix F. Identified and unused lines of Band 18' — 2" 63 Table F.24: Band 18' - 2" bromine (81,81) P(J) . v cm 1 N a i" mv J / kudv cm 2 1 Re \2 Au cm 1 P(50) P(52) P(53) 17477.867 17470.934 17467.375 1.1775 x 1013 1.1311 x 1013 1.8845 x 1013 2.2091 x IO"4 2.2259 x IO-4 3.6337 x IO"4 2.14 x IO"37 2.25 x IO"37 2.25 x IO"37 1.81 x IO"2 2.22 x IO"2 1.98 x IO"2 R(J) y cm'1 x mv J / k„dv cm'2 . \Re 2 Av cm'1 R(53) R(54) R(55) R(56) 17477.315 17473.862 17470.360 17466.783 1.8445 x 1013 1.0816 x 1013 1.7599 x 1013 1.0298 x 1013 4.7498 x IO"4 2.6044 x IO"4 3.4489 X IO"4 3.1334 x IO"4 2.89 x IO"37 2.70 x IO"37 2.20 x IO"37 2.89 x IO"37 1.79 x IO"2 1.88 x IO"2 1.94 x IO"2 2.45 x IO"2 Table F.25: The unused lines from band 18' - 2" bromine (79,79) R(J) . v cm 1 / kvdv cm 2 1 Re \2 Av cm 1 R(58) 17468.766 9.3629 x IO12 3.0098 x IO"4 3.53 x IO"37 2.35 x IO"2 Table F.26: The unused lines from band 18' -2" bromine (79,81) P(J) v cm 1 Nmv"j" / kpdv cm 2 l ^ e l 2 Av cm 1 P(53) 17472.276 2.8370 x IO13 11.5838 x IO"4 20.8 x IO-37 2.07 x IO"2 Table F.27: The unused lines from band 18' -2" bromine (81,81) R(J) v cm 1 N a i" / kvdv cm 2 Re 2 Av cm 1 R(51) 17474.434 1.9245 x IO13 5.2880 x IO"4 3.14 x IO"37 2.22 x IO"2 Appendix G Identified and unused lines of Band 19' — 2" Table G.28: Band 19' - 2" bromine (79,79) P(J) v cm'1 / kudv cm'2 \Re 2 Av cm'1 P(74) P(75) •P(76) 17475.310 17469.938 17464.554 5.1682 x 10" 8.2301 x 1012 4.7136 x 1012 0.3988 x 10"4 2.0805 x 10"4 2.6528 x 10"4 2.74 x 10"37 2.80 x 10"37 2.01 x lO"37 2.27 x 10"2 2.31 x 10"2 2.19 x 10"2 R(J) v cm'1 Nmv"j" / k„dv cm'2 \Re 2 Av cm'1 R(76) R(77) R(78) 17478.640 17473.368 17467.982 4.7136 x 10" 7.4919 x 10" 4.2828 x 10" 1.8104 x 10"4 1.5832 x 10~4 0.9802 x 10"4 2.67 x 10"37 3.00 x lO"37 2.65 x lO"37 2.32 x lO"2 2.18 x 10"2 2.34 x 10~2 Table G.29: Band 19' - 2" bromine (79,81) P(J) v cm 1 N a in * mv J / kudv cm'2 Av cm 1 P(73) P(74) P(75) 17477.024 17471.862 17466.607 1.4541 x 1013 1.3917 x 1013 1.3307 x 1013 2.8446 x 10~4 3.1012 x lO"4 3.0955 x lO"4 2.16 x lO"37 2.46 x 10"37 2.89 x 10"37 2.03 x 10-* 1.94 x 10~2 2.00 x lO"2 R(J) v cm'1 / kt,dv cm'2 i * . r Av cm'1 R(76) R(77) R(78) 17475.257 17470.058 17464.769 1.2711 x 10" 1.2131 x 1013 1.1566 x 1013 10.7176 x 10~4 2.4787 x lO"4 6.0178 x lO"4 2.74 x lO"37 2.34 x 10"37 2.21 x lO"37 2.51 x 10"* 1.91 x 10"2 1.91 x lO"2 64 Appendix H Identified and unused lines of Band 15' — l " Table H.30: Band 15' - l " bromine (79,79) P(J) v cm'1 mv J / kvdv cm 2 Re | 2 Ai/ cm 1 P(57) P(58) P(59) P(60) 17476.913 17473.141 17469.309 17465.411 7.5921 x 1013 4.4271 x 1013' 3.9268 x 1013 4.1680 x 1013 4.6382 x 10"4 2.5729 x IO"4 2.3394 x IO"4 2.4221 x IO"4 2.61 x IO'37 2.48 x 10~37 2.34 x 10~37 2.42 x 10~37 2.34 x IO"2 1.94 x IO"2 2.31 x IO"2 2.09 x 10~2 R(J) v cm'1 Nmv"j" / kvdv cm''2 \ R e 2 Ai/ cm'1 R(61) R(63) 17473.645 17465.929 6.7295 x 1013 6.2957 x 1013 3.8263 x IO"4 3.0085 x IO"4 2.10 x 10~37 2.65 x 10~37 2.07 x IO"2 2.23 x IO"2 Table H.31: Band 15' - l " bromine (79,81) P(J) v cm 1 Nmv"j" / kvdv cm 2 1 Re r Ai/ cm 1 P(55) P(56) P(57) P(58) 17478.132 17474.530 17470.882 17467.161 1.2671 x 1014 1.2348 x 1014 1.2020 x 1014 1.1689 x 1014 6.4400 x 10~4 10.465 x 10~4 6.3559 x 10~4 6.8468 x IO"4 2.27 x 10-37 2.82 x 10~37 2.36 x IO"37 2.62 x 10~37 1.97 x IO"2 2.78 x IO"2 2.19 x 10~2 2.20 x 10~2 R(J) v cm'1 N /' 7II / kvdv cm'2 \ R e 2 Ai/ cm'1 R(58) R(59) R(60) R(61) 17478.691 17475.099 17471.445 17467.732 1.1689 x 1014 1.1354 x 1014 1.1017 x 1014 1.0679 x 1014 6.4681 x IO"4 6.0241 x IO"4 5.5828 x IO"4 5.9345 x IO"4 2.67 x 10~37 2.33 x 10~37 2.23 x 10~37 2:27 x 10~37 2.19 x IO"2 1.97 x IO"2 2.04 x IO"2 2.28 x IO"2 65 Appendix H. Identified and unused lines of Band 15' - " Table H.32: Band 15' - l " bromine (81,81) P(J) v cm 1 TV // 7« mv J / kydv cm 2 1 Re | a Av cm 1 P(53) P(54) P(55) P(56) P(57) 17478.874 17475.459 17471.981 17468.441 17464.839 8.5633 x 1013 5.0208 x 1013 8.1681 x 1013 4.7785 x 1013 7.7571 x 1013 5.1914 x 10~4 2.7060 x lO"4 4.0085 x 10"4 2.4417 x 10"4 6.0178 x 10"4 2.71 x 10"37 2.41 x lO"37 2.19 x lO"37 2.28 x 10"37 2.21 x lO"37 2.36 x lO"2 2.22 x lO"2 2.08 x lO"2 2.17 x lO"2 1.91 x lO"2 R(J) v cm'1 mv J / kvdv cm~2 Re 2 Av cm'1 R(56) R(58) R(59) R(60) 17479.455 17472.572 17469.037 17465.438 4.7785 x 1013 4.5283 x 1013 7.3353 x 1013 4.2731 x 1013 2.1641 x 10"4 2.0538 x 10"4 3.7690 x 10"4 5.8411 x 10"4 2.62 x 10"37 2.00 x 10"37 2.78 x lO"37 2.42 x 10"37 1.90 x lO"2 2.07 x lO"2 2.26 x lO"2 2.11 x lO"2 Table H.33: The unused lines from band 15' — l " bromine (79,79) R(J) v cm 1 N » r" mv J / kudv cm 2 Re 2 Av cm 1 R(60) R(62) 17477.434 17469.834 4.1680 x 1013 3.9074 x 1013 4.3797 x lO"4 1.6549 x 10"4 4.41 x 10"37 1.78 x 10"37 4.41 x lO"* 1.78 x lO"2 Table H.34: The unused lines from band 15' — l " bromine (81,81) R(J) v cm 1 / kvdv cm 2 \Re 2 Av cm 1 R(57) 17476.045 7.7571 x 1013 1.5676 x 10"4 0.89 x 10"37 1.78 x lO"2 Appendix H. Identified and unused lines of Band 15' — l " 67 Table H.35: The F.C.F.used for calculating | Re |2 State Isotope Band F;C.F. (79,79)£r2 14' - 1" 0.00509 (79,81)£r2 14' - 1" 0.00408 (79,79)£r2 15' - 1" 0.00650 (79,81)£r2 15' - 1" 0.00621 (81,81)£r2 15' - 1" 0.00594 B3U0+U (79,79)£r2 17' - 2" 0.02405 (79,81)£r2 17' -2" 0.02378 (81,81)£r2 17' - 2" 0.02324 (79,79)£r2 18' - 2" 0.02487 (79,81)^2 18' - 2" 0.02478 (81,81)£r2 18' - 2" 0.02429 (79,79)Br2 19' - 2" 0.02504 (79,81)£r2 19' - 2" 0.02511 Table H.36: The F.C.F.^79-79)^) used for calculating rrad Band F.C.F. Band F.C.F. Band F.C.F. 14'-0" 0.00060 17'-0" 0.00144 15'-0" 0.00083 14'-1" • 0.00509 17'-1" 0.00951 15'-1" 0.00650 14'-2" 0.01775 17'-2" 0.02405 15V2" 0.02040 14'-3" 0.03145 17'-3" 0.02640 15'-3" 0.03111 14'-4" 0.02639 17'-4" 0.00812 15'-4" 0.01995 14'-5" 0.00543 17'-5" 0.00107 15'-6" 0.00126 14'-6" 0.00264 17'-6" 0.01531 15'-7" 0.00731 14'-7" 0.01859 17'-7" 0.01233 15'-8" 0.01958 14'-8" 0.01447 17'-8" 0.000016 15'-9" 0.00727 14'-9" 0.00018 17'-9" 0.01058 15'-10" 0.00133 14'-10" 0.01026 17'-10" 0.01235 15'-11" 0.01537 Appendix H. Identified and unused lines of Band 15' — l " 68 Table H.37: The F.C.F. used for calculating rrad Isotope Band F.C.F. Band F.C.F. 18'-0" 0.00180 19'-0" 0.00220 18'-1" 0.00.99 19'-1" 0.01238 18'-2" 0.02487 19'-2" 0.02504 18'-3" 0.02273 19'-3" 0.01876 18'-4" 0.00400 19'-4" 0.00137 ( 7 9 , 7 9 ) ^ 18'-5" 0.00358 19'-5" 0.00660 18'-6" 0.01651 19'-6" 0.01571 18'-7" 0.00726 19'-7" 0.00316 18'-8" 0.00106 19'-8" 0.00391 18'-9" 0.01339 19'-9" 0.01348 18'-10" 0.00712 19'-10" 0.00263 Table H.38: The F.C.F.^81'81)^) used for calculating rTad Band F.C.F. Band F.C.F. Band F.C.F. 18'-0" 0.00164 17'-0" 0.00130 15'-0" 0.00074 18'-1" 0.01030 17'-1" 0.00884 15'-1" 0.00594 •18'-2" 0.02429 17'-2" 0.02324 15'-2" 0.01931 18'-3" 0.02378 17'-3" 0.02712 15'-3" 0.03094 18'-4" 0.00525 17'-4" 0.00975 15'-4" 0.02173 18'-5" 0.00253 17'-5" 0.00048 15'-6" 0.00223 18'-6" 0.01608 ' 17'-6" 0.01418 15'-7" 0.00565 18'-7" 0.00877 17'-7" 0.01384 15'-8" 0.01940 18'-8" 0.00041 17'-8" 0.00030 15'-9" 0.00927 18'-9" 0.01250 . 17'-9" 0.00897 15'-10" 0.00048 18'-10" 0.00811 17'-10" 0.01326 15'-11" 0.01402 Appendix H. Identified and unused lines of Band 15' — l " 69 Table H.39: The F.C.F.((79-81)£r2) used for calculating Trad Band F.C.F. Band F.C.F. Band F.C.F. 14'- 0" 0.00056 17'- 0" 0.00138 15'- 0" 0.00079 14'- 1" 0.00482 17'- 1" 0.00924 15'- 1" 0.00621 14'- 2" 0.01714 17'- 2" 0.02378 15'- 2" 0.01985 14'- 3" 0.03106 17'- 3" 0.02684 15'- 3" 0.03102 14'- 4" • 0.02715 17'- 4" 0.00899 15'- 4" 0.02091 14'- 5" 0.00640 17'- 5" 0.00071 15'- 5" 0.00178 14'- 6" 0.00198 17'- 6" 0.01446 15'- 6" 0.00635 14'- 7" 0.01790 17'- 7"' 0.01314 15'- 7" 0.01952 14'- 8" 0.01551 17'- 8" 0.00013 15'- 8" 0.00835 14'- 9" . 0.00046 17'- 9" 0.00976 15'- 9" 0.00083 14'- 10" 0.00914 17'- 10" 0.01309 15'- 10" 0.01472 14'- 11" 0.01736 17'- 11" 0.00045 15'- 11" 0.01145 14'- 12" 0.00327 17'- 12" 0.00817 15'- 12" 0.000001 14'- 13" 0.00415 17'- 13" 0.01255 15'- 13" 0.01126 14'- 14" 0.01662 17'- 14" 0.00055 15'- 14" 0.01296 14'- 15" 0.00640 17'- 15" 0.00766 15'- 15" 0.00029 14'- 16" 0.00155 17'- 16" 0.01201 15'- 16" 0.00896 14'- 17" 0.01514 17'- 17" 0.00044 15'- 17" 0.01385 14'- 18": 0.00930 17'- 18" 0.00787 15'- 18" 0.00092 14'- 19" 0.00028 17'- 19" 0.01164 15'- 19" 0.00728 14'- 20" 0.01324 17'- 20" 0.00028 15'- 20" 0.01451 Appendix H. Identified and unused lines of Band 15' — 1" 70 Table H.40: The F.C.F. used for calculating rrad Isotope Band F.C.F. Band F.C.F. 18'-0" 0.00175 19'-0" 0.00215 18'-1" 0.01076 19'-1" 0.01220 18'-2" 0.02478 19'-2" 0.02511 18'-3" 0.02334 19'-3" 0.01942 18'-4" 0.00463 19'-4" 0.00174 18'-5" 0.00298 19'-5" 0.00593 18'-6" 0.01624 19'-6" 0.01578 (79,81) B j.2 18'-7" 0.00809 19'-7" 0.00378 18'-8" 0.00068 19'-8" 0.00326 18-9" 0.01297 19'-9" 0.01354 18'-10" 0.00802 19'-10" 0.00331 18'-11" 0.00051 19'-11" 0.00348 18'-12" 0.01207 19'-12" 0.01254 18'-13" 0.00715 19'-13" 0.00220 Bibliography [1] Acrivos, J.V., Delios, C, Topsoe, N.V., and Salem, J.R., J. Phys. Chem. 79, 193 (1975). [2] Barrow, R.F., J. Mol. Spectry. 51, 428 (1974). [3] Barrow, R.F., Clark, T.C., Coxon, J.A., and Yee, K.K., J. Mol. Spectry. 51, 428 (1974) [4] Booth, J.L., Dalby, F.W., Parmal, S., and Vanderlinde, J., (to be published). [5] Brown, W.G., Phys. Rev. 39, 777 (1932). [6] Bunker, P.R., Molecular Symmetry and Spectroscopy, (Academic Press, New York, 1979), P.129. [7] Child, M.S., J. Phys. B: Atom. Molec. Phys. 13, 2557 (1980). [8] Clyne A.A. Michael, Heaven C. Michael, and Martinez Ernesto, J.C.S. Faraday II 76,405 (1980). [9] Coxon, J.A., J. Mol. Spectry. 37, 39 (1971). [10] Coxon, J.A., J. Quant. Spectrosc. Radiat. Transfer 11, 443 (1971). [11] Coxon, J.A., J. Quant. Spectrosc. Radiat. Transfer 12, 639 (1972). [12] Gerstenkorn S., Luc P., and Sinzelle J., J. Physique 48, 1685-1696 (1987). 71 Bibliography 72 [13] Herzberg, G., Molecular Spectra and Molecular Structure, (Van Nostrand, New York, 1950), P.20. [14] Herzberg, G., Molecular Spectra and Molecular Structure, (Van Nostrand, New York, 1950), P.50. [15] Herzberg, G., Molecular Spectra and Molecular Structure, (Van Nostrand, New York, 1950), P.382. [16] Herzberg, G., Molecular Spectra and Moleaular Structure, (Van Nostrand, New York, 1950), P.383. [17] Herzberg, G., Molecular Spectra and Molecular Structure, (Van Nostrand, New York, 1950), P.110. [18] Herzberg, G., Molecular Spectra and Molecular Structure, (Van Nostrand, New York, 1950), P.240. [19] Horsley, J.A., and R.F. Barrow, Tans. Faraday Soc. 63, 32 (1967). [20] Huber, K. P., and Herzberg, G., Constants Of Diatomic Molecules. (Van Nostrand, New York, 1979). [21] Atlas Du Spetre De La Molecule De L'lode, Lab Aime Cotton, C.N.R.S.II, Bat.505, 91405-Orsay, France. [22] Richards, W.G., Structure and Spectra of Molecules, (John Wiley and Sons, New York, 1985), P.95. [23] Rideal, E.K., Resonance Radiation and Excited Atoms. (Cambridge University Press, New York, 1934), P.93. Bibliography 73 [24] Robert J. Le Roy, Macdonald, R.G., and Burns,G., J. Chem. Phys. 65,1485 (1976). [25] Siese, M., Tiemann, E., and Wulf, U., Chemical Physics Letters 117, 208 (1985). [26] Steinfeld, I. Jeffrey, Molecules and Radiation: An Introduction to Modern Molec- ular Spectroscopy, (Harper and Row, New York, 1981), P.63. 

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