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The electric dipole moment in the B ³Π₀₊ state of molecular iodine monochloride Wang, Shixin 1993

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THE ELECTRIC DIPOLE MOMENT IN THE B 'Ho+ STATE OFMOLECULAR IODINE MONOCHLORIDEByShixin WangB. A. Sc. (Physics) Peking University, ChinaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESPHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASept. 1993© Shixin Wang, 1993In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.PhysicsThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1W5Date:AbstractThe laser-induced fluorescence spectrum in IC1 of the electronic system B3140+ i--X 1E0+for the (2-0) vibrational band has been measured as a function of the electric field strengthup to 32.5 kV/cm. From the Stark shift measurements, the dipole moment in vibrationallevel v' = 2 of the B 3110+ state, not previously measured experimentally, has been foundto equal 1.122(25) D for I35C1 and 1.116(35) D for I37C1 . Intensity measurements ofthe (2-0) Q(0) and Q(1) of I35C1 have shown that these normally forbidden lines becomeallowed through the mixing of rotational levels generated by the interaction of the dipolemoment with the externally applied electric field. The Stark shift measurement of themagnitude of the dipole moment was confirmed and the sign of the dipole moment wasshown to be the same as that in the ground X 1E0• state.11Table of ContentsAbstract^ iiTable of Contents^ iiiList of Tables^ viList of Figures^ viiiAcknowledgement^ ix1 Introduction 11.1 The dipole moment of IC1 in different electronic states 11.2 Electric field induced transitions ...... 31.3 Present work^...............^. 32 Theory of Stark Effect and Electric Field Induced Transitions 52.1 Stark Effect ^ 52.1.1^The zero field Hamiltonian and its eigenfunctions ^ 52.1.2^The Hamiltonian in the presence of an electric field and its eigen-functions ^ 72.2 Electric field induced transitions of IC1 ^ 92.2.1^Absorption intensities of induced lines of ICI ^ 92.2.2^Fluorescence intensities of induced lines of IC1 123 Apparatus and Spectrum 141113.1 Preparation of experiments^ 143.1.1^Preparation of the Stark cell ^ 143.1.2^Measurement of the electric field 143.1.3^Design of the filling system^ 173.1.4^Getting clean ICI spectrum 193.1.5^Spectroscopic arrangement ............ 233.2 Experimental procedure ^ 253.2.1^Choosing apropriate temperature of the cold finger 253.2.2^Taking the spectra^..........^.^.^. 264 Spectra and Data Analysis 274.1 Selection of the vibrational band^ 274.1.1^Intensity measurement 274.1.2^Stark shift measurement^. . 284.2 Stark splittings in the optical spectrum . .^•^....... 284.2.1^Sample spectrum^.^.^.^.^...........^.^. 284.2.2^Data analysis of Stark splittings ^ 294.3 Induced transitions ^ 394.3.1^Sample spectrum 394.3.2^Saturation ^ 464.3.3^Temperature stability and power variation ^4.3.4^Data Analysis of 4(1,0)40) . • • • • • • • ^44864.3.5^Data Analysis of /6(0)//ifi(5) and /60)//iri(5) ^ 505 Discussion and Conclusion 575.1 Effect of the inhomogeneity of the electric field ^ 575.2 Check of saturation effect at E = 32.5 kV/cm 61iv5.3 Effect of the hyperfine term  ^625.4 Accuracies of different methods  ^635.5 Energy level behaviours at high electric fields  ^645.6 Conclusion  ^66Bibliography^ 70List of Tables1.1 The dipole moment of the A 'Hi state as a function of vibrational level.^22.2 Molecular parameters for the B 3110+ state of IC1 in cm'.^62.3 Dunham Coefficients for the X 1E0+ state of IC1 in cm'. 73.4 Vapour Pressure of Solid Iodine Monochloride.^ 204.5 Measured frequencies with the calculated values for (2-0) bands in theB 3110+—X 1E0+ system in 135C1 and P7C1 . The AJ = +1 lines weremeasured and calculated at zero field; the AJ --= 0 lines were measuredand calculated at E = 29879.3 V/cm   334.6 Fitting results for different value of it"^ 394.7 Fitting results of I35C1 (2-0) Stark components in the B 3110+—X 1E0+ sys-tem ^  424.8 Fitting results of I37C1 (2-0) Stark components in the B 3110+—X lEo+ sys-tem ^  444.9 Average frequencies of 135C1 (2-0) R(7) and R(8) in the B 3140+—X 1Eo+system at different electric fields. . . .^ 454.10 Fitting results of /6(0)//1L(5) as a function of the electric field.  ^534.11 Fitting results of 16(1)/1ii(5) as a function of the electric field.  ^535.12 Fitting results of the linewidth of I'Cl (2-0) P(1,0) in the B 3110+—X lEo+system as a function of the central electric field E0. ^ 59vi5.13 Calculated results of the linewidth of I35C1 (2-0) Q(0) in the electronicB 3I10-1--X 1E0+ system as a function of the central electric field E0.^.^605.14 The fitting results of I35C1 from P(1,0) and from the Stark components ofP(2), P(3).^...... . . .^. ..... . . .^ .^635.15 The coefficients of the eigenvector as a function of electric field in thevibrational level v' = 2 of the B 3110+ state for I35C1 (with ft' = 1.122 D).^675.16 The coefficients of the eigenvector as a function of the electric field in thevibrational level v" = 0 of the X1E0+ state for 135C1^ 685.17 The coefficients of the eigenvector as a function of electric field in thevibrational level v' = 2 of the B 3110+ state for I35C1 (with it' = —1.122 D). 69viiList of Figures3.1 The sketch of the Stark cell.^. 153.2 The circuit for measuring the electric field.^........^163.3 The design of the filling system.^ 183.4 The spectrum of 135C1 at room temperature (about 20°C) ^ 213.5 The spectrum of 135C1 at -55°C^  223.6 Experimental arrangement  244.7 The spectrum showing the effect of the electric field. ^ 304.8 The frequencies of the Stark components of B3110+—X1E0+ (2-0) transitionsin I35C1 as a function of E2 ^  374.9 The frequencies of the Stark components of B3110+—X1E0+ (2-0) transitionsin 137C1 as a function of E2 ^  384.10 The spectrum showing the induced transitions. ^  474.11 /(2f(0)//Rf (5) as a function of the electric field. .^.^.....^544.12 /f //f as a function ^the ^field. Q(1) R(5)^on o  e 554.13 I (o) //j (5) as a function of the electric field (assuming p' = —1.37 D ).^565.14 The skatch of the plate electrodes. ^  58AcknowledgementIt gives me great pleasure to express my heartfelt thanks to my supervisor, Dr. I. Ozier,for his support, guidance and encouragement during the course of the project, for hisextreme patience in reading this thesis and also for his help to my wife. Without hishelp, this thesis would never have been finished. Also, I am very grateful to Dr. F. W.Dalby for his valuable instructions and suggestions. I always felt comfortable to discussproblems with him.In addition, I wish to express my appreciation to Jim Booth, for his tremendouspatience in teaching me the essence of basic research, and for his invaluable assistancewith many aspects of work in this project. My sincere thanks are also due to AlakChanda and Dr. W. Ho, for their constant help and valuable suggestions. Thanks toChrist Boone for helping me to draw the pictures of the experimental designs.Finally, I would like to thank my wife for her constant support, and for her stayingwith me at night when I worked late.ixChapter 1Introduction1.1 The dipole moment of IC1 in different electronic statesIodine monochloride has been the subject of numerous spectroscopic studies over the last6 decades. The molecule shows several unusual properties such as predissociation, levelcrossings, avoided crossings, and the existence of diffuse and continuous spectra. It hastherefore, been of considerable interest to spectroscopists. The spectroscopic propertiesof IC1 have been studied by a number of techniques such as visible absorption spec-troscopy [1, 2, 3, 4], emission spectroscopy [5], laser-induced fluorescence spectroscopy[6, 7, 8, 9], vacuum ultraviolet spectroscopy [10], laser-induced photochemistry [11] andmicrowave and millimeter-wave spectroscopy [12], as well as microwave-optical double-resonance spectroscopy [13, 14]. Information about potential energy curves and levelcrossings in IC1 was obtained in a photofragmentation experiment [15]. Molecular beamexperiments [16, 17] were carried out to obtain information about rotational temper-atures, rotational-translational relaxation, and dissociation of IC1. Brand et al. usedtwo-photon polarization spectroscopy [18, 19] and three-photon resonance spectroscopy[20, 21] to gain information about perturbed electronic states.However, there have been only three publications about the dipole moment of IC1 indifferent electronic states.The Stark effect is the most common method of measuring the dipole moment of amolecule. From the measurements of the Stark shifts in microwave spectra, the dipole1Chapter 1. Introduction^ 2v' it' (D) v' tt' (D) v' it' (D) v' ft' (D)7 2.00(0.15) 11 1.85(0.10) 14 1.75(0.05) 21 1.15(0.15)9 1.95(0.05) 12 1.80(0.10) 17 1.50(0.15) 25 0.60(0.15)10 1.90(0.10) 13 1.60(0.15) 18 1.25(0.10) 27 0.60(0.15)Table 1.1: The dipole moment of the A 3H1 state as a function of vibrational level.moment in the ground electronic state can be determined. The optical Stark effect hasprovided an increasing body of information on excited state dipole moments and canovercome the limitation imposed by the Boltzmann distribution in most microwave andradio-frequency experiments. The sign of the excited state dipole moment relative tothat of the ground state is reflected in the appearance and intensity of forbidden lines,and in the intensity pattern in the band head region.In 1972, Herbst and Steinmetz[22] first measured the Stark effect of IC1 in microwavespectra, and the dipole moment in the ground X1E0+ state was determined to be:yll = 1.24 + 0.02 DIn 1974, Cummings and Klemperer[2] measured the optical Stark effect on spectra forthe A 3 Hi 4-- X 1E0+ band system. The dipole moment of the A 3I-11 state as a functionof vibrational level was found; their results are shown in Table 1.1. From the fit resultsin the band head region for different signs of the dipole moment, it appeared that thesign of the A 3111 state moments is opposite to that of the X 1E0+ state. However, theydid not observe forbidden lines experimentally.In 1993, Friedrich et al. measured high-resolution laser-induced fluorescence spectraof IC1 A 3111 4- X 1E0+ as a function of the electric field. It was found that the field-induced mixing of J states changes the transition probabilities markedly and enriches thespectra with many transitions that would be forbidden in the absence of the field. TheChapter 1. Introduction^ 3transition probabilities fluctuate as the angular lobes of the two pendular wavefunctionsinvolved come in and out of phase when the field strength is varied. They argued thatthe field-dependence of the fluorescence intensity requires the dipole moment to reversesign between the ground X1E0+ and excited A 3111 states.1.2 Electric field induced transitionsThere are several types of transitions in a diatomic molecule that are dipole forbiddenin free space but become allowed in the presence of an external electric field. In 1932,Condon [24] showed that vibration-rotation transitions in a homonuclear molecule wouldbecome allowed in the presence of an electric field because of an induced moment arisingfrom the polarizability. The first measurements of this effect were made in hydrogenby Crawford and Dagg[25]. In 1964, Dows and Buckingham[26] presented a generaltheoretical treatment of electric field induced spectra in diatomic molecules. In 1993,Dagg et al.[27] observed the electric field induced Q branch of the vibrational fundamentalin CO near 2143 cm-1. The dipole moment of CO in the first excited vibrational statehas been found from the intensity measurements.This presents a new method of determining the dipole moment of a molecule.1.3 Present workIn this thesis, we present laser-induced fluorescence spectrum in IC1 of the electronicsystem B 3110+ 4- X 1E0+ for the (2-0) vibrational band measured as a function of theelectric field strength up to 32.5 kV/cm. From the Stark shift measurements, the magni-tude of the dipole moment of the excited B 31-10-1- state was obtained. From the intensitymeasurements, both the sign and the magnitude of the dipole moment were determined.Finally, the dipole moment of the excited B 3110 state in vibrational level v' = 2 wasChapter 1. Introduction^ 4determined to be:^+1.122 ± 0.025 D^for I'Cl^ii =---- +1.116 ± 0.035 D^for 137C1The positive sign of the B 3H0+ state dipole moment here indicates that the sign isthe same as that of the X 1E0+ state. The ground state dipole moment is assumed tocorrespond to I+Cl- and thus the A 3111 moment to I-C1+[2j. Therefore, the B 3110+state dipole moment corresponds to I+ C1.Chapter 2Theory of Stark Effect and Electric Field Induced TransitionsTwo methods were employed to measure the dipole moment in the excited B 'Ho+ stateof ICJ. From the frequency shifts due to the Stark effect, the absolute value of the dipolemoment was determined. From the intensities of the induced transitions, both the signand the magnitude of the dipole moment were obtained.2.1 Stark Effect2.1.1 The zero field Hamiltonian and its eigenfunctionsThe Hamiltonian for the zero field spectrum is:Ho = He + Hy + II,^ (2.1)where He is the electronic term, Hi, the vibrational term and .11r the rotational term.In Eq. 2.1, the hyperfine term Hhyp has been neglected. This term will be discussed inSection 5.3. The eigenfunctions of Ho can be written as IT, 2),J, M >o. Here 7 is theelectronic quantum number and v the vibrational quantum number. J is the quantumnumber for the total angular momentum f exclusive of nuclear spin I. m is the magneticquantum number. The zero subscript indicates the electric field is zero. The quantumnumber will have double primes when we refer to the X' E+ state and will have a singleprime when we refer to the B 3110-F state.In zero field, the eigenvalues of the Hamiltonian for the B 3110-F state of IC1 are given5Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^6v' Ty, By, 106D,, 1012H„,135C1 0 17476.901(10) 0.08580560(33) 0.0591(20) -6.8(25)1 17673.1691(17) 0.08452873(53) 0.0782(24) 4.3(33)2 17855.83584(69) 0.08287411(25) 0.09760(53) -1.15(18)3 18019.2653(20) 0.080371(11) 0.210(12) 3.7(33)137C1 1 0.08099221(19) 0.06825(32)2 17846.4751(14) 0.07946420(50) 0.0878(10) -1.16(43)3 18007.9471(10) 0.0771823(43) 0.1476(43) -5.4(11)Table 2.2: Molecular parameters for the B 3110+ state of IC1 in cm-1.by M. Siese et al. [4]:E (v' , J') = Ty, +^+ 1) - Dv,[J'(J' 1)]2^[J'(J' 1)]3^(2.2)where 71, is the term value, while By,, Dv, and Hy, are the rotational parameters. Ta-ble 2.2 [4] lists all the molecular parameters.In zero field, the eigenvalues of the Hamiltonian for the X1E0+ state of IC1 are givenby H. G. Hedderich et al. [28] by using the well-known Dunham equation [29]:E(v" , J") = E (v" + D'[f(r+1)ti^(2.3)where^is the Dunham coefficient. The Dunham coefficients for the X 1E0+ state ofIC1 are listed in Table 2.3[28]. Different energy expansion forms are used in Eq. 2.2 andEq. 2.3 since we want to use the original results for both states.Since 1 -,---- 0 in both the B 3110+ and X 1E0+ states, B 3110+-X 1E0+ transitions aresimilar to E-E transitions. In zero field, the selection rule on J is AJ = ±1. Theselection rule on M is AM = 0 for parallel polarization and AM = +1 for perpendicularpolarization. Therefore, at zero field, only P and R-Branch transitions are allowed.Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^7Coefficient I35C1 P7C1Y10 384.29416(15) 376.06683(13)Y20 -1.503091(91) -1.439020(45)103Y30 -2.426(15) -2.274YO1 0.114157656(15) 0.109322776(40)101 11 -0.532643(14) -0.499081(39)1061721 -1.2991(32) -1.256(14)106Y02 -0.0402605(61) -0.036943(30)10%2 -0.20933(95) -0.1702(28)11312Y03 -0.0180(12) -0.0354(35)Table 2.3: Dunham Coefficients for the X1E0+ state of ICI in cm'.2.1.2 The Hamiltonian in the presence of an electric field and its eigenfunc-tionsIn the presence of an electric field, the Hamiltonian becomes:HT = HO + HS^ (2.4)where Hs is the Stark Hamiltonian. When an electric field P is applied to a molecule,a coupling occurs between the electric dipole of the molecule rt and the electric fieldstrength P. The corresponding energy operator is the Stark Hamiltonian, which is givenby:(2.5)(2.6)The field is taken to be along the space fixed Z direction. Then Eq. 2.5 becomes:Hs = muzEThe selection rules for Hs are AJ = ±1, AM = 0.The Hamiltonian matrix is set up in the zero-field basis set IT, v , J, M >0 . From Eq.Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^8(2,119) on page 32 in reference [31], we have:[(J +1 + M)(J +1 — M)J1-0< T,v,J,MillsiT,v,J +1,M >0= —,ttE^ (2.7)[(2J 1)(2J + 3)]where IL =< T,^T,V > is the electric dipole moment in the electronic state labelledby T. Here we omit index 0 in wavefunction IT, V > since it is the same as is in zero fieldwhen there is an electric field applied to the molecule. We define:IL" = < 1E0+, v"^I 1E0+, v" >ft' = < 3110+ , litz1 3110+ ,^>Here X,Y and Z represent the directions in space-fixed frame (SFF), while x,y and zrepresent the directions in molecule-fixed frame (MFF).Now the total Hamiltonian matrix is no longer diagonal in J. The M degeneracy ispartially lifted. The states labelled by M with different absolute values are split and thepositive and negative M states remain degenerate. We will use positive M in all ourdiscussions since the results are the same for states labelled by —M values.Here we only consider the case when the electric field is applied along the space-fixedZ direction. By diagonalizing the TIT for each M in an electric field for both X1E0+ andB 3110+ states, we found the eigenvectors having the form:IT", v", J", 1%/i ^E^v", j", M"^(2.8)^= E^vv, >0^(2.9)iiwhere a,,„,,,,p0,(E) and ar,,v,„rx(E) are the (real) coefficients for the X1E0+ and B31-10+states, respectively. These are functions of E. The subscripts e indicates the electric fieldis applied. Although J is no longer a good quantum number, we still use it to label theenergy states; J and M represent values to which the state goes in the limit that E 0.Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^9In the presence of an electric field, given it" and it', the frequencies could be calculatedfor the transitions of interest by diagonalizing HT in both the B 3110+ and X1E0+ statesfor each field strength and M required.2.2 Electric field induced transitions of IC12.2.1 Absorption intensities of induced lines of IC1In transitions in an electric field which is not so strong that the individual M" — M'rotational transitions are resolved, the integrated absorption intensity of a line (allowedor induced) is proportional to the sum over all allowed M" and M' states of the squaresof the transition dipole matrix elements[26]:T11,,11,j11873 7_,v ^j,, EhNIIVF,JIF M"c T MIIT", V" ,^itr^mi 2^(2.10)where indicates the polarization of the absorption line, and can equal X or Y (polarizedperpendicular to the applied electric field) and Z (polarized parallel). Nr",x," ,J" Nu isthe population of the state r", v", J", M" in the presence of an electric field E. Thesuperscript a indicates 1-`1 is the absorption intensity of a transition. The quantum numberK in reference [26] is here to be replaced by S2. This is the sum of the eigenvalues A andE for the components along the internuclear axis of f and S, respectively. Therefore, forIC1 in both the X 1E0+ and B 3110+ states, K = 0; K" and K' are omitted in the aboveformula[26]. In the presence of an electric field, we have:1^hc Tr,/ ,„,j,,,m,/(E)NT/1,04'W" CC kT^Q P(2.11)where^is the energy in wave-number units obtained by diagonalizing HTfor the X 1E0+ state. This energy is a function of electric field. Qp is the partitionChapter 2. Theory of Stark Effect and Electric Field Induced Transitions^10function given by the following expression:Qp = Etr n^mu(E)hc 7 IcT (2. 12)11,0 jl dt/r/Substituting Eq. 2.8 and Eq. 2.9 into Eq. 2.10 we get:(/;);14:),1,1,1,1Y, = 8r3hc^'ji^ T "'V ,J",MM[• E arn,„,,,,p,o,,(E)a..,,,v,,j, ,i, (E) o< T", v", j", M Ipzi T', V', j', M >i,^(2.13).1" ,i'The above equation applies when the transition occurs with the electric field parallel tothe polarization. In this case, the selection rule on M is AM = 0. As a result, only asingle sum on the magnetic quantum numbers is needed in the above formula.To evaluate the matrix elements, the SFF component of ,a is expressed in MFFcomponents [26] :ttz = a zz z + a zo y az /^ (2.14)where azz, azy and az are direction cosines between external and internal coordinates.For a diatomic molecule such as IC1, ,ax = iay = 0. Now we define Az as:AZ =T" 7V" 7 j" M litZI T/ 7 V/T" 7 V" zl 71 I V/ > z j" M la Zzl j/ 7 M >o (2.15)where < 7", v" Luz I r', VI > is the vibronic transition moment. Matrix elements of thedirection cosines have been tabulated (page 31 in reference [31]). By substituting Eq. 2.15into Eq. 2.13, we have:ft^111^1=- 87-3- /lc^< , V 11 ^>2 E22[• E ct,,,,„,,,j,e(E)a-,-,,,,,,J,J, (E) c< j", M jazz' j', M >0I^(2.16)I/Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^11Once it",^and E are known, the right side of the above equation can be calculatedexcept for the factor < 7" , v"1,a,17', v' >2, which is a constant for all the B 3110+-X 1E0+transitions in a same vibrational band.The results of Eq. 2.16 in perturbation limit have been given by Dows and Buckingham[26]. For Q(J) in parallel polarization, they are:(G);;;,v';,° ^= 8r3^Ti ,0 L-12hc 71, V" litz I 71, VI> 2[  it"^r 1ihcB" hcB' 36(2.17)TaZ r",v" „POO873^711^1 1,v ur^n EL <hc 2J" + 1i,„ + it, 12[hcB" hcBd 20J (J + 1)(2J - 1)(2J + 3)7", v" Luz I 71, v' >2+ 1(2.18)where is the population of the state Til v", J". From Eq. 2.17 and Eq. 2.18 wesee that in the electronic system B 3110+-X 1E0+ of IC1, Q-branch transitions are inducedby electric field. 0 and S-branch transitions are induced as well. Eq. 2.16 works for allthe electric field induced transitions.Eq. 2.10 also works for allowed transitions when no electric field is applied if wereplace 7, v", J", M"I by z Ti', v", J", M" 1. By substituting Eq. 2.15 into Eq. 2.10,we can calculate the intensities of all the allowed transitions. The result for P(J) inparallel polarization is:(i;yrr"vviJ,"i873< 711, VII^>2hc^' J"(J" + 1)(4J" - 1)6(2J" - 1)(2J" + 1)(2.19)Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^122.2.2 Fluorescence intensities of induced lines of ICIAs we mentioned earlier, the electric field was applied parallel to the space fixed Zdirection. If a laser beam polarized in Z direction is sent along X direction and lightemitted in Y direction is detected, we can observe fluorescence polarized in both the Zand X directions. These fluorescence intensities are then related to absorption intensitiesby:= Az(f)r,v1;71F(jr17,)\,(y)(r)r,:;1,ivi;ij,,r,Ax (f)rr( fr)r(J ^(/;),Tr",::),'„,„+ rnr(J')(2.20)(2.21)where Fr(J') and F.„7.(J') are the radiative and nonradiative decay rates, respectively;Az(J') and Ax(J') are factors relating the fluorescence and absorption intensities. BothF and A are functions of the upper state rotational quantum number J'. F(f) is relatedto the lifetime T(J') by:T(J') =F(J')F„,r(J') arises primarily from predissociation. It will be a function of the electric field.The total fluorescence intensity observed in Y direction is:=^+1-rr(f) [Ax(f) Az(f)] Fr (J') Frir (P)We define a factor C(J') as:c(f) [x(f)+ z(f)]^Fr(f) Fr(J') F„(J')Then Eq. 2.22 becomes:(2. 22)(2.23)1(If yrimixz^=c(f)(Iar,,v,,J,z (2.24)Chapter 2. Theory of Stark Effect and Electric Field Induced Transitions^13Eq. 2.24 works both when the electric field is applied and when it is zero. When theelectric field is applied, we should use the expression for (4);;;;?ji, given by Eq. 2.16.If the electric field is zero, we should use the expression of (Plir.r.:;',:;;, given by Eq. 2.10(with 7", v", J", M" I replaced by a< r", v", J", M" I ). Both Eq. 2.16 and Eq. 2.24apply in the limit that saturation effects vanish.Chapter 3Apparatus and Spectrum3.1 Preparation of experiments3.1.1 Preparation of the Stark cellAn existing Stark cell used for Br2 has been modified to be suitable for our purposes.Fig. 3.1 shows the sketch of the Stark cell. The cell has two stainless-steel plates whichacted as electrodes. These, unfortunately, are not parallel to each other. The separationof the plates is about 3 8 mm in the middle. The cold finger of the cell allows us to puta cold trap to control the IC1 vapour pressure.3.1.2 Measurement of the electric fieldAs we discussed in Chapter 2, when an electric field is applied to ICI, both the shiftedfrequencies and the intensities of the transitions are functions of the electric field strengthE. Consequently, an accurate measurment of E is important for getting the correct valueof p'.If the potential difference between the two electrodes is V, and the separation of theelectrodes is D at the position where the fluorescence photons were detected, then:E = —14D (3.25)The angle between the electrodes was about 4°. To minimize the effect of inhomogeneitiesof E, the region from which light was collected was kept small. This was done by leavinga small window for the photomultiplier on the side of the Stark cell.14Chapter 3. Apparatus and Spectrum^ 15Figure 3.1: The sketch of the Stark cell.The voltage V, was provided by a Brandenburg regulated high voltage power supplyModel 907, serial No. 36H, which gives up to 60 kV DC high voltage. The output voltagewas tested to be stable better than 0.5% over a period of 10 minutes.To set and monitor the electric field, we built a simple circuit as shown in Fig. 3.2. R4is the internal resistance of the digital voltmeter. The resistances value of the resistorsin Fig. 3.2 are:Ri = 10 MitR2 = 272 MitR3 = 272 kitR4 = 10 MitThe precision values of the resistances are not required.StarkCell:Power supply :Digital Voltmeter0 eR1=---R2R3Chapter 3. Apparatus and Spectrum^ 16Figure 3.2: The circuit for measuring the electric field.Assuming the reading of the multimeter is V, then we have:R2 + R3R4Ve = R3 RR:+R4 VR3 +R4We define K, as:K, = D R3 R4 R3+R4Substituting Eq. 3.26 into Eq. 3.25, we obtain:R2 + RR33+RR44(3.26)(3.27)E = K,V (3.28)Once we fix the laser position, D is fixed and hence K, is a constant. The real conversionfactor K, was measured experimentally. It was found that Kz changed slightly (less than2%) every time we adjusted the laser beam.Chapter 3. Apparatus and Spectrum^ 17This circuit has some advantages. First, by treating K, and p° as variable parame-ters in data fitting, direct measuring of D is avoided. Once Kz is calculated, every Ecorresponding to V can be calculated directly from Eq. 3.28. Second, if electrical dis-charge occurs at high voltage, the potential difference between the electrodes drops tozero quickly and so does the reading of the multimeter. Then we can know there is anelectrical discharge from the reading of the multimeter as soon as it occurs. Third, theresistance R1 in Fig. 3.2 helps to reduce the electrical current when discharge occurs toprevent the damaging in the electrodes and the circuit.The voltage V was measured by a CIRCUIT-TEST model DMR 2208 digital multi-meter. The multimeter was calibrated and found to have an accuracy of 0.5%.3.1.3 Design of the filling systemFig. 3.3 shows the sketch of the filling and part of the pumping systems. The fillingsystem includes an ion gauge with controller (Varian 843), a C12 cell, an ICI cell andan opening to connect to the Stark cell. The pumping system includes an oil diffusionpump, a mechanical pump as fore pump, air cooling fan and a cold trap with 0-ring seal.There are a few important points to be kept in mind when using the pumping andfilling systems. First, during the experiment, the cold trap has to be kept at liquidnitrogen temperature all the time to prevent oil vapour from feeding back to sample cellsand also prevent the ICI vapour from getting into the the diffusion pump. Second, allthe cells has to be pumped out for about 4 hours before using. Third, since ICI mightattack vacuum grease, no grease should be used.)(^sc2C.^■sc3 r" sc50-Cold imp Cold fingerIon gaugesclTo pumpr"c^)sc7ventc6/StalkCell\1c:zil sc4L___a, CellCold fingerICI CellChapter 3. Apparatus and Spectrum^ 18Figure 3.3: The design of the filling system.Chapter 3. Apparatus and Spectrum^ 193.1.4 Getting clean ICI spectrumGetting clean ICI sampleAfter the IC1 cell was pumped out at room temperature for about 4 hours, an IC1 crystalwas placed inside it. When the IC1 crystal was exposed to air, it had absorbed watervapour and formed some HC1 which would attack the stainless steel electrodes. Therefore,it is necessary to remove various impurities, particularly water vapour which got into theIC1 cell while transfering the IC1 crystal. At room temperature, the valve sc5 (refer toFig. 3.3) was opened for about one minute, the water vapour and some IC1 vapour werepumped out. Then the valve sc5 was closed. Since the cold trap was at liquid nitrogentemperature, most of the IC1 vapour was trapped there so that it did not harm the pump.The same procedure was repeated 2 or 3 times, to prepare IC1 for use in the experiment.Getting clean ICI spectra in the presence of electric fieldsThe fluorescence spectrum of IC1 was first looked at in the IC1 cell (refer to Fig. 3.3) atzero electric field, of course. Unfortunately, 12 occurs as a significant impuruty in the IC1at room temperature. 12 has a very strong fluorescence spectrum which occurs in thesame region as the IC1 lines of interest and can mask many of these lines. Steps had to betaken to minimize the 12 concentration in the vapour phase. According to Table 3.4[30j,Ph /Pin -> 0 as T goes lower. Therefore, we can remove 12 signals by reducing the totalvapour pressure of IC1.A dewar containing methanol and water solution was used to control the temperatureof the cold finger of the IC1 cell and hence to control the vapour pressure of the Id. Atits freezing point, the methanol solution temperature is relatively stable. By adjustingthe percentage of the solution, one can change the freezing point. It was found that atabout -60°C the 12 signals disappeared although IC1 signals become weak as well. Fig. 3.4Chapter 3. Apparatus and Spectrum^ 20T,°CPict(Torr)P12(3)(Torr)P,(Torr)IC1+I2(s)10-31312/ Prci-15 1.027 0.006 1.033 5.85-10 1.647 0.011 1.658 6.68-5 2.599 0.018 2.617 6.920 3.833 0.031 3.914 8.085 6.129 0.050 6.179 8.16Table 3.4: Vapour Pressure of Solid Iodine Monochloride.and Fig. 3.5 show the ICI spectrum at two different temperatures.After pumping the Stark cell to 0.4 mT, valve sc2 was closed and valve sc5 was slowlyopened for about 10 seconds while the cold finger of the IC1 cell was kept at -60°C. Thenvalve sc6 was closed (refer to Fig. 3.3). Now the IC1 was transfered into the Stark cell.Even if we transfered the IC1 sample at -60°C, electrical discharge occurred at electricfields as low as 500 V/cm when the Stark cell was kept at room temperature. Thereforewe were forced to use the methanol solution to control the vapour pressure of the IC1 inthe Stark cell so that we could apply a higher voltage to the electrodes.An attempt was made to add some C12 into the Stark cell to help to reduce theI2 signals. This worked to some extent. We observed a pure IC1 spectrum at roomtemperature. Unfortunately, C12 has a very high vapour pressure (6.57 atm. at 20°C).To control the pressure of C12 added into the Stark cell, the C12 cell was kept at dry icetemperature while transfering C12 to the Stark cell. The vapour pressure of C12 at thistemperature (about -78°C) is about 58 Torr which is still too high compare to the vapourpressure of IC1 (11.8 x 10-3 Torr at -60°C). The electrical discharge occurred as soon asthe voltage is on even when the cold finger of the Stark cell was kept at -60°C.Therefore, the only way to remove 12 signals when electric field is on seems to bekeeping ICI at low vapour pressure without adding C12.Chapter 3. Experiment Apparatus and Spectrum^ 21Figure 3.4: The spectrum of I'Cl at room temperature. (about 20°C).Chapter 3. Experiment Apparatus and Spectrum^ 22Figure 3.5: The spectrum of 135 C1 at -55°C.Chapter 3. Apparatus and Spectrum^ 233.1.5 Spectroscopic arrangementA block diagram of the experimental arrangement used for the intensity measurementsis shown in Fig. 3.6.A Coherent INNOVA 400 argon ion laser was tuned to the 514 nm line, and theoutput power was used to pump a Coherent CR-699-21 scanning ring dye laser. R6G dyewas used which allowed the laser to cover from 16260 cm-1 to 17699 cm' . A chopperworking at 1.8 kHz chopped the laser beam and sent a reference signal to the lock-inamplifier. With polarizers P1 and P2 we could decrease the laser intensity to any levelwe needed while keeping the laser light polarized parallel to the applied electric field.An iris was used to keep the diameter of the laser at about 1 mm and ensured thatlaser beam did not hit the electrodes. Photomultiplier PM1 (EMI 9550B) with CorningCS2-60 red pass filter and 100 MI load was used to detect the fluorescence from electricfield region. The Stark cell was wrapped with black tape. Only two small windows atboth ends of the cell were left for the laser beam and one small window on the side of thecell was left for PM1. To ensure that PM1 only saw the signals from between the plates,the small window for PM1 was made facing the middle of the electrodes with a lengthof about 1.5 mm in the horizontal direction and a width of about 0.5 mm in the verticaldirection. A lens with 3.5 cm focal length was placed about 4 cm away from the centerof the plates. A magnified image was obtained at the back focal area where a 4mm x4cmaperture was employed to let only fluorescence from the center pass. PhotomultiplierPM2 (EMI 9550B) with Corning CS2-62 red pass filter and 100 kf2 load was used todetect the fluorescence of 12. The output of PM1 was sent to PAR model 128A lock-inamplifier and was recorded by a double line recorder (PM8252A). The output of PM2was directly recorded by the same recorder.The arrangement used for the Stark shift measurements was the same as shown inChapter 3. Apparatus and Spectrum^ 24Figure 3.6: Experimental arrangement.Chapter 3. Apparatus and Spectrum^ 25Fig. 3.6 except that we did not use polarizer P2. Polarizer P1 ensured that laser polar-ization was parallel to the electric field.3.2 Experimental procedure3.2.1 Choosing apropriate temperature of the cold fingerAfter the ICI sample was transfered into the Stark cell, the cold finger of the Stark cellwas kept at a certain temperature between -40°C and -60°C.We define Td(E) as the highest temperature possible without discharge occurring.Td(E) is a function of E; the higher E, the lower Td(E) is. Tic,/ is defined as the highesttemperature at which the 12 signal can't be detected. Tx/ was found to be about -60°C.It was found from experiment that at lower electric fields, Td(E) > Tics; at electric fieldshigher than 28 kV/cm, Td(E) < T11.Since IC1 has a higher vapour pressure at higher temperature, the temperature T ofthe cold finger was always kept as high as possible to get a good signal to noise ratio. Ofcourse, T should be always less than or equal to Td(E). In the Stark shift measurement,when Td(E) > Tic/ and the Stark components we want to study do not overlap with 12signals, T was chosen to be Td(E). When the Stark components overlap with 12 lines, Tmust satisfy both T < Tin and T < Td(E).In the intensity measurement, T was kept at a constant Td(Eni„) where Erna, was themaximum electric field strength we used. In all cases, Td(En,„,) < Tim. Consequently,there should be no 12 signals in the spectrum. Unfortunately, it was difficult to keepT as constant as needed. Some dry ice had to be added periodically into the methanolsolution in order to stablize the temperature.Chapter 3. Apparatus and Spectrum^ 263.2.2 Taking the spectraWhen the laser beam was sent through the Stark cell, the beam was visually set to passbetween the plates without hitting the electrodes. The laser was tuned to an ICI fluo-rescence line and the position of photomultiplier PM1 was adjusted slightly to maximizethe signal. The signal of PM1 and PM2 were first recorded as a function of frequencywithout an electric field. Then the electric field was applied, the signal of PM1 wasrecorded again. The reading of multimeter was noted each time the voltage was changed.In the Stark shift experiments, an output power P of 60 mW of the dye laser was usedin order to get good signal to noise ratio. In the intensity experiments, P was chosen tobe 40 mW to avoid satuation effects. (See Section 4.3.2.)Chapter 4Spectra and Data Analysis4.1 Selection of the vibrational band4.1.1 Intensity measurementAs we showed in Fig. 3.4, at room temperature, the 12 lines are strong enough to maskIC1 transitions if they overlap. In intensity measurements, according to Eq. 2.17 andEq. 2.18, only the low J induced transitions are strong enough to be observed. If theseQ(J) transitions overlap with 12 transitions, we must choose a temperature low enoughthat the 12 signals do not appear in the spectrum. So we want to select vibrational bandswhere the transitions we want to study do not overlap with any 12 transitions. Then wecan use a high temperature to get a good signal to noise ratio.Some IC1 transitions also caused difficulties. At room temperature, the strongest IC1transitions lie at J P.-, 30. They are about three times more intense than the strongestinduced transition Q(0) at the highest electric field 32.5 kV/cm we used. We can'tmake the necessary measurements if the Q(J) transitions overlap with high J transitions,which, unlike the 12 signals, can't be eliminated by lowering the temperature. Therefore,the vibrational bands we selected must have a clear frequency region where the inducedQ(J) transitions (for J = 0, 1,2 ) do not overlap with any strong IC1 transitions.The vibrational bands should have a relative strong transitions. The transition inten-sities were estimated from the population in the lower X1E0+ state and the Frank-Condonfactors given by M. A. A. Clyne and I. S. McDermid[32].27Chapter 4. Spectra and Data Analysis^ 28It was found that only the (2-0) band in the B 31-10+-x 1E0+ electronic system ofsatisfies the above conditions. For I37C1 , since the ratio of the population of PC1 tois about 3:1, the induced Q(0) is too weak to be measured at the temperature wemust use.4.1.2 Stark shift measurementSince the frequencies of the the Stark components of IC1 are functions of electric field, atsome field they overlap with I2 signals. To take measurement under these circumstances,we must lower the temperature of the cold finger to remove the 12 signals.Only the low J transitions (J = 0, 1, 2, 3) showed significant Stark shifts at electricfields lower than 33 kV/cm. As was the case with the intensity measurement, we need tochoose vibrational bands where the low J Stark components do not overlap with strongICI transitions at most electric fields we used and IC1 has a relative strong transitions.For both P5C1 and I37C1 , only the (2-0) band in the B 3110-1—X 1E0+ system satisfies ourconditions.4.2 Stark splittings in the optical spectrum4.2.1 Sample spectrumFig. 4.7 is the I35Cl spectrum showing Stark splittings in parallel polarization. The firstnumber in the bracket after P, Q or R is the rotational quantum number J and the secondone is the value of M. Since the selection rule is AM 0, only a single value of M isrequired. Vibrational transitions were written in the form (v' — v"). When an electricfield is applied, the P(1) yields only one Stark component, namely P(1,0). This moves tolower frequency as E is increased. P(2) splits into two lines. At low fields, one goes upand one goes down as E is increased. P(3) gives three lines when electric field is applied.Chapter 4. Spectra and Data Analysis^ 29One goes up and two go down.4.2.2 Data analysis of Stark splittingsAccuracy of the frequency measurementFrom the frequencies of the 12 transitions in the ICI spectrum measured at room temper-ature, the frequencies of ICI lines have been calculated.The resolution of our experiment, which is the full width at half maximum (FWHM)of the ICI signals and was measured from experiment, is 0.026 cm-1 at zero field.The scanning speed m is defined as:V1 - V2m =^D12(4.29)where vi and v2 are the frequencies of two transitions in cm-1; D12 is the distance betweenthe line centers of the two transitions in the chart paper (in cm). Of course, we have:D12 -7--- D1 - D2where D1 and D2 are the positions of the transition line centers on the chart paper.The frequencies of 12 transitions A, B and C in Fig. 3.4 were found from 12 atlas[34]to be :VA = 17663.6946 cm-1vB = 17663.9827 cm-1vc = 17664.1886 cm-1The distances between the line centers measured from the chart paper are:DCA =-  7.51 + 0.03 cmDBA ---- 4.36 + 0.02 cmCLIChapter 4. Spectrum and Data Analysis^ 3017663.065 cm-'^ 17663.591 cm'E = 017663.065 cm'^ 17663.591 cm'E =- 29.7 kV/cmFigure 4.7: The spectrum showing the effect of the electric field.Chapter 4. Spectra and Data Analysis^ 31Then the scanning speed is:VU — VA771 DCA= 0.06578 cm-1/cm (4.30)The absolute error of m is written as:Sm = 771 aDCADCA= 0.00026 cm-1/cm^(4.31)Here we neglect the very small errors in frequencies given by reference [34]. Now wecalculate the frequency of transition B from VA, m and DBA.143 = VA + MDBA= 17663.6946 + 0.06578 x 4.36= 17663.9814 cm-1The error in 43 is:= { (svA)2 + [8(mDBA)] 2 1= 8 ( 771DBA)2= (711DBA) X [(-6:7711)= 0.0017 cm-11( aDBA ) 2] 2+DBAThen the calculated frequency of transition B is:V ^17663.9814 ± 0.0017 cm-1This value agrees with the 17663.9827 cm' given by reference [34] within our experi-mental error.Chapter 4. Spectra and Data Analysis^ 32Therefore, no correction is needed for any nonlinearity in the scanning speed m.Table 4.5 lists measured frequencies of some (2-0) transitions in the B 3110+-X 1E0+system in both j35 Cl and 137C1 with the calculated values. The frequencies of the P andR-Branch lines were measured in zero field. Since Q(0), Q(1) and Q(2) are forbiddenat zero field, their frequencies were measured at E = 29879.3 V/cm. The calculatedfrequencies of Q(J) lines at this field were also listed in the table (using the valuefound in the Stark shift fitting); they are the averages of their Stark components. Fromthe table we can see that the measured frequencies of P or R lines usually agree within0.002 cm-1 with the calculated ones. However, the differences between the observedfrequencies of Q lines with the calculated ones are larger and the reason is not fullyunderstood. P(1) always appears as two lines due to the hyperfine effect. The frequencyof P(1) given in the table is the average of the frequencies of the two hyperfine linesand also fits well. It was found from experiments that the frequencies of induced Q(J)transitions are quite insensitive to the electric field.As is explained in next section, the frequency of each Stark component was measuredrelative to an ICI reference line. The maximum error in frequency difference measurementcan be estimated as below. Let us define vs as the Stark component frequency and urthe reference frequency. Then the frequency difference between these two lines is:v„ =^'Ds — Drj (4.32)The error for v„ is:2^„^2 2St/sr = P„ [(±n-) (Uni-/")s r(4.33)where 45D8 is given by:1apsr^[(57)5)2 + (8Dr)21 2Of all the Stark components we measured in 135C1 , P(1,0) had maximum linewidthat 31 kV/cm, 0.6 cm. In addition, at this field P(1,0) had the smallest signal to noiseChapter 4. Spectra and Data Analysis^ 33Transitions Observed(cm') Calculated(cm-1) Obs.-Cal.(cm-1)135 C1 P(1) 17663.8388 17663.8372 0.0016P(2) 17663.5456 17663.5475 -0.0019P(3) 17663.1935 17663.1958 -0.0023R(0) 17664.2269 17664.2308 -0.0039R(4) 17664.2773 17664.2750 0.0023R(5) 17664.1295 17664.1312 -0.0017R(6) 17663.9247 17663.9254 -0.0007R(7) 17663.6563 17663.6577 -0.0014R(8) 17663.3292 17663.3280 0.0012Q(0) 17664.0642 17664.0696 -0.0054Q(1) 17663.9917 17663.9831 0.0086Q(2) 17663.8712 17663.8765 -0.0053137C1 P(1) 17658.5842 17658.5836 0.0006P(2) 17658.3049 17658.3063 -0.0014P(3) 17657.9704 17657.9700 0.0004R(7) 17658.4163 17658.4187 -0.0024Table 4.5: Measured frequencies with the calculated values for (2-0) bands in theB 3110+ -X 1E0+ system in 135C1 and 137C1 . The AJ = +1 lines were measured and calcu-lated at zero field; the AJ ---- 0 lines were measured and calculated at E = 29879.3 V/cm.D sr- mAD:7;:as •8max^DT,axsr- VST(4.35)Chapter 4. Spectra and Data Analysis^ 34ratio of all the components studied, 9:1. Therefore, the maximum value for 8D3 is:0.6SDI:" —9 = 0.067 cmThe reference lines always had a very good signals to noise ratio (about 100:1). Themaximum error for SDr estimated from experiment was 0.02 cm. Therefore, we have8Drsnr" = N/0.0672 + 0.022= 0.070 cm^ (4.34)At 31 kV/cm, for P(1,0), D, = 1.95 cm relative to R(8). Then we have) max 3.6%By using the values given by Eq. 4.30 and Eq. 4.31, the calculated value of 6inini is just0.4%. Therefore, omitting the term Sm/m in Eq. 4.33, we have:The m value measured in Stark splitting experiment was about 0.06182 cm-1/cm. Byusing the value given by Eq. 4.34, the maximum experimental error in Sy, isSzi:ax = 0.0043 cm-1 for 135C1 (4.36)For I37C1 , the maximum linewidth of the Stark components is the linewidth of P(2,1),which is 0.4 cm. The signal to noise ratio of this trasition is 5:1. Dr is 0.02 cm. m is0.06841 cm/cm. By using the same method as we used in 135C1 , the maximum erroris:= 0.0056 cm-1 for FC1 (4.37)The error in general was smaller than those given in Eq. 4.36 and Eq. 4.37. In thedata analysis, the estimated errors were taken to be 0.003 cm-1 for 135C1 and 0.004 cm'for 137C1 . The data were equally weighted in the fits.Chapter 4. Spectra and Data Analysis^ 35Analysis and resultsA non-linear least-square program was used to fit the experimental data. The dipolemoment t"(v" = 0) = 1.24 + 0.02 D of the ground electronic X 1E0+ state of both 135C1and I37C1 was determined by E. Herbst and W. Steinmetz[22]. The value of was heldfixed initially at 1.24 D in the fitting. The room temperature T is 20°C. The dipolemoment ,u'(v' = 2) of the B3110+ state and K, (refer to Eq. 3.28) were treated as variableparameters. The electric field strength was calculated by Eq. 3.28. The fitting model wasprogrammed to diagonalize HT in both the B 3110+ and X 1E0+ states for each electricfield and each M of interest.To avoid the errors in band origin terms, the experimental data were taken by mea-suring the frequency difference between the Stark component and an adjacent high Jline, whose frequency and lineshape should be insensitive to the electric field used here.For I35C1 (2-0) transitions, R(8) and R(7) were chosen as the reference lines and forI37C1 (2-0) transitions R(7) was the reference line. The electric field dependence of thereference frequencies will be discussed in section 4.2.2.To assign the value of M for each of the Stark components, we first tried to fit thethree P(3) components. These correspond to M = 0,1, 2. We tried to calculate thefrequencies of these three Stark components by assigning 1/2 some values around thevalue of ft". It was found that, at certain electric fields, the order of these frequenciescould change when ,u' is assigned different values (at least three different orders arepossible). Therefore, it was necessary to check all the six possible orders. We found thecorrect order is: vp(3,2) < vp(3,1) < vp(3,0), where vp(J,m) is the frequency of transitionP(J,M).The fitted results of I35C1 Stark splittings were shown in Table 4.7. Table 4.8 showthe fitted results of 137C1 Stark splittings. 'Voltage' is the reading V of the multimeter.Chapter 4. Spectra and Data Analysis^ 36The electric field was calculated from Eq. 3.28.Fig. 4.8 and Fig. 4.9 show the fitted results as well as the experimental data. Fromthe figures we can see that the experimental data agreed very well with the fitted resultswithin the experimental error (i. e. 0.003 cm-1 for 135C1 and 0.004 cm-1 for P7C1 ).To this point, ii" has been held fixed at 1.24 D. To take the experimental error in it"into account, 1,u'l was calculated first with it" = 1.22 D and then with tt' = 1.26 D. Thefull set of results is listed in Table 4.6 for both 135C1 and I37C1 . The errors in listed inthe table are the statistical errors only, and neglect the uncertainty in ft". The absoluteerror in p' must be increased to cover the range indicated in Table 4.6. However, as canbe seen from Table 4.6 the ratio / VI is independent of it" (at least over the smallrange of interest); thus for the ratio, only the statistical contribution to the error enters.Finally, the fitted results are:lit'l = 1.122 + 0.025 Dlit'l  = 0.9052 + 0.0053 for^ (4.38)and1,u'l = 1.116 + 0.035 Dlil = 0.900 + 0.014 for I37C1^ (4.39)The absolute values of ft' for I35Cl and I37C1 are equal within the experimental errors.Checking the field dependence of the frequencies of the reference linesA check was made to see whether the reference lines moved significantly with the electricfield.By using the fitted^and K, values with it" = 1.24 D, the frequencies of each Mcomponent of R(7) and R(8) was calculated for each V value used in the experiment.0.20. 10P(3,0)-0 .5-0.60^le+08 2e+08 3e+08 4e+08 5e+08 6e+08 7e+08 8e+08 9e+08-0.4SQUARE OF THE ELECTRIC HELD (vA2 cm^-2)Chapter 4. Spectra and Data Analysis^ 37Figure 4.8: The frequencies of the Stark components of B 31-10_1--x 1E0+ (2-0) transitionsin 135C1 as a function of E2.0.2-0.4-0.5-0.60.1P(3,0)Chapter 4. Spectra and Data Analysis^ 380^le+08 2e+08 3e+08 4e+08 5e+08 6e+08 7e+08 8e+08 9e+08SQUARE OF THE ELECTRIC HELD (v^2 cm^-2)Figure 4.9: The frequencies of the Stark components of B 3110+ -X 1E0+ (2-0) transitionsin 137C1 as a function of E2.liel (D)^lial (D)^K, (1/cm)^itt'l /1/1"11.1044(65) 2568(14) 0.9052(53)1.1225(66) 2527(14) 0.9052(53)1.1406(67) 2486(14) 0.9052(53)1.098(17) 2595(43) 0.900(14)1.116(17) 2553(43) 0.900(14)1.134(17) 2513(42) 0.900(14)135 C1^1.221.241.26FC1 1.221.241.26Chapter 4. Spectra and Data Analysis^ 39Table 4.6: Fitting results for different value of it".Table 4.9 shows calculated results of (2-0) R(7) and R(8) of 135C1. Again 'Voltage' isthe reading of the multimeter. Since from K, and 'V' the electric field can be calculatedimmediately, we did not list the electric field values in Table 4.9. In the electric fieldrange we used, the splitting of R(7) and of R(8) is so small that it can't be resolved by ourexperiment. Hence we only listed the average frequencies in the table. The frequenciesof R(7) and R(8) listed in the table change by less than 0.001 cm-1 as the electric fieldchanges. Since the typical experimental error in the frequencies was 0.003 cm' for I35C1, we can neglect the Stark shifts in R(7) and R(8).The calculated frequencies of (2-0) R(8) of I'Cl at different electric fields show similarbehaviour as the frequencies of the reference lines of I35 C1 . Consequently we did not listthem.4.3 Induced transitions4.3.1 Sample spectrumFig. 4.10 is the fluorescence spectrum of 135C1 showing the electric field induced transitionsin an electric field of the order 31.6 kV/cm. The (2-0) Q(0), Q(1) and Q(2) lines in theB 3110+-X 1E0+ system, which are forbidden at zero field, appear in the spectrum whenChapter 4. Spectra and Data Analysis^ 40TransitionP(J, M)Ohs.(cm-i)Cal.(cm-i)Obs.-cal.(cm-1)Voltage(V)Elec. field(V/cm)ReferencetransitionP(1,0) 0.1488 0.1484 -0.0004 2.1900 5533.0 R(7)P(1,0) 0.1172 0.1150 -0.0022 3.2600 8236.3 R(7)P(1,0) 0.1145 0.1147 0.0002 3.3400 8438.4 R(7)P(1,0) 0.0893 0.0885 -0.0008 4.0700 10282.7 R(7)P(1,0) 0.0569 0.0548 -0.0021 4.9500 12506.0 R(7)P(1,0) 0.0512 0.0468 -0.0044 5.1000 12885.0 R(7)P(1,0) -0.0432 -0.0438 -0.0006 7.5700 19125.4 R(7)P(1,0) -0.0538 -0.0524 0.0014 7.8500 19832.8 R(7)P(1,0) -0.0594 -0.0582 0.0012 8.0000 20211.8 R(7)P(1,0) -0.0668 -0.0652 0.0016 8.2000 20717.1 R(7)P(1,0) 0.1476 0.1479 0.0003 11.5000 29054.4 R(8)P(1,0) 0.1392 0.1362 -0.0030 11.7600 29711.3 R(8)P(1,0) 0.1315 0.1254 -0.0061 12.0000 30317.7 R(8)P(1,0) 0.1236 0.1205 -0.0031 12.2500 30949.3 R(8)P(2,0) -0.0949 -0.1013 -0.0064 3.2600 8236.3 R(7)P(2,0) -0.0945 -0.0985 -0.0040 3.3400 8438.4 R(7)P(2,0) -0.0906 -0.0932 -0.0026 4.0700 10282.7 R(7)P(2,0) -0.0876 -0.0919 -0.0043 4.9500 12506.0 R(7)P(2,0) -0.0873 -0.0889 -0.0016 5.1000 12885.0 R(7)P(2,0) -0.0875 -0.0872 0.0003 6.1600 15563.1 R(7)P(2,0) -0.0886 -0.0911 -0.0025 6.5700 16598.9 R(7)P(2,0) -0.0908 -0.0902 0.0006 7.0500 17811.6 R(7)P(2,0) -0.0927 -0.0899 0.0028 7.3800 18645.4 R(7)P(2,0) -0.0941 -0.0934 0.0007 7.5700 19125.4 R(7)P(2,0) -0.0963 -0.0950 0.0013 7.8500 19832.8 R(7)P(2,0) -0.0976 -0.0979 -0.0003 8.0000 20211.8 R(7)P(2,0) -0.0994 -0.0978 0.0016 8.2000 20717.1 R(7)P(2,0) 0.1851 0.1868 0.0017 11.2300 28372.3 R(8)P(2,0) 0.1798 0.1789 -0.0009 11.5000 29054.4 R(8)P(2,0) 0.1744 0.1764 0.0020 11.7600 29711.3 R(8)P(2,0) 0.1694 0.1718 0.0024 12.0000 30317.7 R(8)P(2,0) 0.1639 0.1638 -0.0001 12.2500 30949.3 R(8)Chapter 4. Spectra and Data Analysis^ 41TransitionP(J, M)Ohs.(cm-1)Cal.(cm')0 b s .- cal.(cm')Voltage(V)Elec. field(V/cm)ReferencetransitionP(2,1) -0.1274 -0.1299 -0.0025 3.2600 8236.3 R(7)P(2,1) -0.1282 -0.1290 -0.0008 3.3400 8438.4 R(7)P(2,1) -0.1365 -0.1389 -0.0024 4.0700 10282.7 R(7)P(2,1) -0.1483 -0.1484 -0.0001 4.9500 12506.0 R(7)P(2,1) -0.1505 -0.1529 -0.0024 5.1000 12885.0 R(7)P(2,1) -0.1672 -0.1702 -0.0030 6.1600 15563.1 R(7)P(2,1) -0.1743 -0.1734 0.0009 6.5700 16598.9 R(7)P(2,1) -0.1829 -0.1852 -0.0023 7.0500 17811.6 R(7)P(2,1) -0.1891 -0.1891 0.0000 7.3800 18645.4 R(7)P(2,1) -0.1927 -0.1951 -0.0024 7.5700 19125.4 R(7)P(2,1) -0.1981 -0.1947 0.0034 7.8500 19832.8 R(7)P(2,1) -0.2010 -0.2004 0.0006 8.0000 20211.8 R(7)P(2,1) -0.2050 -0.2031 0.0019 8.2000 20717.1 R(7)P(2,1) -0.2122 -0.2085 0.0037 8.5600 21626.6 R(7)P(2,1) -0.2187 -0.2143 0.0044 8.8800 22435.1 R(7)P(2,1) -0.2229 -0.2195 0.0034 9.0800 22940.4 R(7)P(2,1) -0.2258 -0.2194 0.0064 9.2200 23294.1 R(7)P(2,1) -0.2285 -0.2258 0.0027 9.3500 23622.5 R(7)P(2,1) -0.2285 -0.2246 0.0039 9.3500 23622.5 R(7)P(2,1) 0.0978 0.1000 0.0022 9.5100 24026.7 R(8)P(2,1) 0.0922 0.0961 0.0039 9.7700 24683.6 R(8)P(2,1) 0.0869 0.0873 0.0004 10.0200 25315.2 R(8)P(2,1) 0.0810 0.0805 -0.0005 10.2900 25997.4 R(8)P(2,1) 0.0762 0.0775 0.0013 10.5100 26553.2 R(8)P(2,1) 0.0707 0.0682 -0.0025 10.7600 27184.8 R(8)P(2,1) 0.0647 0.0662 0.0015 11.0300 27867.0 R(8)P(2,1) 0.0602 0.0590 -0.0012 11.2300 28372.3 R(8)P(2,1) 0.0542 0.0526 -0.0016 11.5000 29054.4 R(8)P(2,1) 0.0484 0.0489 0.0005 11.7600 29711.3 R(8)P(2,1) 0.0429 0.0420 -0.0009 12.0000 30317.7 R(8)Chapter 4. Spectra and Data Analysis^ 42TransitionP(J, M)Ohs.(cm-1)Cal.(cm-1)Obs.-cal.(cm')Voltage(V)Elec. field(V/cm)ReferencetransitionP(3,0) -0.0938 -0.0958 -0.0020 9.5100 24026.7 R(8)P(3,0) -0.0919 -0.0930 -0.0011 9.7700 24683.6 R(8)P(3,0) -0.0902 -0.0910 -0.0008 10.0200 25315.2 R(8)P(3,0) -0.0882 -0.0910 -0.0028 10.2900 25997.4 R(8)P(3,0) -0.0867 -0.0874 -0.0007 10.5100 26553.2 R(8)P(3,0) -0.0850 -0.0862 -0.0012 10.7600 27184.8 R(8)P(3,0) -0.0832 -0.0836 -0.0004 11.0300 27867.0 R(8)P(3,0) -0.0818 -0.0856 -0.0038 11.2300 28372.3 R(8)P(3,0) -0.0801 -0.0848 -0.0047 11.5000 29054.4 R(8)P(3,0) -0.0785 -0.0774 0.0011 11.7600 29711.3 R(8)P(3,0) -0.0770 -0.0754 0.0016 12.0000 30317.7 R(8)P(3,0) -0.0755 -0.0779 -0.0024 12.2500 30949.3 R(8)P(3,1) -0.1373 -0.1381 -0.0008 9.5100 24026.7 R(8)P(3,1) -0.1382 -0.1370 0.0012 9.7700 24683.6 R(8)P(3,1) -0.1391 -0.1411 -0.0020 10.0200 25315.2 R(8)P(3,1) -0.1402 -0.1424 -0.0022 10.2900 25997.4 R(8)P(3,1) -0.1412 -0.1419 -0.0007 10.5100 26553.2 R(8)P(3,1) -0.1423 -0.1438 -0.0015 10.7600 27184.8 R(8)P(3,1) -0.1436 -0.1436 0.0000 11.0300 27867.0 R(8)P(3,1) -0.1447 -0.1446 0.0001 11.2300 28372.3 R(8)P(3,1) -0.1461 -0.1486 -0.0025 11.5000 29054.4 R(8)P(3,1) -0.1476 -0.1467 0.0009 11.7600 29711.3 R(8)P(3,1) -0.1490 -0.1484 0.0006 12.0000 30317.7 R(8)P(3,1) -0.1506 -0.1514 -0.0008 12.2500 30949.3 R(8)P(3,2) -0.1871 -0.1892 -0.0021 9.5100 24026.7 R(8)P(3,2) -0.1899 -0.1884 0.0015 9.7700 24683.6 R(8)P(3,2) -0.1927 -0.1956 -0.0029 10.0200 25315.2 R(8)P(3,2) -0.1957 -0.1975 -0.0018 10.2900 25997.4 R(8)P(3,2) -0.1982 -0.2002 -0.0020 10.5100 26553.2 R(8)P(3,2) -0.2012 -0.2033 -0.0021 10.7600 27184.8 R(8)P(3,2) -0.2044 -0.2043 0.0001 11.0300 27867.0 R(8)P(3,2) -0.2068 -0.2067 0.0001 11.2300 28372.3 R(8)P(3,2) -0.2101 -0.2123 -0.0022 11.5000 29054.4 R(8)P(3,2) -0.2133 -0.2173 -0.0040 11.7600 29711.3 R(8)P(3,2) -0.2163 -0.2170 -0.0007 12.0000 30317.7 R(8)P(3,2) -0.2195 -0.2219 -0.0024 12.2500 30949.3 R(8)Table 4.7: Fitting results of 135C1 (2-0) Stark components in the B 3H0+ -X 1E0+ system.Chapter 4. Spectra and Data Analysis^ 43TransitionP(J, M)Ohs.(cm-1)Cal,(cm-')Obs.-cal.(cm-1)Voltage(V)Elec. field(V/cm)ReferencetransitionP(1,0) 0.1334 0.1377 -0.0043 2.0000 5106.8 R(7)P(2,0) -0.0919 -0.0932 0.0013 3.9700 10137.0 R(7)P(2,0) -0.0880 -0.0914 0.0034 4.5000 11490.3 R(7)P(2,0) -0.0896 -0.0904 0.0008 5.0000 12767.0 R(7)P(2,0) -0.0922 -0.0903 -0.0019 5.5000 14043.7 R(7)P(2,0) -0.0899 -0.0911 0.0012 6.0000 15320.4 R(7)P(2,0) -0.0881 -0.0929 0.0048 6.5000 16597.1 R(7)P(2,0) -0.0955 -0.0957 0.0002 7.0000 17873.8 R(7)P(2,0) -0.0967 -0.0995 0.0028 7.5000 19150.5 R(7)P(2,1) -0.1408 -0.1386 -0.0022 3.9700 10137.0 R(7)P(2,1) -0.1432 -0.1457 0.0025 4.5000 11490.3 R(7)P(2,1) -0.1504 -0.1530 0.0026 5.0000 12767.0 R(7)P(2,1) -0.1572 -0.1608 0.0036 5.5000 14043.7 R(7)P(2,1) -0.1636 -0.1692 0.0056 6.0000 15320.4 R(7)P(2,1) -0.1697 -0.1780 0.0083 6.5000 16597.1 R(7)P(2,1) -0.1904 -0.1872 -0.0032 7.0000 17873.8 R(7)P(2,1) -0.1996 -0.1968 -0.0028 7.5000 19150.5 R(7)P(2,1) -0.2073 -0.2068 -0.0005 8.0000 20427.2 R(7)P(2,1) -0.2167 -0.2170 0.0003 8.5000 21703.9 R(7)P(3,0) -0.4305 -0.4232 -0.0073 7.5000 19150.5 R(7)P(3,0) -0.4248 -0.4198 -0.0050 8.0000 20427.2 R(7)P(3,0) -0.4208 -0.4163 -0.0045 8.5000 21703.9 R(7)P(3,0) -0.4178 -0.4127 -0.0051 9.0000 22980.6 R(7)P(3,0) -0.4133 -0.4092 -0.0041 9.5000 24257.3 R(7)P(3,0) -0.4135 -0.4092 -0.0043 9.5000 24257.3 R(7)P(3,0) -0.4026 -0.4057 0.0031 10.0000 25534.0 R(7)P(3,0) -0.4033 -0.4023 -0.0010 10.5000 26810.7 R(7)P(3,0) -0.3953 -0.3990 0.0037 11.0000 28087.4 R(7)P(3,0) -0.3940 -0.3960 0.0020 11.5000 29364.1 R(7)Chapter 4. Spectra and Data Analysis^ 44TransitionP(J,M)Obs.(cm-1)Cal.(cm-1)Obs.-cal.(cm- 1)Voltage(V)Elec. field(V/cm)ReferencetransitionP(3,1) -0.4530 -0.4497 -0.0033 7.5000 19150.5 R(7)P(3,1) -0.4522 -0.4507 -0.0015 8.0000 20427.2 R(7)P(3,1) -0.4553 -0.4520 -0.0033 8.5000 21703.9 R(7)P(3,1) -0.4585 -0.4536 -0.0049 9.0000 22980.6 R(7)P(3,1) -0.4570 -0.4554 -0.0016 9.5000 24257.3 R(7)P(3,1) -0.4595 -0.4554 -0.0041 9.5000 24257.3 R(7)P(3,1) -0.4552 -0.4575 0.0023 10.0000 25534.0 R(7)P(3,1) -0.4562 -0.4598 0.0036 10.5000 26810.7 R(7)P(3,1) -0.4599 -0.4625 0.0026 11.0000 28087.4 R(7)P(3,1) -0.4630 -0.4655 0.0025 11.5000 29364.1 R(7)P(3,2) -0.4904 -0.4854 -0.0050 7.5000 19150.5 R(7)P(3,2) -0.4932 -0.4902 -0.0030 8.0000 20427.2 R(7)P(3,2) -0.4993 -0.4952 -0.0041 8.5000 21703.9 R(7)P(3,2) -0.5073 -0.5005 -0.0068 9.0000 22980.6 R(7)P(3,2) -0.5125 -0.5060 -0.0065 9.5000 24257.3 R(7)P(3,2) -0.5086 -0.5060 -0.0026 9.5000 24257.3 R(7)P(3,2) -0.5128 -0.5117 -0.0011 10.0000 25534.0 R(7)P(3,2) -0.5159 -0.5176 0.0017 10.5000 26810.7 R(7)P(3,2) -0.5258 -0.5237 -0.0021 11.0000 28087.4 R(7)P(3,2) -0.5295 -0.5300 0.0005 11.5000 29364.1 R(7)Table 4.8: Fitting results of 137C1 (2-0) Stark components in the B3110-F-X1E0+ system.Chapter 4. Spectra and Data Analysis^ 45Volt age(V)Average frequencyof R(7)(cm-1)Average frequencyof R(8)(cm-1)0. 17663.6576 17663.32792.19 17663.6576 17663.32793.26 17663.6576 17663.32793.34 17663.6576 17663.32794.07 17663.6575 17663.32794.95 17663.6575 17663.32795.10 17663.6575 17663.32786.16 17663.6574 17663.32786.57 17663.6574 17663.32787.05 17663.6574 17663.32787.38 17663.6573 17663.32777.57 17663.6573 17663.32777.85 17663.6573 17663.32778.00 17663.6573 17663.32778.20 17663.6573 17663.32778.56 17663.6572 17663.32778.88 17663.6572 17663.32779.08 17663.6572 17663.32779.22 17663.6572 17663.32769.35 17663.6572 17663.32769.51 17663.6571 17663.32769.77 17663.6571 17663.327610.02 17663.6571 17663.327610.29 17663.6571 17663.327610.51 17663.6570 17663.327610.76 17663.6570 17663.327511.03 17663.6570 17663.327511.23 17663.6569 17663.327511.50 17663.6569 17663.327511.76 17663.6569 17663.327512.00 17663.6568 17663.327412.25 17663.6568 17663.3274Table 4.9: Average frequencies of 135C1 (2-0) R(7) and R(8) in the B 3H0+ -X 1E0+ systemat different electric fields.Chapter 4. Spectra and Data Analysis^ 46the field is applied. In zero field, P(1) comes in this region. However, when a field of31.6 kV/cm is applied, the Stark component P(1,0) of P(1) moves to lower frequencyand can't be seen in this frequency region.4.3.2 SaturationIn intensity measurements, we are interested in the relative intensities at different electricfields. If there are strong saturation effects, the simple equations given by Eq. 2.16 andEq. 2.24 do not apply. Therefore, we must test for saturation before we measureAn iris (refer to Fig. 3.6) was used to control the laser beam size before it went throughthe Stark cell. With the beam size fixed, we changed the laser power by adjusting thepolarizer P2 (refer to Fig. 3.6). The polarizer P1 was held fixed in the direction parallelto the electric field.With the beam diameter fixed at about 1 mm, at an electric field of 21 kV/cm, thefluorescence intensities of Q(0) and P(1,0) were measured at 20 mW, 40 mW, 60 mW and75 mW. The measured intensities were proportional to the power of the laser. Therefore,at least at a power as high as 75 mW, no observable saturation effects were found.In the intensity measurements, we used 40 mW laser power and the same beam size.There should be no significant saturation effects. (See Section 5.2.)4.3.3 Temperature stability and power variationIt was found that the intensities of the signals are very sensitive to the cold trap tem-perature which control the IC1 vapour pressure directly. The change in intensities of thesame line was observed even in two consecutive scans when no obvious change in thetemperature of the cold trap was found. Normally it took the dye laser about 10 minutesto finish one scan. Although the methanol solution temperature was supposed to bestable at its freezing point, the temperature could change slightly in 10 minutes since theChapter 4. Spectrum and Data Analysis^ 47t^I^t^1^I17663.744 cm-I 17664.256 cm ^17663.744 cm'^ 17664.256 cm'E =0^ E = 31.6 kVIcmFigure 4.10: The spectrum showing the induced transitions.Chapter 4. Spectra and Data Analysis^ 48solution was exposed to air directly. During the experiment, some dry ice was added tothe methanol solution from time to time to help to stablize the cold trap temperature.The output laser power of the dye laser is a function of the laser frequency. Withina 1 cm scan range, it was estimated that the power could change by the order of 10%.This also gave us trouble in intensity measurements.4.3.4 Data Analysis ofFrom Eq. 2.23 we can see that the factor C(f) depends on Fr(J') and F„,(J1) in theupper state. Because of the possibility of electric field induced predissociation, Fnr(f)can depend on E. Therefore, the ideal situation is to measure 4(1,0)//6(0). Since Q(0)and P(1,0) have same upper states, all lifetime effects and predissociation effects cancel.Therefore, from Eq. 2.24 we have:Ifp(i,o) _  p(i,o)If^IaQ(o)^Q(o)(4.40)The expression of Ia is given by Eq. 2.16. Since we can find K., from Stark shift mea-surements, we can use IC to calculate E if the position of the laser beam relative to theStark cell does not change. Therefore, there is only one parameter ,a' left unknown inthe expression of the ratio /6(0)/4(1,0).Some Stark components of (2-0) band were first measured. In the same way as we fitthe Stark shift data, IC was found to be:K2 = 2596 (1/cm)It was found from experiment that the intensity of Q(0) increases and the intensity ofP(1,0) decreases as the electric field increases. The best electric field to measure the ratioof if^seems to be V = 3.0 V, where /f //fcgo) P(i,o)^ cgo) P(i,o)^I .Chapter 4. Spectra and Data Analysis^ 49At this voltage, we found that:/pf(1,0)11-4(0) --= 1.096The dipole moment in the B 3110+ state of I'Cl was calculated to be:= +1.33 DThis result shows that the sign of fil is positive relative to it". Since the experimentaluncertainty in the magnitude of it' here is very large, we did not consider the error in ii,"and held it" fixed at 1.24 D in the calculation.Since at V = 3.0 V, the frequency difference between P(1,0) and Q(0) is about 0.292cm', the laser power at Q(0) and P(1,0) could be different. In addition, the temperatureof the cold trap was still a problem, even though we chose scanning range to be 0.7 cm-1 toreduce the scanning time between P(1,0) and Q(0). These difficulties can easily accountfor the disagreement between this measurement of the magnitude of il' and the Starkshift measurement given in Eq. 4.38.There are lots of difficulties at other electric fields. When the voltage across themultimeter is lower than 3.0 V, /6(0) becomes weaker; at voltages higher than 3.0 V,'P(1,0)f gets weaker. In both cases, the accuracy is significantly reduced by the inferiorsignal to noise ratio. In addition, the frequency of P(1,0) changes rapidly with theelectric field, while the frequency of Q(0) is almost a constant in the field range we used.Therefore, the frequency difference between P(1,0) and Q(0) increases rapidly when thefield increases. At higher fields, then the change in laser power between P(1,0) and Q(0)is a more serious concern. Therefore, we only measured /./ from 4,(1,0)//6(0) at V = 3.0 V.Due to the difficulties in this method, we checked the sign of ,a' with another method.Chapter 4. Spectra and Data Analysis^ 504.3.5 Data Analysis of Tf //f and IQ (1)f lifQ (0) R(5)^R(5)For Q(J) ( J = 0, 1 ) and R(5) transitions, the upper states are different. Therefore,the ratio of IQ(J) //R(5)f could be affected by the radiative and nonradiative decay rates.However, if the electric field induced predissociation is unimportant, then the field de-pendence of /6( j)//ift(5) can be used to measure til. Of couse it would be better if wecould measure the field-dependence of the absolute intensities of these Q(J) lines. Un-fortunately, we could not control the temperature of the Stark cell to the required level.It was necessary to use the ratio of two transition intensities to get a reliable results. Bychoosing a small frequency difference between these two transitions, the scanning timebetween the two transitions become smaller. Therefore, the effect of temperature driftsis smaller.For the (2-0) band, the induced transitions Q(0) and Q(1) of the B 31I0+-X 1E0+system in I35C1 were measured at different electric fields. The total frequency rangescanned was 0.57 cm-1 and the time for one scan was about 10 minutes. The inducedtransition intensities were normalized to /j(5). Since (2-0) R(5) is 0.0663 cm-1 from Q(0)and 0.1282 cm-1 from Q(1) (see Table 4.5), the power change between these frequenciesshould be much smaller than 10%. Also the scanning time between R(5) and the inducedQ lines were smaller the (1.1 minutes and 2.2 minutes, respectively), so that the errorsin the fluorescence intensities due to the temperature drifts were small.Fitting the data of /I //f and /I I I fQ (0) R(5)^Q (1) R(5)Since the intensity of R(5) is also a function of the electric field, a non-linear least squareprogram was used to fit the experimental data of /6(0)//(5) andAccording to Eq. 2.24,^T6(j)^C(J)F6(j)If — C(6) I a^R(5)^R(5)(4.41)Chapter 4. Spectra and Data Analysis^ 51where J = 0, 1. Assuming the electric field induced predissociation is unimportant, thenC(J)/C(6) is independent of E. We introduce a constantC(J)Cin =C(6)^(4.42)/(4(y) and Ili(5) are given by Eq. 2.16. The fitting model was given by Eq. 4.41; Cr, andwere treated as variable parameters. E was calculated from Eq. 3.28.The value of K, was calculated from measurements of the Stark shifts taken in thesame experiment. For this purpose, splitting measurements were made at ten differentfields. The results were fit as in Section 4.2.2. p" was held fixed at 1.24 D. It was foundthat:= 1.1048 ± 0.0085 DK, = 2598 + 20 (1/cm) for I'ClSince the position of laser beam relative to the electrodes did not change in the sameexperiment, K, found from splitting was used to calculated E in induced transitionfittings.Table 4.10 and Table 4.11 give the results of fitting 16(0)/1ii(5) and '(i)/'(5)' respec-tively. Fig. 4.11 and Fig. 4.12 show the plot of the fitted results with the experimentaldata, where the solid lines are calculated from the fitted C.,-, and fil. From the figures wecan see that the calculated results agree with experimental data within our experimentalerrors.Both the magnitude and the sign of /2 of I'CI were found from the fitting process.The results arePi =----- +1.37 + 0.28 DCr, = 0.1092 + 0.0074Chapter 4. Spectra and Data Analysis^ 52from the /f //f fit andQ(o) R(5)^1It' = +1.15 + 0.34 DC7, = 0.086 ± 0.019from the /6(1)//11(5) fit. In both cases, the value of p" was fixed at 1.24 D. Since the errorin it' here is larger than 20%, we did not consider the effect of the error in it" which isabout 2%.The it' found from /6(0)///fi(5) agrees within experimental error with the one fromThe magnitude of it' obtained here agrees within the error with that obtainedearlier from the Stark shift measurements.To make sure the sign of it' can be decided in this way, by assuming it' = —1.37 D andtreating only C,,, as variable parameter, we fitted /f //f^at different electric fields.Q(0) R(5)The results were plotted with the experimental data in Fig. 4.13. Similar comparisonswere found for a range of negative values of it'• It is quite obvious that the sign of ,a'relative to it" is positive.The method of fitting used in this section was based on the assumption that thefield induced predissociation is unimportant. Since good fits were obtained to the theexperimental data, and the value for Lull agrees with the magnitude we got before, thisassumption appears to be justified.Chapter 4. Spectra and Data Analysis^ 53Voltage(V)Ohs.(dim.)Uncertainty(dim.)Cal.(dim.)Obs.-cal.(dim.)2.00 0.0797 0.0184 0.0785 0.00123.00 0.1369 0.0150 0.1353 0.00154.00 0.1711 0.0143 0.1843 -0.01325.00 0.2338 0.0127 0.2246 0.00926.00 0.2643 0.0148 0.2579 0.00647.00 0.2856 0.0138 0.2859 -0.00038.00 0.3276 0.0146 0.3102 0.01739.00 0.3388 0.0226 0.3316 0.007210.00 0.3415 0.0120 0.3510 -0.009511.50 0.3668 0.0126 0.3774 -0.010512.50 0.3977 0.0129 0.3936 0.0040Table 4.10: Fitting results of /6(0)//1(5) as a function of the electric field.Voltage(V)Ohs.(dim.)Uncertainty(dim.)Cal.(dim.)Obs.-cal.(dim.)12.50 0.2809 0.0124 0.2711 0.009811.50 0.2417 0.0121 0.2419 -0.000210.00 0.1907 0.0115 0.1992 -0.00849.00 0.1654 0.0217 0.1722 -0.00688.00 0.1510 0.0140 0.1472 0.00377.00 0.1154 0.0133 0.1245 -0.00916.00 0.0982 0.0144 0.1042 -0.00595.00 0.0882 0.0124 0.0857 0.00244.00 0.0728 0.0141 0.0677 0.00513.00 0.0565 0.0149 0.0487 0.0078Table 4.11: Fitting results of /60)///fi(5) as a function of the electric field.Chapter 4. Spectra and Data Analysis 54Figure 4.11: /6(0)//ifz(5) as a function of the electric field.Chapter 4. Spectra and Data Analysis^ 550.30.250.20.150.10.05 _-_--2e+08^4e+08^6e+08^8e+08^le+09^1.2e+09SQUARE OF THE ELECTRIC FIELD (v^2 cm^-2)Figure 4.12: /6(1)//i.f1(5) as a function of the electric field.Chapter 4. Spectra and Data Analysis0.45 ^560.050.150.250.35 -0.10.20.30.4 -00^2e+08^4e+08^6e+08^8e+08^le+09^1.2e+09SQUARE OF THE ELECTRIC FIELD (vA2 cm^-2)Figure 4.13: /6(0)//11(5) as a function of the electric field (assuming it' = —1.37 D ).Chapter 5Discussion and Conclusion5.1 Effect of the inhomogeneity of the electric fieldHere we will estimate the angle between the plate electrodes and the effect of the inho-mogeneity of the electric field due to this angle.Fig. 5.14 shows the relative position of the plate electrodes when a lens was used todetect the fluorescence. F and G are points at the edges of the width observed. C0 is thepoint halfway between F and G. Lo, L1 and L2, respectively, are the plate separationscorresponding to Co, F and G. Here we assume the wide side of the plates are parallelto each other and only consider the effect of the angle between the side AB and CD.IG was found from the line center, so it corresponds to the center distance Lo. There-fore, from Eq. 3.27 we have:K R^42 R3+R4Since the voltage is the same across the plates,E0 L1LoE0 L2E2 L0where E0, El and E2 are the electric fields corresponding to the plate separations Lo, L1and L2, respectively.Since FC0 = GC0 and L2 > L0 > L1, we define a positive difference in the distancesAL as:AL = L2 — LO = LO Ll^ (5.45)R2 + noR3j_RD:113^.4LO (5.43)(5.44)57MNWmdow•^II" Lens'Side View To PhotomuhiplierTop ViewAChapter 5. Discussion and Conclusion^ 58Figure 5.14: The skatch of the plate electrodes.By substituting Eq.5.45 into Eq. 5.44 we obtain:Loc—I ELLoEo E2Lo + AL(5.46)We define the FWHM of a transition at zero field as Avo. When the central electricfield E0 at Co was applied, the FWHM of this transition can be approximated by:Au(E0) Avo + Iv(Ei) — v(E2)I (5.47)where v(Ei) and 11(E2) are the frequencies of the same transition at electric field E1 andE2, respectively. By substituting Eq. 5.46 into Eq. 5.47, it can be seen that Av(E0) is afunction only of Eo.The linewidths of (2-0) P(1,0) of 135C1 was measured at different electric fields inStark shift experiment. By using K, = 2527 (1/cm) given by Table 4.6 and the valuesChapter 5. Discussion and Conclusion^ 59Voltage V(V)Ohs. linewidth(cm-1)Cal. linewidth(cm-1)Obs.-cal.(cm')2.19 0.0266 0.0284 -0.0018823.26 0.0256 0.0297 -0.0041993.34 0.0245 0.0299 -0.0054014.07 0.0237 0.0308 -0.0071264.95 0.0294 0.0318 -0.00249612.00 0.0371 0.0370 0.00009012.25 0.0371 0.0371 -0.000001Table 5.12: Fitting results of the linewidth of 135C1 (2-0) P(1,0) in the B 3110+-X 1Eo+system as a function of the central electric field Eo.of the resistances R2 R3 and R4 given in Chapter 4, the value of Lo calculated fromEq. 5.43 was:Lo = 4.070 mmA vo of P(1) was found from experiment to be 0.027 cm-1. The value of jpil was takenfrom Eq. 4.38 and the value of p" was held fixed at 1.24 D. By treating AL as fittingparameter, the linewidths of P(1,0) at different central electric fields were fitted by anon-linear least square program. The value of AL was found to be:AL = 0.053 mmTable 5.12 shows the fitted values with the experimental data for P(1,0).The length of FG has a value of 1.5 mm, which is the width of the window on theside of the Stark cell in horizontal direction. Then the angle a between AB and CD is:a = 2AL1.5 = 0.0706 rad. = 4.05°Visual examination shows this linewidth method overestimates the angle a somewhat.From the change in the linewidths of P(1,0) at different electric fields, we can seethat the inhomogeneity of E increases the error in the frequency measurement. SinceChapter 5. Discussion and Conclusion^ 60Voltage V(V)Calc. linewidth(cm-1)Voltage V(V)Calc. linewidth(cm-1)2.19 0.02706 8.88 0.027323.26 0.02706 9.08 0.027343.34 0.02706 9.22 0.027354.07 0.02703 9.35 0.027364.95 0.02701 9.51 0.027385.10 0.02701 10.02 0.027426.16 0.02709 10.29 0.027456.57 0.02712 10.51 0.027477.05 0.02716 10.76 0.027497.38 0.02719 11.03 0.027527.57 0.02721 11.23 0.027537.85 0.02723 11.50 0.027568.00 0.02724 11.76 0.027588.20 0.02726 12.00 0.027618.56 0.02729 12.25 0.02763Table 5.13: Calculated results of the linewidth of 135C1 (2-0) Q(0) in the electronicB 31I0+-X 1E0+ system as a function of the central electric field Eo.the lineshape remains symmetric for most Stark components at high electric fields, thesystemetic errors do not increase. These effects had been taken into account by choosingthe maximum linewidth in the error calculation for the Stark shift fitting. (See section4.2.2.)To check the effect of the inhomogeneity of E on induced Q(J) lines, the linewidthof P5C1 (2-0) Q(0) was calculated using the fitted AL value and the value of jit'l givenby Eq. 4.38. liT, = 2527 (1/cm) was taken from Table 4.6 and it" was fixed at 1.24 D asbefore. The calculated results are listed in Table 5.13The maximum change in the calculated linewidth of Q(0) is 0.0006 cm'. This ismuch smaller than our experimental error, which is at least 0.003 cm-1. Therefore,the inhomogeneity of E does not effect the intensity of induced Q(J) lines within ourChapter 5. Discussion and Conclusion^ 61experimental error.5.2 Check of saturation effect at E = 32.5 kV/cmIn the intensity measurements, we showed that there are no observable saturation effectsfor Q(0) at 75 mW and E = 21 kV/cm. When we took data, a laser power of 40 mWwas used. Since the highest electric field we used in the intensity measurements was 32.5kV/cm, we must check whether saturation effect is significant at this field with a powerof 40 mW.When saturation effects are taken into account, the absorption coefficient 7 can bewritten:^7 = 70 (1 —^S) (5.48)where S is a saturation parameter that indicates the level of saturation and -yo is theabsorption coefficient in the limit that S --* 0. From Eq. (13-76) in reference [35], wehave:^s oc 'laser 7^ (5.49)where /laser is the intensity of the laser.To compare S at 21 kV/cm and 32.5 kV/cm, we notice that 7 can be related to theintegrated absorption intensity Ia by (Eq. (VI,64) in reference [36]):^P = i -y dv^ (5.50)Since both the lineshape and the linewidth Av of Q(0) are constants in the field rangewe used, we have:(5.51)where -ymax is the absorption coefficient on resonance. By substituting Eq. 5.51 intora'E=21 kV/cm = 0.809r_k=32.5 kV/cmChapter 5. Discussion and Conclusion^ 62Eq. 5.49 we obtain:Tlaser^TaSE=21 kV/cm = 1E=21 kV lcm'E=21 kV/cm (5.52)SE-325 kVIcm^11.1=363r2.5 kV/ cm IaE=32.5 kV/ cmBy using it' = 1.122 D and it" = 1.24 D, the ratio of Ia at these two different fields wascalculated to be:(5.53)Then we have:SE=21 kV/cm SE=32.5 kV /cmilaserE=21 kV/cm x 0.809' laserE=32.5 kV /cm75 mW ^ x 0.80940 mW = 1.51 (5.54)where a is the laser beam size which was a constant in intensity measurements. SinceSE=32.5 kV/ cm < SE=21 kV/cm and no saturation was observed at 21 kV/cm, it follows thatno saturation existed at 32.5 kV/cm for the power level used.Q(1) is more difficult to be saturated than Q(0); so there were no saturation effectsfor Q(1) in the experimental conditions we used in the intensity measurements.5.3 Effect of the hyperfine termWe have neglected the hyperfine term in all our data analysis. Therefore, it is necessaryto check the effect of this term.In our experiment, only (2-0) P(1) (for both 135C1 and I37C1 ) showed hyperfinesplitting at zero and low fields (refer to Fig. 4.10). At electric fields higher than 3 kV/cm,P(1,0) only appeared as a single line. We fitted the data of P(1,0) and the data of P(2)and P(3) Stark components in the Stark shift measurements of I35C1 separately. In bothcases (with tt" = 1.24 D), the frequencies calculated from fitted parameters agreed withChapter 5. Discussion and Conclusion^ 63lit'l (D)^K, (11 cm)P(1,0) only^1.140+0.024^2502+51Without P(1,0) 1.1182+0.0070^2527+15Table 5.14: The fitting results of I35C1 from P(1,0) and from the Stark components ofP(2), P(3).the experimental data within our experimental error (0.003 cm-'). The results of theleast square analysis are listed in Table 5.14. From the table we can see that the resultsof 10 agreed within the errors. Both sets of results agreed with the set given by Eq. 4.38where we fitted the Stark components of P(1), P(2) and P(3) at the same time.Therefore, the neglected hyperfine term is unimportant in this experiment.5.4 Accuracies of different methodsWe used two methods to measure pi of IC1 in this work: the Stark shift measurementand the intensity measurement. The Stark shift measurement is the more accurate wayto determine the magnitude of p'. There are several reasons for this. First, in the Starkshift measurement, saturation is not a concern. Therefore, we can always use high laserintensity to get good spectrum. Second, the temperature drifts which affects the vapourpressure of IC1 increase the error in the intensity measurement, since the number of IC1molecules is proportional to the vapour pressure. In the Stark shift measurement, all weneed to do with the cold trap temperature is to fix the temperature in a region where nodischarge occurs, or no I2 signals appears (if the Stark components we interested overlapwith I2 transitions). Third, the laser power is a function of laser frequency; this alsoincrease the experimental error in the intensity measurement.Although the magnitude of fi' calculated from the intensity measurements has a largererror than the one we got from the Stark shift measurements, it was possible to determineChapter 5. Discussion and Conclusion^ 64the sign of //' relative to that of p"•Since the isotope effects on the dipole moment are expected to be small, the sign ofin the B '110+ state for I37C1 should be the same as that for I35C1 . Although we onlydetermined that the sign of til for I35 C1 is positive, we conclude the sign of it' for I37C1 ispositive too.The final results are that in the vibrational level v' = 2 of the B '110+ state:+1.122 + 0.025 D0.9052 + 0.0053^for= +1.116 + 0.017 D0.900 ± 0.014^for 137C1^ (5.55)The ratio p' / ,tt" is determined more accurately than pl itself, because the experimentalerror in ,tt" only affects the absolute value of in the data analysis.5.5 Energy level behaviours at high electric fieldsWhen an electric field is applied to a molecule, the energy levels with same M value willmix to form new energy states.Table 5.15 and Table 5.16 show the coefficients of the eigenvectors at different electricfields in the B 3110+ and X 1E0+ states of 135C1 , respectively. To see the effect of thesign of Table 5.17 gives the same calculated resultes of the B 3110+ state by assumingthe sign of pi is negative. The coefficient ar,„4,i(E) is defined by Eq. 2.8 and Eq. 2.9 forthe X 1E0+ and B 3110+ state, respectively. The results were calculated by diagonalizing8 x 8 HT matrix for M = 0 in different electronic states. Only six coefficients were shownin the tables. Each set of coefficients arj,j(E) (j = 1,2, ,8) is determined only towithin an overall sign. (e. g. Any row can be multiplied by —1.) In Tables 5.15 to 5.17,Chapter 5. Discussion and Conclusion^ 65the convention is adopted that^is positive.The eigenyalues shown in the tables for the X1E0+ and B3II0+ states are quite differentsince different energy expansion forms were used.At low electric field E = 2596 V/cm, the mixing of state j,0 >6 and jj + 1,0 >o isquite small. aj,i(E) has the maximum absolute value when J j for both the X 1E0+and B 3110+ states. 1J, 0 >e is mainly formed by the zero field eigenvector 1j J, 0 >.At a field E = 28556 V/cm, the eigenvector 1J, 0 >, is mainly formed by mixing ofthree states (ie. j = J —1, J, J —1 ). In the B3110+ state, when J 1, and a j,,i,+1have the maximum absolute values. The maximum electric field we used in experimentswas around this value.At an electric field of 49324 V/cm, the mixing between becomes more complicated.For example, for the B3II0+ state, 1J = 2,0 >e is mainly formed by lj = 0,0 >0 , 1, 0 >0and 1j = 3,0 >0.Comparing the results in Table 5.17 with those in Table 5.15, we can see that thechange of the sign of p' changes the sign of some of the coefficients of the eigenvectorand does not affect the eigenvalues. This explains why we can find only the magnitudeof ft' from the Stark shifts. The change in the signs of the coefficients is summarized as:7,^_(-1)j-ri a j,,j, (5.56)where 4,,a, and (7,71,i1 are the coefficient a J,,j, when ft' is positive and negative, respectively.From Table 5.15 to Table 5.17 and Eq. 5.56, it can be seen that the leading terms in thesum on j" and j' in Eq. 2.16 have the same sign when ft' is positive and have oppositesign when ft' is negative. To see the effect of the sign of relative to fL" from anotherpoint of view, we substitute a positive ft' and a negative p' into Eq. 2.17. It turns outthat for a positive p', the intensity of the induced Q(0) transition is stronger than it isif ft' is negative. At high electric fields where the perturbation theory does not apply,Chapter 5. Discussion and Conclusion^ 66the results are similar except that the intensity of Q(0) is no longer proportional to thesquare of the electric field.Therefore, we can find the sign of it' from the intensities of the induced transitions.5.6 ConclusionIn this paper, we have presented a detailed study on the dipole moment in the B 3110+state of both 135C1 and 137C1 . The more accurate value of the magnitude of //' invibrational level v' = 2 was determined from the Stark shift measurement. From theintensity measurement of the electric field-induced transitions in I35 C1 , both the signand the magnitude of ,a' were obtained. Combining the results for these two methods,the dipole moment in the B 3II0+ state of ICI was obtained for the first time. The resultsare summarized in Eq. 5.55.Chapter 5. Discussion and Conclusion^ 67= 1.122 D, M = 0E = 2596 V/cmj'^0 1 2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.0047 0.9863 -0.1647 0.0043 0.0000 0.0000 0.00001 0.1686 0.1646 0.9834 -0.0761 0.0015 0.0000 0.00002 0.4983 0.0083 0.0757 0.9958 -0.0498 0.0008 0.00003 0.9955 0.0002 0.0023 0.0498 0.9981 -0.0371 0.00054 1.6588 0.0000 0.0000 0.0011 0.0371 0.9989 -0.02965 2.4880 0.0000 0.0000 0.0000 0.0006 0.0296 0.9993E = 28556.00 V/cmi'^0 1^2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.2828 0.7147 -0.6172 0.3249 -0.0516 0.0032 -0.00011 0.2101 0.6505 0.4172 -0.6107 0.1719 -0.0174 0.00102 0.5841 0.2510 0.6237 0.5556 -0.4805 0.0915 -0.00793 1.0360 0.0553 0.2322 0.4459 0.7728 -0.3790 0.05734 1.6816 0.0078 0.0445 0.1168 0.3671 0.8670 -0.31055 2.5029 0.0008 0.0053 0.0168 0.0698 0.3064 0.9118E = 49324.00 V/cm./,^ 0 1^2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.5798 0.6307 -0.4723 -0.5832 -0.1957 0.0262 -0.00181 0.1094 -0.3530 0.0877 -0.6660 0.6018 -0.2460 0.03892 0.6684 0.6813 0.5882 0.1189 0.4104 -0.0845 0.00833 1.1257 0.1129 -0.5672 0.4272 0.3838 -0.5565 0.15964 1.7292 0.0244 -0.3073 0.1376 0.4986 0.6244 -0.48495 2.5336 0.0038 -0.0825 0.0278 0.1838 0.4637 0.7481Table 5.15: The coefficients of the eigenvector as a function of electric field in the vibra-tional level v' = 2 of the B 3H0+ state for I35C1 (with ft' = 1.122 D).Chapter 5. Discussion and Conclusion^ 68= 1.24 D, M = 0E = 2596 V/cmin^0^1 2 3 4 5J" E(J")(cm-1) Coefficients of the eigenvector0 191.7668 0.9910^-0.1340 0.0028 0.0000 0.0000 0.00001 192.0013 0.1340^0.9891 -0.0612 0.0010 0.0000 0.00002 192.4550 0.0054^0.0610 0.9973 -0.0401 0.0005 0.00003 193.1380 0.0001^0.0015 0.0401 0.9987 -0.0299 0.00034 194.0490 0.0000^0.0000 0.0007 0.0299 0.9993 -0.02385 195.1878 0.0000^0.0000 0.0000 0.0004 0.0238 0.9995E = 28556.00 V/cmft^0^1^2 3 4 5J" E(J")(cm-1) Coefficients of the eigenvector0 191.4844 0.7499^-0.6119 0.2500 -0.0280 0.0014 0.00001 192.0711 0.6260^0.5349 -0.5558 0.1143 -0.0092 0.00042 192.5343 0.2104^0.5582 0.6898 -0.4059 0.0602 -0.00423 193.1733 0.0392^0.1649 0.3831 0.8514 -0.3132 0.03754 194.0691 0.0046^0.0254 0.0775 0.3072 0.9131 -0.25425 195.2010 0.0004^0.0024 0.0088 0.0462 0.2520 0.9425E = 49324.00 V/cmju^0^1^2 3 4 5J" E(J")(cm-1) Coefficients of the eigenvector0 191.1686 0.6633^-0.6020 0.4275 -0.1213 0.0115 -0.00061 192.0001 0.6739^0.2326 -0.6309 0.3028 -0.0455 0.00352 192.6462 0.3132^0.6726 0.2923 -0.5791 0.1683 -0.02083 193.2508 0.0871^0.3498 0.5348 0.5773 -0.4890 0.10714 194.1105 0.0160^0.0922 0.2138 0.4566 0.7497 -0.4117195.2279 0.0021^0.0152 0.0446 0.1270 0.4007 0.8331Table 5.16: The coefficients of the eigenvector as a function of the electric field in thevibrational level v" = 0 of the X1E0+ state for 135C1 .Chapter 5. Discussion and Conclusion^ 69= -1.122 D, M = 0E = 2596 V/cm./'^0 1 2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.0047 0.9863 0.1647 0.0043 0.0000 0.0000 0.00001 0.1686 -0.1646 0.9834 0.0761 0.0015 0.0000 0.00002 0.4983 0.0083 -0.0757 0.9958 0.0498 0.0008 0.00003 0.9955 -0.0002 0.0023 -0.0498 0.9981 0.0371 0.00054 1.6588 0.0000 0.0000 0.0011 -0.0371 0.9989 0.02965 2.4880 0.0000 0.0000 0.0000 0.0006 -0.0296 0.9993E = 28556.00 V/cm./3^0 1^2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.2828 0.7147 0.6172 0.3249 0.0516 0.0032 0.00011 0.2101 -0.6505 0.4172 0.6107 0.1719 0.0174 0.00102 0.5841 0.2510 -0.6237 0.5556 0.4805 0.0915 0.00793 1.0360 -0.0553 0.2322 -0.4459 0.7728 0.3790 0.05734 1.6816 0.0078 -0.0445 0.1168 -0.3671 0.8670 0.31055 2.5029 -0.0008 0.0053 -0.0168 0.0698 -0.3064 0.9118E = 49324.00 V/cm../'^0 1^2 3 4 5J' E(J')(cm-1) Coefficients of the eigenvector0 -0.5798 0.6307 0.4723 -0.5832 0.1957 0.0262 0.00181 0.1094 0.3530 0.0877 0.6660 0.6018 0.2460 0.03892 0.6684 0.6813 -0.5882 0.1189 -0.4104 -0.0845 -0.00833 1.1257 -0.1129 -0.5672 -0.4272 0.3838 0.5565 0.15964 1.7292 0.0244 0.3073 0.1376 -0.4986 0.6244 0.48495 2.5336 -0.0038 -0.0825 -0.0278 0.1838 -0.4637 0.7481Table 5.17: The coefficients of the eigenvector as a function of electric field in the vibra-tional level v' = 2 of the B 31-10+ state for I35C1 (with p' = -1.122 D).Bibliography[1] W. 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