Photoionization of iodine atoms: Rydberg series which convergeto the I+„1S0…] I„2P3/2… threshold

Marie Eypper,1 Fabrizio Innocenti,1 Alan Morris,1 Stefano Stranges,2 John B. West,3

George C. King,4 and John M. Dyke1,a�

1School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom2Department of Chemistry and INSTM Unit “La Sapienza,” University of Rome, Rome, Italy; ISNM-CNR sez.Roma La Sapienza, 34012 Basovizza, Trieste, Italy; and Laboratorio TASC-INFM-CNR, 34012Basovizza, Trieste, Italy3STFC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, United Kingdom4Department of Physics, Manchester University, Manchester M13 9PL, United Kingdom

�Received 26 March 2010; accepted 17 May 2010; published online 24 June 2010�

Relative partial photoionization cross sections and angular distribution parameters � have beenmeasured for the first and fourth �5p�−1 photoelectron �PE� bands of atomic iodine by performingangle-resolved constant-ionic-state �CIS� measurements on these PE bands between the 1D2 and 1S0

�5p�−1 ionic thresholds in the photon energy region of 12.9–14.1 eV. Rydberg series arising from the5p→ns and 5p→nd excitations are observed in both the first PE band, I+�3P2�← I�2P3/2�, and thefourth PE band, I+�1D2�← I�2P3/2�, CIS spectra. For each Rydberg state, the resonance energy,quantum defect, linewidth, line shape, and photoelectron angular distribution parameter � have beendetermined. For the �-plots for each PE band, only resonances corresponding to 5p→nd excitationsare observed; no resonances were seen at photon energies corresponding to the 5p→ns resonancesin the CIS spectra. The �-plots are interpreted in terms of the parity unfavored channel with jt=4being the major contributor at the 5p→nd resonance positions, where jt is the quantum number forangular momentum transferred between the molecule, and the ion and photoelectron. Comparison ofthe results obtained with those published for bromine shows reasonably good agreement for the CISspectra but poor agreement for the �-plots. It appears that parity unfavored channels are playing agreater role in the valence �np�−1 ionization of atomic iodine than in the corresponding ionization ofatomic bromine. © 2010 American Institute of Physics. �doi:10.1063/1.3447382�

I. INTRODUCTION

The understanding of atomic and molecular photoioniza-tion has been significantly advanced in recent years by ex-perimental measurements made with synchrotronradiation.1–3 For closed-shell atoms, such as inert gases, theinteraction between experiment and theory has been veryfruitful in that it led to a detailed understanding of the photo-ionization processes.4–8 Open shell atoms and molecules aremore challenging to study experimentally in that they aredifficult to prepare in sufficient number densities for photo-ionization experiments as they are often short lived in the gasphase because of their reactivity. Nevertheless, the study ofopen shell atoms and molecules with photoionization is veryimportant as it opens up new areas of investigation in thateffects such as interchannel coupling, and spin-orbit interac-tion can be studied. The results obtained provide reliable datato test calculations, for example, of photoionization crosssections and angular distribution parameters that take theseinteractions into account. In particular, it should be notedthat, unlike the closed-shell case, removal of a single elec-tron can give rise to several possible ionic states, which inthe presence of the outgoing electron will give a number offinal states. Careful treatment of the coupling between thesefinal states is necessary in a reliable theoretical model.

The halogens have the valence electron configuration¯ns2np5 in their ground states, one electron less than theirclosed shell neighbors, the inert gases. They offer ideal testcases for studying the effects introduced by the np5 openshell and allow a comparison of the results obtained withthose of the inert gases. In this work, we report angle re-solved photoionization experiments on iodine atoms. Theground state electronic configuration of atomic iodine is¯5s25p5. This gives rise to two states 2P3/2 and 2P1/2 sepa-rated by 0.94 eV with the 2P3/2 state lying lower.9 The 2P1/2state is effectively not populated under equilibrium condi-tions at room temperature. The �5p�−1 ionization from the2P3/2 ground state gives 3P2, 3P1, 3P0, 1D2, and 1S0 ionicstates with the following ionization energies determinedfrom photoabsorption measurements:9,10

I+�3P2� ← I�2P3/2� 10.451 eV,

I+�3P0� ← I�2P3/2� 11.251 eV,

I+�3P1� ← I�2P3/2� 11.330 eV,

I+�1D2� ← I�2P3/2� 12.153 eV,a�Author to whom correspondence should be addressed. Electronic mail:

jmdyke@soton.ac.uk.

THE JOURNAL OF CHEMICAL PHYSICS 132, 244304 �2010�

0021-9606/2010/132�24�/244304/11/$30.00 © 2010 American Institute of Physics132, 244304-1

I+�1S0� ← I�2P3/2� 14.109 eV.

The �5s�−1 ionization gives 3P2,1,0 and 1P1 ionic states withionization energies 20.607, 20.894, 21.038, and 23.348 eV,respectively.10,11

Calculations of total and partial cross sections and angu-lar distribution parameters of atomic iodine as a function ofphoton energy have been performed at different levels ofsophistication.12–15 The most relevant for this present work,and the only study to include contributions to the computedphotoionization cross sections from autoionization of excitedRydberg states, is the work of Robicheaux and Greene.12

They calculated total photoionization cross sections foratomic iodine up to the 5s25p4 thresholds using the R-matrixapproach combined with multichannel quantum defecttheory to extend wave functions to larger distances. Angulardistribution parameters have also been calculated as afunction of photon energy by Combet Farnoux et al.13 andManson et al.14 Both of these studies used the independentparticle approximation, although the work of CombetFaknoux et al.13 improved the continuum wave functionsbeyond the independent particle level with a coupled channelmethod.

I atoms were first observed by PES using a HeI �21.22eV� photon source by de Lange and co-workers,16 where apartial photoelectron spectrum of the �5p�−1 ionization region�10.0–15.0 eV� was obtained. I atoms were prepared via theBr+I2 gas-phase reaction. Later, a complete HeI PE spec-trum of iodine atoms in this ionization energy region wasobtained by Berkowitz et al.17 and Dyke et al.,18 and therelative band intensities were interpreted using an intermedi-ate coupling model. I atoms were prepared in these studiesby heating solid silver iodide and from the F+HI gas-phasereaction, respectively.

Caldwell and Krause and co-workers19–25 carried out ex-tensive angle resolved PE studies of the halogen atoms F, Cl,and Br using monochromatized synchrotron radiation. Theymeasured partial cross sections and partial differential crosssections following ionization of both inner and outer shellelectrons. A summary of their work is presented in a paperpublished in 2004.19 Atomic bromine is immediately aboveiodine in the Periodic Table. Its PE spectrum from ionizationfrom the 4p valence shell shows the same bands as the iodine�5p�−1 ionization, Br+ 3P2,1,0, 1D2, and 1S0←Br 2P3/2.18

Caldwell and co-workers20 measured the constant-ionic-state�CIS� spectra for all bromine �4p�−1 PE bands except theBr+�3P2�←Br�2P3/2� band. Rydberg series converging toeach available �4p�−1 threshold were observed and analyzed.The angular distribution of the ejected photoelectron wasalso studied. The asymmetry parameter � was determined byrecording each CIS spectrum at two different angles withrespect to the polarization direction of the photon beam.Atomic chlorine and fluorine have also been studied in thisway.19,22–25 Unfortunately, the microwave discharge sourceused by Caldwell and co-workers, which involved passingthe flowing vapor of the appropriate molecular diatomichalogen through a microwave discharge to make the halogenatoms F, Cl, and Br, could not be used to make I from I2

because the vapor pressure of I2 at room temperature is too

low. As a result, atomic iodine is the halogen that has beenleast studied. In particular, no angle resolved CIS measure-ments have been made on the �5p�−1 PE bands of this atom.However, related measurements at higher photon energyhave been made on photoionization of atomic iodine withmonochromatized synchrotron radiation using laser dissocia-tion of molecular iodine to produce iodine atoms.26–28 Re-sults have been reported for relaxation of the 4d→5p reso-nance �Ref. 26; photon energy range of 45–54 eV�, forexcitation of the 4d electrons into excited states with n�5�Ref. 27; photon energy range of 44–80 eV� and for autoion-ization of the 5s→np resonances �Ref. 28; photon energyrange of 18.0–23.0 eV�. It is notable that although the iodine4d→np spectrum resembles the analogous 3d→np spectrumof Br, this and other iodine spectra are more complex thantheir equivalent Br spectra and require more sophisticatedcalculations in order to assign the observed spectral features.

A number of studies have been made of the electronicabsorption spectrum of atomic iodine. Early work was per-formed in 1962 by Minnhagen11 who revised the analysis ofthe photographic electronic absorption work of Kiess andCorliss.29 He also determined accurate term values for thefive I+ 5s25p4 states and demonstrated that neutral iodineexcited states are best described by Jcl �or JK� coupling.Later, Huffman et al.10 recorded the absorption spectra of allatomic halogens and confirmed the ionization limits obtainedby Minnhagen for iodine atoms. Berkowitz et al.30 observedRydberg series converging to the four higher ion core limitsby mass analyzed photoionization spectra of iodine atomsproduced by vaporizing AgI. Sarma and Joshi31 later as-signed Rydberg series converging to the I+ 3P2,1,0 thresholdswith principal quantum number up to n=20. More recently,Gu et al.32 observed two Rydberg series �one ns and one ndseries� built on the I+ 3P1 ion core and resolved states withprincipal quantum number up to n=47 by combining multi-photon ionization with time of flight photoelectron spectros-copy and mass spectrometry.

As part of our ongoing program to study photoionizationof short-lived reactive atoms with synchrotron radiation,which has so far involved O,33 N,34 and S,35 we presentresults of angle resolved PE experiments on iodine atoms inthe photon energy range of 12.9–14.1 eV. CIS spectra of thefirst and fourth �5p�−1 PE bands of I atoms are reportedwhich reveal Rydberg series which converge to the I+�1S0�← I�2P3/2� �5p�−1 limit. The objectives are to obtain relativepartial photoionization cross sections and the asymmetry pa-rameter � as a function of photon energy and to analyze thespectra to obtain information on photoionization dynamicsand excited state electronic structure. This follows an initialinvestigation of atomic iodine I and iodine monofluoride IFby photoelectron spectroscopy �PES� and threshold photo-electron spectroscopy �TPES� in which I and IF were pre-pared by reacting F atoms with CH2I2 in a flow tube.36 PEand TPE spectra were recorded with different I to IF ratios todetermine the relative intensities of I atom PE bands at 21.22eV photon energy and to obtain improved adiabatic ioniza-tion energies and vibrational spectroscopic constants for thetwo lowest ionic states of IF.

244304-2 Eypper et al. J. Chem. Phys. 132, 244304 �2010�

II. EXPERIMENTAL

In this work, experiments were carried out at the Elettrasynchrotron photon source on the Polar beamline BL4.2R asdescribed previously.33–37 The photoelectron spectrometerused was specifically designed to study reactive intermedi-ates with PES, TPES, and CIS spectroscopy using synchro-tron radiation.36–39 Measurements were carried out either byrecording PE spectra, in which the photon energy is fixed, orby recording CIS spectra, where the intensity of a particularatomic band is monitored as a function of photon energy.Both CIS and PE spectra were recorded in constant passenergy mode by scanning the voltage on a lens which accel-erates �or decelerates� the photoelectrons before they enterthe energy analyzer. The voltages on the hemispheres of thespectrometer are also scanned with the voltage on the lens tomaintain their difference constant. This ensures constant passenergy and spectral resolution.

The degree of linear polarization �P=1� of the radiationis well established.40 The asymmetry parameter � was mea-sured for the first and fourth �5p�−1 bands of iodine atomsover the photon energy range of 12.9–14.1 eV by recordingthe CIS spectra at two angles �0° and 54° 44�� with respect tothe direction of polarization of the photon source, as de-scribed previously.33–35

Iodine atoms were produced as in our earlier study of Iand IF by PES and TPES �Ref. 36� from the following con-secutive rapid reactions which occur on reacting F withCH2I2:

primary reaction:

F + CH2I2 → CH2I + IF,

main subsequent reactions:

F + CH2I → �CH2IF�† → CH2F + I

→CHF + HI,

CH2I + CH2I → �CH2ICH2I�† → CH2CHI + HF.

A high yield of F atoms was produced by flowing 5% F2

in helium through a microwave discharge at 2.45 GHz in thesidearm of a glass inlet system.41,42 This also has an innerinlet which is used to transport the target reaction molecules�in this case CH2I2� to the reaction region. The intensities ofthe bands in the experimental PE and CIS spectra were nor-malized by the photon flux and the transmission correction ofthe spectrometer.43,44 Test experiments were carried out inSouthampton in order to determine the optimum pressuresand mixing distance above the photon beam which maximizethe intensity of the I atom features. The optimum partialpressure readings were �p�CH2I2�=1�10−6 mbar,�p�F2 /He�=5�10−6 mbar, and �p�Ar�=3�10−7 mbar.These partial pressure readings were made using an ioniza-tion gauge connected to the main vacuum chamber and weremeasured with respect to the background pressure in thevacuum chamber �1�10−7 mbar�. They were used to repro-duce experimental conditions. Spectra which showed themost intense I atom bands were obtained at a mixing dis-tance of 4 cm above the photon beam. A typical PE spectrum

recorded under these conditions in the ionization region of10.3–12.3 eV is shown in Fig. 1. This was recorded at aphoton energy of 21.22 eV at an angle of 54° 44� with re-spect to the polarization direction of the photon beam. Thespectrum shown in this figure contains contributions from Iand IF. Our earlier work has shown that the I atom bandsI+�3P2�← I�2P3/2� and I+�1D2�← I�2P3/2� are not overlappedby IF features, whereas the I atom bands I+�3P0�← I�2P3/2�and I+�3P1�← I�2P3/2� are overlapped with vibrational com-ponents of the second band of IF. In our earlier work,36 spec-tra were recorded with different I:IF ratios by changing themixing distance above the photon beam. From the spectraobtained, the relative intensities of the I and IF contributionsto Fig. 1 were established. Because the first and fourth I atombands are not overlapped with any IF bands, they were se-lected for the CIS experiments and, for each band, CIS spec-tra were recorded from 12.9 eV up to the fifth �5p�−1 I atomthreshold at 14.11 eV, I+�1S0�← I�2P3/2�, with a step size of 2meV at two angles �0° and 54° 44�� with respect to thepolarization direction of the photon source.

III. FUNDAMENTAL BACKGROUND

A. CIS spectra

CIS spectra recorded for the two selected PE bands eachshow resonances which are parts of Rydberg series converg-ing to the 1S0 ionic state. To assign the series, it is helpful todraw up a table �Table I� of the excited states to which tran-

FIG. 1. PE spectrum recorded for the reaction F+CH2I2 at h�=21.22 eVover the ionization energy range of 10.3–12.3 eV, showing atomic I and IFfeatures �see text�.

TABLE I. Allowed Rydberg states, which converge to the I+ 1S0 ionic state,to which transitions are allowed from the ground state I¯5s25p5�2P3/2� andwhich autoionize to the ionic states I+

¯5s25p4�3P2� or I+¯5s25p4�1D2� in

the Jcl coupling scheme.

Excited states �Jcl�J final

Ionic state after autoionization

I+ 3P2 I+ 1D2

5s25p4�1S0�ns 2S1/2 �00�1/2 5s25p4�3P2�+�d 5s25p4�1D2�+�d5s25p4�1S0�nd 2D5/2 �02�5/2 5s25p4�3P2�+�s /�d 5s25p4�1D2�+�s /�d5s25p4�1S0�nd 2D3/2 �02�3/2 5s25p4�3P2�+�s /�d 5s25p4�1D2�+�s /�d

244304-3 CIS spectroscopy of I atoms J. Chem. Phys. 132, 244304 �2010�

sitions are allowed from the ground state ¯5s25p5�2P3/2� andwhich autoionize to the ionic states I+

¯5s25p4�3P2� andI+¯5s25p4�1D2�, respectively, in the Jcl coupling scheme

�also known as JK coupling�. In this coupling scheme, thetotal angular momentum of the ion core Jc couples with theorbital angular momentum of the electron l to give K. Thespin of the Rydberg electron s is then coupled to K to givethe total angular momentum J.

The resonances seen in experimental CIS spectra oftenshow an asymmetric profile. This is due to interference be-tween the direct and indirect ionization processes and resultsin a characteristic Fano profile,45,46 where the cross sectioncan be expressed as45

��E� = �a ��q + ��2

1 + �2 + �b. �1�

In this equation, �a and �b represent two portions of thecross section which correspond, respectively, to transitions tostates of the continuum that do and do not interact with thediscrete autoionizing state. � is the reduced energy which canbe expressed as follows:

� =E − En

1/2�, �2�

where En is the resonance energy and � is the natural widthof the autoionizing state which represents the bound-continuum mixing of the resonance state. The q parametercharacterizes the line profile. Neglecting the backgroundcross section, the resonance has a maximum at �max=1 /qand is zero at �0=−q. The sign of q thus determines whetherthe maximum occurs before or after the minimum. The mag-nitude of q indicates qualitatively the relative probabilities ofthe transition to the Rydberg state and direct ionization.45

In this work, codes for fitting resonances in the experi-mental CIS spectra to a convolution of the Fano profile andthe instrumental function F�E ,�, where is the energyresolution measured by the full width at half maximum, werewritten, where the total cross section is expressed as

��E,� = �−

��En − E� . F�E,�dE . �3�

A Gaussian function was used as the instrumental functionwith an energy width of 3 meV, which is consistent with thephoton width previously determined for the CIS spectra re-corded for oxygen atoms in earlier work at Elettra.33 Fanofitting of the resonances in this way allows the resonancepositions En as well as the parameters q and � to be estab-lished.

The effective quantum number �n�=n−�� and principalquantum number �n� of each Rydberg state can then be de-termined from47

En = E −R

�n − �n�2 , �4�

where R is the Rydberg constant for iodine atoms�109 736.84 cm−1� and En are the observed resonance ener-gies of the Rydberg states. This equation can then be used,with known En and n values, to obtain the ionization energy

E and the quantum defect �n of the series. This Fano fittingprocedure follows closely that carried out previously for CISspectra of N and S atoms.34,35

B. Angular distribution plots

The Bethe–Cooper–Zare formula48 can be used to assistinterpretation of results of angular distribution experimentsof light closed-shell atoms. However, this formula assumesL-S coupling in the initial and final states, neglects angularmomentum exchange between the escaping electron and theion core, and neglects configuration mixing in the initial andfinal states.6 This approach is not expected to be appropriatefor iodine, an element where configuration mixing and relax-ation effects are important and where JK coupling is the mostappropriate coupling scheme for valence states.11

To obtain some guidance as to what might be expectedfor values of the angular distribution parameter �, both onand off resonances, it was considered valuable to use angularmomentum transfer theory49 to investigate possible values ofthe �-parameter for parity favored and unfavored ionizationchannels.

Photoionization can be accompanied by a transfer of an-gular momentum between the neutral atom and the atomicion including the spin of the photoelectron. The photoioniza-tion process can be represented schematically as49

X�J0�0� + h��jh� = 1, �h� = − 1�

→ X+�Jc�c� + e−1�lsj,�e = �− 1�l� , �5�

where X�J0�0� and X+�Jc�c� represent the atom and ion,respectively, with total angular momentum J and parity �.�Parity of an atomic state is determined by li for that state.It is even for li even and odd for li odd.�

The angular momentum transferred between the atom,and the ion and photoelectron jt is defined by

j�t = j�h� − l� = J�c + s� − J�o, �6�

where J�0+j�h�=J�c+s�+l�.Conservation of parity � also implies

� h� � �0 = �c � �e, �7�

which in the electric dipole approximation reduces to

�c � �o = �− 1�l+1. �8�

The parity transfer �t is defined as the difference in paritiesbetween the neutral and ionic states. If �t matches jt �bothodd or both even�, then the ionization is parity favored.When �t and jt are not matched �one odd, the other even�,then the ionization is parity unfavored and the asymmetryparameter �unf is �1.

Table II shows values of the asymmetry parameter � atdifferent values of angular momentum transfer jt obtainedfrom the work of Dill and Fano49,50 by Chang.51 In general,the asymmetry parameter is given as a weighted average ofthe possible ��jt� contributions as follows:

244304-4 Eypper et al. J. Chem. Phys. 132, 244304 �2010�

� =1

��Jcs��

jt

fav.

��jt�fav��jt�fav − �jt

unf.

��jt�unf� . �9�

The results shown in Table II can be used to obtain values of��jt� for specific ionization channels and thus help under-stand the experimental �-plots.

Considering the case of direct ionization from theground state of I to the ground state of I+, i.e.,

I�¯5s25p5�2P3/2 + h� → I+�¯5s25p4�3P2 + e−. �10�

For this ionization, j�t=2� +1� /2−3� /2, which givesjt=0 ,1 ,2 ,3 ,4. Also �t is odd, and as l must be even �asremoval of a p electron in the atom will give an s or d freeelectron�, �c�o must be odd.

Inspection of Table II shows that when l is even, jt=0 isnot possible.

Also, for

�i� jt=1, l=0 or 2, and ��jt�=0 or 1, respectively.�ii� jt=2, l=2, ��jt�=−1, this channel is parity unfavored.�iii� jt=3, l=2 or 4, ��jt�=2 /7 or 5/7, respectively.�iv� jt=4, l=4, ��jt�=−1, this channel is parity unfavored.

When jt is odd, it matches the parity transfer �t, which isalso odd. In contrast, when jt is even, the ionization channelis parity unfavored and �=−1.

For direct ionization to the fourth state of I+,

I�¯5s25p5�2P3/2 + h� → I+�¯5s25p4�1D2 + e−. �11�

As the J quantum number of the ion is equal to 2 �Jc=2� asin the above example �Eq. �10��, the results derived abovefor the first PE band of iodine atoms also apply to the fourthband. For nonresonant photon energies, the �-plots for thesetwo bands will therefore be a weighted average of parityfavored and unfavored partial cross sections.

For resonant photon energies, the decay from the reso-nant state to the ionic state must also be considered, e.g.,

I��¯5s25p4, 1S0,nd�2D3/2,5/2 → I+�¯5s25p4�3P2 + e−,

�12a�

I��¯5s25p4, 1S0,ns�2S1/2 → I+�¯5s25p4�3P2 + e−,

�12b�

where in each case the resonant state is considered to be amember of a Rydberg series which converges to theI+¯5s25p4 1So ionic limit. These processes do not involve a

photon and as a result Eq. �8� changes for these autoioniza-tions to

�c�o = �− 1�l .

The excited neutral states in Eqs. �12a� and �12b� haveJ=1 /2 �from ns resonant states�, 3/2, and 5/2 �from nd reso-nant states�.

Taking as an example an autoionization from an excitedstate with J=1 /2, then j̄t between the excited atom I� and theatomic ion including the spin of the photoelectron is

2� +1� /2−1� /2=1, 2, and 3. In this case, l is even, �c�o iseven, and �t is even.

These jt values �1, 2, and 3� are already present in thedirect ionization process. Autoionization via one of thesechannels will therefore enhance the roles of channels that arealready present in direct ionization.

A similar situation also applies to autoionization from anexcited state with J=3 /2. Possible jt values are 1, 2, 3, and 4which are the same as those for direct ionization.

However, decay from an excited state with J=5 /2 willhave

j̄t = 2� + 1�/2 − 5�/2 = 0,1,2,3,4,5.

Again, l is even, �c�o is even, and �t is even. These jt valuesmean that there will be one new channel with jt=5.

The same analysis applies to the I+�¯5s25p4� 1D2 ionicstate in Eqs. �12a� and �12b� as the ionic state J value is 2both for the 3P2 and 1D2 ionic states. This analysis indicatesthat autoionization may enhance the contributions of somechannels in direct ionization, and it can also give rise to extrachannels, with new jt values, which are not present in directionization. Also, it can be seen that jt values of 1, 2, and 3 areobtained from �¯5s25p4 , 1S0 ,ns� resonant sates and jt valuesof 1, 2, 3, 4, and 5 are obtained from �¯5s25p4 , 1S0 ,nd�resonant states.

IV. RESULTS AND DISCUSSION

A. CIS spectra

The CIS spectra obtained during this work are in goodagreement with the spectra obtained by Berkowitz et al.30

from mass-analyzed photoionization of atomic iodine. Thisstudy30 measured the total I+ ion yield as a function of pho-ton energy and, unlike the present work, is not sensitive tothe final ionic state. The assignments given by Berkowitz etal. are consistent with those given by Huffman et al.10 in agas-phase optical absorption study. However, in the presentwork higher resolution was achieved, enabling analysis ofthe CIS resonance profiles using Fano fitting. Also � param-eter plots as a function of photon energy were obtained fromthe CIS spectra obtained at two different angles with respectto the radiation polarization direction.

TABLE II. The asymmetry parameter � for different values of the angularmomentum transfer quantum number jt �Refs. 50 and 51�. �The angularmomentum transfer is defined as the angular momentum transferred betweenthe atom and the ion and photoelectron �see text�.�

jt lodd � leven �

0 1 21 1 �1 0 0

2 12 1 1/5 2 �1

3 4/53 3 �1 2 2/7

4 5/74 3 3/9 4 �1

5 6/9

244304-5 CIS spectroscopy of I atoms J. Chem. Phys. 132, 244304 �2010�

Figures 2�a� and 2�b� show the CIS spectra of theI+�3P2�← I�2P3/2� band recorded in the photon energy regionof 12.9–14.1 eV at angles of �=0° and 54°44�, respectively,with respect to the direction of polarization of the photonsource. Corresponding spectra for the I+�1D2�← I�2P3/2� bandare shown in Figs. 3�a� and 3�b�. These spectra show twoclearly distinguishable Rydberg series converging to theI+�1S0� threshold, one of which is broader than the other.This general pattern was observed in all CIS spectra recordedat �=0° and �=54°44� for these two PE bands in this pho-ton energy region. The shapes of the resonances wereslightly different for the CIS spectra recorded for the first andfourth PE bands �see Figs. 2 and 3� while the resonanceswere similar in shape for CIS spectra recorded for the samePE band at the two different angles with respect to the pho-ton beam polarization direction. According to Table I, thesame transitions are allowed from the ground stateI¯5s25p5�2P3/2� to the excited states I�

¯5s25p4�1S0� ns ornd, whether the ionic state after autoionization is theI+¯5s25p4�3P2� or the I+

¯5s25p4�1D2� state. From thistable, it can be seen that three series which converge to theI+�1S0� threshold are allowed, one ns and two nd series.Since only two series are observed and the quantum defectsobtained for them correspond to the assignment of one nsand one nd series,52 it is assumed that the splitting between

the two expected nd�2�5/2,3/2 states for a given n value is toosmall to be resolved in this work. Of the two observed series,the nd series is expected to be broader than the ns series, ashas been observed in other halogens and rare gases, exceptfor the atoms of the first row.53 The series observed in thepresent work closely resemble those obtained for bromine�for the Br+ 1S0←Br�2P3/2� �4p�−1 CIS spectrum�20 and xe-non �for the �5p�−1 CIS spectrum�.54 This behavior, of com-ponents of the 5s25p4�1S0�ns series being sharper than com-ponents of the 5s25p4�1S0�nd series, is also expected fromthe R-matrix calculations of Robicheaux and Greene12 onatomic iodine.

Fano fitting was used to find the position En and fittingparameters q and � of each resonance. From Eq. �4�, theeffective quantum number n� and principal quantum numbern were derived for each Rydberg state. The results obtainedare shown in Tables III and IV. Also included in these tablesis the value of the product �n�3, the reduced linewidth. TableIII presents the values obtained for resonances seen in thefirst band CIS, I+�3P2�← I�2P3/2� at 54°44�, while Table IVpresents the values obtained for the fourth band CIS,I+�1D2�← I�2P3/2� at 54°44�. Inspection of these tablesshows that as n goes up, �, the linewidth, goes down as theRydberg state lifetime goes up. �n�3 is expected to be con-stant within a series.46 Also, the q value, the line profile

FIG. 2. CIS spectra of the first PE band of iodine atoms �I+�3P2�← I�2P3/2�� recorded at angles of �a� �=0° and �b� �=54°44� in the photonenergy region of 12.9–14.1 eV, showing autoionizing resonances convergingto the I+�1S0� threshold at 14.109 eV.

FIG. 3. CIS spectra of the fourth PE band of iodine atoms �I+�1D2�← I�2P3/2�� recorded at angles of �a� �=0° and �b� �=54°44� in the photonenergy region of 12.9–14.1 eV, showing autoionizing resonances convergingto the I+�1S0� threshold at 14.109 eV.

244304-6 Eypper et al. J. Chem. Phys. 132, 244304 �2010�

index, is expected to show a smooth trend with increasing n.The agreement with the expected trends is only moderate�see Tables III and IV� although the errors in the valuesobtained are significant. Inspection of Tables III and IV, andthe corresponding results obtained at �=0°, shows that the qvalues are negative for the 5s25p4�1S0� ns resonances seen inboth the I+�3P2�← I�2P3/2� and I+�1D2�← I�2P3/2� CIS spectrarecorded at �=0° and 54°44�, whereas for the 5s25p4�1S0�nd �2�5/2,3/2 resonances the q values are positive for theI+�3P2�← I�2P3/2� channel and negative for the I+�1D2�← I�2P3/2� channel.

Once this fitting procedure had been completed, the fit-ted ns and nd resonance profiles could be plotted separately.Examples of this are shown in Figs. 4 and 5 for the CISspectra recorded at �=0° for the I+�3P2�← I�2P3/2� and the

I+�1D2�← I�2P3/2� ionizations, respectively. The shapes of thend �Figs. 4�a� and 5�a�� and ns �Figs. 4�b� and 5�b�� reso-nances can be seen more clearly from these spectra.

The position of the resonances En at the two angles andfor the two different PE bands is in good agreement �seeTables III and IV�. From these values, the I+�1S0�← I�2P3/2�ionization threshold and the quantum defect can be obtainedfor each observed series �Eq. �4��. The results are shown inTable V. The derived I+�1S0�← I�2P3/2� ionization energiesare in good agreement with the value obtained by Huffman etal.10 and Berkowitz et al.30 of 14.109 eV within experimentalerror. Radler and Berkowitz52 showed that the quantum de-fect of Xe was 4 for ns series and 2.3 for nd series andinvestigations of resonances in atomic chlorine and brominehave shown to give in general the same quantum defects as

TABLE III. Energy of resonances converging to the I+�1S0� threshold at 14.109 eV recorded in the CIS spectrafor the first I+�3P2�← I�2P3/2� band of iodine atoms at �=54°44�. Also shown are the effective and principalquantum numbers n� and n, the fitting parameters q, �, �2, and �n�3 for each Rydberg state.

En

�eV� n� n q�

�meV� �n�3

�i� ns �0� 12 series

13.258�0.0008 4.00�0.01 8 −1.75�0.35 8.5�2.8 0.54�0.1813.576�0.002 5.50�0.02 9 −0.64�0.55 8.6�3.2 1.43�0.5313.736�0.001 6.04�0.03 10 −1.78�0.72 7.0�2.6 1.55�0.64

Not seen 1113.900�0.001 8.06�0.06 12 −2.21�1.41 4.5�2.3 2.37�1.2113.951�0.001 9.29�0.10 13 −0.89�0.72 1.5�3.1 1.20�2.52

�ii� nd �2�5/2,3/2 series13.056�0.001 3.59�0.01 6 2.30�0.14 24.4�1.8 1.13�0.0813.468�0.001 4.61�0.01 7 2.82�0.18 12.2�1.4 1.19�0.1413.681�0.001 5.64�0.02 8 2.69�0.17 10.0�1.0 1.79�0.1813.803�0.001 6.66�0.03 9 3.00�0.42 6.9�1.4 2.04�0.4013.878�0.001 7.67�0.05 10 2.09�0.34 6.2�1.8 2.82�0.8413.929�0.001 8.70�0.08 11 2.75�0.82 6.3�1.8 4.13�1.2113.966�0.002 9.74�0.12 12 2.84�1.52 7.4�1.5 6.83�3.4813.990�0.002 10.70�0.16 13 1.81�1.01 6.5�2.8 7.98�3.48

TABLE IV. Energy of resonances converging to the I+�1S0� threshold at 14.109 eV recorded in the CIS spectrafor the fourth I+�1D2�← I�2P3/2� band of iodine atoms at �=54°44�. Also shown are the effective and principalquantum numbers n� and n, the fitting parameters q, �, �2, and �n�3 for each Rydberg state.

En

�eV� n� n q�

�meV� �n�3

�i� ns �0� 12 series

13.261�0.001 4.00�0.01 8 −1.19�0.18 10.2�0.8 0.66�0.1013.575�0.001 5.05�0.01 9 −0.92�0.24 6.8�1.4 0.88�0.1813.744�0.001 6.10�0.03 10 −0.77�0.23 5.4�1.3 1.24�0.2913.839�0.001 7.10�0.04 11 −2.99�1.62 7.6�2.4 2.71�0.8713.905�0.001 8.17�0.07 12 −0.68�0.22 5.3�1.4 2.89�0.79

�ii� nd �2�5/2,3/2 series13.060�0.001 3.60�0.01 6 −1.93�0.38 24.9�2.8 1.16�0.1413.472�0.001 4.62�0.01 7 −1.42�0.24 8.9�1.6 0.88�0.1613.685�0.001 5.66�0.02 8 −1.43�0.24 8.9�1.6 1.61�0.2813.806�0.001 6.70�0.04 9 −1.56�0.34 6.8�1.4 2.05�0.4613.880�0.001 7.71�0.06 10 −1.70�0.71 8.4�2.3 3.85�1.0813.930�0.001 8.72�0.08 11 −4.09�1.97 10.5�2.9 6.97�1.96

244304-7 CIS spectroscopy of I atoms J. Chem. Phys. 132, 244304 �2010�

their rare gas neighbors.55,56 This is consistent with the as-signment for the ns�0�1/2 and nd�2�5/2;3/2 series made in thispresent work as quantum defects found for these series areapproximately 2.3 for the broad nd�2�5/2;3/2 series and ap-proximately 3.7 for the sharper ns�0�1/2 series �see Table V�.

B. �-plots

More information on the series can be obtained by look-ing at the asymmetry parameter � plotted as a function ofphoton energy. Beta plots were obtained from the ratio of theexperimental intensities in the CIS spectra at the two differ-ent angles, �=0° and �=54°44�. Figure 6�a� shows the betaplot of the first band of iodine atoms, I+�3P2�← I�2P3/2�,whereas Fig. 6�b� shows the beta plot of the fourth band ofiodine atoms, I+�1D2�← I�2P3/2�. The resonance positions inthe CIS spectra have been marked on these figures for refer-ence. These spectra are different from the CIS spectra as theresonances have similar shapes for the two bands and aresymmetric. However, the values of the beta parameter aredifferent in Figs. 6�a� and 6�b�; off resonance, the beta pa-rameter for the first band of iodine atoms has a mean value ofapproximately �0.3. It shows a broad oscillating backgroundwith values changing from �0.4 to �0.10 and sharp reso-nances going to �0.5 �see Fig. 6�a��. The beta parameter forthe fourth band of iodine atoms has a mean value of �0.6across the photon energy range with dips at the resonancesgoing to �0.85. Comparison of Figs. 2, 3, and 6 shows that

only the nd�2�5/2;3/2 series is seen in the beta plots; the nsseries is not seen. As stated earlier, the beta parameter foriodine atoms at any photon energy for these two PE bandswill be a weighted average of parity favored and parity un-favored ionization channels. In Figs. 6�a� and 6�b�, the back-ground is approximately �0.30 and �0.60, respectively, soboth parity favored �� zero or positive� and unfavored chan-nels ��=−1� are clearly playing a part �see Table II�.

The first resonance in Fig. 6�a� has a minimum of �0.47and a width of 22 meV. The second one has very similarcharacteristics with a minimum at �0.48 and a width of 21meV. The following resonances have a minimum of approxi-mately �0.4 with widths decreasing from 15 to 7 meV. Theresonances in Fig. 6�b� decrease regularly in intensity with aminimum of �0.90 and a width of 33 meV for the firstresonance and a minimum of �0.65 with a width of 8 meVfor the last observed resonance. The fact that the resonancesare more negative than the general background level showsthat the parity unfavored channels are enhanced on reso-nance. This seems to be the case even more strongly for the�-parameter plot shown in Fig. 6�b� where the resonanceshave minima close to �1.0.

Extensive angular distribution studies have been carriedout on the outermost �np�−1 ionizations of the inert gases, Ne,Ar, Kr, and Xe,49,54,57,58 in which the variation of � with

FIG. 4. Fano fits of the resonances converging to the I+�1S0� threshold at14.109 eV recorded for the I+�3P2�← I�2P3/2� band of iodine atoms at anangle �=0°.

FIG. 5. Fano fits of the resonances converging to the I+�1S0� threshold at14.109 eV recorded for the I+�1D2�← I�2P3/2� band of iodine atoms at anangle �=0°.

244304-8 Eypper et al. J. Chem. Phys. 132, 244304 �2010�

photon energy has been compared with the variation of thecross section. These studies showed that, in general, reso-nances are expected in the �-plots when resonances are ob-served in the CIS plots. The shape of the resonances in the�-plots can vary from one resonance to another, being sym-metric or asymmetric. In most cases, the � parameter is posi-tive, except at resonances, which usually has a minimumbelow 0. Specifically, in xenon54,57,58 the nd and ns reso-nances are seen in both the CIS and �-plots, with the ndresonances being broad and the ns resonances sharp, in boththe CIS and �-plots. Comparing the �-plots of iodine andxenon, the nd resonances are seen in both iodine and xenon,

but the ns resonances are not seen in iodine. This is probablydue to an increase of the exit channels accessible in iodinearising from the increased coupling possibilities of the freeelectron with the ion in the case of the open shell iodineatom compared to xenon. Also, the fact that the � parameteris always negative in the present work and becomes morenegative on resonances indicates that the parity unfavoredterms play a significant role with interference terms and in-terchannel coupling also probably contributing. As statedearlier, the jt values of 1, 2, and 3 are expected from�¯5s25p4 , 1S0 ,ns� resonant states and jt values of 1, 2, 3, 4,and 5 are expected from �¯5s25p4 , 1S0 ,nd� resonant states.As l must be even, the values of jt=1, 3, and 5 correspond toparity favored channels which have � values which are zeroor positive. For jt=2 or 4, the channels are parity unfavoredand have �=−1 �see Table II�. As the �-plots in Fig. 6 showonly nd resonances, not ns resonances, with � values morenegative than the negative background level, it appears thatthe jt=4 channel is the major contributor to the � values onresonance seen in Fig. 6, as the jt=2 channel will be avail-able for autoionization from the ns resonances.

Surprisingly, the �-plots for iodine atoms do not looklike the corresponding plots for bromine atoms �Fig. 10 ofRef. 20�, even though the corresponding CIS plots are verysimilar for the two atoms. As in the case of xenon53,56,57 inbromine nd and ns resonances are seen in the CIS and�-plots with the ns resonances sharp and the nd resonancesbroad.20 In iodine, ns and nd resonances are seen in the CISplots but only nd resonances are seen in the �-plots as de-scribed above. Further work will involve recording CIS and�-plots of the first and fourth PE bands of I to higher photonenergies and CIS and �-plots of the first PE band to theI+�1D2� and I+�3P1� �5p�−1 thresholds.

V. CONCLUSIONS

In this study CIS spectra have been recorded for the firstand fourth PE bands of atomic iodine, the I+�3P2�← I�2P3/2�and I+�1D2�← I�2P3/2� ionizations, in the photon energyrange of 12.9–14.1 eV. Resonances were observed in thesespectra corresponding to excitation to Rydberg states whichare parts of series which converge to the I+�1S0� ionizationthreshold. These were assigned to excitation to one ns andone nd series, although the observed nd series is thought to

TABLE V. Ionization energies and quantum defects obtained from the fit of series converging to the I+�1S0�threshold at 14.109 eV. Also shown is the difference in meV from the value given in Refs. 10 and 30 �14.109eV�.

E

�eV���E�toRef.7�meV� �

ns�0�1/2 series �=0° First band 14.1114�0.0027 2.4 3.79�0.10Fourth band 14.1121�0.0039 3.1 3.77�0.15

�=54°44� First band 14.1122�0.0086 3.2 3.77�0.36Fourth band 14.1111�0.0042 2.1 3.65�0.15

nd�2�5/2,3/2 series �=0° First band 14.1116�0.0021 2.6 2.35�0.06Fourth band 14.1116�0.0013 2.6 2.24�0.03

�=54°44� First band 14.1128�0.0010 3.8 2.34�0.30Fourth band 14.1137�0.0029 4.7 2.27�0.07

FIG. 6. Beta plots recorded over the photon energy region from 12.9 to 14.1eV. Spectrum �a� was recorded for the I+�3P2�← I�2P3/2� band of iodineatoms whereas spectrum �b� was recorded for the I+�1D2�← I�2P3/2� band ofiodine atoms. The resonance positions in the CIS spectra have been markedfor reference.

244304-9 CIS spectroscopy of I atoms J. Chem. Phys. 132, 244304 �2010�

consist of two unresolved series, nd5/2 and nd3/2. Each Ryd-berg resonance was fitted to a Fano profile to determine theresonance position. The resonance positions were then fittedto obtain the ionization energy and quantum defect from thetwo series. The results obtained agree with values obtainedfrom previous work using optical spectroscopy10,31 andphotoionization mass spectroscopy.30

�-parameter plots were obtained for the first time for thefirst and fourth bands of iodine atoms up to the I+ 1S0 thresh-old in the same photon energy range as the CIS spectra.These �-plots show unexpected behavior in that althoughresonances are seen in the �-plots at the same positions asthe nd resonances in the CIS spectra, no resonances wereobserved in the �-plots at the positions of the ns resonancesseen in the CIS spectra. Also, in these plots, � is negativeoff-resonance and becomes more negative on-resonance.This is in contract to the equivalent �-plots for xenon and thelighter halogen atoms, notably bromine, which show reso-nances in the same positions as the resonances in the CISspectra, and which have positive values off-resonance andare negative on-resonance. It appears that parity unfavoredchannels are playing a greater role in iodine than bromine orxenon. At nonresonant photon energies, the jt=2 and jt=4channels make significant contributions, whereas at photonenergies at nd resonant positions, the jt=4 channel domi-nates.

In the theoretical studies13,14 which calculated the � pa-rameter as a function of photon energy, � was computed tobe always positive at different photon energies and to varysmoothly as a function of photon energy. However, boththese studies used the independent particle approximationand did not take into account the contributions from resonantstates. The demands on any theoretical method to reproducethe experimental results are clearly quite high. It must in-clude interchannel coupling and other electron correlationterms, the effects of resonant states as well as relativisticeffects. However, such calculations will be rewarding in thatthey should lead to greater insight being obtained from themeasurements.

ACKNOWLEDGMENTS

The authors are grateful to EPSRC for supporting thiswork. M.E. thanks the EU Early Stage Research TrainingNetwork �SEARCHERS� for financial support. We alsothank Dr. N. Zema and the technical staff of the Polar beam-line �BL4.2R� at Elettra, Trieste for help and advice.

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244304-11 CIS spectroscopy of I atoms J. Chem. Phys. 132, 244304 �2010�

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