Photoelectron angular distribution and ion vibrational branching ratio: The (2+1)photon ionization of E 1Πstatealigned CO moleculesG. Sha, D. Proch, and K. L. Kompa Citation: The Journal of Chemical Physics 99, 7687 (1993); doi: 10.1063/1.465698 View online: http://dx.doi.org/10.1063/1.465698 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/99/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Photoelectron angular distributions and vibrational branching ratios of CO (2+1)photon ionization via the B1Σ+ state J. Chem. Phys. 99, 4334 (1993); 10.1063/1.466087 Rotational branching ratios and photoelectron angular distributions in resonance enhanced multiphotonionization of HBr via the F 1Δ2 Rydberg state J. Chem. Phys. 95, 7872 (1991); 10.1063/1.461316 Resonance structure in the vibrationally resolved photoelectron branching ratios and angular distributionsof the 2π− 1 channel of NO J. Chem. Phys. 87, 5125 (1987); 10.1063/1.453680 Photoionization of the E F excited state of H2: Calculation of vibrational branching ratios andphotoelectron angular distributions J. Chem. Phys. 87, 3934 (1987); 10.1063/1.452947 Photoionization dynamics of excited molecular states. Photoelectron angular distributions and rotationaland vibrational branching ratios for H2 C 1Π u , v=0–4 J. Chem. Phys. 85, 3379 (1986); 10.1063/1.450959

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Photoelectron angular distribution and ion vibrational branching ratio: The (2+ 1)-photon ionization of E 1rr-state-aligned CO molecules

G.Sha DaHan Institute of Chemical Physics, Chinese Academy of Sciences, P. O. Box 110, Dalian 116023, People's Republic of China

D. Proch and K. L. Kampa Max Planck Institutftir Quantenoptik, P.O. Box 1513, 85740 Garching; Germany

(Received 8 April t993; accepted 30 July 1993)

We report vibrational level channeling and photoelectron angular distributions which characterize the single-step photoionization of the E I II Rydberg state of CO. Particular atten­tion is paid to the influence of the intermediate state's rotational preparation and its spatial alignment. The two-photon excitation is tuned to populate the lowest possible J values of E, which permits us to isolate a single magnetic sublevel of this intermediate state. Vibrational branching is found to be insensitive to the choice of the excitation line and does not match the predictions suggested by the Franck-Condon factors for a CO E III(uI) ->CO+ X 2~+ (u+) direct ionization. A competitive autoionization from the three-photon-energy state S 1 may be responsible for this anomalous behavior. The phenomenological pattern of photoelectron distri­butions can in all cases be rationalized on the basis of the intermediate state alignment. A separate chapter of the discussion is devoted to P(2) pumping, since it provides a particularly simple situation where all excited molecules are oriented with their axes parallel to the light vector E, which makes this case tractable to a quantitative calculation. Its results show quali­tative agreement with the experimental observations. The remaining discrepancy can be attrib­uted to the autoionization which has not been considered in the calculation.

I. INTRODUCTION

In a preceding paper, I we have reported the results of a study of the photoelectron angular distribution (PAD) and the ion vibrational branching ratio (VBR) observed in the process of CO (2+ 1) resonance-enhanced multipho­ton ionization (REMPI) via the B l~+inten;nediate state. In the presentation at hand, we wish to communicate data and interpretation from an analogous single color experi­ment which employed the two-photon accessible E 1 II state. This will allow a comparison with the results that have been obtained for the B state which, just as E, belongs to a Rydberg series converging to the CO+ (X 2~ +) elec­tronic ground state. However, the knowledge to be gained from the present effort promises to be of greater depth and detail since we may examine the influence of the interme­diate state's rotational and alignment status on VBR and PAD. In the B-state study, we had been unable to prepare selected rotational levels of the intermediate resonance since the two-photon excitation spectrum of X 1 ~ + -> B 1 ~ + exhibited but a congested Q branch.' This failure barred the access to essential information, such as the relative contribution of individual partial waves to the overall emission pattern. It is well established2 that the angular distribution of photoelectrons ejected during REMPI is determined not only by the character of the partial wave of the outgoing electron, but also by the align­ment of the intermediate state. If, e.g., the initial orienta­tion is random, as it is in many single-photon ionization studies which use synchrotron radiation in the vacuum ultraviolet wavelength regime, the only nonvanishing an-

isotropic term of the Legendre polynomial series which describes the PAD is f3 (or a2), with all higher contribu­tions vanishing.

An experiment which demonstrates the rotational res­olution of both the intermediate and the ionic states has recently been published by Allendorf et al. 3 A fit of the data of this PAD study of NO-which has been resonantly ionized via the A 2~ + intermediate state-to a theoretical model allowed us to identify the photoelectron partial waves which contribute to the overall emission pattern. By varying the angle between the polarizations of excitation and ionization lasers, the authors also observed some ef­fects of intermediate state alignment on the PAD. The experiment which we report here provides rotational reso­lution of the CO E 1 II intermediate state by line-selective excitation. Since the resolving power of our electron time­of-flight (TOF) instrument proved insufficient to identify contributions from individual rotational levels, we re­stricted the selection of excitation routes to those which populate the lowest Jlevels (J=O, 1, or 2). The number of ionic rotational levels which can be populated by photo­ionization out of a single rotational level of the intermedi­ate state is usually quite limited. For pump lines which are members of the P or R branches, previous laser-induced fluorescence (LIF) measurements of Fujii et al. 4 have shown N+ =Ni to hold, with N representing the rotational quantum numbers of ion and intermediate, respectively. Low-J excitation, in some cases, offers the benefit of "align­ment resolution." We have chosen this term to designate the population of one single magnetic sublevel of the inter­mediate, which allows us to identify any orientational ef-

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7688 Sha, Proch, and Kompa: Photoionization of CO

fects in a straightforward manner. P(2) excitation, as a special case, will align all excited molecules with their axes parallel to the electric vector of the light field. This specific situation permits us to calculate a theoretical PAD which shows a pattern of the same character as the experimental data. Further information to be gained from the present study is on the anomalous behavior of ionization via E III as evidenced by the vibratiomil branching ratio. We will interpret this anomaly and discuss the impact of autoion­ization as a competitive process to the direct route.

II. EXPERIMENT

Since the experimental setup has been described previ­ously in detail, I the account which follows is sketchy and just serves as a reminder. An excimer-pumped dye laser is frequency-doubled (BBO-I) to cover the wavelength range 210<..1.<215 nm. Its output pulses are attenuated to a few tens of micro joules to minimize Coulombic repulsion, which gives rise to a broadening of the TOF peaks and hence to a loss of energy resolution. Laser beam, gas jet, and drift tube axes are mutually orthogonal. The photo­electron signal from the channel plate detector is processed by a TEK7612 digitizer. Control over the direction 9 of the laser's polarization with respect to the flight tube axis is afforded by a rotatable Fresnel rhomb. Photoelectron spec­tra as a function of 9 were recorded· within the range 0.<9<90° in increments of 10°. Care was taken to design a data acquisition routine which minimizes the deleterious impact of declining laser performance.

.?l-'ijj

" .!'l " '" > :;:; 0

'" ""

.?l-'ijj

" 2 " ., ~ 0

Qi

""

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0 215.125

1.5

1.2

0.9

0.6

0.3

0.0 210.250

(a) S(O) S(1)

Q(I)

S(2) R(I) P(2)

.I I R(3) I 215.150 215.175 215.200 215.225 215.250

Wavelength [nm]

,.. ~ ... -(b) S(1)

S(O)

~ R(I) Q{l)

S(2)

'. ,

210.275 210.300 210.325 210.350

Wavelength [nm]

FIG.!. Wavelengths of two-photon excitation from CO[X 1 ~+ (v=O)] to CO*[E In(v;)] measured inthe TOF experiment. (a) Vi=O; (b) Vi= I.

(a) S(O) 1,;xc:ilnI.iOII

=30 °

=60 ° 8=90°.

450 475 500 525 550 575 600 625 650

Time of Flight [nl!l]

+

ii V =0 0

(~=45 (b) R(I) Excitation s:t '\ till

° Uj \ 8=0 s:t 0 ,.. .... Cl CD ..... CD 0 .... 0 .<l 11. -~-~ .. - .. -=::

450 475 500 525 550 575 600 625 650

Time of Flight [ns]

V =0 ii (c) P(2} Excitation = till .... -til

= 0 ,.. .... Cl CD ..... CD 0 .... + l V =4 11.

450 475 500 525 550 575 600 625 650

Time of Flight [nl!l]

FIG. 2. Photoelectron time-of-flight spectra of CO (2+ 1) REMPI via E(Vi=O) at different angles between laser polarization and drift tube axis. Excifation line (a) S(O); (b) R(l); (e) P(2) .

III. RESULTS

The three-photon REMPI process relies on the se­quence

2hv CO[X l};+ (v" =0)] ->CO*[E lII(vi=O or 1)]

lhv ->CO+ [X 2~+ (v+)] +e-.

We open each set of measurements (Le., VI =0 or 1) by assigning the two-photon absorption spectra recorded as a wavelength-dependent ion signal either in a CO-filled (Pco< 1 mbar) ionization cf)ll, or in the TOF instrument which, to this end, is operated as a mass spectrometer. Photoelectron time-of-flight information is then collected. for each of these resonance lines. The ionization spectra ·displayed as Figs. l(a) and l(b) show the positions and relative intensities of the various excitation lines and their assignment for Vj=O and 1, respectively. The neutral CO molecules are supplied from a pulsed adiabatic expansion

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Sha, Proch, and Kompa: Photoionization of CO 7689

(a)

S(O)

(b)

R(l)

(c)

P(2)

j/i --~/"/"" ~:>'. -- --

FIG. 3. Photoelectron angular distributions of CO (2+ 1) REMPI via E(Vi=O). Excitation line (a) S(O); (b) R(1); (c) P(2).

which confines the absorption to a few intense lines perti­nent to J" =0, 1, and 2. Figure 2 displays the photoelectron TOF spectra originating from Vi=O at different e (as marked) which were observed following excitation by the

TABLE I. The (2+ 1) REMPI of CO via theE iI1(Vi=O,I) intermediate state. The fit of Legendre polynomials to v+ = vi data. a2k is normalized to ao=l.

VI Excitation a2 a4 a6

0 S(O) 0.52 0.16 0.30 S(1) 0.67 0.27 0.09 R(l) 0.54 -0.75 0.05 Q(l) 0.7 0.21 0.19 P(2) 0.77 0.58 0.05

S(O) 0.65 -0.04 0.13 S(1) 0.47 -0.12 0.08 Q(1) 1.23 0.20 0.(13

TABLE II. The (2+ 1) REMPI of CO via the E lI1(v;=O,1) intermedi­ate state-vibrational branching ratios. To facilitate the discussion, we reproduce the VBRs pertinellt to ionization via the B i~+ state from Ref.l.a

Ei I1(v;=O,I) vi Excitation v+~O v+=l v+=2

Q S[O) S(l) R(!)

. P(2)

I S(O) R(l)

0.65 (0.12) 0.58 (0.13 )

JJ.59 0.11 0.65 0.09

0.89 0.9 .

_,,~_B i~+(v;=O,I)

Vj v+=O v+=1 v+=2

o 1

0.509 0.099

.0.305 0.901

0.133

0.15 0.15 0·18 0.13

0.11 0.1

:aEstimated values are enC(losed'in parentheses.'

v+=3 v+=4

0.06 0.02 0.08 0.06 0.09 0.03 0.09 0.04

0.039 0.014

·seO), R(1), and P(2) lines [see Figs. 2(a), 2(b), and -2(c)]. The PADs obtained for these respective cases are presented as Figs. 3(a)-3(c).

The photoelectron emission pattern which character­Izes a (2 + I) -photon ionization may be expressed analyt­ically by a series of Legendre polynomials2

,5

3

Iere) = L a2kP2k( cos-e). k=O .

(1)

The coefficients a2k which are the result of a fit of Eq. (1) to the experimental data are listed in Table I for the des­ignated Llv::::Otrlmsitionsfrom Vi=O and 1. .

The distribution among the vibrational states v+ can be described by the relationship

Ie(v!) Ri=~le(vn '

where

(2)

(3)

represents the total photoelectron signal from level v+ emitted into the full solid angle. It is extracted from the corresponding PAD. A compilation of the VBR is given in Table II. These figures must be compared to the calculated Franck-Condon factors for the ionizing transition which are listed in Table III.

TABLE III. Calculated Franck-Condon factors for the direct ionizing transition CO E 1I1(vj=0 or 1)->CO+X2~+(V+). As an approxima­tion, Morse wave functions (Ref. 25) were used according to Halmann and Laulicht (Ref. 26).

Vj=O vj=1

v+=O 0.997619 0.002273 v+=1 0.002128 0.979384 v+=2 0.000 169 O.OHi 796 v+_=3 0.000096 0.001077

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7690 Sha, Proch, and Kompa: Photo ionization of CO

IV. DISCUSSION

A. Anomalous behavior of the CO+ vibrational branch­ing ratio

As shown in Table II, the VBRs pertinent to v+ =Vi channels assume values of 0.58-0.65 for Vi=O and :::::0.9 for v·= 1. These figures are almost independent of the excita­tion line chosen which indicates the absence of any signif­icant influence of the rotational status nor the alignment of the E state on the VBR of the ion. This insensitivity finds a straightforward explanation--each line prepares a de­fined rotational and alignment status of the molecule in a space-fixed frame. VBRs, on the other hand, are deter­mined only by the status with reference to the molecular frame provided there is no vibration-rotation interaction for these low-J cases. The E In Rydberg state of CO has an equilibrium internuclear distance of re= 1.1152 A. (Ref. 6) which almost equals that of CO+(X 2~+) (re= 1.1151 A.) (Ref. 6). The Franck-Condon principle then states a pro­pensity for v+ =Vi transitions. The calculated F-C factors for the ionizing transition COrE In(Vi=O or 1)]-+CO+[X 2~+ (v+)] (Table III) thus show a vanishing probability for Llv=foO processes. This is in apparent dis­agreement with the observeo branching ratios compiled ~n Table II. Similar inconsistencies have been encountered In

REMPI studies on H2 (via C In) (Ref. 7), O2 (via C 3ng )

(Ref. 8), and CO (via B I~+).I In their theoretical study of low-lying I~+ and In

states of CO, Cooper and Kirby9 conclude for the domi­nant configuration of the E In state

At R=R =2.13ao (=1.13 A.), lif2if3if4if5al1r431T e 3 2

=(···)5al1T431T; and for 2.65<R<3.0ao ( ... ) 5al1T 211, where 31T is a C 3p orbital. E(Vi=O) is certainly in the 3P1T configuration quoted for its equilibrium distance. The value of lVe=2153.8 cm-;..llisted for this state6 permits a rough estimate on the position of the turning points of v·= 1 (Table III and Fig~2 of Cooper's paper9) which are f~und to be -2.05 and 2.3 a.u., respectively. It seems hence justified to treat Vt=O and vi= 1 alike and to ignore the influence of configurations other than 3p1T. Perturba­tions by other nearby states such as C I ~ + should also be unimportantlO,ll since E is prepared in its lowest rotational levels only.

Chupka 12 has suggested several possible causes for the anomalous behavior which occurs during the photoioniza­tion of unperturbed single configuration Rydberg mole­cules, including Cooper minima, electronic shape reso­nance, and autoionization. Of these, we hold the latter to be relevant. According to photoionization data measured by Cook et aI., 13 the accumulated three-photon energy at Ao=215.2 nm [ionization via E(v~=O)] coincides with the preionization peak around 717 A. Three photons of Al =210.3 nm [to pump E(Vi= 1)], on the other hand, termi­nate in the region of a preionization valley. This circum­stance may explain why an excitation routed through E(Vi =0) fans out to channels V+=foVi while pumping of E(Vi = 1) predominantly tends to prepare v+ = 1 ions.

In the context of energetics at the three-photon level, we also realize that a third photon may pump a transition

137835 cm-1 Sl

113029 cm-1 I.P. ~--------====

92930 cm-1 E

Ocm-1 X _ ....... _-

co co+

FIG. 4. Transition from E to SI' which belongs to Tanaka's sharp series -(n=3), by the absorption of a third photon. This state, then, undergoes autoionization E(" '4UZbT45u,3p1T) ""SI ( .. '4ul1T45UZ,3p1T) .... CO+ X(···4UZI1T45u)+e-.

from E to SI which is a member of Tanaka's sharp series (n=3), converging to CO+(B 2~+).6,14 The electronic configuration of SI is 1if2if3if4a11T45az, 31TY The tran­sition from E to this state can be imagined as an inner-shell 4a-+5a process, while the 3P1T electron acts as a spectator. As illustrated in Fig. 4, autoionization .of SI yields CO+(X2~+,v+)+e- [and also CO+(A 2n,v+)+e- as our photoelectron spectra reveal]. The Franck-Condon factors of the autoionizing transition CO*(SI'V') -+CO+ (X,v+) plus those of the direct process CO*(E,Vi) -+CO+ (X,v+) will contribute to the ion's vi­brational distribution. This argument does indeed offer a plausible and satisfactory explanation for the differences in VBR observed for the two vibrational states Vi of E. A third photon of AO excites E(Vi=O) to SI (v' = 1) [AI-E(Vi= 1) to SI (v' =3)]. The Franck-Condon factors for the ionizing step CO(SI'V')-+CO+(X,v+) have been calculated for v' under consideration (Table IV). We may now attempt to fit the experimental VBRs, assuming that only some frac­tion K of all ions owes its existence to direct ionization (E-+X), whereas the complement (l-K) is due to auto­ionization (SI-+X), Optimal agreement between observa­tion and calculation is produced by adjusting K=0.5 in the case of E(Vi=O) and K=0.8 for E(Vi=1). The calculated branching ratios resulting from this procedure are listed in

TABLE IV. Calculated Franck-Condon factors for the autoionizing tran­sition CO SI(V'= lor 3) .... CO+ X2~+ (u+ )'. u'= 1 and 3 of Sl h~ve ~een populated from E(u;=O) and v;= I, respectively. As an appr~XlmatIon, Rydberg-Klein-Rees (RKR) potentials were used. The rotatIOnal con­stant B. of SI was assumed to be equal to that of CO+ B 2~ + (Ref. 6) to which this Rydberg state converges.

u'=1 u'."" 3

u+=O 0.3266 0.0055 v+=1 0.1619 0.1430 v+=2 0.3059 0.3493 v+=3 0.1657 0.0024 u+';"4 0.0349 0.1549 u+=5 0.0045 0.2473 u+=6 0.0005 0.0784

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Sha, Proch, and Kompa: Photo ionization of CO 7691

TABLE V. Calculated vibrational branching ratios of CO+(v+). For REMPI via E(v[=O), equal contributions from direct and autoionizing channels have been assumed. The E( Vi= 1) data are best reproduced by attributing 80% to the direct and 20% to the indirect routes.

o 1

0.660 0.003

0.080 0.815

0.155 0.083

0.085 0.001

0.Ql8 0.031

Table V and compared to the experimental observation in Fig. 5.

While the assumption of a competition between direct and autoionizing channels explains the observed VBR of REMPI via the E state very well, the reasons behind the anomaly in the VBR of the analogous process via B remain a puzzling question. Our attempts to solve it by invoking some similar autoionization approach have failed. We sup­pose that a more sophisticated ab initio calculation may reveal the intrinsic mechanism of ionization via the B state.

B. The effect of intermediate state alignment on the PAD

The angle-resolved emission pattern is known to con­vey information on the character of the ejected photoelec­trons, including their partial wave composition [I, A., m (see Table VI)] and phase shifts. Many such details remain hidden to experiments which measure the one-step photo­ionization of isotropic (i.e., thermal ground state) mole­cules since a2 is the only non vanishing term in the analyt­ical notation for the PAD [see Eq. (1)]. The distillation of the desired knowledge from the PADs which accompany molecular REMPI is, however, often hampered by compli-

(a)

1.0,---.,----,-----r---,----,---,

'-__ ---'I E;XP.

CALC.

0.8 1>(2) EXCITATION

0.2

0.0~~0~-~1~-~2~-~3---~4~

VIBRATIONAL LEVEL OF CO+

TABLE VI. List of symbols. Excited intermediate and ionic states are labeled by SUbscript "I" and superscript "+," respectively.

N Angular momentum due to nuclear rotation and orbital angular momentum, with space-fixed and molecule-fixed projections M and A.

J Total angular momentum (without contribution from nuclear spin) with space-fixed projection M J •

S Total electron spin with space-fixed projection Ms. Se Spin of the photoelectron with space-fixed projection

Ms· Orbital angular momentum of the photoelectron in partial wave "f' with space-fixed and molecule-fixed projections m and A..

fLo

fL

p

Space-fixed projection of the dipole photon's unit angular momentum; fLo=O for linearly polarized light. Molecule-fixed projection of the dipole photon's unit angular momentum. Kronig symmetry index; p= 1 for f parity, p=O for e parity. All other quantum numbers for final and intermediate state designation.

cations introduced by the intermediate state alignment. The observed emission distribution represents a summation to which, depending on the particulars of the excitation mechanism, molecules with different M quantum numbers may have contributed. (The nomenclature that we have adopted is summarized in Table VI).

The present text reports PADs observed as a result of REMPI pumped by the two-photon S(O), R(1), or P(2) transitions. These lines populate low Jj which means a par­ticularly simple intermediate state alignment as only one IMI must be considered in each case. S(O) excitation will connect Jg=O, Mg=O to J j =2, Mj=O since a

1.0

EXP.

CALC.

0.8

Z R(I) EXCITATION

0 1-1

~ ...:l 0.6 ;:J p., 0 p.,

I'<l

~ 0.4

.~ ...:l

~ 0.2

~-'-O.O \I • 0 1 2 3 4

(b) VIBRATIONAL LEVEL OF CO+

FIG. 5. A comparison between calculated and experimental CO+ vibrational population distribution. (a) For REMPI via E(Vi=O); (b) for E(Vi= l).

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7692 Sha, Proch, and Kompa: Photoionization of CO

J I = 2 MI = 0

(0) E

J I = 2 MI =-1 J I = 2 MI =+1

(b) ----~~~----.. E

JI= 1 MI=-1 J I = MI =+1 (c) --------,-+.--,-----~. E

FIG. 6. Alignment of the angular momentum vector J j of the intermedi­ate state E lIT as effected by two-photon excitation by (a) S(O); (b) R(l); (c) P(2).

!::.M =0 selection rule holds (in the case of linearly polar­ized pump light). Figure 6(a) -shows a vector diagram which illustrates this angular momentum alignment of the intermediate state. In the treatment of R ( I) excitation that we begin with, we adopt the reasoning of Bray and Hochstrasser16 as illustrated in Fig. 7(a). The two-photon absorption may be conceived along two alternate ways:

and

fL~ (J-+J+ 1) . fLU (J+ I-+J+ 1).

Both take off from Jg = 1, M g= ± 1,0. As tlIe transition amplitude for the single-photon J -+J (and J + I-+J + 1)

(a) j

fJl \J it

'r-J--- - _. J

fJlI III

(b) j

'n; J-1

fJl fJ it

'r- J -- --- --- 'n~ J-1 J

fJu III __ ..L. ___ ......J __ , r: J

FIG. 7. The structure of the two-photon transition amplitude of I~+ --+ I IT - showing the detailed J dependence of particular transitions in the case of (a) R-branch and (b) P-branch excitation. IL" and ILl represent the parallel (~--+~ or IT--+IT) and perpendicular (~--+IT) transitions, respectively.

step is proportional to M (for linearly polarized light),16 the Mg=O sublevel cannot be excited by either sequence. The only accessible intermediate state therefore is Ji= 2, Mi= ± 1, which is oriented at 45° or 135° with respect to E [see Fig. 6(b)]. With a glance at Fig. 7(b) as a visual aid, an analogous argument applies for P(2) excitation which hence terminates in Ji= 1, Mi± 1, being parallel to E [Fig. 6(c)]. We are now able to correlate the PADs displayed in Fig. 3 to the alignment of the involved intermediate state.

S (0) pumping addresses the II + sublevel of E. Since bothCO(E 1II) andCO+(X2~+) are examples of Hund's case (b), the ionizing transition follows the selection rule17,18

(4)

For the case at hand, the Kronig symmetry indices are Pi=O (II+) andp+=O (~+). The Rydberg orbital of the E 1 II state is 3p1r(l= 1) and we may approximately assume a spherical potential of the ion core. Regarding the fl.l = ± 1 selection rule, we derive 1 =0 and 2. Equation (4) thus yields N+ -Ni= ± 1, ±3, ... , which has been observed in a laser-induced-fluorescence experiment performed on ions.4 In the classical limit, the transition dipole moment in this case can be shown to be perpendicular to J. 19 The photoelectrons will then be ejected preferably along theE direction.

R(1) excitation populates the II- sublevel (Pi= 1) when we obtain N+ -Ni=even according to Eq. (4). In fact, N+ -Ni=O has been observed.4 The transition dipole moment should now be along the Ji direction with the maximum photoelectron intensity at 45° and 135° and two nodes at 0° and 90°, which is in good agreement with the experimental PAD shown in Fig. 3 (b).

For the final case of P(2) excitation, we resort to a similar argument as for R (1) and deduce a transition mo­ment which is along Ji • The observation indeed confirms the expectation of maximum photoelectron signal at 0° and 180° [Fig. 3(b)].

While the above qualitative arguments invoked to ex­plain the shape of PE distributions seem convincingly plau­sible, we have met serious difficulties in the attempt to calculate quantit(Jtive emission characteristics because the partial wave analysis is hampered by too many unknown parameters. The only example which does not suffer from this drawback is P(2) excitation as will be demonstrated in the chapter to follow.

c. Theoretical calculation of PAD for REMPI by P(2) excitation

In this section, we shall compare calculated properties with observation. For details of the mathematical formal­ism, please turn to the "Appendix," the adopted nomen­clature is listed in Table VI. Our deliberations start from Eqs. (Al)-(A3) which have been derived by Wang and McKoy.20 The relationships apply to Hund's case (b) and to A-degenerate states. They also properly consider the effects of spin on the photoionization process. In the present CO(E) -+ CO+ (X) ionization, we may simplify Eq. (A2) to yield Eq. (A8) by setting Si=O, Ai=l, and

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Sha, Proch, and Kompa: Photo ionization of CO 7693

FIG. 8. Theoretical photoelectron angular distribution observed from CO (2+ 1) REMPI via E lII(vi=O) by P(2) excitation (solid line). The dashed line represents a Legendre polynomial fit through the experimen­tal data which are marked as dots.

A + =0. As discussed in Sec. IV B, 1 may be either 0 or 2. The key dynamical factor which determines the photoion­ization transition is the vibrationally averaged dipole ma­trix element21

11pJ..=(-i)I· exp (i7J/)· J X:+(R) ·r~i·XVi(R) . dR,

where

1}'t(R) = ('l' k/) .. (r,R) I r· YljL I 'l',(r,R».

11p.;"'s are, in principle, computable by ab initio methods. The possibility to calculate the PAD which results from P(2) excitation without explicit knowledge of these aver­aged matrix elements rests on the particularly uncompli­cated alignment of the intermediate state which greatly reduces the complexity of the problem. As shown in Fig. 6 ( c ), J,= 1 and is parallel to E. A, represents the projection of J, on the molecular axis. For a n state, it assumes the value A,= 1. The molecular axis must therefore be oriented parallel to E. The photon dipole moment is thus perpen­dicular to the molecular axis and J.L must be zero. From the triangle relation of 3j symbols in Eq. (A8), we obtain At = -A,= -1 and A=J.L-At = 1. The requirement to sat­isfy I> I AI leaves 1=2 as the only partial wave that P( 2) pumping may give rise to. Thus, in dealing with Eq. (A8), we must henceforth only consider 11AjL(l=2, A= 1, J.L=O). In the calculations of the angular dependence of photoelec­tron emission, which make use of Eqs. (A9)-(AI2), 1210

cancels if we normalize the Legendre coefficients. A; 'a result of this procedure, we obtained ao=: I, a2 =0.43, and a4=0.57. While a4 reproduces the experimental value very well, a2 is apparently too small. Figure 8 shows a polar coordinate display of the theoretical PAD superposed on the measured data. Though quantitative agreement is found only between 0° and ;::: 50°, the shape of the emission pattern, including the existence of two nodes, is correctly predicted, which adds to our confidence in the validity of this model. The partial failure to reproduce the measured

distribution cannot be rationalized by the presence of the state C I ~ + since any perturbation caused by it cannot affectJhejcomponents of the E In A doublet, according to the Kronig selection rule I1J=O and +~-.

It should be kept in mind that the calculation pre­sented here has tacitly assumed direct ionization as the only route connecting CO*(E) to CO+. Any participation of autoionization mechanisms, as discussed above, will ob­viously result in discrepancies between calculation and ex-

, periment since this competing process will be characterized by ~ .~ AD whic~ differs from that due to direct ionization.

v . .cONCLUSION

The unperturbed single-configuration Rydberg state E In served as the intermediate resonance for a (2+ 1)­photon ionization study of CO. Considerate choice of wavelength permitted us to prepare selected states of vi­bration, rotation, and molecular alignment. The ionizing step tended to favor I1v=O transitions only from E(v,= 1), whereas pumping of E(Vi=O) resulted in a distribution of ion vibrational states. This apparent noncompliance with the Franck-Condon principle is due to a competition be­tween direct ionization and autoionization from the S 1

state, which can be accessed from E by one-photon absorp­tion. The spatial distribution of photoelectrons ejected dur­ing ionization reflects the alignment of the involved inter­mediate state. Discrepancies between observed and calculated emission patterns again point to a contribution from an autoionizing channel, whereas a perturbation from C I ~ + may be excluded.

ACKNOWLEDGMENTS

G.S. recognizes the ample support which the National Natural Science Foundation oj China and the Max Planck Gesellschaft have bestowed on him. All authors enjoyed and benefited from the willing cooperation of Werner Knott, Christoph Rose, and Hans Bauer.

APPENDIX

To calculate the PAD of the single-photon ionization process

CO(E In,Vi,Ni,Mi,Pi)

->CO+ (X 2~+ ,v+ ,N+ ,M+) +e-, we will start from Eqs. (33) and (34) as formulated in Ref. 20 because both electronic states involved can be treated as Hund's case (b). The transition matrix element is

(Al)

with

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7694 Sha, Proch, and Kompa: Photoionization of CO

(Ni Si J. ) (N+ S+ J+ ) (S+ Se Si ) ( N+ Ni Nt) X -~Jj M+ Ms -Ms. -M+ Mi MSj Ms+ -MJ+ Ms+ e I

Mi mt

(Nt 1 X -mt f..Lo

1 ) P' [ L ( N+ -m (1+(-1» I[AJ.t;Ms• -A+ Ni Nt) Ai At

(Nt 1 -At f..L ~A)

and

( N+ + LI[AJ.t;Ms.(-I)P

j -A+

P' =M+ +MJ+ -Mi+f..Lo-Ni-N+

+Si-A+-f..L+~'

Ni Nt) (Nt -Ai At -At

(A3)

(A4)

I[AwM is the generalized vibrationally averaged dipole ma-, s. trix element [Eq. 22(c) in Ref. 20].

For a nonvanishing matrix element of Eq. (Al), P" must be even. Two-photon pumping effected by members of the P or R branch populates the II - sublevel (p i= 1 ) and p+ =0 for CO+ X 2l: +. As we have reasoned in Sees. IV B and IV C, 1 may assume the values 0 and 2, and N+ -Ni=O. P(2) excitation prepares an intermediate state with the internuclear axis parallel to E, thus f..L=0. Since A + =0, the triangle relation of the 3j symbols N+, N i , Nt and Nt> 1, I requires that At= T 1 and A= ± 1. In accor­dance with the relation I> I A I, 1=1=0 must hold for P(2) pumping. If we insert the corresponding values for Ai, At, and A, the symmetry relation of 3 j symbols yields

(N+ Ni Nt) (Nt 1 I) o 1 -1 1 0 -1

(Nt 1

X -1 0

Ni

-1

(AS)

We notice that N+ +Ni+2Nt+ 1 +I=odd. As au symme­try is satisfied, I[AJ.t=h-A,-w The equality of the two terms which are enclosed in square brackets ofEq. (A2) is now easy to see.

If we make use of the algebraic expressions of 3j sym­bols22 and consider Si=O, we have

and (A6)

where S+ = 1/2. Using the above equations, we may write

1

f..L ~A) ], (A2)

=( _1)P'+N/-M/+S+-Ms+. (2)-112= (_I)P(2)-1I2, (A7)

where P=P' + Ni - Mi + S+ - M s+ . P must be even as can be seen by inserting the known values of f..Lo=Si=A + =f..L=0 and N+=Ni=1 into Eq. (A3) and using the tri­angle relation of N+, S+, J+ (from which follows MJ+ =M+ + Mt). We finally obtainP = M+ + MJ+ - 2Mi -Ms+ =2· (M+ -MJ = even.

Bringing into play Eqs. (AS), (A6), and (A7), ex­pression (A2) can be reduced to yield

(N+ S+ J+ ) ( N+ Ni Nt)

X M+ Ms+ -MJ+ -M+ Mi mt

( Nt 1

~m) X -mt f..Lo

( N+ Ni Nt) (Nt 1

~A)' X LI[AJ.t;Ms, -A+ Ai At -At f..L

(A8)

The angle-resolved photoelectron intensity is obtained by squaring the photoelectron matrix element of Eq. (AI)

(A9)

In computing Ie, it must be kept in mind that we must sum over 1 and A coherently as a consequence of the interfer­ence between outgoing photoelectron channels, but inco­herently over Nt, m, and other quantum numbers.3

,23 In the case at hand, the only partial waves not to vanish are 1=2 and A= 1, such that no interference exists. We may write

(AW)

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Sha, Proch, and Kompa: Photoionization of CO 7695

TABLE VII. Calculated values of CI.m' KL,m' and aL of Eq. (A12) and nonnalized Legendre coefficients a2k-

KL,ml ,j4;

qm L=O L=2 L=4 ad.j4; aZk

1=2, m=O 0.502 0.639 0.857 L=O, 1.25 ao=l m=1 0.418 0.319 -0.571 L=2, 0.538 a2 = 0.43 m=2 0.334 -0.639 0.143 L=4, 0.718 a4=0.57

Each set of quantum numbers in Eq. (A9) determines one value of Clm' the square of which contributes to Ie(e) independently.

From the relationship24

(21 + I )(2/' + 1) (2L+ 1) * ( m' '\' Y1m Y 1m= -1) ~ L,M 417'

/'

-m' ~) y* L,ML

(All)

where [=['=2, m=m', ML=O, and L=O, 2, and 4. We. eventually obtain, by combining Eqs. (A9), (AlO), and (All),

(AI2)

where

(T" 2 2 2 aO=V4;(C2,0' KO,0+C2,1 ~ KO,1 +C2,2' KO,2)'

(5 2 2 2 a2 = V4;( C 2,0' K 2,0+ C 2,1 . K 2,1 + C 2,2' K 2,2)'

19-2· 2 ·-2

a4=V4;(C2,0' K 4,0+C2,1 . K4,1+ C 2,2' K4,2)'

The calculated values of the parameters Cl,m' K L,m' ao, a2' and a4 are listed in Table VII.

IG. ·Sha, D. Proch, C. Rose, and K. L. Kompa, J. Chern. Phys. (to be published).

2p. Larnbropoulos, in Advances in Atomic and Molecular Physics (Aca­demic, New York, 1976), Vol. 12, p. 87.

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Chern. Phys. 87, 3288 (1987). sp. J. Miller, W. A. Chupka, J. Winniczek, and M. G. White, J. Chern. Phys. 89, 4058 (1988).

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( 1990). These authors invoke a perturbation of Ii by the nearby C 11; + curve. Their observations were made forbigh values of J' though, which differs from the conditions prevailing in our experiment.

12W. A. Chupka, J. Chem.l'hys. 87, 1488 (1987). 13G. R. Cook, H. Metzger, and M. Ogawa, Can. J. Phys. 43,1706 (1965). 14M. Ogawa and S. Ogawa, J. Mol. Spectrosc. 41, 393 (1972). 15 A. Dadouch, G. Dujardin, L. Hellner, M. J. Besnard-Ramage, and B. J.

Olsson, Phys. Rev. 43, 6057 (1991). 16R .. G. Bray and R. M. Hochstrasser, Mol. Phys. 31, 412 (1976). 17J. Xie and R. N. Zare, J. Chern. Phys. 93, 3033 (1990). 18S. N. Dixit and V. C. McKoy, Chern. Phys. Lett. 128,49 (198/J). 19D. C. Jacobs and R. N. Zare, J. Chern. Phys. 85, 5457 (1986). 20K. Wang and V. C. McKoy, J. Chern. Phys. 95, 4977 (1991). 21 S. N. Dixit, D. L. Lynch, V. C. McKoy, and W. M. Huo, Phys. Rev. A

32, 1267 (1985). 22R. N. Zare, Angular Momentum (Wiley, New York, 1988), p. 62. 23D. Dill, Phys. Rev. A 6, 160 (1972). 24S. N. Dixit and P. Lambropoulos, Phys. Rev. A 27, 861 (1983). 25K. Cashion, J. Mol. Spectrosc. 10, 182 (1963). 26M. Halmann and I. Laulicht, J. Chern. Phys. 43, 438 (1965).

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