Photoionization of CF4 in the VUV region

Journal of Electron Spectroscopy and Related Phenomena 130 (2003) 101–109 www.elsevier.com / locate / elspec

Photoionization of CF 4 in the VUV region a,b a, c d E.M. Nascimento , L.E. Machado *, L.M. Brescansin , M.-T. Lee a

˜ Carlos, SP, Brazil ´ , UFSCar, 13565 -905 Sao Departamento de Fısica b ´ , UFBa, 40210 -340 Salvador, BA, Brazil Instituto de Fısica c ´ ‘ Gleb Wataghin’, UNICAMP, 13083 -970 Campinas, SP, Brazil Instituto de Fısica d ˜ Carlos, SP, Brazil ´ , UFSCar, 13565 -905 Sao Departamento de Quımica Received 23 October 2002; received in revised form 19 March 2003; accepted 19 March 2003

Abstract We present calculated results of photoionization cross sections and photoelectron angular distributions for ionization out of the five outermost valence orbitals of CF 4 for photon energies ranging from near threshold to 55 eV. The Schwinger variational iterative method, using an exact static-exchange plus a model correlation–polarization potential, is applied to obtain the continuum photoelectron orbitals. The quantitative agreement between our calculated results and the experimental data is fair. Moreover, our study is capable of identifying most structures seen in experimental results for both cross sections and asymmetry parameters.  2003 Elsevier B.V. All rights reserved. Keywords: Photoionization cross sections; Photoionization asymmetry parameters; CF 4 ; SVIM PACS: 33.80.-b; 33.80.Eh

1. Introduction In recent years, there has been an increasing interest in the study of fluoromethanes, due to their importance in different fields of research, such as plasma and atmospheric chemistry, among others [1]. These gases are chemically stable and have great ability to absorb infrared radiation, thus contributing to the greenhouse effect. Tetrafluoromethane (CF 4 ) is an important member of these species and has been widely used in semiconductor manufacturing processes [2]. In the last few years, efforts have been *Corresponding author. Tel.: 155-16-260-8226; fax: 155-16261-4835. E-mail address: [email protected] (L.E. Machado).

made to reduce the use of this compound in plasma processing, due to its contribution to the global warming. The interaction of radiation with CF 4 molecules has been the subject of continuous investigation from both experimental and theoretical points of view for a long while. In particular, partial photoionization integral cross sections (s ) and photoelectron angular distribution or asymmetry parameters ( b ) have been measured for more than fifteen years [3] over a wide photon energy range. Vacuum–UV photofragmentation [4] and, very recently, dissociative photoionization [5] of CF 4 were also studied experimentally. On the other hand, theoretical investigations on the valence-shell photoionization of CF 4 are much more scarce, mainly due to the difficulties involved in the

0368-2048 / 03 / $ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0368-2048(03)00090-2

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determination of accurate photoelectron continuum wavefunctions. The only two articles reporting calculated values of s and b have used the multiplescattering (MS-Xa ) [6,7] and the multiple-scattering with atomic amplitudes (MSAA) [7] methods, both of non-ab initio nature. It is worth noticing that a strong disagreement has been observed between the results of the two MS-Xa calculations, in the magnitude of s and b as well as in the identification of the structures appearing in the experimental results. In particular, the MS-Xa calculation of Stephens et al. [6] presents shape-resonant structures near thresholds, which are usually not observed either in the experimental results or in other calculations [7]. Also, in all previous calculations [6,7] no discussion on the broad structure seen in the experimental s at higher photon energies was made. In this paper we present a theoretical study on the photoionization of CF 4 . We report calculated partial photoionization cross sections and photoelectron asymmetry parameters for the five outermost valence orbitals, namely, 1t 1 , 4t 2 , 1e, 3t 2 and 4a 1 , for photon energies ranging from near the ionization potentials to 55 eV. Our main interest in this paper is the identification of the structures seen in the experimental data, thus contributing to clarify their physical origin. In the present study we employ the Schwinger variational iterative method (SVIM) [8] to obtain accurate Hartree–Fock photoelectron orbitals which are used to derive s and b. This procedure has already been applied to study photoionization of several small molecules [9–12]. It has proven to be numerically robust and capable of providing a quantitative description of the photoionization dynamics in several molecular systems studied to date. Although this method was developed in the early 1980s for photoionization studies of linear systems [8,13,14], it has been extended to nonlinear polyatomic molecules [9–12,15–17] and still constitutes one of a few tools capable of performing ab initio calculations of photoionization cross sections and asymmetry parameters. On the other hand, considering the one-electron nature of SVIM, the comparison of our data obtained at the exact static-exchange plus model correlation–polarization (SEP) level with the experimental results would provide information on the role played by important physical effects, e.g.,

target electronic correlation, multichannel coupling, etc., not included in our calculations. The paper is organized as follows. In Section 2 we briefly review the method used for obtaining the photoelectron orbitals and matrix elements along with some numerical details of the calculation. In Section 3 we present our calculated photoionization cross sections and photoelectron asymmetry parameters and compare them with available experimental data. Finally, in Section 4 we summarize our conclusions.

2. Theory and calculation Details of the method have been given elsewhere [8,12], so only the essential aspects will be discussed here. The photoelectron differential cross sections averaged over molecular orientations are given by: ds (L,V ) s (L,V ) ) ]] 5 ]] [1 1 b (L,V P2 (cos u )], kˆ 4p dVkˆ

(1)

where s (L,V ) is the total photoionization cross section, obtained with the length (L) or velocity (V ) form of the dipole moment operator. For nonlinear molecules, s (L,V ) is given by:

O

4p 2 E (L,V ) s (L,V ) 5 ]] uI p m u 2 , 3c p m lhv lhv

(2)

where E is the photon energy, p is one of the irreducible representations (IR) of the symmetry group of the molecule and h distinguishes between different bases for the same IR corresponding to the same value of l. The index m labels components of vectors belonging to the same IR and v designates components of the dipole moment operator. ) In Eq. (1), b (L,V is the asymmetry parameter kˆ which can be written as: 3 1 ) b (L,V 5 ] ]]]] (1100u20) kˆ m (L,V ) 2 5 uI plhv u

O

p m lhv

O

3

(L,V )

pm (21)m92m v I lhv

m (L,V ) * p m p9 m 9 I lp9h9v 9 b lhm b l 9h9m9

p m lhvmm v p9 m 9l 9h9v9m9m v 9 v m v p v 9 mv 9 3 b plvm b [(2l 1 1)(2l9 1 1)] 1 / 2 v l 9v9m v 9

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3 (11 2 m v9 m v u2M9)(l9l00u20)(l9l 2 m9mu2 2 M9). (3) (L,V )

m The quantities I plhv appearing in Eqs. (2) and (3) are the partial-wave components of the dynamical ) coefficients I (L,V k,nˆ ,

S D OI

4p ) ] I (L,V k,nˆ 5 3

1/2

p m (L,V ) lhv

X plhm (kˆ )X p1vv mv (nˆ )

(4)

p m lhv

where (L )

I k,nˆ 5 (k)

1/2

(2) kCi ur ? nˆ uC k l

(5)

and (k)1 / 2 ) ]] I (V 5 kCi u=? nˆ uC (2) k,nˆ k l. E

(6)

In Eq. (4) X plhm are the symmetry-adapted functions [18], that are related to the usual spherical harmonics by

Ob

X plhm (rˆ ) 5

m

pm lhm lm

Y (rˆ ),

(7)

whereas in Eqs. (5) and (6) Ci is the target ground state wave function, Ck the final state wavefunction of the system (ion plus photoelectron), the superscript ( 2 ) denotes the incoming-wave boundary condition, nˆ represents the unit vector along the radiation polarization direction and k is the photoelectron momentum. In the present study, Ci is a one-determinant wavefunction calculated self-consistently at the Hartree–Fock (SCF–HF) level. The final molecular state is described by a single electronic configuration in which the ionic orbitals are constrained to be identical to those of the initial ground state. In this approximation, the photoelectron orbital is a solution ¨ of the one-electron Schrodinger equation

F

G

1 k2 2 ] = 2 1V SEP(r) 1 ] f k(2) (r) 5 0, 2 2

(8)

with V SEP(r) 5VN21 (r) 1Vcp (r)

(9)

where VN21 (r) is the static-exchange potential of the molecular ion and Vcp (r) is a correlation–polarization model potential. In our calculation, VN 21 (r) is obtained exactly from the SCF–HF target wavefunction

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within the framework of the frozen-core (FC) approximation. A parameter-free model potential introduced by Padial and Norcross [19] is used to account for the correlation–polarization contributions. In that model, a short-range correlation potential between the photoelectron and the target electrons is defined in an inner region and an asymptotic-form polarization potential in an outer region. The first crossing of the correlation and polarization potential curves defines the inner and the outer regions. To proceed, Eq. (8) is rewritten in an integral form, the Lippmann–Schwinger equation, and is solved using an iterative procedure based on the Schwinger variational principle. This method provides continuum wavefunctions that are shown to converge to the exact solutions for a given photoelectron–target interaction potential [20]. The SCF–HF ground state wavefunction used in the present calculation was obtained using the [9s5p / 5s3p] contracted Gaussian basis of Dunning [21] on the C center, augmented with three s (a 5 0.0473, 0.0125 and 0.0045), three p (a 5 0.0365, 0.0125, 0.0035) and three d (a 50.626, 0.15, 0.0375) uncontracted functions, and the [9s5p / 4s2p] contracted Cartesian Gaussian basis set of Dunning [21] on the F centres, augmented with one uncontracted d function (a 5 1.58). At the equilibrium geometry of the ground state [18,19], this basis set gives an SCF energy of 2 435.76738 a.u., in excellent agreement with the calculated value 2 435.76776 a.u. of Winstead et al. [22]. In order to verify the influence of the basis sets on the calculation of both s and b, test runs were carried out using a larger basis set including more diffuse functions centered on both C and F nuclei. No relevant differences in those quantities were observed. The only empirical parameters used in the Padial and Norcross model [19] for the polarization part of the Vcp potential are the molecular ion polarizabilities that are required to adequately describe the asymptotic form of that part of the potential. In the present case the experimental value a0 5 25.93 a.u. [23] for the spherical polarizability of neutral CF 4 was used instead of the corresponding ionic one. In the generation of the correlation part of Vcp we have used the FC electronic density of the CF 41 ion. The numerical calculation of the scattering wavefunctions was performed using our SVIM

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codes, developed for molecular systems with symmetries reducible to C2v . The potential field of 2 2 2 all degenerate ionic ( T 2 , T 1 , E) states was constructed assuming that the corresponding C2v -reduced components (A 1 , A 2 , B1 and B2 ) of the hole orbital were equally depopulated. This procedure was adopted in our recent study on the photoionization of silane [12] and has proved to yield results in good agreement with experiment. The cross sections were evaluated by adding up the dipole-allowed contributions: a 1 → ka 1 , kb 1 , kb 2 ; a 2 → ka 2 , kb 1 , kb 2 ; b 1 → ka 1 , ka 2 , kb 1 ; and b 2 → ka 1 , ka 2 , kb 2 , while the asymmetry parameters were obtained as an average over the components taking the corresponding cross sections as weights. All matrix elements arising in the SVIM calculation were evaluated using a single-center expansion truncated at l max 5 20. All allowed h # l values were retained for a given l. In order to verify the convergence in the partial-wave expansion of the continuum wavefunction, some test calculations were carried out also with l max 5 22. No relevant differences have been noticed in the calculated cross sections with these two cutoff parameters, showing that the calculations have already converged. The basis set used to construct the trial solution of Eq. (8) is given in Table 1. All cross sections shown below were converged within 6 iterations.

3. Results and discussion Our calculated partial photoionization cross sections and photoelectron angular distributions for ionization of the ground state of CF 4 leading to the different ionic states will be presented separately below.

3.1. 1 t1 ( I.P. 5 16.191 eV) Fig. 1(a) shows our calculated s, in both dipolelength (DL) and dipole-velocity (DV) forms, for the photoionization out of the 1t 1 orbital of CF 4 , along with the experimental data of Carlson et al. [3] and with the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] and the MSAA theoretical results of Rosi et al. [7]. According to Stephens et al.

[6], the experimental s of Carlson et al. [3] exhibit three structures, namely, a small shoulder centered at photon energies around 17 eV, a shoulder at around 24 eV and a broad peak extending from 25 to 35 eV, approximately. The MS-Xa results of Stephens et al. [6] and the MSAA results of Rosi et al. [7] have shown a very sharp peak near threshold, identified by them as a t 2 shape resonance. This structure is not reproduced by the MS-Xa results of Rosi et al. [7]. According to these authors, this peak is of unphysical nature and would be shifted to below threshold by the use of an appropriate interaction potential in the calculation of the continuum wave functions. In addition, the MS-Xa results of Stephens et al. [6] show a very broad structure centered at around 28 eV, considered by them as a nonresonant increase in the cross sections. Also, the shoulder at around 24 eV was assigned as the result of an interchannel coupling with one or more other valence levels. The broad structure was also seen at around 26 eV in both calculations of Rosi et al. [7], who identified it as a shape resonance of e symmetry. On the other hand, our calculated s show no structure near threshold, thus indicating that the small experimental shoulder around 17 eV is probably due to a statistical fluctuation. Also our results confirm Rosi et al.’s hypothesis of an unphysical nature of the sharp peaks in their and Stephens et al.’s cross sections near threshold. In fact, our calculation has shown only two structures, centered at around 25 and 34 eV. Based on an eigenphase sum analysis, the first one was identified as a t 2 shape resonance that should correspond to the experimental shoulder at around 24 eV, in contrast to Stephens et al.’s interpretation. Also, the second structure was identified as an a 1 broad shape resonance that should be associated with the 25–35 eV broad experimental peak, now in contrast with Rosi et al.’s assignment. It is interesting to note that the positions of our resonances are shifted to higher energies typically by a few eV. This type of shift is frequently observed in calculations using the oneparticle approximation [11,12]. Fig. 1(b) shows our calculated b, in both DL and DV forms, along with the experimental data of Carlson et al. [3] and of Novak et al. [24] and the MS-Xa theoretical results of Stephens et al. [6] and of Rosi et al. [7]. All the theoretical results show a minimum at around 18–20 eV, in good agreement

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Table 1 Starting basis sets used for the trial continuum wavefunction a Symmetry

Center

Basis functions b

Exponents

ka 1

C

s z x 2, s x z x 2, s y z x 2, xy y xy, x xy, y yz y xy, s y z x 2, x xz s x z x 2, x xy,

16.0, 8.0, 4.0, 2.0, 0.5, 0.1, 0.025 5.0, 2.0, 0.5, 0.05 0.2, 0.05 24.0, 12.0, 6.0, 3.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 1.0 24.0, 12.0, 6.0, 3.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 1.0 8.0, 2.0, 0.5, 0.12, 0.03 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 1.0 8.0, 4.0, 1.6, 0.8, 0.4, 0.2, 0.05, 0.01 1.0 16.0, 8.0, 4.0, 2.0, 0.5, 0.1, 0.025 1.0, 0.25 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 1.0, 0.25 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 1.0, 0.25 16.0, 8.0, 4.0, 2.0, 0.5, 0.1, 0.025 1.0, 0.25 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 1.0, 0.25 24.0, 8.0, 3.0, 1.5, 0.75, 0.25, 0.05, 0.01 1.0, 0.25

F1

F2

ka 2

C F1 F2

kb 1

C F1 F2

kb 2

C F1

F2

y 2, z 2

y 2 , z 2 , xz

y 2 , z 2 , yz

yz xz

yz

y 2 , z 2 , yz

y 2 , z 2 , xz xz

a

The basis sets are given for the C2v -reduced components of the scattering functions in the T d symmetry. Cartesian Gaussian basis functions are used. They are defined as f a ,l,m,n,A (r) 5 N(x 2 A x )l ( y 2 A y )m (z 2 A z )n exp(2a ur 2 Au 2 ), with N a normalization constant. b

with the experimental minimum at around 20 eV. This minimum is probably associated with the experimental shoulder seen at around 24 eV. It is interesting to note that despite this minimum being also present in the MS-Xa calculation of Rosi et al. [7], no corresponding structure in their calculated s is observed. In addition, the very shallow depression at around 25 eV seen in our data is probably associated with the broad a 1 shape resonance, shifted to lower photon energies. Quantitatively, the differences between the DL and DV results, as seen in Figs. 1(a) and 1(b), are known to be generally due to the neglect of both electronic correlation in the target wavefunction [8]

and multichannel coupling effects in the photoelectron wavefunction [25].

3.2. 4 t2 ( I.P. 5 17.416 eV) Fig. 2(a) shows our calculated s for the photoionization out of the 4t 2 orbital of CF 4 in both DL and DV forms, along with the experimental results of Carlson et al. [3] and with the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] and the MSAA theoretical results of Rosi et al. [7]. For this photoionization channel, the experimental s of Carlson et al. [3] exhibit two main structures, namely, a broad enhancement of cross sections

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Fig. 1. (a) Photoionization cross sections for the 2 T 1 (1t 21 1 ) state of CF 1 4 . Solid line, present dipole-length results; dotted line, present dipole-velocity results; short-dashed line, MS-Xa results of Stephens et al. [6]; dashed line, MSAA results of Rosi et al. [7]; long-dashed line, MS-Xa results of Rosi et al. [7]; full circles, experimental results of Carlson et al. [3]. (b) Asymmetry parame1 ters for the photoionization of the 2 T 1 (1t 21 1 ) state of CF 4 . Solid line, present dipole-length results; dotted line, present dipolevelocity results; short-dashed line, MS-Xa results of Stephens et al. [6]; long-dashed line, MS-Xa theoretical results of Rosi et al. [7]; full circles, experimental results of Carlson et al. [3]; open triangles, experimental results of Novak et al. [24].

centered at around 21 eV (composed by three partially resolved peaks as stated by Stephens et al. [6]) and a broad maximum centered at around 33 eV. Accordingly, our calculation also exhibits two resonant structures. An eigenphase sum analysis has shown that these structures can be assigned as t 2 and a 1 shape resonances, centered at around 26 and 36 eV, respectively, which can probably be associated with the experimental main structures. As in the previous sub-section, the features interpreted by Stephens et al. as three partially resolved peaks are also probably due to a statistical fluctuation. Again, the peaks in the MS-Xa and the sharp increase in the

1 Fig. 2. Same as Fig. 1, but for the 2 T 2 (4t 21 2 ) state of CF 4 .

MSAA near-threshold calculations of Stephens et al. [6] and Rosi et al. [7], respectively, seem to be of an unphysical nature. Quantitatively, our DV results are in general better agreement with the experimental s. The disagreement between our DL and DV cross sections can again indicate the need for inclusion of target electronic correlation and / or multichannel coupling effects in the calculations. In Fig. 2(b) we show our b for this photoionization channel. The experimental results of Carlson et al. [3] and Novak et al. [24] and the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] are also shown for comparison. The experimental b of Carlson et al. [3] exhibit two local minima at around 24 and 32 eV, respectively. Our calculated data show a depression at around 28 and a minimum at around 34 eV, which would correspond to the t 2 and a 1 shape resonances, respectively, seen in our cross sections. The minima seen in both MS-Xa results for b above 20 eV could be associated with possible resonances shifted to higher energies, not addressed by the authors [6,7]. Quan-

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titatively both our DL and DV results systematically overestimate the experimental values of the asymmetry parameter for this channel.

3.3. 1 e ( I.P. 5 18.504 eV) Fig. 3(a) shows our calculated s for photoionization out of the 1e orbital of CF 4 along with the experimental data of Carlson et al. [3] and the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] and the MSAA theoretical results of Rosi et al. [7]. Our calculation shows two enhancements in s, located at around 23 and 36 eV, which are in fair agreement with the corresponding experimental energy positions at around 22.5 and 32.5 eV. The calculated s of Stephens et al. have also shown two maxima, however located at about 19 and 25 eV, respectively. An eigenphase sum analysis has shown that our first maximum corresponds to a shape resonance of t 2 symmetry, as also assigned by Stephens et al. [6] to their peak at 19 eV. In addition, our analysis showed that our second maximum, at 36

107

eV, also corresponds to a t 2 shape resonance, in contrast to that pointed out by Stephens et al. [6] who interpreted their maximum at 25 eV as being nonresonant. It is also possible to notice an enhancement in s in the MS-Xa results of Rosi et al. [7] around 22 eV, although no comments were made by the authors on it. Fig. 3(b) shows our calculated b in both DL and DV forms, along with the experimental data of Carlson et al. [3] and Novak et al. [24] and the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7]. The experimental data of Carlson et al. [3] have exhibited a minimum at around 23 eV, which could be associated with the enhancement in the experimental s around 22.5 eV. The MS-Xa calculation of Stephens et al. [6] has also shown a minimum structure, although shifted to 21 eV. On the other hand, our calculation has shown a shallow minimum located at around 28 eV. We believe that this minimum is associated with the second t 2 shape resonance, although shifted 8 eV to lower energy relative to the position of the maximum structure in our s. A deeper minimum associated with the first resonance has probably been shifted to below threshold in our calculation.

3.4. 3 t2 ( I.P. 5 22.042 eV)

Fig. 3. Same as Fig. 1, but for the 2 E(1e 21 ) state of CF 41 .

Fig. 4(a) shows our calculated photoionization cross sections for the 3t 2 orbital of CF 4 along with the experimental data of Carlson et al. [3] and with the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] and the MSAA theoretical results of Rosi et al. [7]. The experimental s of Carlson et al. [3] exhibit two structures, namely, a peak centered at photon energies around 23 eV and a very broad structure extending from 28 to 50 eV, approximately. The MS-Xa results of Stephens et al. [6] have shown two very sharp peaks near threshold, identified by them as a t 2 and an a 1 shape resonance. These structures are not reproduced by the MS-Xa results of Rosi et al. [7]. In addition, both MS-Xa calculations [6,7] have also shown a very broad structure centered at around 40 eV. No comments on this structure were made by the authors. On the other hand, our calculation shows one broad peak centered around 30 eV and a shoulder at around 36 eV. Our

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2

21

1

Fig. 4. Same as Fig. 1, but for the T 2 (3t 2 ) state of CF 4 .

1 Fig. 5. Same as Fig. 1, but for the 2 A 1 (4a 21 1 ) state of CF 4 .

3.5. 4 a1 ( I.P. 5 25.035 eV) eigenphase sum analysis has shown that the broad peak indeed corresponds to a t 2 shape resonance, which can be associated with the experimental peak at around 23 eV. However, that analysis was unconclusive whether that shoulder (at around 36 eV) can or cannot be related to a shape resonance. Fig. 4(b) shows our calculated asymmetry parameter for this photoionization channel, along with the experimental data of Carlson et al. [3], Novak et al. [24] and the theoretical results of Stephens et al. [6] and Rosi et al. [7]. Our calculated results, both in DL and DV forms, show a broad minimum located at around 38 eV. From our previous experience, the minima in b corresponding to an assigned resonance are usually shifted towards lower photon energies. For this reason, we are not confident to associate that minimum in b with the t 2 shape resonance. As discussed in the previous photoionization channel, a minimum associated with the t 2 resonance has probably also been shifted to below threshold in our calculation.

Fig. 5(a) shows our calculated photoionization cross sections for the 4a 1 orbital of CF 4 along with the experimental data of Carlson et al. [3] and with the MS-Xa theoretical results of Stephens et al. [6] and Rosi et al. [7] and the MSAA theoretical results of Rosi et al. [7]. A very broad enhancement in s is seen in the experimental data near 38 eV. Stephens et al.’s calculation predicted a very sharp t 2 shape resonance near the photon energy of 26 eV. However, this structure was not associated by them with the experimental one because it was located 13 eV below the experimental energy position. On the other hand, the experimental structure is well reproduced by our calculations, though shifted towards higher energies ( | 41 eV). An eigenphase sum analysis has shown that this feature is in fact a t 2 shape resonance. The MSAA results of Rosi et al. [7] have also shown a broad enhancement centered at around 31 eV. Nevertheless, no comments on this structure were addressed by the authors.

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In Fig. 5(b) we show our results for the asymmetry parameter for the photoionization from the 4a 1 orbital of CF 4 along with the experimental data of Carlson et al. [3] and of Novak et al. [24] and with the MS-Xa theoretical results of Stephens et al. [6]. There is a good qualitative agreement between our calculated results and both experimental data. Our calculation predicts a minimum at around 28 eV and 30 eV, for the DV and DL forms, respectively, which agrees reasonably well with the experimental data of Carlson et al. [3]. This minimum, although shifted to lower energies, can probably be associated with that same t 2 shape resonance seen in the cross sections. It is interesting to note that the MS-Xa results of Stephens et al. [6] also show a minimum at about the same energy region.

4. Concluding remarks We have reported cross sections and asymmetry parameters for the photoionization of the five outermost valence orbitals of CF 4 , both in length and velocity forms. To our knowledge, this is the first theoretical study that reports results of these physical quantities for valence-shell photoionization of CF 4 at the SEP level. Although our calculated cross sections in general do not agree quantitatively well with the available experimental data, our method was capable of identifying most of the structures seen both in s and b. The significant discrepancies between the calculated dipole-length and dipole-velocity cross sections are probably due to the lack of electronic correlation in our target wave function and / or multichannel coupling effects.

Acknowledgements This research was partially supported by Brazilian agencies CNPq, FINEP-PADCT, CAPES-PADCT and FAPESP.

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