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Rydberg series of valence and core excited inert-gas atoms: Effects of electron relaxation
CHEMICAL PHYSICS LETTERS
me 79, number 3
RYDBERG EFFECTS
SERIES OF VALENCE OF ELECTRON
AND CORE EXCITED
RELAXATION
1 May 1981
INERT-GAS ATOMS:
+
S. BARONI, A. QUATTROPANI Laboratoire
de Physique
Th&onque. Ecole Polytechnrque
F&d&ale de Luusanne, Lausanne. Switzerland
and A. BALDERESCHI Laboratoire
de Physique Appliquie,
Ecole Poly:echnique
F&d&ale de Luusanne, Lausanne. Switzerland
Received 23 January 1981
The sinularitiesbetween core and valence Rydberg series observed in inert-gasatoms are explained by the electron density relaxation which extends up to the outer atomic shell, regardlessof the localization of the hole.
xperimental interest has been growing [l-6] on 2ydberg series of inert-gas atoms corresponding te excitation of a core or valence electron from orbital {v, h} to excited orbitals {n, I}. nalysis of the various Rydberg series of a given .gas atom has led us to notice that the {n, I} values, i.e. the energy difference between ex1states and the corresponding ionization limit, are bstindependent on the hole quantum numbers L} when multiplet structure is subtracted. Even in :xtreme limit of the Rydberg series associated the K edge {Y = 1, X = 0), the observed term :s [ 1,3] differ little from the well-known valence
[61-
hese results are hardly understandable within the : frozen-core method based on atomic orbitals In this method rhe excited electron is assumed to : in the field of the nucleus and of all the other rons “frozen” in a given configuration independent re outer electron (field of the “residue”). Using the .als of the atomic ground state, the electronic ;e density of the residue and therefore the effecBeld felt by the excited electron depends strongly te localization of the hole _ kially supported by the ConsiglioNazionale delle Bicerche, ne, Italy. 9-2614/81/0000-0000/$02.50
In this letter, we show that in inert-gas atoms, the electronic relaxation [8], due to the creation of a core hole, is very strong and such that similar Rydberg series are obtained for both core and valence excitations in agreement with experimental findings. We study both core and valence excitations using the H-F frozen-core method based on (i) the SCF orbitals of the atomic ground state as calculated in ref. [9] (frozenatom scheme) and (ii) the SCF orbitals of the ion with a {Y, X} hole whrch have been calculated in the present work (frozen-ion scheme). While electronic relaxation is disregarded in the former scheme, most of it is included in the latter. Indeed, even in the frozen-ion scheme, we neglect the difference among the electronic relaxations of different {n, I) states for the same {Y, X) Rydberg series and for all states we use the orbitals of the ion corresponding to the series limit. This approximation is justified by the delocalized characrer of the {n, r} excited orbitals and has been verified by full SCF calculations of the excited atom for several series among those reported in this work. We first show that large differences exist between the charge distribution of the residue to be employed in the frozen-atom and in the frozen-ion schemes. To this end, we defme an “effective {v, X) hole” through its radial charge density
0 North-Holland Publishing Company
509
Volume 79. number 3
CHEMICAL PHYSKS
(1) where PC{ (r) IS the electronic charge density of the {v, A) IOII and depends on the scheme, and p(r) IS the SCF electromc charge density of the neutral atom m its ground state. In the frozen-atom scheme P,,h(rj represents the negative charge density of the {?I, X} orbltal of the atonuc ground state. Includmg relaxation, eq. (1) defies the charge density of an effective hole. The strong eiectromc relaxation associated mth the creation of a core hole IS dlustrated m fig 1 where we compare pi,(r) of argon obtamed m the frozen-atom and the frozen-Ion schemes Wrthout relaxation p,&-) extends about one half atomic un,t, whlie relavatlon expands the “effective hole” up to the outer atorruc shell. Furthermore, the integrated charge of the outer lobe of p&) calculated m the frozen-ion scheme IS about one posttlve charge urut. Our results m&cate that this relaxation-Induced transfer occurs for all core holes. The effect of relaxation IS of course less dramatIC for valence holes. Tlus IS vlsuahzed m the insert of fig 1 for the 3p hole UI argon. We now show that the redlstrlbutlon of the electronic charge IS responsible for the observed slmllarlty among Rydberg senes associated with different holes. We calculate the H-F energy of the center of gravity of the {v, X} + {n, I) multlplets and we simply report the term values of the vanous states, which allow one
Fg 1. Radial charge dlstriiutlon of the Is “effecuve hole” pls(r) III argon [see eq (l)] as obtamed III the frozen-Ion (sohd lme) and III the frozenatom (broken hne) schemes. The msert shows the 3p “effective hole” m argon. obtamed m the two schemes
510
1 May 1981
LETTERS
to make a stralghtforwnrd comparison of the different Rydberg series H-F results obtamed using both the frozen-atom scheme and the frozen-ion scheme are reported m table 1 (Ne) and table 2 (Ar), together with available experimental data. We stress that all the data reported m tables 1 and 2 refer to the statlstlcdl average of the multlplet energies corrcspondmg to a given electroruc configuratIon In those cases where some members of the multlplet are not known experimentally, calculated spllttmgs are employed rn order to perform the average. The results reported m tables 1 and 2 show that. wtile the frozen-atom term values strongly depend on the hole, relaxation explams the observed slmllarltles of the Rydberg series Furthermore, the term values evaluated m the frozen-Ion scheme agree with expertment wltlun a few percent. The devlatlons are mostly due to differences rn the correlation energies between the excited state and the appropriate series hmit MoreTable 1 Average term values (III eV) of wlence and core Rydberg series m neon Euperlmental values (cup ) arc reported together with those obtamed m the frozen-ion (i-1) and m the frozen-atom (FA) schemes n,l
u, A 1s ill
3s cup. FI FA
___ ---__ 50 4 803 5 816
-__
?s [2]
2~ I6l
4671 4.945
4 899 4 698 5 000
4s cup FI FA
1 873 2071
1 840 1.899
I 890 1 846 1911
3p cup. FI FA
3 040 2 980 3 969
2 978 2.915 3 095
2.975 2 903 3 056
4p exp. Fl I-A
1410 1 370 1 598
1 370 1.348 1401
1 365 1 344 1 390
3d cup Fl FA
151.5 1.521
i.516 1 520
1 535 1516 1519
4d exp. FI FA
0 852 0 856
0853 0 855
0.857 0.853 0 855
CHEMICAL
Volume 79. number 3
1 May 1981
PHYSICS LE’ITERS
Tab!e 3 Average term v;tiues (m eV) of valence and core Rydberg senes m argon Expenmental values (exp ) are reported together with those obtamed m the frozen-Ion (FI) and m the frozenatom (FA) schemes Il,I
4s exp FI FA
v, A Is [2]
2s
2P 141
3s [S]
3~ 161
3 938 5 103
3 909 4.649
4 246 3 927 4 731
3 820 4 055
4 167 3 819 4 045
1 609 1 664
1 609 1 660
1 684
5s e\p FI FA
1 642 1871
i 634 1 790
1 70 1.639 1 805
4~ exp FI FA
2 730 2 601 3 463
2 584 3 040
2 672 2 585 3 057
2 677 2 530 2 639
2 648 2.5 I4 2.594
5P e’Q FI FA
1 260 1 240 1,448
1 234 I 360
1 234 1.364
1 260 1 216 1.250
I 2.50 1210 1 236
3d cup. FI FA
i-584
3 006
1604 2 790
1.602 2.791
1612 1 759
1.733 I 592 I 678
4d exp FI FA
0 896 1 327
0910 I.303
0 958 0 908 1.304
0913 i -007
0 976 0.901 0.955
1.701
over, for a gven {n, I} such devlatlons are almost mdependent on the hole quantum numbers (u, Xl. Thrs fact suggests that correlation effects can be estrmated through the equivalent core model (Z + 1 model). Regardless of the hole quantum numbers {Y, A}, the correction to a gven term value of an inert-gas atom IS well reproduced by the correctIon which apphes to the correspondmg valence exerted state of the 2 + 1 alkali metal atom. For example, for the excited 4s orbltrd m argon the 2 + 1 model based on data from refs. [6,9] suggests an mcrease of the term values of 0.34 eV mdependent of the quantum numbers of the hole. The energy corrections necessary to explain the experlmental data for 2p and 3p hoks are 0.32 and 0.35 eV respectively. in the frozen-atom scheme, the electromc charge titnbution depends strongly on the shell m which the hole is created and this fact determines the large dependence of the term values on the pru~cipal quan-
0
2
4 t-
bul
Fig 2 Integrated charge drstnbut!ons &h(r) of “effecttve holes” III argon [see eq C!)j as obtamed UI the frozen-Ion scheme. The mserf shows the integrated charge drstnbutrons
evaIuated III the frozen-tom scheme. Sofid lmes (broken hnes) refer to s-I&e (Q-Ike) holes The prmclpal quantum numbers v are mdicated
turn number v of the hole. As shown prevtously, the charge densrty varratrons are strongIy reduced by the electronic relaxation. The resulting effective field felt by the outer electron 1s thus nearly independent on the hole quantum number, gving nse to similar Rydberg senes m correspondence to holes created m different shells Thus effect IS vlsuahzed m fig. 2, where we present the mtegrated charge density
Qv,dr) =
1(r’)2&,,A(rrldr’ ,
(3
0
of the various “effective holes” m argon. We stress that neglectmg relaxatron the function Qy,A(r) would depend strongly on (Y, A) as shown by the frozenatom results gven m the msert of fig. 2. The most compact way to emphasize the mdependence of the hole quantum numbers (v, X) of the Rydberg series is the defmltlon of the corresponding quantum defects, wtuch account for the short-range correctrons to the coulombrc potent&. The experimental and theoretlcal values of the quantum defects &I (P. h} for several Rydberg series m neon and argon are gxven m tables 3 and 4. These defects have been obtamed from term values vrlth Iarge principal quantum number n. The superiority of the frozen-Ion approach compared to the frozen-atom one for the evaluation of 511
Volume
?9, number
CHEMICAL
3
Table 3 Quantum defects 61 (v, A} for core and valence Rydberg serves m neon as calculated III the frozen-atom (FA) and III the frozen-ion (FI) schemes. Experunental values are also given for comparison I
“, A ls [II
2s [2]
2~ [61
s exp FI FA
1 30 142
1 27 1 31
1.31 1 28 1 32
P exp FI FA
0 84 1 05
0 83 081 0 87
0 83 0 81 0 86
d exp. FI FA
000 0.02
001 0.01
0.02 0.01 001
PHYSICS LETTERS
1 hfay 1981
show that this supenonty IS even stronger when one deals with core tramtlons and also applies to the evaluation of term values. We finally remark that not all atoms are expected to have the sunllarlty of Rydberg series which we have discussed here for neon and argon. Atoms with low Z are weakly polanzable and should not show the strong electromc relaxation responsible for thus slmdarlty. On the contrary, heavier atoms have larger polarlzablhtles and therefore our results can be extended to the heavier Inert-gas atoms krypton and xenon. The authors gratefully acknowledge contrlbutrons from J.-J. Fomey and P Malllefer m the prehnunary
stages of tius work.
References Table 4
Quantum defects 61 {v, A} for cme and valence Rydberg
senes in argon as calculated UI the frozen-atom (I-A) and m the frozen-ron (FI) schemes. Experunental values are also gwen for comparison 1
S
p
d
y, h ls [31
2s [4]
2P ISI
3s
3~ [6]
FI FA
2.11 2 28
2 10 2.22
2.1 I 2 23
208 2 13
2.14 2.08 2.12
exp FI FA
I 7 1 67
1.90
1 66 1.81
1.66 1 81
1 67 1.64 1 68
1.68 1 63 1 67
cup. FI FA
0.14 0 78
0 18 0.76
0 30 0 17 076
0 18 0.40
0 30 0 15 0 29
tXp.
transition energies has been dlscussed by Hlrao et al. [ 101 m the case of valence excitations. Our results
512
[II F Wurlleurmer,
Compt Rend Acad. SCI (Parts) 1 (1970) B875; A.P. HItchcock and C E. Bnon, J Phys. B13 (1980) 3269 121 K. Codlmg, R P. hladden and D L Ederer, Phys Rev. 155 (1967) 26, P. hlltchell, J A. Baxter and J. Comer, J Phys B13 (1980) 2817. I31 M. Bremlg. hl H Chen, G-E. Ice, F Parente, B Crasemann and G S Brown, Phys Rev A22 (1980) 520.
[4] G C. Kmg, hl Tronc, F H Read and R C. Bradford, J. Phvs BIO (1977) 2479. . 151 R.P. Madden, D L Ederer and K. Codhng. Phys. Rev 177 (1969) 136 161 C E hfoore, NBS Cucular 467 (NatIonal Bureau of Standards, Washmgron, 1971) 171 W. Hunt and W A. Goddard Ill, Chem Phys Letters 3 (1969)414. ISI P S. Bagus, Phys Rev. 139 (I 965) A6 19. PI E Clement1 and C Roettl, At Data Nucl Data Tables 14 (1974). r101 K Huao and S Huzmaga. Chem Phys. Letters 45 (1977) 5.5
me 79, number 3
RYDBERG EFFECTS
SERIES OF VALENCE OF ELECTRON
AND CORE EXCITED
RELAXATION
1 May 1981
INERT-GAS ATOMS:
+
S. BARONI, A. QUATTROPANI Laboratoire
de Physique
Th&onque. Ecole Polytechnrque
F&d&ale de Luusanne, Lausanne. Switzerland
and A. BALDERESCHI Laboratoire
de Physique Appliquie,
Ecole Poly:echnique
F&d&ale de Luusanne, Lausanne. Switzerland
Received 23 January 1981
The sinularitiesbetween core and valence Rydberg series observed in inert-gasatoms are explained by the electron density relaxation which extends up to the outer atomic shell, regardlessof the localization of the hole.
xperimental interest has been growing [l-6] on 2ydberg series of inert-gas atoms corresponding te excitation of a core or valence electron from orbital {v, h} to excited orbitals {n, I}. nalysis of the various Rydberg series of a given .gas atom has led us to notice that the {n, I} values, i.e. the energy difference between ex1states and the corresponding ionization limit, are bstindependent on the hole quantum numbers L} when multiplet structure is subtracted. Even in :xtreme limit of the Rydberg series associated the K edge {Y = 1, X = 0), the observed term :s [ 1,3] differ little from the well-known valence
[61-
hese results are hardly understandable within the : frozen-core method based on atomic orbitals In this method rhe excited electron is assumed to : in the field of the nucleus and of all the other rons “frozen” in a given configuration independent re outer electron (field of the “residue”). Using the .als of the atomic ground state, the electronic ;e density of the residue and therefore the effecBeld felt by the excited electron depends strongly te localization of the hole _ kially supported by the ConsiglioNazionale delle Bicerche, ne, Italy. 9-2614/81/0000-0000/$02.50
In this letter, we show that in inert-gas atoms, the electronic relaxation [8], due to the creation of a core hole, is very strong and such that similar Rydberg series are obtained for both core and valence excitations in agreement with experimental findings. We study both core and valence excitations using the H-F frozen-core method based on (i) the SCF orbitals of the atomic ground state as calculated in ref. [9] (frozenatom scheme) and (ii) the SCF orbitals of the ion with a {Y, X} hole whrch have been calculated in the present work (frozen-ion scheme). While electronic relaxation is disregarded in the former scheme, most of it is included in the latter. Indeed, even in the frozen-ion scheme, we neglect the difference among the electronic relaxations of different {n, I) states for the same {Y, X) Rydberg series and for all states we use the orbitals of the ion corresponding to the series limit. This approximation is justified by the delocalized characrer of the {n, r} excited orbitals and has been verified by full SCF calculations of the excited atom for several series among those reported in this work. We first show that large differences exist between the charge distribution of the residue to be employed in the frozen-atom and in the frozen-ion schemes. To this end, we defme an “effective {v, X) hole” through its radial charge density
0 North-Holland Publishing Company
509
Volume 79. number 3
CHEMICAL PHYSKS
(1) where PC{ (r) IS the electronic charge density of the {v, A) IOII and depends on the scheme, and p(r) IS the SCF electromc charge density of the neutral atom m its ground state. In the frozen-atom scheme P,,h(rj represents the negative charge density of the {?I, X} orbltal of the atonuc ground state. Includmg relaxation, eq. (1) defies the charge density of an effective hole. The strong eiectromc relaxation associated mth the creation of a core hole IS dlustrated m fig 1 where we compare pi,(r) of argon obtamed m the frozen-atom and the frozen-Ion schemes Wrthout relaxation p,&-) extends about one half atomic un,t, whlie relavatlon expands the “effective hole” up to the outer atorruc shell. Furthermore, the integrated charge of the outer lobe of p&) calculated m the frozen-ion scheme IS about one posttlve charge urut. Our results m&cate that this relaxation-Induced transfer occurs for all core holes. The effect of relaxation IS of course less dramatIC for valence holes. Tlus IS vlsuahzed m the insert of fig 1 for the 3p hole UI argon. We now show that the redlstrlbutlon of the electronic charge IS responsible for the observed slmllarlty among Rydberg senes associated with different holes. We calculate the H-F energy of the center of gravity of the {v, X} + {n, I) multlplets and we simply report the term values of the vanous states, which allow one
Fg 1. Radial charge dlstriiutlon of the Is “effecuve hole” pls(r) III argon [see eq (l)] as obtamed III the frozen-Ion (sohd lme) and III the frozenatom (broken hne) schemes. The msert shows the 3p “effective hole” m argon. obtamed m the two schemes
510
1 May 1981
LETTERS
to make a stralghtforwnrd comparison of the different Rydberg series H-F results obtamed using both the frozen-atom scheme and the frozen-ion scheme are reported m table 1 (Ne) and table 2 (Ar), together with available experimental data. We stress that all the data reported m tables 1 and 2 refer to the statlstlcdl average of the multlplet energies corrcspondmg to a given electroruc configuratIon In those cases where some members of the multlplet are not known experimentally, calculated spllttmgs are employed rn order to perform the average. The results reported m tables 1 and 2 show that. wtile the frozen-atom term values strongly depend on the hole, relaxation explams the observed slmllarltles of the Rydberg series Furthermore, the term values evaluated m the frozen-Ion scheme agree with expertment wltlun a few percent. The devlatlons are mostly due to differences rn the correlation energies between the excited state and the appropriate series hmit MoreTable 1 Average term values (III eV) of wlence and core Rydberg series m neon Euperlmental values (cup ) arc reported together with those obtamed m the frozen-ion (i-1) and m the frozen-atom (FA) schemes n,l
u, A 1s ill
3s cup. FI FA
___ ---__ 50 4 803 5 816
-__
?s [2]
2~ I6l
4671 4.945
4 899 4 698 5 000
4s cup FI FA
1 873 2071
1 840 1.899
I 890 1 846 1911
3p cup. FI FA
3 040 2 980 3 969
2 978 2.915 3 095
2.975 2 903 3 056
4p exp. Fl I-A
1410 1 370 1 598
1 370 1.348 1401
1 365 1 344 1 390
3d cup Fl FA
151.5 1.521
i.516 1 520
1 535 1516 1519
4d exp. FI FA
0 852 0 856
0853 0 855
0.857 0.853 0 855
CHEMICAL
Volume 79. number 3
1 May 1981
PHYSICS LE’ITERS
Tab!e 3 Average term v;tiues (m eV) of valence and core Rydberg senes m argon Expenmental values (exp ) are reported together with those obtamed m the frozen-Ion (FI) and m the frozenatom (FA) schemes Il,I
4s exp FI FA
v, A Is [2]
2s
2P 141
3s [S]
3~ 161
3 938 5 103
3 909 4.649
4 246 3 927 4 731
3 820 4 055
4 167 3 819 4 045
1 609 1 664
1 609 1 660
1 684
5s e\p FI FA
1 642 1871
i 634 1 790
1 70 1.639 1 805
4~ exp FI FA
2 730 2 601 3 463
2 584 3 040
2 672 2 585 3 057
2 677 2 530 2 639
2 648 2.5 I4 2.594
5P e’Q FI FA
1 260 1 240 1,448
1 234 I 360
1 234 1.364
1 260 1 216 1.250
I 2.50 1210 1 236
3d cup. FI FA
i-584
3 006
1604 2 790
1.602 2.791
1612 1 759
1.733 I 592 I 678
4d exp FI FA
0 896 1 327
0910 I.303
0 958 0 908 1.304
0913 i -007
0 976 0.901 0.955
1.701
over, for a gven {n, I} such devlatlons are almost mdependent on the hole quantum numbers (u, Xl. Thrs fact suggests that correlation effects can be estrmated through the equivalent core model (Z + 1 model). Regardless of the hole quantum numbers {Y, A}, the correction to a gven term value of an inert-gas atom IS well reproduced by the correctIon which apphes to the correspondmg valence exerted state of the 2 + 1 alkali metal atom. For example, for the excited 4s orbltrd m argon the 2 + 1 model based on data from refs. [6,9] suggests an mcrease of the term values of 0.34 eV mdependent of the quantum numbers of the hole. The energy corrections necessary to explain the experlmental data for 2p and 3p hoks are 0.32 and 0.35 eV respectively. in the frozen-atom scheme, the electromc charge titnbution depends strongly on the shell m which the hole is created and this fact determines the large dependence of the term values on the pru~cipal quan-
0
2
4 t-
bul
Fig 2 Integrated charge drstnbut!ons &h(r) of “effecttve holes” III argon [see eq C!)j as obtamed UI the frozen-Ion scheme. The mserf shows the integrated charge drstnbutrons
evaIuated III the frozen-tom scheme. Sofid lmes (broken hnes) refer to s-I&e (Q-Ike) holes The prmclpal quantum numbers v are mdicated
turn number v of the hole. As shown prevtously, the charge densrty varratrons are strongIy reduced by the electronic relaxation. The resulting effective field felt by the outer electron 1s thus nearly independent on the hole quantum number, gving nse to similar Rydberg senes m correspondence to holes created m different shells Thus effect IS vlsuahzed m fig. 2, where we present the mtegrated charge density
Qv,dr) =
1(r’)2&,,A(rrldr’ ,
(3
0
of the various “effective holes” m argon. We stress that neglectmg relaxatron the function Qy,A(r) would depend strongly on (Y, A) as shown by the frozenatom results gven m the msert of fig. 2. The most compact way to emphasize the mdependence of the hole quantum numbers (v, X) of the Rydberg series is the defmltlon of the corresponding quantum defects, wtuch account for the short-range correctrons to the coulombrc potent&. The experimental and theoretlcal values of the quantum defects &I (P. h} for several Rydberg series m neon and argon are gxven m tables 3 and 4. These defects have been obtamed from term values vrlth Iarge principal quantum number n. The superiority of the frozen-Ion approach compared to the frozen-atom one for the evaluation of 511
Volume
?9, number
CHEMICAL
3
Table 3 Quantum defects 61 (v, A} for core and valence Rydberg serves m neon as calculated III the frozen-atom (FA) and III the frozen-ion (FI) schemes. Experunental values are also given for comparison I
“, A ls [II
2s [2]
2~ [61
s exp FI FA
1 30 142
1 27 1 31
1.31 1 28 1 32
P exp FI FA
0 84 1 05
0 83 081 0 87
0 83 0 81 0 86
d exp. FI FA
000 0.02
001 0.01
0.02 0.01 001
PHYSICS LETTERS
1 hfay 1981
show that this supenonty IS even stronger when one deals with core tramtlons and also applies to the evaluation of term values. We finally remark that not all atoms are expected to have the sunllarlty of Rydberg series which we have discussed here for neon and argon. Atoms with low Z are weakly polanzable and should not show the strong electromc relaxation responsible for thus slmdarlty. On the contrary, heavier atoms have larger polarlzablhtles and therefore our results can be extended to the heavier Inert-gas atoms krypton and xenon. The authors gratefully acknowledge contrlbutrons from J.-J. Fomey and P Malllefer m the prehnunary
stages of tius work.
References Table 4
Quantum defects 61 {v, A} for cme and valence Rydberg
senes in argon as calculated UI the frozen-atom (I-A) and m the frozen-ron (FI) schemes. Experunental values are also gwen for comparison 1
S
p
d
y, h ls [31
2s [4]
2P ISI
3s
3~ [6]
FI FA
2.11 2 28
2 10 2.22
2.1 I 2 23
208 2 13
2.14 2.08 2.12
exp FI FA
I 7 1 67
1.90
1 66 1.81
1.66 1 81
1 67 1.64 1 68
1.68 1 63 1 67
cup. FI FA
0.14 0 78
0 18 0.76
0 30 0 17 076
0 18 0.40
0 30 0 15 0 29
tXp.
transition energies has been dlscussed by Hlrao et al. [ 101 m the case of valence excitations. Our results
512
[II F Wurlleurmer,
Compt Rend Acad. SCI (Parts) 1 (1970) B875; A.P. HItchcock and C E. Bnon, J Phys. B13 (1980) 3269 121 K. Codlmg, R P. hladden and D L Ederer, Phys Rev. 155 (1967) 26, P. hlltchell, J A. Baxter and J. Comer, J Phys B13 (1980) 2817. I31 M. Bremlg. hl H Chen, G-E. Ice, F Parente, B Crasemann and G S Brown, Phys Rev A22 (1980) 520.
[4] G C. Kmg, hl Tronc, F H Read and R C. Bradford, J. Phvs BIO (1977) 2479. . 151 R.P. Madden, D L Ederer and K. Codhng. Phys. Rev 177 (1969) 136 161 C E hfoore, NBS Cucular 467 (NatIonal Bureau of Standards, Washmgron, 1971) 171 W. Hunt and W A. Goddard Ill, Chem Phys Letters 3 (1969)414. ISI P S. Bagus, Phys Rev. 139 (I 965) A6 19. PI E Clement1 and C Roettl, At Data Nucl Data Tables 14 (1974). r101 K Huao and S Huzmaga. Chem Phys. Letters 45 (1977) 5.5