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Scattering of slow electrons from excited atoms: The dominant role of the polarization potential
Physics Letters A 173 (1993) 78-82 North-Holland
PHYSICS LETTERS A
Scattering of slow electrons from excited atoms: The dominant role of the polarization potential L o u c a s G . C h r i s t o p h o r o u 1 and Eugen I l l e n b e r g e r Institut )~r Physikalische und Theoretische Chemie, Freie Universitiit Berlin, Takustrasse 3, W: 1000 Berlin 33, Germany Received 3 September 1992; revised manuscript received 19 November 1992; accepted for publication 20 November 1992 Communicated by B. Fricke
The total electron scattering cross sections from ground state and excited atoms are correlated with their static polarizabilities.
The systematic study o f the interactions o f slow electrons with excited a t o m s and molecules is just beginning, although calls for such studies trace back decades. Experimental and theoretical studies on electron scattering from v i b r a t i o n a l l y / r o t a t i o n a l l y excited molecules revealed many and often profound changes in the scattering [ 1,2 ] and electron a t t a c h m e n t / d e t a c h m e n t [1,3 ] cross sections. Large increases have been reported also in electron scattering from [ 1,4 ] and in particular in dissociative a t t a c h m e n t o f electrons to [ 1,5 ] electronically excited molecules. Similarly, experimental and theoretical studies on electron-excited a t o m interactions have shown that often e n o r m o u s increases in the electron scattering and ionization occur [ 6 ]. Such studies include those on electron scattering from excited He [7,8], Ar [9], Na [ 10-15 ] and Ba [ 16 ] a t o m s a n d electron impact ionization o f excited H [ 17,18 ], He [ 19-23 ], Ne [22,24], Ar [22], Ba [25] and Sr [26] atoms. The results o f optical m e t h o d s [ 6,27 ] also show consistently larger cross sections for the excited atoms, and the limited theoretical studies on excited atoms [28 ] support the experimental findings and indicate the d o m i n a n t role played by the dipole polarizability in the scattering process. In this Letter we draw attention to a rather quanHolder of the Alexander von Humboldt Senior US Award; Permanent address: Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 78
titative correlation between the total electron scattering cross section and the static dipole polarizability o f the ground and excited states o f a t o m s as is predicted by Vogt and W a n n i e r [29]. Vogt and W a n n i e r considered the m o t i o n o f ions or electrons in gases when the interaction potential between the two is simply the polarization function i e2of
V(r)-
2 r4 '
(l)
where e is the elementary charge, a is the atomic ( m o l e c u l a r ) polarizability and r is the distance between the electron and the atom. F r o m a q u a n t u m mechanical description o f the polarization potential, they obtained for the capture cross section the expression ryv,w = 4 ~ ( e 2 a / m v 2 ) 1/2
(2)
where m and v are, respectively, the mass and the velocity o f the electron. The av,w in ( 2 ) is twice the classical capture cross section for spiralling orbits over a wide range o f v [29]. Equation ( 2 ) can be written as av.w=4~aZ( of / 2 E ) t/2
= 2 . 4 8 7 × l O - ' 6 ( a / E ) '/2
(3)
where ao is the Bohr radius ( 5 . 2 9 1 7 2 × 10 - 9 c m ) , of is in atomic units (1 a . u . = a o3 = 0 . 1 4 8 2 ~ 3 ) , E is the electron energy in atomic units (1 a . u . = 1 hartree =27.21165 eV) and av,w is in cm 2.
0375-9601/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 173, number 1
PHYSICS LETTERS A
25 January 1993
Table 1 Static dipole polarizabilities, ~t, of ground state and excited atoms (in atomic units a3; ao3 = 0.1482 X 10-24 era3= 0.1482 A 3) Atom
a(a~)
He
ISo !.366 1.382 1.384 1.383 [1.381
Ar
23S [30] [31] [32] [33] ")
3 tSo 11.07 [32,36] e) [ll.07]
Na
32S~/2 160.0 [39] 159.2 [38] ~) 159.5 [40] 162.6 [41] 164.64 [42] ¢~ 164.8 [43] 165.02 [44] 165.5 [45] [161.91 e>
K
4 ISo 286.7 [39] 287.6 [441 288.1 [41] 292.8 [38] ¢) 301.4 [43] 305.0 [42] ¢) 308.57 [45] [298.9] a)
2 IS
312.6 [30] 316.2 [311 316.2 [32] b~ [315.01
773.1 [30] 802.3 [31] 803.3 [34] b) [792.9]
33p2 313.1 [371 ~) 323.2 [38] ¢) [318.2] Sstates(4s)
2939 [46] 2962 [39] f)
S states ( 5 s)
4585 [46]
P states (3 p ) 362 [461 368.4 [39] B~ 441.2 [45] 341.1 [47] ¢) 367.3 [39] 355.4 [47] e),h) 368.9 [39] [362.2] °
Na*(32p1/2) Na*(32p1/2)
Na*(3 2p3/2) Na* ( 3 2p3/2)
P states (4 p)
625 [46] 645.37 [45] 655.0 [48] c~ 622.9 [39] 635.0 [39]
K*(4 2P1/2) K*(4 2p3/2)
a~ The bracketed values are the ones used in fig. 1 and throughout the present discussion. For a review of atomic (and molecular) polarizabilities see ref. [ 35 ]. b) See this reference for a listing of earlier theoretical values. o All these values are experimental; the rest are the results of calculations. d~ Average of the two experimental values. e~ Values listed in column b of table 5 of this reference. f~ For the 42S~/2 state. g~ Average for the P states as quoted in ref. [ 39 ]. h~ Average of ix(3 2p3/2, M j = +_½) and a ( 3 2P3/2, Mj-- -I- 3 ) given in this reference. i~ Average of the two values listed for Na*(32pa/2).
In table 1 are listed the static dipole polarizabilities f o r t h e g r o u n d s t a t e o f H e , A r a n d N a a n d f o r some of their excited states for which total electron
s c a t t e r i n g cross s e c t i o n s h a v e b e e n m e a s u r e d ; also l i s t e d i n t a b l e 1 a r e r e l e v a n t d a t a f o r K. T h e g r o u n d s t a t e r a r e gas a t o m s h a v e low v a l u e s o f a d u e to t h e i r 79
Volume 173, number 1
PHYSICS LETTERS A
closed-shell structure, but when excited, the loosely bound electron increases their polarizability substantially. On the other hand, the polarizability of the alkali atoms is already large in their ground state since a single outer valence electron is loosely bound in an s-orbital of large radius. The ot of the excited alkali atoms is larger compared to the ground state, but the relative increase is not as large as for the rare gas atoms. In fig. 1 are plotted the measured total electron scattering cross sections which are available in the literature for these species as a function of ( a / E)1/2 along with the prediction of eq. (3). The cross sections decrease monotonically with increasing E. The experimental measurements - especially those for the alkali metals - are in a rather good agreement with the predicted dependence of the cross section, a~,.~ on (or~E) j/2. The magnitude of c~ largely accounts for the scattering (it is interesting to note (fig. 1 ) that even the electron scattering cross section for
10©0 ........
100
A ~i i •" ~_ ~ .....
oy OZ~
¢,)
2
O'v,w
IC)
C
10
/
yO,~e
•
1
10
100
(a/E) 1/e (au) 1/z
1000
Fig. 1. Total electron scattering cross sections plotted versus (a/E)t/2for (O) He (1 ISo) [49], ( 0 ) He*(2tS) [8], (V) He*(23S) [8], (A) He*(23S) [7], (A) Na(32Si/2) [50], (rq) Na*(32P3/2) [ 10-12], (m) Ar*(3p2+3po) [9] and (O) K(4 ISo) [501. a~,~ (eq. (3)),
80
25 January 1993
the ground state of He approaches a~,wat high energies); the effect of the core and resonance phenomena seem not to be significant. The dominant role of the dipole polarizability can be further seen from the measurements on the differential electron scattering cross sections for ground state and excited atoms. Thus the measurements of Miiller-Fiedler et al. [ 51 ] on the differential electron scattering cross sections for the transitions e ( E ~ 30 eV) + He*(2 3S) ~He*(2 3P) + e ( E ' )
(4)
and e ( E ~ 3 0 e V ) + H e ( l tS)-+He*(2 3P) + e ( E " )
(5)
(i.e., for excitation by 30 eV electrons of the 2 3p excited state of He, respectively, from the excited state 2 3S and from the ground state 1 ~S) showed that the cross section for the excited state (reaction (4)) is up to 105 times larger compared to the ground state (reaction (5)). The maximum enhancement is for small angles (forward scattering) as is to be expected (Flannery and McCann [ 28 ] ) for the distant collisions involved in the electron-induced dipole scattering. The excited state enhancement is expected to be a function of the excited state itself and of the electron energy [ 51 ]. It can, thus, be concluded from these rather limited studies that electron scattering from excited atoms (and perhaps to a lesser degree from electronically excited molecules) can be as much as 105 times larger compared to their respective ground states depending on the excited state, the electron energy and the scattering angle. These increases are principally the consequence of the larger polarizabilities of the excited states. The Vogt-Wannier "limiting case" formula ( 3 ) predicts reasonably well the magnitude of the total electron scattering cross section and clearly indicates that the cross section can be very large depending on the magnitude of both a and E. For example, for a = 3 × 103 a.u. and E = 5 meV, O.v,w: 10-12 c m 2 ))l
We acknowledge useful discussions with Professors H. Baumg~irtel, K.H. Bennemann, B. Brutschy, #1
The polarizabilities of high-lying excited electronic states can be very large. Polarizabilities of the order of 10 10ao3 have been measured for atoms in Rydberg orbitals [35 ].
Volume 173, number 1
PHYSICS LETTERS A
V. Bonacic-Koutecky and J. Koutecky of the Freie Universit~it Berlin, Professor H. Hotop and H. Ehrhardt of Kaiserslautern University, and Drs. P.G. Datskos and L.A. Pinnaduwage of Oak Ridge National Laboratory. We also thank Dr. S. Trajmar for a preprint of ref. [ 6 ]. LGC thanks the HumboldtStiftung for the Senior US Scientist Award. Research sponsored, in part, by the US Department of Energy under Contract DE-ACOS-84 OR 214 00 with Martin Marietta Energy Systems, Inc.
References [ 1 ] L.G. Christophorou, Electron-excited molecule interactions, Invited general lecture, in: Proc. XXth Int. Conf. Phenomena ionized gases, Il Ciocco, Italy, 8-12 July 1991, in press. [2] S.J. Buckman, M.T. Eiford and D.S. Newman, J. Phys. B 20 (1987) 5175; G.N. Haddad and M.T. Elford, J. Phys. B 12 (1979) L743; J. Ferch, C. Masche, W. Raith and L. Wiemann, Phys. Rev. A 40 (1989) 5407; L.G. Christophorou, P.G. Datskos and J.G. Carter, Chem. Phys. Lctt. 186 (1991) 11. [3]L.G. Christophorou, A.A. Christodoulides and D.L. McCorkle, in: Electron-molecule interactions and their applications, Vol. 1 (Academic Press, New York) ch. 6; L.G. Christophorou, P.G. Datskos and J.G. Carter, Ber. Bunsenges. Phys. Chem. 96 (1992) 448. [4 ] R.I. Hall and S. Trajmar, J. Phys. B 8 ( 1975 ) L293. [ 5 ] L.G. Christophorou, S.R. Hunter, L.A. Pinnaduwage, J.G. Carter, A.A. Christodoulides and S.M. Spyrou, Phys. Rev. Lett. 58 (1987) 1316; L.A. Pinnaduwage, L.G. Christophorou and S.R. Hunter, J. Chem. Phys. 90 (1989) 6275; L.A. Pinnaduwage, L.G. Christophorou and A. Bitouni, J. Chem. Phys. 95 ( 1991 ) 274; L.A. Pinnaduwage and L.G. Christophorou, Chem. Phys. Lett. 186 (1991)4; P.D. Burrow, J. Chem. Phys. 59 (1973) 4922; D.S. Belic and R.I. Hall, J. Phys. B 14 ( 1981 ) 365; C. Bottcher and R.D. Buckley, J. Phys. B ! 2 ( 1979 ) L497; T. Jaffke, M. Meinke, R. Hashemi, L.G. Christophorou and E. lllenberger, Chem. Phys. Lett. 193 (1992) 62. [ 6 ] S. Trajmar and J.C. Nickel, Cross section measurements for electron impact on excited atomic species, submitted to At. Mol. Opt. Phys. [7 ] R.H. Neynaber, S.M. Trujillo, L.L. Marino and E.W. Rothe, in: Proc. 3rd Int. Conf. on Phys. electr, atom. coll., (NorthHolland, Amsterdam, 1964) p. 1089. [ 8] W.G. Wilson and W.L. Williams, J. Phys. B 9 (1976) 423. [9] R. Celotta, H. Brown, R. Molofand B. Bederson, Phys. Rev. A3 (1971) 1622. [ 10] N.D. Bhaskar, B. Jaduszliwer and B. Bederson, Phys. Rev. Left. 38 (1977) 14.
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[ 11 ] B. Jaduszliwer, R. Dang, P. Weiss and B. Bederson, Phys. Rev. A 21 (1980) 808. [ 12] B. Jaduszliwer, G.F. Shen, J.-L. Cai and B. Bederson, Phys. Rev. A31 (1985) 1157. [ 13 ] M. Zuo, T.Y. Jiang, L. Vuskovic and B. Bederson, Phys. Rev. A41 (1990) 2489; T.Y. Jiang, M. Zuo, L. Vuskovic and B. Bederson, Phys. Rev. Lett. 68 (1992) 915. [ 14] I.V. Hertel and W. Stoll, J. Phys. B 7 (1974) 583. [ 15 ] H.W. Hermann, I.V. Hertel, W. Reiland, A. Stamatovic and W. Stoll, J. Phys. B 10 (1977) 251. [ 16] D.F. Register, S. Trajmar, S.W. Jensen and R.T. Poe, Phys. Rev. Lett. 41 (1978) 749. [17] A.J. Dixon, A. yon Engel and M.F.A. Harrison, Proc. R. Soc. A 343 (1975) 333. [ 18 ] P. Defiance, W. Claeys, A. Cornet and G. Poulaert, J. Phys. B 1 4 ( 1 9 8 1 ) III. [ 19] W.L. Fite and R.T. Brackmann, in: Proc. VIth Int. Conf. on Ionization phenomena in gases, ed. P. Hubert (SERMA, Paris, 1964) p. 21. [20] L Vriens, T.F.M. Bonsen and J.H. Smit, Physica 40 (1968) 229; L. Vriens and A.H.M. Smeets, Phys. Rev. A 22 (1980) 940. [21 ] D.R. Long and R. Geballe, Phys. Rev. A 1 (1970) 260. [ 22 ] A.J. Dixon, M.F.A. Harrison and A.C.H. Smith, Proc. VIIIth Int. Conf. on Phys. electr, atom. coll., Belgrade (Book of Abstracts, 1973) p. 405. [23] A.J. Dixon, M.F.A. Harrison and A.C.H. Smith, J. Phys. B 9 (1976) 2617. [24] K. Fujii, M. Johnston, J.C. Nickel and S. Trajmar, in: Abstracts of contributed papers XVlIth Int. Conf. on Phys. electr, atom. coll., Brisbane, Australia ( 1991 ) p. 166. [25] S. Trajmar, J.C. Nickel and T. Antoni, Phys. Rev. A 34 (1986) 5154. [26] I.S. Aleksaldin and I.I. Shafranyosh, Ukr. Fiz. Zh. (USSR) 19 (1974) 1843. [27 ] V.A. Gostev, D.V. Elakhovskii, Yu. V. Zaitsev, L.A. Luizova and A.D. Khakhaev, Opt. Spektrosk. 48 (1980) 251; A.A. Mityureva and N.P. Perkin, Opt. Spektrosk. 38 ( 1975 ) 229; 66 (1989) 710; A.A. Mityureva, N.P. Perkin and V.V. Smirnov, Opt. Spektrosk. 66 (1989) 463; 67 (1989) 461; A.A. Mityureva, V.V. Smirnov and T. Yu. Grigoreva, in: Abstracts of contributed papers XVIIth Int. Conf. on Phys. electr, atom. coll., Brisbane, Australia ( 1991 ) p. 691; B. Stumpfand A. Gallagher, Phys. Rev. A 32 ( 1985 ) 3344; D.LA. Rail, F.A. Sharpton, M.B. Schulman, L.W. Anderson, J.E. Lawler and C.C. Lin, Phys. Rev. Lett. 62 ( 1989 ) 2253. [28] D. Husain, A.L. Choudhury, A.K. Rafiqullah, C.W. Nestor Jr. and F.B. Malik, Phys. Rev. 161 ( 1967 ) 68; E.J. Robinson, Phys. Rev. 182 (1969) 196; D.G. Truhlar, S. Trajmar, W. Williams, S. Ormonde and B. Tortes, Phys Rev. A 8 (1973) 2475; R.S. Oberoi and R.K. Nesbet, Phys. Rev. 8 (1973) 2969; D.L. Moores, D.W. Norcross and V.B. Sheorey, J. Phys. B 7 (1974) 371; I.V. Hertel and W. Stoll, J. Phys. B 7 (! 974) 570;
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M.R. Hannery and K.J. McCann, Phys. Rev. A 12 (1975) 846; M.R. Flannery, W.F. Morrison and B.L. Richmond, J. Appl. Phys. 46 ( 1975 ) 1186; D. Ton-That, S.T. Manson and M.R. Flannery, J. Phys. B l0 (1977) 621; D. Ton-That and M.R. Hannery, Phys. Rev. A 15 (1977) 517; R.K. Sharma, G.P. Gupta and K.C. Mathur, J. Phys. B 13 (1980) 3677; W.C. Fon, K.A. Berrington, P.G. Burke and A.E. Kingston, J. Phys. B 14 (1981) 2921; D. Margreiter, H. Deutsch and T.D. M~irk, Contrib. Plasma Phys. 30 (1990) 487. [29] E. Vogt and G.H. Wannier, Phys. Rev. 95 (1954) 1190. [30] M.W. Miiller, A. Merz, M.-W. Ruf, H. Hotop, W. Meyer and M. Movre, Z. Phys. D 21 ( 1991 ) 89. [31]G.A. Victor, A. Dalgarno and A.J. Taylor, J. Phys. B l (1968) 13. [ 32 ] A. Dalgarno and A.E. Kingston, Proc. R. Soc. A 259 (1960) 424. [ 33 ] R.M. Glover and F. Weinhold, J. Chem. Phys. 65 (1976) 4913. [34] R.M. Glover and F. Weinhold, J. Chem. Phys. 66 (1977) 185. [ 35 ] T.M. Miller and B. Bederson, Adv. At. Mol. Phys. 13 ( 1977 ) 1.
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[ 36 ] A. Dalgarno, Adv. Phys. 11 ( 1962 ) 281. [37] E. Pollack, E.J. Robinson and B. Bederson, Phys. Rev. A 134 (1964) 1210. [38] R.W. Molof, H.L. Schwartz, T.M. Miller and B. Bederson, Phys. Rev. A 10 (1974) 1131. [39] G. Lamm and S. Szabo, J. Chem. Phys. 72 (1980) 3354. [40] P.F. Gruzdev, G.S. Soloveva and A.I. Sherstyuk, Opt. Spektrosk. 59 (1985) 299. [41 ] W. Miiller, J. Flesch and W. Meyer, J. Chem. Phys. 80 (1984) 3297. [42] W.D. Hall and J.C. Zorn, Phys. Rev. A 10 (1974) 1141. [43]P. Fantucci, S. Polezzo, V. Bonacic-Koutecky and J. Koutecky, Z. Phys. D 13 (1989) 355. [ 44 ] E.A. Reinsch and W. Meyer, Phys. Rev. A. 14 ( 1976 ) 915. [45] P.C. Schmidt, M.C. B/Shm and A. Weiss, Ber. Bunsenges. Phys. Chem. 89 ( 1985 ) 1330. [46] F. Vign6-Maeder, Chem. Phys. 85 (1984) 139. [47 ] H.T. Duong and J.-L. Picqu6, J. Phys. (Paris) 33 (1972) 513. [48] R. Marrus and J. Yellin, Phys. Rev. 177 (1969) 127. [49] R.E. Kennedy and R.A. Bonham, Phys. Rev. A 17 (1978) 1844; J.C. Nickel, K. Imre, D.F. Register and S. Trajmar, J. Phys. B 18 (1985) 125. [50] A. Kasdan, T.M. Miller and B. Bederson, Phys. Rev. A 8 (1973) 1562. [ 51 ] R. MiJller-Fiedler, P. Schlemmer, K. Jung, H. Hotop and H. Ehrhardt. J. Phys. B 17 (1984) 259.
PHYSICS LETTERS A
Scattering of slow electrons from excited atoms: The dominant role of the polarization potential L o u c a s G . C h r i s t o p h o r o u 1 and Eugen I l l e n b e r g e r Institut )~r Physikalische und Theoretische Chemie, Freie Universitiit Berlin, Takustrasse 3, W: 1000 Berlin 33, Germany Received 3 September 1992; revised manuscript received 19 November 1992; accepted for publication 20 November 1992 Communicated by B. Fricke
The total electron scattering cross sections from ground state and excited atoms are correlated with their static polarizabilities.
The systematic study o f the interactions o f slow electrons with excited a t o m s and molecules is just beginning, although calls for such studies trace back decades. Experimental and theoretical studies on electron scattering from v i b r a t i o n a l l y / r o t a t i o n a l l y excited molecules revealed many and often profound changes in the scattering [ 1,2 ] and electron a t t a c h m e n t / d e t a c h m e n t [1,3 ] cross sections. Large increases have been reported also in electron scattering from [ 1,4 ] and in particular in dissociative a t t a c h m e n t o f electrons to [ 1,5 ] electronically excited molecules. Similarly, experimental and theoretical studies on electron-excited a t o m interactions have shown that often e n o r m o u s increases in the electron scattering and ionization occur [ 6 ]. Such studies include those on electron scattering from excited He [7,8], Ar [9], Na [ 10-15 ] and Ba [ 16 ] a t o m s a n d electron impact ionization o f excited H [ 17,18 ], He [ 19-23 ], Ne [22,24], Ar [22], Ba [25] and Sr [26] atoms. The results o f optical m e t h o d s [ 6,27 ] also show consistently larger cross sections for the excited atoms, and the limited theoretical studies on excited atoms [28 ] support the experimental findings and indicate the d o m i n a n t role played by the dipole polarizability in the scattering process. In this Letter we draw attention to a rather quanHolder of the Alexander von Humboldt Senior US Award; Permanent address: Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 78
titative correlation between the total electron scattering cross section and the static dipole polarizability o f the ground and excited states o f a t o m s as is predicted by Vogt and W a n n i e r [29]. Vogt and W a n n i e r considered the m o t i o n o f ions or electrons in gases when the interaction potential between the two is simply the polarization function i e2of
V(r)-
2 r4 '
(l)
where e is the elementary charge, a is the atomic ( m o l e c u l a r ) polarizability and r is the distance between the electron and the atom. F r o m a q u a n t u m mechanical description o f the polarization potential, they obtained for the capture cross section the expression ryv,w = 4 ~ ( e 2 a / m v 2 ) 1/2
(2)
where m and v are, respectively, the mass and the velocity o f the electron. The av,w in ( 2 ) is twice the classical capture cross section for spiralling orbits over a wide range o f v [29]. Equation ( 2 ) can be written as av.w=4~aZ( of / 2 E ) t/2
= 2 . 4 8 7 × l O - ' 6 ( a / E ) '/2
(3)
where ao is the Bohr radius ( 5 . 2 9 1 7 2 × 10 - 9 c m ) , of is in atomic units (1 a . u . = a o3 = 0 . 1 4 8 2 ~ 3 ) , E is the electron energy in atomic units (1 a . u . = 1 hartree =27.21165 eV) and av,w is in cm 2.
0375-9601/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 173, number 1
PHYSICS LETTERS A
25 January 1993
Table 1 Static dipole polarizabilities, ~t, of ground state and excited atoms (in atomic units a3; ao3 = 0.1482 X 10-24 era3= 0.1482 A 3) Atom
a(a~)
He
ISo !.366 1.382 1.384 1.383 [1.381
Ar
23S [30] [31] [32] [33] ")
3 tSo 11.07 [32,36] e) [ll.07]
Na
32S~/2 160.0 [39] 159.2 [38] ~) 159.5 [40] 162.6 [41] 164.64 [42] ¢~ 164.8 [43] 165.02 [44] 165.5 [45] [161.91 e>
K
4 ISo 286.7 [39] 287.6 [441 288.1 [41] 292.8 [38] ¢) 301.4 [43] 305.0 [42] ¢) 308.57 [45] [298.9] a)
2 IS
312.6 [30] 316.2 [311 316.2 [32] b~ [315.01
773.1 [30] 802.3 [31] 803.3 [34] b) [792.9]
33p2 313.1 [371 ~) 323.2 [38] ¢) [318.2] Sstates(4s)
2939 [46] 2962 [39] f)
S states ( 5 s)
4585 [46]
P states (3 p ) 362 [461 368.4 [39] B~ 441.2 [45] 341.1 [47] ¢) 367.3 [39] 355.4 [47] e),h) 368.9 [39] [362.2] °
Na*(32p1/2) Na*(32p1/2)
Na*(3 2p3/2) Na* ( 3 2p3/2)
P states (4 p)
625 [46] 645.37 [45] 655.0 [48] c~ 622.9 [39] 635.0 [39]
K*(4 2P1/2) K*(4 2p3/2)
a~ The bracketed values are the ones used in fig. 1 and throughout the present discussion. For a review of atomic (and molecular) polarizabilities see ref. [ 35 ]. b) See this reference for a listing of earlier theoretical values. o All these values are experimental; the rest are the results of calculations. d~ Average of the two experimental values. e~ Values listed in column b of table 5 of this reference. f~ For the 42S~/2 state. g~ Average for the P states as quoted in ref. [ 39 ]. h~ Average of ix(3 2p3/2, M j = +_½) and a ( 3 2P3/2, Mj-- -I- 3 ) given in this reference. i~ Average of the two values listed for Na*(32pa/2).
In table 1 are listed the static dipole polarizabilities f o r t h e g r o u n d s t a t e o f H e , A r a n d N a a n d f o r some of their excited states for which total electron
s c a t t e r i n g cross s e c t i o n s h a v e b e e n m e a s u r e d ; also l i s t e d i n t a b l e 1 a r e r e l e v a n t d a t a f o r K. T h e g r o u n d s t a t e r a r e gas a t o m s h a v e low v a l u e s o f a d u e to t h e i r 79
Volume 173, number 1
PHYSICS LETTERS A
closed-shell structure, but when excited, the loosely bound electron increases their polarizability substantially. On the other hand, the polarizability of the alkali atoms is already large in their ground state since a single outer valence electron is loosely bound in an s-orbital of large radius. The ot of the excited alkali atoms is larger compared to the ground state, but the relative increase is not as large as for the rare gas atoms. In fig. 1 are plotted the measured total electron scattering cross sections which are available in the literature for these species as a function of ( a / E)1/2 along with the prediction of eq. (3). The cross sections decrease monotonically with increasing E. The experimental measurements - especially those for the alkali metals - are in a rather good agreement with the predicted dependence of the cross section, a~,.~ on (or~E) j/2. The magnitude of c~ largely accounts for the scattering (it is interesting to note (fig. 1 ) that even the electron scattering cross section for
10©0 ........
100
A ~i i •" ~_ ~ .....
oy OZ~
¢,)
2
O'v,w
IC)
C
10
/
yO,~e
•
1
10
100
(a/E) 1/e (au) 1/z
1000
Fig. 1. Total electron scattering cross sections plotted versus (a/E)t/2for (O) He (1 ISo) [49], ( 0 ) He*(2tS) [8], (V) He*(23S) [8], (A) He*(23S) [7], (A) Na(32Si/2) [50], (rq) Na*(32P3/2) [ 10-12], (m) Ar*(3p2+3po) [9] and (O) K(4 ISo) [501. a~,~ (eq. (3)),
80
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the ground state of He approaches a~,wat high energies); the effect of the core and resonance phenomena seem not to be significant. The dominant role of the dipole polarizability can be further seen from the measurements on the differential electron scattering cross sections for ground state and excited atoms. Thus the measurements of Miiller-Fiedler et al. [ 51 ] on the differential electron scattering cross sections for the transitions e ( E ~ 30 eV) + He*(2 3S) ~He*(2 3P) + e ( E ' )
(4)
and e ( E ~ 3 0 e V ) + H e ( l tS)-+He*(2 3P) + e ( E " )
(5)
(i.e., for excitation by 30 eV electrons of the 2 3p excited state of He, respectively, from the excited state 2 3S and from the ground state 1 ~S) showed that the cross section for the excited state (reaction (4)) is up to 105 times larger compared to the ground state (reaction (5)). The maximum enhancement is for small angles (forward scattering) as is to be expected (Flannery and McCann [ 28 ] ) for the distant collisions involved in the electron-induced dipole scattering. The excited state enhancement is expected to be a function of the excited state itself and of the electron energy [ 51 ]. It can, thus, be concluded from these rather limited studies that electron scattering from excited atoms (and perhaps to a lesser degree from electronically excited molecules) can be as much as 105 times larger compared to their respective ground states depending on the excited state, the electron energy and the scattering angle. These increases are principally the consequence of the larger polarizabilities of the excited states. The Vogt-Wannier "limiting case" formula ( 3 ) predicts reasonably well the magnitude of the total electron scattering cross section and clearly indicates that the cross section can be very large depending on the magnitude of both a and E. For example, for a = 3 × 103 a.u. and E = 5 meV, O.v,w: 10-12 c m 2 ))l
We acknowledge useful discussions with Professors H. Baumg~irtel, K.H. Bennemann, B. Brutschy, #1
The polarizabilities of high-lying excited electronic states can be very large. Polarizabilities of the order of 10 10ao3 have been measured for atoms in Rydberg orbitals [35 ].
Volume 173, number 1
PHYSICS LETTERS A
V. Bonacic-Koutecky and J. Koutecky of the Freie Universit~it Berlin, Professor H. Hotop and H. Ehrhardt of Kaiserslautern University, and Drs. P.G. Datskos and L.A. Pinnaduwage of Oak Ridge National Laboratory. We also thank Dr. S. Trajmar for a preprint of ref. [ 6 ]. LGC thanks the HumboldtStiftung for the Senior US Scientist Award. Research sponsored, in part, by the US Department of Energy under Contract DE-ACOS-84 OR 214 00 with Martin Marietta Energy Systems, Inc.
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