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Low-energy electron impact excitation of the lowest-lying autoionizing level in Li
Volume 97, number 2
LOW-ENERGY
13 May 1983
CHEMICAL PHYSICS LETTERS
ELECTRON
OF THE LOWEST-LYING
IMPACT EXCITATION AUTOIONIZING
LEVEL
IN Li
S.N. TIWARY * Department of Applied Mathematics and i%eoretical Physics. Tjie Queen ‘s University of Belfast. Belfast BT7 INN. Northern Ireland Received 14 February 1963; in final form 9 March 1983
We have calculated the electron impact total cross sections for the excitation of the lowest-lying autoionizing level gcnerated due to the core-excitation 1s22s 2Se - ls2s2 2Se transition in the lithium atomic system usins Hartree-Fock wakefunctions for both initial and final states within the R-matrix method in the low bombarding energy region. Our results show that the energy dependence of cross sections is significantly different in natnre from all earliertheoretical predictions
Studies of autoionization in alkali-metal atoms are of growing interest for theoreticians because the single electron in the outermost shell makes the problem simpler. while the relatively large number of electrons in the next lower shell provides an amplification to the inner-shell process. In general, the excitation of an inner-shell electron leads to autoionization since the level generated due to the inner-shell electron is em-
bedded in and interacts with the associated continuum state. These levels play a very important role in explaining the structure observed in the electron impact total ionization cross section curves. Consequently, a reliable theoretical estimate of the total cross sections for the excitation of autoionizinglevelsin alkali atoms is of special interest_ For the first time we [l-4] have calculated the electron impact total cross sections for the excitation of the lowest-lying autoionizing level in alkali-metal atoms using Hartree-Fock (HF) wavefunctions for both initial and final states within the first Born approximation (FBA), modified first Born approximation (MFBA), Vainshtein approximation (VPSA) and asymptotic Green’s function approximation (AGFA). Similar calculations have been performed by Liepinsh and Peterkop [5] and Srivastava et al. [6] for the elec* Permanentaddress: Department of Physics. Bihar University, Muz.. Bihar, India.
0 009-2614/83/0000-0000/S
03.00 0 1983 North-Holland
for the excitation of level in alkali atoms
Iron impact total cross sections the lowest-lying autoionizing
within the framework of the FBA, Glauber approsimation (GA) and Crothers and McCarroll method (CMM). All these calculations are based on the highenergy approximations and the interaction between the autoionizing state wiviththe associared continuum has not been taken into account. Our main goal of this work is to investigate the effect of the R-matrix method [7,8] on the electron impact total cross sections for the core-excitation 1~~2s ?Se + 1~2s~ ?Se transition in the lithium atomic system employing the same Hartree-Fock orbital wavefunctions [9] as used by other authors within the FBA, GA and CMhl in order to have a physically meaningful comparison. The wavefunction describing the electron andlithium atomic system is represented by [lo]
(1) where ~j are channel functions formed from zhe target states. Uj are the continuum basis orbitals and C+are bound configurations formed from the atomic orbitals. The coefficients aijk and bj~ are obtained by diagonal221
\blume
97. number 2
13 May 1983
CHEhlICAL PHYSICS LETTERS
ELECTRON
IMPACT ENERGY
(eV)
)
1‘1g. 1. Total electron
impact excitation cross section for the lowest-lying autoionizing level in Li. present R-ruatrb results: - - - results due to Liepinsh and Peterkop using the HI- wavefunction [S]; ----FBA results due to Srivastava et al. [6]; ______.____results due to Liepinsh and Peterkop [S] using the wavefunctions of Green et al. [ 111: -------, Glauber approsiruat~on results due to Srivastava et al.
izing the total hamiltonian
in the basis defined
in eq.
(I). Fig. 1 displays the present R-matrix results with other theoretical data of Liepinsh and Peterkop [5] and Srivastava et al. [6]. Several features of imporiance emerge from fig. 1. Firstly, the R-matrix results sbo\~ the different behaviour in the energy dependence of the cross sections whereas all other theoretical predictions exhibit a broad and flat maximum in the incident energy range of =SO-115 eV. It may be due to the fact that all theoretical models employed in this calculation are not valid in the low-energy region excepr the R-matrh method. Secondly, it is clear from fig. I that thr R-matrix cross section decreases monoronicdlly with increase of incident energy and goes towards the Clauber approximation curve after = 120 eV. The good agr2ement brtween the R-matrix and GA results above =Z120 eV reflects the reliability of the R-matrix calculation because the GA cross section 333 ___
should be reliable after the maximum attained in the cross section curve. There are two factors which limit the accuracy of our present R-matrix calculations for the cross section of thq inner-shell excitation in lithium. They are (1) the wavefunction of the target state and (2) the number of states incorporated in the calculation. In order to obtain reliable cross sections, one should use full configuration interaction (CI) wavefunctions and several target states_ Our present calculations suffer from these two factors but probably not too much because the correlation may be not be very important in Li and the overlap between the initial and final states will be negligible_ We have not used CI wavefunctions and many states for computational reasons. It would be interesting to see the effect of electron correlation on the cross section. The author
wishes to express his gratitude
to
Volume 97, number 2
CHEMICAL
Drs. K.A. Berrington and H-R-J. Walters for fruitful discussions and encouragement.
References [l] S.N. Tiwary and D-K. Rai. Phys. Lett 43A (1973) 411. [2] S.N. Tiwary and D.K. Rai, J. Phys. B 8 (1975) 1109. [ 31 S.N. Tiwary, Ph.D. Thesis, Banaras Hindu University (1976). [4] S.N. Tiwary. J. Phys. B 14 (1981) 2951. [S] A.K. Liepinsh and R. Peterkop, J. Phys. B 11 (1978) L27. [6] R. Srivastava, C.S. Singh and D.K. Rai, J_ Phys. B 15 (1982) 1899.
PHYSICS
LEITBRS
13 May 1983
171 K-A. Berrington.P.G. Burke,M.LeDoumeuf. IV-D. Robb. K-T_ Taylor and Vo Ky Jan. Computer Phyr Commun. 14 (1978) 367. [8] P-G. Burke, A. Hibbert and IV-D. Robb. J. Phys. B 4 (1971) 153. [9] E. Qementi and C. Roetti. At. Data Nucl. Data Tables 14 (1974) 177. [IO] P-G. Burke and W-D. Robb, in: Advances in atomic and molecular physics, Vol. 11, eds D.R. Bates and B. Bederson (Academic Press, New York, 1975) pp. 143-214. [ 111 A.E.S. Green, D.L. Selhn and AS. Zachor. Phys. Rev. 184 (1969) 1.
223
LOW-ENERGY
13 May 1983
CHEMICAL PHYSICS LETTERS
ELECTRON
OF THE LOWEST-LYING
IMPACT EXCITATION AUTOIONIZING
LEVEL
IN Li
S.N. TIWARY * Department of Applied Mathematics and i%eoretical Physics. Tjie Queen ‘s University of Belfast. Belfast BT7 INN. Northern Ireland Received 14 February 1963; in final form 9 March 1983
We have calculated the electron impact total cross sections for the excitation of the lowest-lying autoionizing level gcnerated due to the core-excitation 1s22s 2Se - ls2s2 2Se transition in the lithium atomic system usins Hartree-Fock wakefunctions for both initial and final states within the R-matrix method in the low bombarding energy region. Our results show that the energy dependence of cross sections is significantly different in natnre from all earliertheoretical predictions
Studies of autoionization in alkali-metal atoms are of growing interest for theoreticians because the single electron in the outermost shell makes the problem simpler. while the relatively large number of electrons in the next lower shell provides an amplification to the inner-shell process. In general, the excitation of an inner-shell electron leads to autoionization since the level generated due to the inner-shell electron is em-
bedded in and interacts with the associated continuum state. These levels play a very important role in explaining the structure observed in the electron impact total ionization cross section curves. Consequently, a reliable theoretical estimate of the total cross sections for the excitation of autoionizinglevelsin alkali atoms is of special interest_ For the first time we [l-4] have calculated the electron impact total cross sections for the excitation of the lowest-lying autoionizing level in alkali-metal atoms using Hartree-Fock (HF) wavefunctions for both initial and final states within the first Born approximation (FBA), modified first Born approximation (MFBA), Vainshtein approximation (VPSA) and asymptotic Green’s function approximation (AGFA). Similar calculations have been performed by Liepinsh and Peterkop [5] and Srivastava et al. [6] for the elec* Permanentaddress: Department of Physics. Bihar University, Muz.. Bihar, India.
0 009-2614/83/0000-0000/S
03.00 0 1983 North-Holland
for the excitation of level in alkali atoms
Iron impact total cross sections the lowest-lying autoionizing
within the framework of the FBA, Glauber approsimation (GA) and Crothers and McCarroll method (CMM). All these calculations are based on the highenergy approximations and the interaction between the autoionizing state wiviththe associared continuum has not been taken into account. Our main goal of this work is to investigate the effect of the R-matrix method [7,8] on the electron impact total cross sections for the core-excitation 1~~2s ?Se + 1~2s~ ?Se transition in the lithium atomic system employing the same Hartree-Fock orbital wavefunctions [9] as used by other authors within the FBA, GA and CMhl in order to have a physically meaningful comparison. The wavefunction describing the electron andlithium atomic system is represented by [lo]
(1) where ~j are channel functions formed from zhe target states. Uj are the continuum basis orbitals and C+are bound configurations formed from the atomic orbitals. The coefficients aijk and bj~ are obtained by diagonal221
\blume
97. number 2
13 May 1983
CHEhlICAL PHYSICS LETTERS
ELECTRON
IMPACT ENERGY
(eV)
)
1‘1g. 1. Total electron
impact excitation cross section for the lowest-lying autoionizing level in Li. present R-ruatrb results: - - - results due to Liepinsh and Peterkop using the HI- wavefunction [S]; ----FBA results due to Srivastava et al. [6]; ______.____results due to Liepinsh and Peterkop [S] using the wavefunctions of Green et al. [ 111: -------, Glauber approsiruat~on results due to Srivastava et al.
izing the total hamiltonian
in the basis defined
in eq.
(I). Fig. 1 displays the present R-matrix results with other theoretical data of Liepinsh and Peterkop [5] and Srivastava et al. [6]. Several features of imporiance emerge from fig. 1. Firstly, the R-matrix results sbo\~ the different behaviour in the energy dependence of the cross sections whereas all other theoretical predictions exhibit a broad and flat maximum in the incident energy range of =SO-115 eV. It may be due to the fact that all theoretical models employed in this calculation are not valid in the low-energy region excepr the R-matrh method. Secondly, it is clear from fig. I that thr R-matrix cross section decreases monoronicdlly with increase of incident energy and goes towards the Clauber approximation curve after = 120 eV. The good agr2ement brtween the R-matrix and GA results above =Z120 eV reflects the reliability of the R-matrix calculation because the GA cross section 333 ___
should be reliable after the maximum attained in the cross section curve. There are two factors which limit the accuracy of our present R-matrix calculations for the cross section of thq inner-shell excitation in lithium. They are (1) the wavefunction of the target state and (2) the number of states incorporated in the calculation. In order to obtain reliable cross sections, one should use full configuration interaction (CI) wavefunctions and several target states_ Our present calculations suffer from these two factors but probably not too much because the correlation may be not be very important in Li and the overlap between the initial and final states will be negligible_ We have not used CI wavefunctions and many states for computational reasons. It would be interesting to see the effect of electron correlation on the cross section. The author
wishes to express his gratitude
to
Volume 97, number 2
CHEMICAL
Drs. K.A. Berrington and H-R-J. Walters for fruitful discussions and encouragement.
References [l] S.N. Tiwary and D-K. Rai. Phys. Lett 43A (1973) 411. [2] S.N. Tiwary and D.K. Rai, J. Phys. B 8 (1975) 1109. [ 31 S.N. Tiwary, Ph.D. Thesis, Banaras Hindu University (1976). [4] S.N. Tiwary. J. Phys. B 14 (1981) 2951. [S] A.K. Liepinsh and R. Peterkop, J. Phys. B 11 (1978) L27. [6] R. Srivastava, C.S. Singh and D.K. Rai, J_ Phys. B 15 (1982) 1899.
PHYSICS
LEITBRS
13 May 1983
171 K-A. Berrington.P.G. Burke,M.LeDoumeuf. IV-D. Robb. K-T_ Taylor and Vo Ky Jan. Computer Phyr Commun. 14 (1978) 367. [8] P-G. Burke, A. Hibbert and IV-D. Robb. J. Phys. B 4 (1971) 153. [9] E. Qementi and C. Roetti. At. Data Nucl. Data Tables 14 (1974) 177. [IO] P-G. Burke and W-D. Robb, in: Advances in atomic and molecular physics, Vol. 11, eds D.R. Bates and B. Bederson (Academic Press, New York, 1975) pp. 143-214. [ 111 A.E.S. Green, D.L. Selhn and AS. Zachor. Phys. Rev. 184 (1969) 1.
223