EGAS41 - Swansea University

41 st EGAS CP 95 Gdańsk 2009
The relativistic J-matrix method in elastic scattering of slow
electrons from Argon atoms
P. Syty 1,∗ , J.E. Sienkiewicz 1
1 Department of Theoretical Physics and Quantum Informatics, Gdansk University of
Technology, Gabriela Narutowicza 11/12, 80-233 Gdansk, Poland
∗ Corresponding author: sylas@mif.pg.gda.pl
The J-matrix method is an algebraic method in quantum scattering theory. It is based on
the fact that the radial kinetic energy operator is tridiagonal in some suitable bases. Nonrelativistic
version of the method was introduced in 1974 by Heller and Yamani [1] and
developed by Yamani and Fishman a year after [2]. Relativistic version was introduced
in 2000 by P. Horodecki [3].
Some preliminary applications of relativistic J-matrix method to scattering have been
presented for some square-type potentials [4], using the newly developed Fortran 95 code
JMATRIX [5]. These tests proved that the method correctly describes the scattering
process.
The main advantage of the method is that it allows to calculate phase shifts for many
projectile energies with relatively small computational time. Also, the non-relativistic
limit in relativistic calculations is properly achieved. This fact was expected, since the
basis sets used in relativistic calculations satisfied the so called kinetic balance condition.
In this contribution we present relativistic scattering phase shifts together with total
and differential cross sections in elastic scattering of slow electrons from Argon atoms,
calculated using the modified relativistic J-matrix method [6]. To improve convergence,
some mathematical and numerical techniques has been applied. Scattering potential has
been calculated using the well-known GRASP92 package [7], and the scattering solution
has been written in terms of series od the Laguerre, Gaussian and complete oscillator
basis functions. We compare the results with other theoretical (e.g. these obtained using
the multiconfiguration Dirac-Fock method [8]) and experimental (e.g. measured at high
scattering angles [9]) data.
References
[1] E. Heller, H. Yamani, Phys. Rev. A 9, 1201 (1974)
[2] H. Yamani, L. Fishman, J. Math. Phys. 16, 410 (1975)
[3] P. Horodecki, Phys. Rev. A 62, 052716 (2000)
[4] P. Syty, TASK Quarterly 3 No. 3, 269 (1999)
[5] http://aqualung.mif.pg.gda.pl/jmatrix/
[6] P. Syty, W. Vanroose, P. Horodecki, proceedings of the 41st EGAS conference (2009)
[7] F.A. Parpia, C. Froese Fischer, I.P. Grant, Comput. Phys. Commun. 94, 249 (1996)
[8] P. Syty, J.E. Sienkiewicz, J. Phys. B: At., Mol. and Opt. Phys. 38, 2859 (2005)
[9] B. Mielewska, I. Linert, G.C. King, M. Zubek, Phys. Rev. A 69, 062716 (2004)
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