FIZIKA A 15 (2006) 3 , 193208
THE STUDY OF ATOMIC TRANSITIONS BY USE OF NUMEROV TECHNIQUE IN SCHEMATIC MODEL
SMAIL BOUGOUFFA
Department of Physics, Faculty of Science, Taibah University, P.O.Box 344,
Madinah, Saudi Arabia
Received 25 May 2005; Revised manuscript received 23 February 2006
Accepted 28 June 2006 Online 23 February 2007
The calculation of a partial cross section in atomic collision theory when the
collision is inelastic and there is not a possibility of particle exchange
requires the solution of a system of coupled differential equations. The Numerov
technique is applied to the solution of schematic model equations, which
simulate the solution of real problems but are themselves exactly solvable. We
have investigated the 3^{2}S transition in sodium as an excellent
application of a near resonance and strong coupling situation in the case of twostate
approximation. The results are compared with those obtained by the Bethe and
resonance distortion approximations. The difference can be ascribed to the use
of the set of twochannel differential equations rather than the set of threechannel
equations used in other approximations, and to the simplified treatment of the
interaction potentials.
PACS numbers: 34.30, 34.80.Bm, 34.50.Fa, 34.80.Dp, 34.80.Nz
UDC 539.186
Keywords: electronatom collisions, atomic transitions, close coupling
approximation, coupled differential equations, Numerov technique
