 
FIZIKA A 8 (1999) 2 , 5164
THEOREM ON SEPARATION OF COUPLED DIFFERENTIAL EQUATIONS, RESONANCE
EFFECTS AND THRESHOLD BEHAVIOUR
SMAIL BOUGOUFFA
Faculty of Science and Engineering, University of Science and
Technology, P. O. Box 14353, SANA'A, Yemen
CAO XUAN CHUAN and PAUL FAUCHER
URA 1362du CNRS, Observatoire de la cote d'Azur, B. P. 229, F06304,
Nice Cedex, France
Received 7 January 1999; Accepted 2 November 1999
The aim of this work is to show the importance of the theorem on the separation of
coupled differential equations in elastic scattering when the electron energy is below the
threshold necessary to produce excitation of the state 1 from the ground state 0. We apply
a schematical model to study the resonance effects in electronhydrogen scattering. We are
concerned with the behaviour of various crosssections in the neighbourhood of the
threshold of a new mode of scattering in which the electron possesses any quantized
angular momentum, and examine the effects of the change in the centrifugal potentials in
the case 1s2s2p closecoupling approximation. We conclude by discussing the threshold
behaviour and its relation to resonance effects.
PACS numbers: 34.80.Bm
UDC 539.186
Keywords: electronhydrogen scattering, theorem on the separation of coupled
differential equations, scattering near thresholds, resonance effects
