Ph.D. Thesis: Solving the quantum scattering problem for systems of two and three charged particles
by
Mikhail Volkov(Stockholm University, Department of Physics)
→
Europe/Stockholm
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Description
A rigorous formalism for solving the Coulomb scattering problem is presented in this thesis.
The approach is based on splitting the interaction potential into a finite-range part and a longrange
tail part. In this representation the scattering problem can be reformulated to one which is
suitable for applying exterior complex scaling. The scaled problem has zero boundary conditions at
infinity and can be implemented numerically for finding scattering amplitudes. The systems under
consideration may consist of two or three charged particles.
The technique presented in this thesis is first developed for the case of a two body single
channel Coulomb scattering problem. The method is mathematically validated for the partial
wave formulation of the scattering problem. Integral and local representations for the partial wave
scattering amplitudes have been derived. The partial wave results are summed up to obtain the
scattering amplitude for the three dimensional scattering problem. The approach is generalized
to allow the two body multichannel scattering problem to be solved. The theoretical results are
illustrated with numerical calculations for a number of models.
Finally, the potential splitting technique is further developed and validated for the three body
Coulomb scattering problem. It is shown that only a part of the total interaction potential should
be split to obtain the inhomogeneous equation required such that the method of exterior complex
scaling can be applied. The final six-dimensional equation is reduced to a system of three
dimensional equations using the full angular momentum representation. Such a system can be
numerically implemented using the existing full angular momentum complex exterior scaling code
(FAMCES). The code has been updated to solve the three body scattering problem.
