Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas

Abstract

In evaluating differential cross section of elastic scattering, different theories were applied to low-momentum and relativistic particles. For low-momentum motion, Lippmann-Schwinger scattering equation was applied, called fundamental formula; while for relativistic particles, a general scattering theory was used which calculates S matrix. In this paper, Lippmann-Schwinger equation is applied uniformly to both low-momentum and relativistic particles. The cross sections are valuated to the first order of Born approximation. One-body time-independent Green's functions for relativistic free particles are given. Compared to the general scattering theory, the fundamental theory has a clearer physical picture and the approximations made are more explicit.

28 pages, 2 figures, 4 tables

References in corpus (3)

• Solving Klein's paradox
• The modified fundamental equations of quantum mechanics
• New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments

Cited by in corpus (4)

• A generalized scattering theory in quantum mechanics
• Many-body theories for negative kinetic energy systems
• Liouville equation in statistical mechanics is not applicable to gases composed of colliding molecules
• A physical mechanism of the generation of stable positive kinetic energy systems and a qualitative explanation of the proportions of the four ingredients in the universe