Boundary Conditions for the Description of Nuclear Reactions

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Abstract
The present paper deals with a phenomenological description of nuclear reactions by means of boundary conditions. The several stages of the reaction (initial particles, compound nucleus, etc.) are described in their respective configuration spaces; and the state representing the whole system is given by a wave function in Fock space. The wave equations and the boundary conditions are deduced with the help of an analogy to vibration problems. The interaction leading to the nuclear reaction appears as a boundary condition between the different components of the Fock type wave function. A discussion is given of elastic scattering and of two-particle nuclear reactions, showing that the present procedure gives the same dependence of the cross sections on energy as the Breit-Wigner resonance formula and its generalizations. A sketch is given of the extension of the present ideas to multiple particle reactions. The whole treatment is nonrelativistic.

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