O potencial nucleon-nucleon devido à troca de um píon: cálculo e características

Abstract

Nuclear physics has as its fundamental piece the interaction between nucleons (name used to designate indistinctly protons and neutrons). From the point of view of particle physics, these interactions are carried out by the exchange of particles, the most important in these processes being the pion. Based on this premise, the necessary calculations were developed to find the nucleon-nucleon potential due to the exchange of a pion (One Pion Exchange Potential, OPEP), starting with a survey of concepts necessary to perform the calculation, such as Dirac notation and Feynman rules. The entire calculation follows the techniques of Quantum Field Theory. The procedure was carried out step by step to facilitate the understanding of the subject by those who want to begin studying this area. The final result is a potential involving two of the five spatial structures that make up the NN potential: the central potential and the tensor potential. Both are described by the Yukawa function, which is essentially a potential like the electrostatic one (i.e., with 1/r behavior) multiplied by a decreasing exponential, with a coefficient (in the exponent) inversely proportional to the pion mass, in full agreement with the short range observed in the strong interaction. We present the behavior of these OPEP terms for distances up to 7 fm. The Yukawa function is singular at the origin, which arises from the limitations of OPEP, i.e., the non-relativistic approximation, and because nucleons are considered point particles. We present here a common way to get around this problem, which is the use of the so-called form factors. They mathematically impose an effective size for the nucleons.