THE CORRELATION BETWEEN NUCLEON-NUCLEON INTERACTION, PAIRING ENERGY GAP AND PHASE SHIFT FOR IDENTICAL NUCLEONS IN NUCLEAR SYSTEMS.

Abstract

The correlation between nucleon-nucleon interactions 𝑉(𝑟) and the pairing energy gap Δ is studied theoretically. When two nuclear particles collide due to the interaction, they get scattered after approaching within a distance of the nearest approach or scattering length 𝑎 which leads to deviation from original path and this leads to phase shift 𝛿𝑙. Hence there will be a relation between 𝛿𝑙, 𝑎 and 𝑉(𝑟). This is what has been calculated by assuming a particular form of interaction potential 𝑉(𝑟), and in this case Yukawa potential has been used. The theoretical calculations leads to a singlet 1S0 scattering length of 𝑎=−18.3 𝑓𝑚 which is very close to the value of 𝑎=−19.3 𝑓𝑚 reported in the literature. Working on the bare nucleon-nucleon interaction in 1S0 channel calculations were done using Yukawa potential, which shows that phase shift 𝛿𝑙(𝑘𝐹) is directly related to Fermi momentum 𝑘𝐹.