The Correlation between Nucleon-Nucleon Interaction, Pairing Energy Gap and Phase Shift for Identical Nucleons in Nuclear Systems

The correlation between nucleon-nucleon interactions 𝑉(𝑟) and the pairing energy gap ∆ is studied theoretically. When two nuclear particles collide due to the interaction, they get scattered after approaching within 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 lead to a singlet So 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 1So channel calculations were done using Yukawa potential, which shows that phase shift 𝛿 𝑙(𝑘𝐹) is directly related to Fermi momentum 𝑘𝐹. (author)