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

Willy K Koech,Ken M Muguro,Kapil M Khanna,Godfrey S Murunga

doi:10.4236/jhepgc.2019.52018

Abstract

Assuming some known nucleon-nucleon interactions, and using the relations between phase shift δ and nucleon-nucleon interaction potential V (r) ; the relation between nucleon-nucleon interaction and scattering length a; the relation between energy gap Δ, and scattering length a; an equation is obtained between energy gap Δ and Fermi momentum kF via the phase shift δ (kF). Assuming 1s0 (singlet) pairing between the nucleons, the energy gap Δ has been calculated and it is found that Δ = 3.0 MeV at Fermi momentum kF = 0.8 fm-1.

Highlights

When one particle approaches another particle, and they are in the field of force of each other; they interact and scatter
When the Fermi momentum kF of the interacting nucleons is zero, the value of phase shift δ0, is equal to zero in the ground state as seen from Figure 2, this show that an increase in Fermi momentum kF leads to an increase in phase shift δ0
It can be concluded that scattering length influences the energy gap with different values of Fermi momentum

Summary

Introduction

When one particle approaches another particle, and they are in the field of force of each other; they interact and scatter. In BCS approximation, the pairing energy gap is calculated by solving the BCS equation with the free-space nucleon-nucleon interaction and free particles in intermediate states in the scattering process; the effects of the neutron medium on the normal state excitations and the pairing interaction are neglected [5] [6]. Substituting the values of V (r ) from Equation (3) and Equation (5) in Equation (2) and substituting the values of V (k, k′) in Equation (1) we can get the relation between ∆ (k ) and V0 clearly emphasizing of the there exists a close relationship between the pairing energy gap and the interaction potential. Exact value of ∆ (k ) can be calculated [8]

Theoretical Derivations

Results and Discussion

Conclusion

Suggestions