The calculation of Binding Energy and Incompressibility, Pressure, and Velocity of Sound of Infinite Nuclear matter Using New One Boson Interaction.

M T Aper,J O Fiase,F Gbaorun

doi:10.46912/napas.51

Abstract

The use of effective nucleon – nucleon (N N) interactions for the determination of nuclear matter properties such as, binding energy per nucleon, incompressibility,K of infinite nuclear matter, pressure 0 and velocity of sound of nuclear matter has been a subject of great interest to nuclear physicists for many decades. The effective interaction usually involved in these calculations has been the Michigan three Yukawa (M3Y) effective interactions whose origin is from G- matrix approach. In this research work however, we have used a newly developed interaction known as new one boson (NOB) effective interaction to carry out similar calculations. This new interaction is based on the Lowest Order Constrained Variational (LOCV) technique. The interaction reproduces the saturation energy of spin and isospin infinite nuclear matter of approximately -16MeV at the normal nuclear matter saturation density consistent with the best available density-dependent interaction derived from the G-matrix approach. The results of the incompressibility obtained using the NOB interaction ranges from 304 to 309 MeV. These values are in good agreement with the values of incompressibility obtained for similar calculations using the M3Y – Reid effective interaction, in which values for K range from 304 to 310 MeV. The results of 0 pressure and velocity of sound of infinite nuclear matter obtained in the present calculations are also in excellent agreement with results of other workers. The results of our present calculations indicate that, the NOB interaction has passed the basic test for an effective interaction. The NOB may therefore be applied to other nuclear matter and optical model calculations to ascertain its reliability.

Highlights

The study of nuclear matter properties using effective N- N interaction has received a lot of attention for some time
The velocity VS of sound in standard nuclear matter is expressed as Results and Discussion Fig.1gives the graph of the calculated values of the binding energy per nucleon for infinite nuclear matter plotted with the requirement that the nuclear binding energy be reproduced at the correct nuclear matter density
The theoretical estimate of K0 by infinite nuclear matter model (INM)by Satpathy et al (1988), claims a well-defined and stable value of K0 = 288 ± 20 MeV and the present estimate is in good agreement with the value of K0 obtained by INM which rules out any values lower than 200 MeV

Summary

Introduction

The study of nuclear matter properties using effective N- N interaction has received a lot of attention for some time now. A number of effective interactions have been developed by many authors to study the interaction between nucleons inside the nucleus (Bertsch et al, 1977; Dartmans and Amos, 1994). According to Misicu (2007), the M3Y interaction has been derived by fitting its matrix elements into an oscillator basis (the oscillator parameters were chosen to reproduce the ground state of 16O) to the elements of the G–matrix obtained with the Reid soft-core N - N interaction. The results of some nuclear matter calculations carried out with the M3Y – type interaction compared favourably with the results obtained from that of the G – matrix calculations (Fiase et al, 2011)

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Conclusion