Energy-Density Relation for Nuclear Matter

Abstract

In most previous calculations of nuclear matter the energy has been calculated only at the equilibrium density, which density has been determined by a minimum condition. In the present paper the author's theory of nuclear matter is applied to a study of the complete energy-density relation of nuclear matter, in the neighborhood of the equilibrium density. The emphasis here is not upon duplicating the accepted value for the equilibrium binding energy, but rather upon a study of the leading (diagonal) contribution of the quasi-particle interaction term $g_1\left(k_1{k}_2\right|k_3{k}_4)$, which is the matrix element of a reaction matrix $G_1$. It is shown that $g_1\left(k_1{k}_2\right|k_1{k}_2)$ must be evaluated partly by using observed nucleon-nucleon scattering phase shifts and partly by calculating the close-in behavior of the two-nucleon wave function, and that this second part receives a large contribution from the deuteron state. Curves are given for the dependence of $g_1\left(k_1{k}_2\right|k_1{k}_2)$ on the density and the center-of-mass momentum. It is also shown that $g_1\left(k_1{k}_2\right|k_1{k}_2)$ is sensitive to the size of the nucleon repulsive core, but not upon the character of the attraction, when agreement with scattering data has first been achieved. Finally, a comparison of $g_1\left(k_1{k}_2\right|k_1{k}_2)$ with the prediction of first-order perturbation theory is made.