The Saturation Requirements for Nuclear Forces

The inequalities between the coefficients $M$, $H$, $B$, $V$, representing the proportions of Majorana, Heisenberg, Bartlett and ordinary interactions in the symmetric Hamiltonian, arising through considerations of saturation and of the instability of odd-odd nuclei heavier than ${\mathrm{N}}^{14}$ are represented graphically (Fig. 1). The allowed values of $M$, $H$, $B$, $V$ correspond to a part of a plane bounded by three straight lines. These inequalities are sufficient for saturation at infinitely high density of nuclear particles and all conditions derivable from the necessity of saturation for the potential energy in the high density condition are derivable from those listed. The limits set on the interactions in the ${}_{}{}^3{}_{}{}^{}P$ and ${}_{}{}^1{}_{}{}^{}P$ states by the inequalities are discussed. The results are summarized in Table I, Eqs. (7) and (8) and in the adjoining section. The sufficiency of the conditions is discussed in Section 2. The physical limitations are gone into in Section 3.