Spin Condition in the Cluster Variation Method and Its Application to the Neutron Matter

A kinematical study is made on the relation between the spin-singlet and spin-triplet pair distribution functions in the many-body system of spin-1/2 particles, and a group of inequalities is derived from the positiveness of the square of the "local spin" which is the total spin of a subsystem confined in a certain local region. This spin condition is applied to the neutron matter in the two-body approximation of the cluster variation method, and a conditional Euler-Lagrange equation is derived for the ground state. Although the solution of the Euler-Lagrange equation has a long-range tail, the conditional energy minimum can be obtained from it. Numerical results show that the spin condition compensates the kinematical defects due to the truncation of the cluster series in a fairly wide density region and is useful to eliminate unnatural solutions.