The Evaluation of the Energy Matrix of the Tensor Forces

Abstract

It is shown how the use of tensor operators enables a simple calculation of the tensor forces in nuclear configurations by the usual spectroscopic methods. The number of independent parameters necessary to define the energy in the nuclear configuration $l^n$ (or $j^n$) is found to be $2l$ (or $2j$), whereas it is shown to be only [$\frac{4l}{3}$] (or [$2j+\frac{2}{3}$]) in the $l^n$ (or $j^n$) configuration of equivalent nucleons. The energy matrix is given by means of a closed formula for the case of $d^n$ and ${\left(d_{\frac{5}{2}}\right)}^n$ configurations (of equivalent nucleons). It is found that in the latter configuration the order of levels for a short-range potential (of the tensor forces) is the same as for short-range central forces.