Two-body shell model matrix elements by Taylor-series method

By using the Taylor-series method, i.e., by expanding the two-nucleon wave functions in the relative coordinates around the c.m. of the system, the analytical expressions of the two-body shell model matrix elements with infinite and finite well single particle wave functions are obtained. The first term in this expression describes the zero range forces. For harmonic oscillator single particle wave functions the connections with the Talmi-Moshinsky method are deduced. Also, it is shown that only the first term in the expansion of the two-nucleon wave functions is needed for the correct evaluation of the two-body shell model matrix elements. (author)