Note on the Validity of Methods Used in Nuclear Calculations

Abstract

A study has been made of several of the methods used to approximate the solutions of nuclear problems, especially the Schrödinger perturbation scheme and the linear variation method. The advantages of individual particle coordinates and relative coordinates are considered, the latter being more accurate. The methods are evaluated chiefly by application to the deuteron, where the possibility of an exact solution permits a check on the rapidity of convergence of the methods employed. The second Schrödinger approximation has been summed for this case, and the convergence is found to be rapid. However, the degree of approximation obtained is poorer than that readily obtainable from the linear variation scheme, using the same functions. This has been verified also for ${\mathrm{H}}^3$ and ${\mathrm{He}}^4$. For ${\mathrm{H}}^2$ the Schrödinger scheme is found to be improved by decreasing the scale parameter (increasing the width) of the exponential functions from 0.60 to 0.45. For the linear variation method, this is not the case, at least if the functions are limited to those of double and quadruple excitation.