Methods of Calculation of Radial Wave Functions and New Tables of Coulomb Functions

Abstract

In connection with the tabulation of Coulomb wave functions special methods of obtaining numerical results having an accuracy of about one percent have been developed and are reported. Some of the methods are applicable also to other problems. Many of them are concerned with the calculation of the second solution of an ordinary differential equation of second order making use of the first solution. The present paper contains an introduction to the use of new Coulomb Functions tables which cover ranges of parameters required for the calculation of nuclear reactions of protons, deuterons and alpha-particles from hydrogen to oxygen in the energy range of a few Mev. The ranges covered are 0 to 6 for $\ensuremath{\rho}$, 0 to 3.98 for $\ensuremath{\eta}$. For alpha-particles the tables suffice for the treatment of reactions up to about 10 Mev for $Z=9(F) \mathrm{and}5$ Mev for $Z=2(\mathrm{He})$. For protons the tables cover an energy range of roughly 4 times that for alpha-particles.