Gaussian Radial Dependence Research Articles

The Elastic Scattering of Neutrons by Tritons and3He

Cross sections and phase shifts for the elastic scattering of neutrons by tritons and 3He are calculated over the energy range 1 to 14 MeV using central forces. Resonating group wave functions are employed to derive integro-differential equations for which accurate solutions are obtained with the aid of an electronic computer. The two-body interaction has exchange properties of either the Serber or the symmetrical type and a gaussian radial dependence with constants consistent with the binding energies of the alpha particle and the deuteron. The calculated angular distributions are found to depend sensitively on the exchange nature of the interaction, although the available experimental data are unsufficient to distinguish between the interactions considered.

Studies in jj -coupling. III. Nuclear energy levels

The wave functions for the configurations j n , with j = 3/2, 5/2 and 7/2, obtained in part II of this series according to the particular scheme of part I, are here used to obtain the central force energy matrices for nuclear configurations. The ordering of energy levels is studied as a function of the nature of the force with especial reference to its range, and the results are presented in the form of energy-level diagrams. The ordering of levels predicted to hold in parts I and II when forces are of short range is shown to occur with practical ranges; but for light nuclei in particular it is demonstrated that levels of very high angular momentum may sometimes occur near to the ground state. The results are found to be largely independent of the precise nature of the forces provided they are of reasonably short range and are attractive in the 1 S state of two like particles; for definiteness, however, the diagrams have been drawn for a Rosenfeld symmetrical exchange force of Gaussian radial dependence. The effect of using other types of central interaction is discussed qualitatively. The lowest excited states of even-even nuclei are seen to have a simple interpretation in jj -coupling.