A method for calculating spectra in light nuclei

Abstract

Harmonic oscillator well eigenfxmctions, classified according to the group SU^, are used as a set of zero order approximations to nuclear states, A selection rule is used to put the representation; of SU^ in their order of importance. A method is developed for calculating energy levels, with theses tates, by a variational procedure using a central force only. The appearance of rotationalf eatures for even nuclei in the ds-shell is discussed, using only the states of the leading representation, and the low lying energy levels of X8 pQ 2Zi. 0 , Ne and Mg are calculated. The agreement with the K = 0 bands as good but the K = 0 and K = 2 band spacing in I3g^ is too small for any exchange mixture. The mixing of bands in Mg , for Rosenfeld exchange, is of the right kind to give almost the correct branching ratio for E2 transitions from the s econd 2^ state. Mixing of representations is small and the changes in the spectrum from the leading representation only slight. Initial calculations are given an the use of the deformed, harmonic oscillater well eigenfunctions as a set of zero order states. It is found that there is very little difference between the deformation parameters which minimise the deformed harmonic oscillator potential and the Gaussian two body potential.

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