Few-nucleon SU(3) parentage coefficients and α-particle spectroscopic amplitudes for core excited states in s-d shell nuclei

Abstract

The SU(6)/SU(3) factors of few-nucleon fractional parentage coefficients in 1s-0d shell nuclei are calculated directly without being generated recursively from one-nucleon c.f.p. Tabulations are given for x-nucleon reduced matrix elements, ( x = 4, 3, 2, 1), connecting states of high SU(3) symmetry, where the x-nucleon states are limited to states of totally symmetric space and oscillator quanta symmetry, i.e. SU(3) representations (80), (60), (40), (20) for states of space symmetries [4], [3], [2], [1]. Together with the SU(3)/R(3) factors calculated by Draayer, these reduced matrix elements make it possible to predict spectroscopic amplitudes for reactions in which the x-nucleon groups are transferred in unexcited (0s) internal states. In a specific application, α-particle spectroscopic amplitudes are calculated for core-excited states in s-d shell nuclei, reached by the transfer of (0p) −1(1s0d) −3, or (0p) −2(1s0d) −2 groups in pickup reactions and (1s0d) 3(1p0f) 1 or (1s0d) 2(1p0f) 2 groups in stripping reactions, where states in the final residual nuclei are approximated by SU(3) strong coupling states, (free of spurious c.m. excitation), corresponding ot the largest possible intrinsic deformations in these nuclei. The effect of a difference in α-particle size parameters in projectile and residual nuclei is discussed.