Alpha-particle spectroscopic amplitudes and the su(3) model

Abstract

Formulas for calculating spectroscopic amplitudes for emission or transfer of α-particles are developed in the framework of the harmonic-oscillator shell model with SU(3) classification. These formulas are applied to some interesting states of ²⁰Ne, e.g., low-lying (sd)⁴ shell-model states, members of the lowest K = 0⁻ band with SU (3) label (90), and 2khω excited states with SU(3) label (10, 0). Spurious c.m. motion is removed. The formulas are also applied to the ground and some excited states of ¹⁶O. The ¹⁶O wave functions of Brown and Green are used in an investigation of how the mixing among 0p-0h, 2p-2h, and 4p-4h states affects the wave function for relative motion between the α-cluster and the mass-12 nucleus. These calculations indicate much larger α reduced widths for states which are mainly 4p-4h than for states which are mainly 0p-0h or 2p-2h. Spectroscopic amplitudes are also calculated for some ¹⁶O and ¹²C states described as linear chains of α-particles.