Alpha-particle state in extended Elliot model

The microscopic model of alpha-particles (A P) of (2s-1d)-nuclei basing on the Hamiltonian of SU(3) symmetry including, in addition to the Elliot model one Q3, QL2, and Bergram terms, is developed. Multi-cluster but not two body resonating group model (RGM) anzatz for the description of the AP resonances is used. The wave function (WF) for this model is presented. It is noted, that WF of any such resonance is a linear combination of few Elliot shell model WFs. The most important property of the Hamiltonian chosen in that if the clusters consisting the system are oscillator magic ones than the matrix elements of it do not contain exchange terms. The AP states are defined as resonance ones with same global quantum numbers as the α+core channel. So in comparison with presented semi-microscopic model one is in the same sense the next step to pure microscopic approach. Fitting the parameters of the Hamiltonian is based mainly on the spectra of low-lying AP states of nuclei known from the spectroscopic tables and, to a smaller degree, on a few high-spin states obtained in the reproducing experiment. This procedure resulted to a reasonable description of the AP level density in any two-fold spin-energy area. This true both for poor spectrum of magic α-core system and level-rich spectra of the nuclei in the middle of (2s-1d)-shell