Structure of the shell-model wave functions of ²²Na and ²²Ne

Abstract

The structure of the shell-model wave functions for the T=0 and J=3,4 and 5 states of ²²Na and the T=1 and J=0,2 and 4 states of ²²Ne has been studied to test the existence of an intrinsic wave function. The SU₃ representation is very convenient for the purpose and has been employed. Good intrinsic wave functions are found for both nuclei. There is a slight J-dependence in the case of ²²Na. The intrinsic wave function of ²²Na is almost purely a single determinant and it compares well with the Hartree-Fock solution. An attempt is made to explain the J-dependence on the basis of the theory of Peierls and Thouless. The intrinsic wave function of ²²Ne shown considerable two-particle correlation. The amount of this correlation is of the same order as that of the pairing correlation predicted by a self-consistent Hartree-Fock-Bogolyubov calculation. An explanation of the observed difference in the character of the two intrinsic wave functions is suggested. The interaction employed in this calculation is close to a Serber exchange, Yukawa potential with the usual spin dependence. It cannot be regarded as a very satisfactory choice. Thus no attempt is made to compare the level spacings. However the level ordering is found to be satisfactory.