Application of Time-Dependent Hartree-Fock Theory toNe20: Odd-Parity Bands

The constraint that the ${\mathrm{O}}^{16}$ "core" be inert with respect to particle-hole excitations in ${\mathrm{Ne}}^{20}$, imposed in a recent calculation, is relaxed. In this time-dependent Hartree-Fock treatment of ${\mathrm{Ne}}^{20}$, excitations are considered in which a particle from the energetically highest level in the core is promoted to a level in the $s-d$ shell. The wave function describing the core particle is assumed to be given by the shell model. The single-particle wave functions and energy spectra ascribed to the outer four particles are those obtained by a static Hartree-Fock calculation done previously. Such excitations give rise to excited "intrinsic" states of odd parity, the lowest lying of which correspond to the observed odd-parity rotational bands. The agreement between the observed and calculated band positions gives credence to the assumption, proposed in the earlier calculation, that the ${\mathrm{O}}^{16}$ core is nearly spherical in ${\mathrm{Ne}}^{20}$ despite the deformation of the orbitals of the outer particles.