Linear chain states with zero-range and other Skyrme interactions

Abstract

With the usual Skyrme interactions, e.g., Skyrme III, the energies of the bandheads of the linear-alpha-chain states in 12C and 16O come about a factor of two too high in energy. On the other hand, the Nilsson model gets the energies about right. In an analytic model using a zero-range Skyrme interaction with asymptotic deformed harmonic oscillator wave functions, the energies of the linear chain states come down considerably and are in better agreement with experiment. In more sophisticated Hartree-Fock calculations with the above zero-range interaction, these states come down too low in energy, but the overall analysis suggests lowering the magnitude of the finite-range terms in the Skyrme interactions in order to get the linear chain states at the right energies. The zero-range Skyrme interaction gives a close realization of the Nilsson model when a constraint of volume conservation is imposed.