16O Core Research Articles

Deformed state admixtures in18O

Following the suggestion by Brown, we have considered a model of the nucleus 18O in which, in addition to the usual shell-model picture of two neutrons coupled to an inert 16O core, we have also included a collective deformed state represented by a two-proton excitation in a deformed but axially symmetric shell-model potential. For a given model interaction (the Kallio-Kolltveit interaction), four fitted parameters (the oscillator constant, the effective charge and the single-particle spectrum) and two variational parameters (the deformation parameters) we have managed to reproduce the lowest eight known positive parity states to a good approximation in 18O and the two principal E2 transition rates. The predicted eigenvectors are in good agreement with the stripping experiments of Moreh and Daniels.

Structure of finite nuclei and the free nucleon-nucleon interaction: An application to 18O and 18F

The intention of this work is to investigate the applicability of the free nucleon-nucleon potential determined by the scattering data in the shell-model description of finite nuclei. The potential is chosen to be that of Hamada and Johnston. We have chosen 18O and 18F as our first numerical calculations. A major part of the work reported here concerns the evaluation of the shell-model reaction matrix elements. They are evaluated using the separation method for the singlet-even and triplet-even states and the reference spectrum method for the singlet-odd and triplet-odd states. The second-order Born term for the triplet-even tensor force is found to be very important. It can be calculated conveniently and with good accuracy using the closure approximation with an energy denomiator of ≈ 220 MeV. Assuming the singlet-particle wave functions to be those of a harmonic oscillator well, the single-particle energy levels of 0 d 5 2 , 1 s 1 2 and 0 d 3 2 for 170 are calculated by letting the valence nucleon interact with 16O core. The results are very encouraring. The 0 d 5 2 −0 d 3 2 splitting is found to come mostly from the triplet-odd 1 · s force through the reaction matrix Hartree-Fock process. The spectra of 18O and 18F are satisfactorily reproduced by diagonalizing the model interaction GΘ 3 p1 h in the sd shell, except for the states which are presumed to be largely deformed; G is the reaction matrix and Ω 3p1h is the wave operator which takes care of the corrections arising from the one-particle-one-hole excitation of the 16O core. It is found that the conventional shell-model effective interactions are well reproduced by the model interaction deduced from the free nucleon-nucleon potential.

Core excitation of 20Ne

Odd parity states of 20Ne arising from excitation of the 16O core are studied using the SU(3) classification scheme. A K = 0, L = 0 −, 2 −, 4 −,… band is predicted to begin at about 10 MeV. The E2 transitions between such states are discussed.

XXIX. Collective effects in nuclei of mass 18 and 19

Abstract In an intermediate coupling shell model calculation for the nuclei of mass 18 and 19, Elliott and Flowers (1955) determined the positions of the low lying levels in the absence of any collective effects. They found, however that certain E2 transition rates in 17O and 19F could not be explained without collective motion and that the introduction of weak coupling of the Bohr and Mottelson (1953) type between the surface and the nucleons outside the 16O core gave simultaneous agreement in 17O and l9F. In this note we consider the effects of such weak coupling, and show that although it enhances the E2 transition rates in 19F by a factor of order 5, the changes in level positions and magnetic moment, are negligible.