Abstract
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.
Published Version
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