The effective Hamiltonian which was determined empirically by Koops and Glaudemans is tested in shell model calculations for the nuclei in the full(1 P3/2,0]5/2, 1 Pl/J space. The resulting energy spectra are compared with the experimental spectra and results of previous calculations. The overall agreement with experiment is as satisfactory for these nuclei as for the Ni and Cu isotopes, by which the Hamiltonian was determined. It is noticed that the spectra of 67Zn and 67'69Ga calculated in this work are similar to those provided by the Alaga model.
Electromagnetic properties of Zn, Ga, and Ge are studied by using the nuclear shell model. Empirically determined M1 operators are found to be very successful to explain M1 transitions, moments, and mixing ratios. Many E2 properties are also understood by the present shell-model calculations with effective charges.
One of the possible improvements of the Hatree-Fock (HF) method of variation after projection (VP), which consists in the use of an angular momentum eigenstate as a trial wave function. The eigenstate is projected from a determinant whose single-particle orbitals are variationally determined. This method has been applied to the simple nuclei and compared with the HF method. 1 >• 2 > The comparisons have shown that the two methods give practically identical results in the case of 20 Ne. However, the comparison is incomplete for 44 Ti, 2 > and is completed in this short note.Two protons and two neutrons in the (f, p) shell are treated as active particles. The axial symmetry and the time-reversal invariance are assumed for the four-particle determinant. One proton and one neutron are embedded in the single-particle orbit and other particles are assumed to occupy the orbit obtained from the first one by a rotation of an angle 11: about they-axis. The former orbit is expanded by the harmonic oscillator wave functions with the magnetic quantum number m=1/2. The expansion coefficients are assumed to be real and are treated as variational parameters.The projection of the angular momuntum is done analytically and the final formulae for the matrix elements
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