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The intent of the work reported here has been to ascertain which properties of nuclei with 20

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One of the classic weaknesses of the shellmodel analysis of nuclear structure is its general inability to describe the observed magnetic moments and beta-decay transition probabilities. The failure is usually attributed to the sensitivity of the single-particle matrix elements to small configuration admixtures which introduce large changes in the single-particle matrix elements without appreciably affecting the energies of the states involved. It is clear that some explanation of this sort is necessary for s l/2 and p 1/2 particles, since in those cases there is very little uncertainty in the nuclear wave function corresponding to a pure configuration. But in shells of high single-particle spin the trouble may not lie in the assumption of a pure configuration, but rather in the additional assumptions usually made to obtain many-particle wave functions. This note will show in the specific case of the f ll2 shell that proper many-particle wave functions can explain much of the experimental data for magnetic moments and beta-decay transitions without invoking configuration mixing.The calculations of the single-particle operators were made for all nuclei in the f 7/2 shell which have at most two particles (holes) in one of the unfilled shells, and an arbitrary number of par-ticles (holes) in the other. This includes most of the nuclei in the shell. The wave functions used were energy eigenfunctions determined by diagonalizing the energy matrix of the residual interactions between all the nucleons in the shell. The interaction energies were taken to be (in MeV) 0, 1.035, 1.509, 2.248, 2.998, 1.958, 3.400, and 0.617, for angular momenta J = 0-7, respectively. This spectrum is consistent with all available experimental data on the spectrum of Sc 42 . 1 * 2 The interaction energies have been chosen to be charge independent so that the resulting wave functions are states of definite isotopic spin.Following Talmi's procedure, the many-body energy matrix elements were calculated using standard fractional parentage techniques. 3 The details of the calculation and the energy eigenvalues and eigenf unctions calculated by this method will be described in a forthcoming paper now in preparation.The beta-decay transition probabilities were calculated in terms of the single-particle transition probability, log//= 3. 65, taken from the experimental value for the 7-6 transition in the Sc 42 -Ca 42 decay. 4 The results are shown in Table I. In general, the predicted log ft values are raised to around 5.0, which closely matches the Table I. Log/* values.