Shell-Model Structure ofCa42−50

Physical Review C1970Vol. 2(1), pp. 186–212

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J.B. McGrory, B. H. Wildenthal, E.C. Halbert

Abstract

The low-lying states of the calcium isotopes $^{42}\mathrm{Ca}$ through $^{50}\mathrm{Ca}$ are discussed within the framework of the conventional shell model. An inert $^{40}\mathrm{Ca}$ core is assumed. Calculations are made in several basis-vector spaces involving active $0{f}_{\frac{7}{2}}$, $1{p}_{\frac{3}{2}}$, $0{f}_{\frac{5}{2}}$, $1{p}_{\frac{1}{2}}$, and $0{g}_{\frac{9}{2}}$ neutron orbits. In one set of calculations, we use a "realistic" effective interaction derived for this mass region by Kuo and Brown. The shell-model results suggest that, in this effective interaction, the interactions of ${f}_{\frac{7}{2}}$ neutrons with ${p}_{\frac{3}{2}}$, ${p}_{\frac{1}{2}}$, and ${f}_{\frac{5}{2}}$ neutrons are too strong. In other calculations, with a modified Kuo-Brown interaction, we find the calculated spectra for the low-lying states of the calcium isotopes are in agreement with observed spectra, with several significant exceptions. The exceptions are that the second ${0}^{+}$ and ${2}^{+}$ states observed in $^{42}\mathrm{Ca}$, $^{44}\mathrm{Ca}$, and $^{46}\mathrm{Ca}$ are not accounted for in the calculation. Calculated spectroscopic factors for ${f}_{\frac{7}{2}}$ transfers are in good agreement with experimental spectroscopic factors, and the observed centroids of the ${p}_{\frac{3}{2}}$ single-particle strengths are reasonably well reproduced. Our results also indicate that "core-excitation" effects are significant above about 2.5 MeV in $^{42}\mathrm{Ca}$ through $^{48}\mathrm{Ca}$.

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Abstract

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