State-Dependent Effective Charge in the2p−1fShell

Abstract

Motivated by a desire to understand the electric quadrupole transition rates in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, calculations of the effective charge for both neutrons and protons were carried out, first with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as a core and then with ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$. The calculation was done in perturbation theory using the Kallio-Kolltveit interaction. Concerning state dependence, it was first observed and then proved that in the limit in which energy differences in the $2p-1f$ shell were small compared with $2\hslash \omega$ excitations, the effective charge depended on the initial and final orbital angular momentum of a given transition, but when these $l$'s were specified, it was independent of the initial and final $j$ values. The effective-charge correction was much bigger for a neutron than for a proton. This may have the effect of reducing the isovector part of the quadrupole operator and hence causing $\Delta T=1\mathrm{}$ transitions to be inhibited. The effective charge is substantially larger with ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$ as a core than with ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as a core, but is somewhat too small to explain the $E2\mathrm{}$ transition from the first excited $2_1^{}{}_{}{}^{+}$ stage to ground. The effect of state dependence in the examples considered was to change certain $E2\mathrm{}$ rates by a factor of 1.5 to 2. In ${}_{}{}^{58}{}_{}{}^{}\mathrm{N}1\mathrm{}$, the $E2\mathrm{}$ ratio $2_2^{}{}_{}{}^{+}$→$0_1^{}{}_{}{}^{+}$/$2_2^{}{}_{}{}^{+}$→$2_1^{}{}_{}{}^{+}$, if calculated with shell-model wave functions, is extremely sensitive to the two-body interaction that is used. For example, it is about sixty times smaller (and closer to experiment) if Kuo's matrix elements, which are derived from a realistic interaction, are used rather than matrix elements chosen to give a least-squares fit to the energy levels of the nickel isotopes. If only one of the matrix elements obtained from the energy fit is changed by 0.3 MeV, the ratio becomes forty-two times smaller, also closer to the experimental value. The possibility that a lowlying $2^{+}$ state was basically a $3p-1h$ state was examined. The lowest two such states had very weak $E2\mathrm{}$ transitions to ground and therefore did not at all resemble the one-phonon state or the electric quadrupole state. By themselves, these states fail as candidates, not only for the

Keywords

• MMULTISCRIPTS
• MROW
• INLINE
• HTTP
• XMLNS
• WWW.W3.ORG/1998/MATH/MATHML

This publication has 18 references indexed in Scilit:

• 58Ni(p, p′γ)58Ni angular correlation measurements
  Nuclear Physics A, 1967
• Quadrupole matrix elements in O17 and F17
  Nuclear Physics, 1964
• Collective Enhancement ofE2Matrix Elements in Light Nuclei
  Physical Review B, 1959
• Effective Charge of Neutrons in Nuclei
  Physical Review B, 1959
• Weak Collective Effects in the Nuclear Shell Model
  Physical Review B, 1957
• Weak Collective Effects in the Nuclear Shell Model
  Proceedings of the Physical Society. Section A, 1957
• XXIX. Collective effects in nuclei of mass 18 and 19
  Philosophical Magazine, 1956
• Configuration Mixing and Quadrupole Moments of Odd Nuclei
  Physical Review B, 1955
• Configuration Mixing and Magnetic Moments of Nuclei
  Progress of Theoretical Physics, 1954
• The Magnetic Moments of Spin Nuclei
  Proceedings of the Physical Society. Section A, 1953

Read more Read more

Cited by 58 articles