Collective Enhancement ofE2Matrix Elements in Light Nuclei

Abstract

Several electric quadrupole transitions in nuclei in the neighborhood of ${\mathrm{O}}^{16}$ are discussed. The well-known strong enhancement of the single-nucleon matrix elements is interpreted as resulting from the virtual excitation of a collective 2+ state in the ${\mathrm{O}}^{16}$ core. It is found that an energy of 18 Mev for this state gives a satisfactory account of all of the experimental data. The enhanced matrix elements are expressed in terms of an effective charge, which is calculated in detail within the framework of the nuclear shell model. The value of the effective charge depends on the particular independent-nucleon states involved in the transition and is found to be approximately 0.5, 0.7, and 0.9 for $2s-1d$, $1d-1d$, and $1p-1p$ matrix elements, respectively. Of special interest is the result that the ${\mathrm{N}}^{14}$ quadrupole moment should possess the relatively large value of 3×${10}^{-26\mathrm{}}$ ${\mathrm{cm}}^2$, or about three times the simple shell-model value. This prediction has recently been confirmed by high-energy electron scattering measurements. The relation of the present work to previous theoretical treatments of enhancement by the methods of the hydrodynamic model and of configuration mixing is discussed. The Appendix on center-of-mass effects contains an explicit demonstration of the cancelling of the classical recoil quadrupole moment of ${\mathrm{O}}^{17}$ by a quantum mechanical exchange term.