The Effects of Deformation on Isovector Electromagnetic and Weak Transition Strengths

Abstract

The summed strength for transitions from the ground state of ${}^{12}C$ via the operators $\vec{s}t,\vec{\ell }t,r{Y}^{\prime }t,r[Y^{\prime }s{]}^{\lambda }t$ and $r[Y^{\prime }\ell {]}^{\lambda }t$ are calculated using the $\Delta N=0$ rotational model. If we choose the z component of the isospin operator $t_z$, the above operators are relevant to electromagnetic transitions; if we choose $t_{+}$ they are relevant to weak transitions such as neutrino capture. In going from the spherical limit to the asymptotic (oblate) limit the strength for the operator $\vec{s}t$ decreases steadily to zero; the strength for the operator $\vec{\ell }\tau$ (scissors mode) increases by a factor of three. For the last three operators - isovector dipole, spin dipole and orbital dipole (including the twist mode) it is shown that the summed strength is independant of deformation. The main difference in the behavior is that for the first two operators we have in-shell transitions whereas for the last three operators the transitions are out of shell.

14 pages, latex

References in corpus (6)

• Evidence for ${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$ Oscillations from the LSND Experiment at LAMPF
• Weak reactions on 12C within the Continuum Random Phase Approximation with partial occupancies
• Measurements of the reactions 12C + nu_mue -> mu- + 12N g.s. and 12C + nu_mu -> mue- + 12N
• Neutrino-nucleus reactions on ^{12}C and ^{16}O
• Correlation between the quenching of total GT+ strength and the increase of E2 strength
• Neutrino nucleus scattering

Cited by in corpus (3)

• Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines
• Quasideuteron states with deformed core
• Double beta decay to the first $2^{+}$ state within a boson expansion formalism with a projected spherical single particle basis