Nuclear Structure and Parity Impurities

Abstract

Nuclear-structure calculations, relevant to the evaluation of irregular gamma-ray transition amplitudes (parity-forbidden multipoles), have been performed. General expressions have been derived for the case of one-particle states in odd-$A$ nuclei with spherical or spheroidal shape. In particular, the pseudoscalar operator $\mathbf{\ensuremath{\sigma}}\mathbf{\ifmmode\cdot\else\textperiodcentered\fi{}}\mathbf{p}$ is discussed. The case of regular $M1$ plus irregular $E1$ transition is considered as an application. Results are derived for the transitions of 482 keV in ${\mathrm{Ta}}^{181}$, 343 keV in ${\mathrm{Lu}}^{175}$, and 14 keV in ${\mathrm{Fe}}^{57}$. For ${\mathrm{Ta}}^{181}$, it is possible to calculate the magnitude and the sign of the nuclear matrix-element ratio $R$. Comparing the theoretical result for the circular polarization, $P\ensuremath{\propto}\mathrm{FR}$, with recent measurement, gives the following limits for the amplitude factor $F:9\ensuremath{\lesssim}{10}^{7}\ifmmode\times\else\texttimes\fi{}F\ensuremath{\lesssim}110$. This result agrees in sign and order of magnitude with estimates derived from the current-current theory of weak interactions.