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 $\mathbf{\sigma }\mathbf{·}\mathbf{p}$ is discussed. The case of regular $M1\mathrm{}$ plus irregular $E1\mathrm{}$ 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, $P\propto \mathrm{FR}$, with recent measurement, gives the following limits for the amplitude factor $F:9\mathrm{}\lesssim {10}^7\times F\lesssim 110$. This result agrees in sign and order of magnitude with estimates derived from the current-current theory of weak interactions.