Structure of Low-Energy Collective $0^{-}$-States in Doubly Magic Nuclei and Matrix Elements of the P-odd and P- and T-odd Weak Interaction

Abstract

The structure of the collective low-energy $J^{\pi }=0^{-}$ (T=0 and T=1) modes is studied for a doubly magic nucleus in a schematic analytic model of RPA. The $0^{-}$ phonon states ($T=0,1$) lie at energies $E_{T=0}(0^{-})\text{alt}\omega$ and $E_{T=1}(0^{-})>\omega$, where $\omega$ is the oscillator frequency. The matrix elements of P-odd and P- and T-odd weak one-body potentials connecting the ground state to these $0^{-}$-states, $W_{coll}$, are enhanced by the factor $\sim 2(\frac{\omega }{E}{)}^{1/2}{A}^{1/3}\sim 10$ as compared to the single-particle value $w_{sp}$ what can result in values $|W_{coll}|\sim 20-30eV$ if standard values of DDH parameters are used for $w_{sp}$. Similar enhancement arises in the P- and T-odd case.

Comments: 15 pages, REVTEX 3, 2 figures