Isospin mixing and Coulomb mixing in ground states of even-even nuclei

In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small.

Figure 1

Isovector states in nuclei with $N>Z$. A single-particle isovector operator $Q_{\mu }^{\left(\mathrm{IV}\right)}$, has three components, $Q_{-1}^{\left(\mathrm{IV}\right)}$, $Q_0^{\left(\mathrm{IV}\right)}$, and $Q_{+1}^{\left(\mathrm{IV}\right)}$. In the parent nucleus, $Q_0^{\left(\mathrm{IV}\right)}$ excites $|T+1,T;\alpha \rangle$ and $|T,T;\alpha \rangle$. In the analog nucleus ($N-1,Z+1$), $Q_{-1}^{\left(\mathrm{IV}\right)}$ excites $|T+1,T-1;\alpha \rangle$, $|T,T-1;\alpha \rangle$, and $|T-1,T-1;\alpha \rangle$. In the nucleus ($N+1,Z-1$), $Q_{+1}^{\left(\mathrm{IV}\right)}$ excites $|T+1,T+1;\alpha \rangle$ only.

Figure 2

The distribution of IVM strength (a) and Coulomb strength (b) in ${}^{208}\mathrm{Pb}$. The discrete RPA peaks for both operators were smoothed by using the same Lorentzian averaging with the width of 1 MeV.