Effects of particle-hole excitations to nuclear Schiff moments in Xe isotopes

The existence of the permanent electric dipole moment of a fundamental particle implies violation of time reversal invariance. The electric dipole moment of a diamagnetic neutral atom is mainly induced by the nuclear Schiff moment. In this study the Schiff moments induced by the interaction which violates parity and time reversal invariance are calculated for various Xe isotopes using the shell-model wave functions. The contributions to the Schiff moment from one-particle and one-hole excitations turn out to be very different from orbital to orbital. It is also found that the contributions from the core excitations are larger than other particle-hole contributions.

Figure 1

The schematic illustration of three types of $1p1h$ excitations considered in this study.

Figure 2

The proton-single-particle energy for each orbital taken for ${}^{129}\mathrm{Xe}$ in units of MeV. The energy of the $0g_{7/2}$ orbital is adjusted to be zero. Orbitals which are not connected by the Schiff moment operator are not shown.

Figure 3

The calculated results of $a_{\left(T\right)}$ for (a) $T=0$, (b) $T=1$, and (c) $T=2$ as functions of mass number $A$ for Xe isotopes (in units of ${10}^{-3}e{\mathrm{fm}}^3)$. The squares, diamonds, triangles, and circles represent $a_{\left(T\right)}^{\mathrm{type}\text{−}\mathrm{I}},a_{\left(T\right)}^{\mathrm{type}\text{−}\mathrm{II}},a_{\left(T\right)}^{\mathrm{type}\text{−}\mathrm{II}}$, and $a_{\left(T\right)}$, respectively.

Figure 4

(a) The strength functions of Schiff moment operator as a function of the energy denominator $E_{\mathit{\text{ph}}}$ for isoscalar $\left(T=0\right)$ contributions of ${}^{129}\mathrm{Xe}$. (b) The same as in (b), but for $V_{\pi \left(T\right)}^{PT}$ operator. (c) The same as in (a), but for partial contribution to the Schiff moment. The summation of partial contributions to the Schiff moment is also shown.

Figure 5

(a) Energy weighted sum function for the Schiff moment operator as a function of the energy denominator $E_{\mathit{\text{ph}}}$ for ${}^{129}\mathrm{Xe}$. (b) The same as in (a), but for $V_{\pi \left(T\right)}^{PT}$ operator with the isoscalar $\left(T=0\right)$ component.