Screening of nucleon electric dipole moments in atomic systems

The electric dipole moments (EDMs) of diamagnetic atoms are expected to be sensitive to charge-parity violation, particularly in nuclei through the nuclear Schiff moment. I explicitly demonstrate that the well-known form of the Schiff moment operator originating from the nucleon EDM is obtained by considering the screening of the nucleon EDMs in a neutral atom. Consequently, an additional contribution to the Schiff moment arises from the screening of the nuclear EDM induced by the interaction of the nucleon EDMs with the protons. This correction to the Schiff moment of ${}^{199}\mathrm{Hg}$ is evaluated in the independent particle model.

Figure 1

(a) The second-order and (b) the third-order contributions of the $P, T$-odd $\pi NN$ interaction ${\tilde{V}}_{\pi NN}$ to the energy shift of an atom immersed in an external electric field. The black circles represent the $P, T$-odd vertices. The electric charges of proton and electron are denoted by $q_N$ and $q_e$, respectively. The $P, T$-odd $\pi NN$ coupling constant is denoted by ${\overline{g}}_{\pi NN}$.

Figure 2

Schematic illustration of how the $P, T$-odd $\pi NN$ interaction ${\tilde{V}}_{\pi NN}$ induces the atomic EDM ${\mathit{d}}_{\text{atom}}$. The $P, T$-odd $\pi NN$ interaction induces the nuclear Schiff moment as well as the nuclear EDM. The interaction of the nuclear Schiff moment with the electrons $V_{\text{NSM-1}}$ violates $P$ and $T$ symmetries both in the nucleus and in the electron system. Finally, the $P, T$ violation in the electron system generates the atomic EDM.

Figure 3

The external interaction of (a) the nucleon EDMs and (b) the atomic EDM induced by the interaction of the nucleon EDMs with the electrons. The vertices with $d_N$ indicate the interactions of the nucleon EDM.

Figure 4

The leading-order contribution of the nucleon EDMs to the atomic EDM ${\mathit{d}}_{\text{atom}}$. The $P, T$-odd $eN$ interaction due to the finite-size effect ${\tilde{V}}_{\text{NSM-2}}$ appears in the pointlike nucleus limit.

Figure 5

(a) The second-order and (b) the third-order contributions of the interactions between the nucleon EDMs and the protons.