Electric dipole moment of ${}^{13}\mathrm{C}$

We calculate for the first time the electric dipole moment (EDM) of ${}^{13}\mathrm{C}$ generated by the isovector charge conjugation-parity (CP)-odd pion exchange nuclear force in the $\alpha$-cluster model, which describes well the structures of low-lying states of the ${}^{13}\mathrm{C}$ nucleus. The linear dependence of the EDM of ${}^{13}\mathrm{C}$ on the neutron EDM and the isovector CP-odd nuclear coupling is found to be $d_{{}^{13}\mathrm{C}}=-0.33d_n-0.0020{\overline{G}}_{\pi }^{\left(1\right)}$. The linear enhancement factor of the CP-odd nuclear coupling is smaller than that of the deuteron, due to the difference of the structure between the $1/2_1^{-}$ state and the opposite-parity ($1/2^{+}$) states. We clarify the role of the structure played in the enhancement of the EDM. This result provides good guiding principles to search for other nuclei with large enhancement factor. We also mention the role of the EDM of ${}^{13}\mathrm{C}$ in determining the new physics beyond the standard model.

Figure 1

The radial shape of the bare pion exchange CP-odd nuclear force $V\left(r\right)$ and its folding potential $V_{\alpha -N}\left(r\right)$. The CP-odd coupling constant was factored out.

Figure 2

Jacobi coordinates to express the EDM of ${}^{13}\mathrm{C}$.

Figure 3

Convergence of the EDM of ${}^{13}\mathrm{C}$ displayed in the function of the number of channels, with 343 bases for each. The CP-odd coupling constant ${\overline{G}}_{\pi }^{\left(1\right)}$ was factored out.

Figure 4

Parity-odd transitions contributing to the EDM of ${}^{13}\mathrm{C}$ in the leading order of perturbation. The dashed lines represent the dissociation thresholds into ${}^{12}\mathrm{C}\left(0^{+}\right)+n$ or ${}^{12}\mathrm{C}\left(2^{+}\right)+n$ states. The gray bands correspond to the continuum states.