Electric dipole moment of $^{13}$C

TL;DR

This paper calculates the electric dipole moment of $^{13}$C using an $ ext{alpha}$-cluster model, revealing its dependence on neutron EDM and CP-odd nuclear forces, and discusses implications for new physics beyond the standard model.

Contribution

First calculation of $^{13}$C EDM considering isovector CP-odd forces within an $ ext{alpha}$-cluster model, highlighting structural effects on EDM enhancement.

Findings

$^{13}$C EDM linearly depends on neutron EDM and CP-odd coupling.

The enhancement factor for $^{13}$C is smaller than for deuteron.

Structural differences influence the EDM enhancement in nuclei.

Abstract

We calculate for the first time the electric dipole moment (EDM) of $^{13}$C generated by the isovector CP-odd pion exchange nuclear force in the $\alpha$-cluster model, which describes well the structures of low lying states of the $^{13}$C nucleus. The linear dependence of the EDM of $^{13}$C on the neutron EDM and the isovector CP-odd nuclear coupling is found to be $d_{^{13}{\rm C}} = -0.33 d_n - 0.0020 \bar G_\pi^{(1)}$. 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 $^{13}$C in determining the new physics beyond the standard model.