Effect of nuclear quadrupole moments on parity nonconservation in atoms

Nuclei with spin $I\ge 1$ have a weak quadrupole moment which leads to tensor contribution to the parity nonconserving interaction between nuclei and electrons. We calculate this contribution for atoms of current experiment interest ${\mathrm{Yb}}^{+}$, Fr, and ${\mathrm{Ra}}^{+}$. We have also performed order of magnitude estimates and found strong enhancement of the weak quadrupole effects due to the close levels of opposite parity in many lanthanoids (e.g., Nd, Gd, Dy, Ho, Er, Pr, Sm) and Ra. Another possibility is to measure the parity-nonconservation (PNC) transitions between the hyperfine components of the ground state of Bi. Since nuclear weak charge is dominated by neutrons this opens a way of measuring quadrupole moments of neutron distribution in nuclei.

Figure 1

Coulomb corrections to the weak matrix elements. Cross stands for the weak quadrupole interaction; summation over complete set of $n{p}_{3/2}$ states is assumed. (a) The $6p\text{−}5d$ or $5d\text{−}4f$ matrix elements. (b) The $6s\text{−}4f$ matrix element. (c) The two-electron matrix element between the $4f6s$ and $5d^2$ states (e.g., in Nb).