Time reversal violating magnetic quadrupole moment in heavy deformed nuclei

The existence of permanent electric dipole moments (EDMs) and magnetic quadrupole moments (MQMs) violate both time reversal invariance ($T$) and parity ($P$). Following the $CPT$ theorem they also violate combined $CP$ symmetry. Nuclear EDMs are completely screened in atoms and molecules while interaction between electrons and MQMs creates atomic and molecular EDMs which can be measured and used to test $CP$-violation theories. Nuclear MQMs are produced by the nucleon-nucleon $T$, $P$-odd interaction and by nucleon EDMs. In this work we study the effect of enhancement of the nuclear MQMs due to the nuclear quadrupole deformation. Using the Nilsson model we calculate the nuclear MQMs for deformed nuclei of experimental interest and the resultant MQM energy shift in diatomic molecules of experimental interest ${}^{173}\mathrm{YbF}$, ${{}^{177,179}\mathrm{HfF}}^{+}$, ${}^{181}\mathrm{TaN}$, ${}^{181}{\mathrm{TaO}}^{+}$, ${}^{229}\mathrm{ThO}$ and ${}^{229}{\mathrm{ThF}}^{+}$.