Weak quadrupole moment, quadrupole distribution of neutrons and Lorentz invariance violation in deformed nuclei

摘要

Collective effects in deformed atomic nuclei present possible avenues ofstudy on the non-spherical distribution of neutrons and the violation of thelocal Lorentz invariance. We introduce the weak quadrupole moment of nuclei,related to the quadrupole distribution of the weak charge in the nucleus. Theweak quadrupole moment produces tensor weak interaction between the nucleus andelectrons and can be observed in atomic and molecular experiments measuringparity nonconservation. The dominating contribution to the weak quadrupole isgiven by the quadrupole moment of the neutron distribution, therefore,corresponding experiments should allow one to measure the neutron quadrupoles.Using the deformed oscillator model and the Schmidt model we calculate thequadrupole distributions of neutrons, $Q_{n}$, the weak quadrupole moments,$Q_{W}^{(2)}$, and the Lorentz Innvariance violating energy shifts in$^{9}$Be, $^{21}$Ne , $^{27}$Al, $^{131}$Xe, $^{133}$Cs, $^{151}$Eu,$^{153}$Eu, $^{163}$Dy, $^{167}$Er, $^{173}$Yb, $^{177}$Hf, $^{179}$Hf,$^{181}$Ta, $^{201}$Hg and $^{229}$Th.