Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation

The nuclear matrix elements for the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean field theory to calculate these matrix elements in $^{21}$Ne, $^{23}$Na, $^{131}$Xe, $^{173}$Yb and $^{201}$Hg. These are the first microscopic calculations of the nuclear matrix elements for the momentum quadrupole tensor that go beyond the single-particle estimate. We show that they are strongly suppressed by the many-body correlations, in contrast to the well known enhancement of the spatial quadrupole nuclear matrix elements.