Local Lorentz invariance violating (LLIV) and Einstein equivalence principle violating (EEPV) effects in atomic experiments are discussed. The EEPV effects are strongly enhanced in the narrow 7.8 eV transition in the ₉₀²²⁹Th nucleus. The nuclear LLIV tensors describing the anisotropy in the maximal attainable speed for massive particles (analog of the Michelson-Morley experiment for light) are expressed in terms of the experimental values of the nuclear quadrupole moments. Calculations for nuclei of experimental interest ₅₅¹³³Cs, ₃₇⁸⁵Rb, ₃₇⁸⁷Rb, ₈₀²⁰¹Hg, ₅₄¹³¹Xe, and ₁₀²¹Ne are performed. The results for ₁₀²¹Ne are used to improve the limits on the proton LLIV interaction constants by 4 orders of magnitude.
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V. V. Flambaum (2016) studied this question.