  The Lorentz invariance and Einstein equivalence principle violating effects
in the narrow 7.8 eV transition in 229Th nucleus may be 100 000 times larger
than in atoms. This transition may be investigated using high precision laser
spectroscopy methods, has a very small width, and suppressed systematic
effects. Similar values of the effects are expected in 73 eV 235U nuclear
transition which is coming within the reach of the laser spectroscopy.
Mossbauer transitions give another possibility.
