spacetime symmetry of special relativity, Lorentz invariance is

a basic component of the standard model of particle physics

and general relativity, which to date constitute our most successful

descriptions of nature. Deviations from exact symmetry would

radically change our view of the universe and current experiments

allow us to test the validity of this assumption. In this talk, I will

describe how we can use current and future beta-decay experiments

to search for some key signals of the violation of Lorentz invariance.

nuclei with 94<Z<98, accessed via inelastic and transfer reactions,

using heavy stable beams on radioactive targets. These complement

spectroscopic investigations of elements with 100<Z<104 using

fusion-evaporation reactions. The physics of the highest neutron

orbitals at and beyond N=150 will be discussed. Valence orbitals here

can originate from above the spherical shell gaps that are believed to

be responsible for the stability of superheavy elements. Thus, a precise

mapping of single particle states in this deformed region can provide

guidance and constraints for theories that attempt to predict the next

higher spherical magic numbers.