In the shell model of nuclei, protons and neutrons move in a phenomenological nuclear potential much in the same manner as electrons move in Coulomb based potential in the shell model of atoms. As in the atomic case, the protons and neutrons of certa
in nuclear energy levels will have a non-zero orbital angular momentum (i.e. l =/= 0) and will therefore experience a centripetal potential and a centripetal acceleration. We advance the hypothesis, based on justification via the path integral formalism, that if one associates an Unruh temperature with this quantum centripetal acceleration then there is a potentially experimentally observable effect on certain nuclei -- the shifting of the naive expectations of the relative occupation of the ground and lowest lying energy levels. In particular we find that this effect should be most prominent in Li-7 nuclei. We speculate that this effect of the Unruh temperature might offer an answer to the Li-7 problem in Big Bang Nucleosynthesis.
We propose a test for the circular Unruh effect using certain atoms - fluorine and oxygen. For these atoms the centripetal acceleration of the outer shell electrons implies an effective Unruh temperature in the range 1000 - 2000 K. This range of Unru
h temperatures is large enough to shift the expected occupancy of the lowest energy level and nearby energy levels. In effect the Unruh temperature changes the expected pure ground state, with all the electrons in the lowest energy level, to a mixed state with some larger than expected occupancy of states near to the lowest energy level. Examining these atoms at low background temperatures and finding a larger than expected number of electrons in low lying excited levels, beyond what is expected due to the background thermal excitation, would provide experimental evidence for the Unruh effect.
