Effects of variation of hyperfine splitting(structure) in atomic physics

Abstract

The possible variation of the fundamental constants is currently a very popular research topic. Theories unifying gravity and other interactions suggest the possibility of spatial and temporal variation of physics constants in the universe. Current interest is high because in superstring theories which have additional dimensions compactified on tiny scales any variation of the size of the extra dimensions results in changes in the 3-dimensional coupling constants. String theory also suggest the space to be noncommutative i.e., the space coordinates do not commute with each other. In this paper we study the hyperfine splitting in the framework of the noncommutative quantum mechanics(NCQM) developed in the literature. We show that the energy difference between two excited F = I + ½ and the ground F = I − ½ states in a noncommutative space(NCS) is bigger than the one in commutative case, so the radiation wavelength in NCSs must be shorter than the radiation wavelength in commutative spaces. We also find an upper bound for the non-commutativity parameter. Since in the very tiny string scale or at very high energy situation the effects of non-commutativity of space may appear so the hyperfine splitting is not constant and changes as energy changes(high energy situation). The results would be of interest both for theoretical and optical spectroscopists.