2015/06/30 by Calvin W. Johnson · 1 citation
Physics and Astronomy · #nucl-th #astro-ph.SR #nucl-ex
paper · pdf · doi:10.1016/j.physletb.2015.08.054
published as Phys. Lett. B 750, 72 (2015) · 5 pages, 4 figures; minor revisions; references updated; title revised; matches accepted version
arxiv created 2015/08/27 · arxiv updated 2015/09/02
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).