The Casimir effect at the nucleus (2402.01776v1)

Abstract: In this report, the impact of the Casimir effect in the near-nuclear environment on electrons, in particular of the K-shell, is investigated. It has long been known that the experimentally measured binding energies of the inner electrons, especially for heavy elements, agree only to a very limited extent with the theoretical solutions of the Schroedinger and Dirac equations. This report presents a modification for the potential of electrons near the nucleus by investigating the impact of the Casimir effect on the innermost electrons. It can be shown that with this approach the calculated binding energies agree much better with the literature values from spectroscopy, especially for heavy elements. In addition, the innermost electrons are apparently influenced much more strongly than previously assumed by the nature of the nuclear surface, in particular the deviation from the spherical geometry, e.g. the multipole moments and not least the range of the strong interaction. This effect is not to be confused with the quantum-mechanical quadrupole energy (Casimir 1936), which is determined by spin interactions between nucleus and electron, but the effect discussed in this report is a distance dominated effect of the s-electrons to the nucleus. It offers the possibility of investigating the nucleus structure and isotope effects on the binding energies much more precisely than expected, e.g. by spectroscopy, and thus gaining new insights into the respective nuclear structure and geometry. At the same time, this approach shows that the probability of the electrons staying close to the nucleus is apparently significantly higher than assumed in previous atomic models. This may also increase the transition probabilities of electron capture, and thus the model enables a higher accuracy for the calculation of the theoretical half lifetimes for electron capture decay.