2025/06/19 by Adkins, G. S., Jentschura, U. D. · 1 citation
#Atomic Physics (physics.atom-ph) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2506.15973
In exotic atomic systems with hadronic constituent particles, it is notoriously difficult to estimate the strong-interaction correction to energy levels. It is well known that, due to the strength of the nuclear interaction, the problem cannot be treated on the basis of Wigner-Brioullin perturbation theory. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates for the search of New Physics in the low-energy sector of the Standard Model. In order to render this endeavor feasible, it is necessary to estimate the strong-interaction correction to the atomic energy levels. We thus derive a generalized Deser-Trueman formula for the induced energy shift for a general hydrogenic bound state with principal quantum number n and orbital angular momentum quantum number~ℓ, and find that the energy shift is given by the formula delta E = 2 alphan, L betaL (ah/a0)^(2 L + 1) Eh/n3, where alphan,0 = 1, alphan,L is the product from s=1 to s=L of the expression (s^(-2) - n^(-2)), betaL = (2 L + 1)/[(2 L + 1)!!]2, where Eh is the Hartree energy, ah is the hadronic radius and a0 is the generalized Bohr radius. The square of the double factorial, [(2ℓ + 1)!!]2, in the denominator implies a drastic suppression of the effect for higher angular momenta.