Higher-order nuclear-polarizability corrections in atomic hydrogen

Abstract

Nuclear-polarizability corrections that go beyond unretarded-dipole approximation are calculated analytically for hydrogenic (atomic) S-states. These retardation corrections are evaluated numerically for deuterium and contribute -0.68 kHz, for a total polarization correction of 18.58(7) kHz. Our results are in agreement with one previous numerical calculation, and the retardation corrections completely account for the difference between two previous calculations. The uncertainty in the deuterium polarizability correction is substantially reduced. At the level of 0.01 kHz for deuterium, only three primary nuclear observables contribute: the electric polarizability, α E , the paramagnetic susceptibility, β M , and the third Zemach moment, r 3 (2) . Cartesian multipole decomposition of the virtual Compton amplitude and its concomitant gauge sum rules are used in the analysis.

Nuclear polarizability of helium isotopes in atomic transitions

“…However, the uncertainty of the experimental result of Wang et al [16] for the isotope shift between 6 He and 4 He, ν iso = 43 194 772(56) kHz, is about four times larger than ν pol , and therefore the nuclear polarizability correction at this precision level is not very significant.…”

“…The relative magnitude of the nuclear polarizability to the nuclear finite size for 6 He is about 0.35 %, so it alters the charge radius determination at this precision level. However, the uncertainty of the experimental result of Wang et al [16] for the isotope shift between 6 He and 4 He, ν iso = 43 194 772(56) kHz, is about four times larger than ν pol , and therefore the nuclear polarizability correction at this precision level is not very significant.…”

“…In this case the polarizabilityα( 6 He) was calculated from two different B(E1) distributions. The first one corresponds to the experimental distribution extracted by Aumann et al [10] from the Coulomb breakup of 6 He on lead at 240 MeV/u. These data are represented by the dots in Fig.…”

“…This is the main approximation of our approach, which may not always be valid. It was checked however that higher order polarizabilities are quite small (below 1 kHz) for deuterium [5,6], and this should be similar for He isotopes. Within this low electromagnetic momentum approximation, the nuclear polarizability correction to the energy is given by the following formula [7] (in unitsh = c = 1, e 2 = 4 π α):…”

“…The second B(E1) distribution corresponds to a theoretical calculation, and was obtained in [11] by evaluating the matrix element of the dipole operator between the ground state and the 1 − continuum states. These states where obtained by solution of the Schrödinger equation, assuming a three-body model for the 6 He nucleus, with pairwise neutron-neutron and neutron-α interactions, plus an effective three-body force. The B(E1) obtained in this calculation is represented in Fig.…”