Density Shift and Broadening of Transition Lines in Antiprotonic Helium

Abstract

The density shift and broadening of the transition lines of antiprotonic helium have been evaluated in the impact approximation using an interatomic potential calculated ab initio with the symmetry-adapted perturbation theory. The results help to remove an uncertainty of up to 10 ppm in the laser spectroscopy data on antiprotonic helium and are of importance in experimental tests of bound state QED and CPT invariance.

Shift and broadening of resonance lines of antiprotonic helium atoms in liquid4He

“…The very good agreement of the theoretical results of Refs. [5,25] with the experimental data taken at a broad range of helium gas densities up to 127 g/l should be attributed to (1) the use of an accurate pair-wise state-dependent potential for the interaction of antiprotonic and ordinary helium atoms, calculated ab initio with the symmetrized Rayleigh-Schrödinger theory [6]; (2) the use of curvilinear classical trajectories of the perturbers determined by the interaction potential for the initial state of the transition; and (3) the fact that the conditions which justify the impact approximation and the approximation of binary collisions -typical collision duration smaller by an order of magnitude than the average interval between collisions, emitter excitation energies much larger than the thermal collision energies, uncorrelated motion of the perturbers, etc. -are satisfied for the densities and temperatures in consideration.…”

“…We therefore put the results of Ref. [5] in a form that allows us to use phenomenological data about the liquid helium target density instead of the theoretical calculations, and this way we obtain a reliable estimate of the collisional shift of the spectral lines. Unfortunately, the line broadening cannot be evaluated this way since similar naive approaches are known to produce wrong values, as pointed out in Ref.…”

“…[5,25] the density shift and broadening of the spectral lines of antiprotonic helium atoms in gaseous helium were evaluated in the frame of the semiclassical approach of P.W. Anderson [26].…”

“…These high-accuracy goals required various systematic effects to be accounted for, the density broadening and shift of the spectral lines being among the most important among them [4]. The density effects have been evaluated for a gaseous target in the semiclassical approach [5] using a pairwise interaction potential of an antiprotonic and an ordinary helium atom, calculated ab initio in the frame of the symmetrized RayleighSchrödinger theory [6], and the results were in agreement with the experimental data taken at helium gas densities up to 127 g/l [1]. The attempts of the ASACUSA collaboration at CERN for the laser spectroscopy of antiprotonic atoms in liquid helium [7] made us revisit the subject, since the collective degrees of freedom in the liquid phase (sound waves in the liquid consisting of the neutral 4 He atoms) provide a new mechanism for shifting and broadening the atomic spectra, in addition to those investigated in gaseous helium.…”

“…III, we evaluate the line shift due to collisions ofpHe + with 4 He atoms by making use of the quasistatic limit of the results of Ref. [5] in a form that allows for exploiting the experimental data on the pair correlation function in liquid 4 He. Unfortunately, this method cannot be extended to the evaluation of the line broadening.…”