One- and two-photon resonant spectroscopy of hydrogen and anti-hydrogen atoms in external electric fields

Abstract

The resonant spectra of hydrogen and anti-hydrogen atoms in the presence of an external electric field are compared theoretically. It is shown that nonresonant corrections to the transition frequency contain terms linear in the electric field. The existence of these terms does not violate space and time parity and leads to a difference in the resonant spectroscopic measurements for hydrogen and anti-hydrogen atoms in an external electric field. The one-photon 1s − 2p and the two-photon 1s − 2s resonances are investigated.

Influence of external electric fields on multi-photon transitions between the 2s, 2p and 1s levels for hydrogen and antihydrogen atoms and hydrogen-like ions

“…The relation (8) involves the nonrelativistic electron momentum operator p = −i∇, the electron spin operator ŝ = 1 2 σ (σ are the Pauli matrices) and (...) A A denotes the matrix element with the Schrödinger wavefunctions. In the dipole approximation the first term of the integrand in equation (7) describes the E1 photon emission, that in the case of A = 1s, A = 2s is forbidden by parity; the second term corresponds to the M1 photon emission. Due to the orthogonality of the radial wavefunctions ψ 2s and ψ 1s the M1 transition probability as described by equation ( 7) is nonzero only due to the factor e −ikr and due to the relativistic corrections to the Schrödinger wavefunctions.…”

“…The possibility of the CPT-tests is connected with the modern extra-accurate resonance frequency measurements in hydrogen [4,5]. In [6][7][8] it was shown that a specific difference in the H and H atomic spectra arises even in the absence of the CPT-violation, if an external electric field is present. In principle, a difference also arises for the frequency measurements if nonresonant (NR) corrections are taken into account.…”

Quenching of para-H2with an ultracold antihydrogen atomH¯1Sultanov1, Adhikari2, Guster3 2010Phys. Rev. A61230View full textAdd to dashboardCite

“…Some theoretical studies have been carried out for the H + H system at thermal energies using quantum-mechanical methods [21][22][23][24][25][26]. Also, discussions on the importance and applications for this system, especially in connection with Bose-Einstein condensation [27], ultracold collisions [16,22], and its static and dynamic properties [28], can be found in the literature.…”

Proton size from precision experiments on hydrogen and muonic hydrogen atoms

“…The first attempts to calculate NR corrections to them were made in [16,19], where the negligibly small contributions for the 1s−2s transition frequency with respect to the current level of experimental accuracy were found. Theoretical analysis of such experiments is complicated by the presence of an external electric field acting on the excited atom with a time delay, see [17,18,33]. Reference can also be made to the result of [17], where the nonresonant correction 0.17 MHz for the Lyman-α spectral line was found taking into account the hyperfine splitting, while the uncertainty of the frequency measurement is about 6 MHz.…”