Pressure shifts in high-precision hydrogen spectroscopy: II. Impact approximation and Monte-Carlo simulations

Abstract

We investigate collisional shifts of spectral lines involving excited hydrogenic states, where van der Waals coefficients have recently been shown to have large numerical values when expressed in atomic units. Particular emphasis is laid on the recent hydrogen 2S-4P experiment (and an ongoing 2S-6P experiment) in Garching, but numerical input data are provided for other transitions (e.g., involving S states), as well. We show that the frequency shifts can be described, to sufficient accuracy, in the impact approximation. The pressure related effects were separated into two parts, (i) related to collisions of atoms inside of the beam, and (ii) related to collisions of the atoms in the atomic beam with the residual background gas. The latter contains both atomic as well as molecular hydrogen. The dominant effect of intra-beam collisions is evaluated by a Monte-Carlo simulation, taking the geometry of the experimental apparatus into account. While, in the Garching experiment, the collisional shift is on the order of 10 Hz, and thus negligible, it can decisively depend on the experimental conditions. We present input data which can be used in order to describe the effect for other transitions of current and planned experimental interest.

Two-photon frequency comb spectroscopy of atomic hydrogen

“…Most of the measurements in this work have been done at a temperature of 7 K, which is much smaller than the temperature of the background gas (≈ 300 K). A model for the collisional shift experienced by a slow atomic beam that is emerged in a gas of faster moving atoms has been developed in [69] and is described by:…”

“…where n is a number density of the particles of the background gas, and T B is the temperature of the background gas with a particle mass of m B . The coefficient ξ (6) ω = −4.325 × 10 −17 rad m 2 (m/s) 2/5 has been obtained in [69]. It is based on the calculation of the van-der-Waals interaction coefficients derived in [68].…”

Precision measurement of quasi-bound resonances in H$_2$ and the H + H scattering length

“…The H + H scattering process is of fundamental interest in physics, playing a role in the formation of molecular hydrogen in the universe [83], frequency shifts in the hydrogen maser [84], the magnitude of pressure shifts in the 1S-2S transition of atomic hydrogen for a determination of the Rydberg constant [85,86], and for the formation of a Bose-Einstein condensate in hydrogen [87]. Because of the light atomic mass, non-adiabatic effects are especially important in this collision process and the question about the correct treatment of these was vividly discussed in the literature [88] (and references therein).…”

Measurement of the $2$S$_{1/2}-8$D$_{5/2}$ transition in hydrogen

“…During a collision with a water molecule, a hydrogen atom experiences a varying electric field which can drive population in the 8D state to nearby states, quenching the 8D state and broadening the line [30]. We have employed Monte Carlo simulations of these H-H 2 O collisions to estimate the shift and broadening, similar to [31]. From these simulations we have found that any associated pressure shifts are below the ∼1 Hz level and insignificant at our current level of precision.…”