Abstract
To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient α R A for producing the negative hydrogen ion H − or its antimatter equivalent, the positive antihydrogen ion H ¯ + , we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of H ¯ + has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results.
Highlights
The Antiproton Decelerator (AD) facility at CERN [1] has provided the foundation for a variety of experiments (e.g., [2,3,4]) over more than a decade
We found the analytic form for the rate coefficient α RA for attaching a positron to antihydrogen to form H as a series convergent for temperatures of 400 K and below, which may be used to estimate formation rates
As our result is for attachment from the 1s antihydrogen state, it depends on the trapped antihydrogen having been held for long enough to ensure that it will have decayed to the ground state from the likely excited state in which it is formed [7,8]
Summary
The Antiproton Decelerator (AD) facility at CERN [1] has provided the foundation for a variety of experiments (e.g., [2,3,4]) over more than a decade Small numbers of these anti-atoms are trapped by the ALPHA and ATRAP collaborations using specialized magnetic minimum neutral atom traps [5,6,7], with confinement times of many minutes being routine at ALPHA [8]. Measurements for H in their quest to investigate possible violations of CPT symmetry, experimental limits on its charge [10], and preliminary limits on the gravitational interaction of the anti-atom [11] Building on the latter idea, the GBAR collaboration [12,13,14] means to measure the gravitational attraction of matter versus antimatter using neutral H atoms, but cooling them sufficiently is difficult because of their neutrality. Tests of the new form confirm the numerical integrals of prior work
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