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Canadian Journal of Physics

Spin-exchange scattering cross sections for hydrogen atoms at low temperatures

A. J. Berlinsky, Bernie D. Shizgal

Published Jun 1, 1980• 31 citations
Publisher

Abstract

Calculations are presented of the low energy (0 < E ≤ 10−2 eV) spin exchange and frequency shift cross sections for (H,H) scattering, and of their thermal averages for 0 < T < 10 K. In particular, the behaviour of the cross sections in this low energy limit and the role of resonances due to orbiting collisions is studied in detail. A comparison is made with recent nmr measurements on gaseous atomic hydrogen at liquid helium temperatures. The results of this work suggest further useful experiments at low temperatures.

DOI
10.1139/p80-119

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Journal of Physics Conference Series•Nov 1, 2007•9 citations
Calculations are presented of the low energy (0 < E ≤ 10−2 eV) spin exchange and frequency shift cross sections for (H,H) scattering, and of their thermal averages for 0 < T < 10 K. In particular, the behaviour of the cross sections in this low energy limit and the role of resonances due to orbiting collisions is studied in detail. A comparison is made with recent nmr measurements on gaseous atomic hydrogen at liquid helium temperatures. The results of this work suggest further useful experiments at low temperatures.
Potential scattering and spin-exchange scattering cross sections in the energy range from 10 -3 cm -1 to 100 cm -1 have been calculated numerically for hydrogen atoms in collision based on the most accurate Kołos-Woniewicz adiabatic potentials available at present. The scattering lengths for the singlet and triplet states are calculated to be a 0 s =0.595 a.u. and a 0 t =1.34 a.u., respectively. The quasi-bound state with ν=14 and l =4 is found to be at E =1.675 cm -1 above the dissociation limit. The thermally averaged spin-exchange cross section has the low temperature limit \barσ ex (0 K)=0.982 A 2 with a minimum \barσ ex (2.5 K)=0.329 A 2 .
Abstract Motivated by the needs of atomic tritium sources for neutrino mass experiments and Doppler-free two-photon 1 S–2 S spectroscopy in atomic deuterium and tritium, we present calculations of energy-dependent elastic scattering cross sections of hydrogen isotopes (H, D, and T) on helium isotopes ( 3 He and 4 He) in the temperature range 1 mK to 300 K. The tritium-on-helium cross sections are found to be enhanced over their hydrogen-on-helium counterparts by a near-threshold resonant s -wave bound state at low energy, similar to one that has been predicted in the triplet T–T system. While the energy-dependent cross sections span a wide range at low energy due to this s -wave enhancement, they tend toward a common value at high energy where the scattering becomes effectively geometric in nature.
We present a unified multichannel approach to calculate electron spin-exchange and spin-flipping transition cross sections for collisions of H with H, H with T, and T with T. We use the theory to calculate the hyperfine quenching cross sections for collision energies that range from 111 mK to thermal temperatures. We show that spin-flipping transitions are induced by the splitting of the $b {}^{3}{\ensuremath{\Sigma}}_{u}$ Born-Oppenheimer potential via the long-range magnetic interactions among electrons. We find that the spin-flipping cross sections in the tritium dimer are about a magnitude larger than that predicted by mass scaling the H-H cross sections. For the former, we show that the spin-exchange cross sections are several magnitudes larger, at cold temperatures, than that of the hydrogen system. We compare the results of the multichannel approach with those obtained using approximate methods such as the degenerate internal-state, the elastic, and Born approximations and discuss their respective range of validity.
We have calculated cross sections and rate coefficients for elastic scattering, ionization, and double excitation transfer in collision of two hydrogen atoms in the 2s state. We find that for collision energies between 5 × 10-10 a.u. and 10-6 a.u. elastic scattering has the largest cross section. For temperatures below 0.02 K ionization is the dominant loss process, while for higher temperatures double excitation transfer dominates. Our results for the total loss rate are found to be within a factor 2 or 3 of the error bars of recent measurements.
In sufficiently large magnetic fields, the weakly bound levels of H2 acquire finite lifetimes owing to hyperfine predissociation and become manifest as scattering resonances in spin-polarized atomic hydrogen (H↓). In this work we investigate in detail the contribution to the reaction kinetics in H↓ due to the resonance, denoted [Formula: see text], arising from the predissociation of the (v,J) = (14,4) level of H2. To characterize the formation and disintegration of [Formula: see text], we calculate the predissociation as a function of both the applied magnetic field and the dissociation energy, D, of the level. Recombination occurs when [Formula: see text] is stabilized in collisions that cause transitions to lower molecular levels. For low H↓, densities, collisions with atoms of the saturated 4He vapour dominate; we calculate the cross section in the distorted wave Born approximation and also use a coupled-channels approach. At higher densities, stabilization occurs in collisions with H↓ as well; the effect of proton exchange between the atom and the molecule is derived. Previous experiments, analyzed neglecting proton exchange, are reanalyzed including this; the dissociation energy D is not as well determined by the data as was previously thought. Prospects for future experiments are discussed.
We consider two types of collisional processes with excited antiprotonic helium systems. (i) Transitions between hyperfine structure sublevels in ( He + ) n LFJ are considered at T ≤ 25 K using the coupled-channels method and a model of scalar and tensor interactions between antiprotonic and ordinary He atoms. Inelastic cross sections for the single and double spin-flip transitions are less than elastic ones by four and seven orders of magnitude, respectively. The cross sections show a resonance behaviour at E ∼ 1–4 K, and therefore the relaxation rates, density shift and broadening of the M1 spectral lines decrease with increasing temperature from 3 to 25 K. (ii) Stark transitions and induced annihilation during collisions of the ( He 2+ ) nl ion with He atoms at E ∼ 10 K are considered for all l -states at n ∼ 30 in the framework of the coupled-channels method. In order to take into account complex energy shifts of the ns and np -states, we introduce modified boundary conditions in these channels. The main contribution to elastic scattering, Stark transitions and induced annihilations during collisions comes from the long-range polarization interaction. Admixtures of ns and np -states to nl -states ( l ≥ 2) during collisions induce the effective annihilation cross sections for the initial l up to 15, but don't affect the Stark cross sections for states with nearly-circular orbits. The calculated values for both types of processes are compatible with recent experimental data.