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arXiv:2509.13426 · Physical Review A

Elastic and spin-changing cross sections of spin-polarized atomic tritium

M. G. Elliott, B. J. P. Jones

Published Nov 20, 2025• 1 citation
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Abstract

The rates of elastic and inelastic scattering processes of spin-polarized atomic tritium are vital inputs for the design and operation of experiments using cold, magnetically trapped tritium atoms. Elastic scattering dominates the total cross section and dictates the thermophysical properties of the vapor, determining the efficiency of magnetic evaporative cooling and the fluid dynamical properties of the trapped atom cloud. Spin-changing cross sections in both exchange and dipolar channels determine the trap lifetime of the various hyperfine states, imposing constraints on the required atomic tritium supply rate to maintain a given trap density. Motivated by the needs of next-generation spectrometers that will study the tritium beta end point to infer the mass of the neutrino, we present new calculations of the elastic, spin-exchange, and dipolar cross sections for spin-polarized atomic tritium. Cross sections and rate constants are reported for magnetic field strengths of 0--10 T and temperatures from 0 to 100 K in all relevant Zeeman-hyperfine channels for both tritium and hydrogen. Results are benchmarked against past calculations for atomic hydrogen and the limited available results for tritium, and extend far into the regimes where past calculations have not been available.

DOI
10.1103/v6gz-jmjq

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The rates of elastic and inelastic scattering processes of spin-polarized atomic tritium are vital inputs for the design and operation of experiments using cold, magnetically trapped tritium atoms. Elastic scattering dominates the total cross section and dictates the thermophysical properties of the vapor, determining the efficiency of magnetic evaporative cooling and the fluid dynamical properties of the trapped atom cloud. Spin-changing cross sections in both exchange and dipolar channels determine the trap lifetime of the various hyperfine states, imposing constraints on the required atomic tritium supply rate to maintain a given trap density. Motivated by the needs of next-generation spectrometers that will study the tritium beta end point to infer the mass of the neutrino, we present new calculations of the elastic, spin-exchange, and dipolar cross sections for spin-polarized atomic tritium. Cross sections and rate constants are reported for magnetic field strengths of 0--10 T and temperatures from 0 to 100 K in all relevant Zeeman-hyperfine channels for both tritium and hydrogen. Results are benchmarked against past calculations for atomic hydrogen and the limited available results for tritium, and extend far into the regimes where past calculations have not been available.
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.
In this paper, the Lippmann-Schwinger (LS) formalism is applied to spin-polarized atomic tritium (T↓). The total and viscosity cross sections of T↓- T↓ collisions are calculated, using two triplet-state potentials: a Morse- and a Silvera- type potentials. Also, the scattering length and the binding energy of T↓ atoms are calculated. Our results are found to be in good agreement with previous calculations. Our results for the Morse potential are smaller in magnitude than those for the Silvera potential, because the Morse-potential well is shallower than that of the Silvera potential. In the low-energy limit, the cross sections are dominated by S-wave scattering. In this limit, the S-wave scattering length a0< 0 for both potentials. This means that the interaction between the T↓ atoms is attractive. The Ramsauer-Townsend (RT) effect and phase transitions in the cross sections are found at low temperatures. The effect of the D-wave scattering appears as a resonance-like behavior in the total cross section. This peak corresponds to a quasi-bound state.
We present theoretical calculations of thermally averaged elastic cross sections and spin-relaxation rate coefficients in the temperature range 0.1 to $300\ensuremath{\mu}\mathrm{K}$ for magnetically trapped, doubly polarized cesium atoms. The calculations reproduce the recent experimental results of Arndt et al. (1997) and S\"oding et al. (1998) for cases where the ${a}^{3}{\ensuremath{\Sigma}}_{u}$ ground state potential of Cs2\mathrm{Cs}{}_{2}Cs2​ possesses a large scattering length ( ∣A3∣>35nm|{A}_{3}|>35\mathrm{nm}∣A3​∣>35nm) and the magnitude of the second-order spin-orbit interaction is scaled to reproduce room temperature scattering data.
The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
We have measured the elastic collision cross section for spin polarized atomic cesium. Neutral cesium atoms are optically cooled, then loaded into a dc magnetic trap. We infer the scattering rate from the rate at which anisotropies in the initial energy distribution are observed to relax. The cross section for F=3, mF{\mathit{m}}_{\mathit{F}}mF​=-3 on F=3, mF{\mathit{m}}_{\mathit{F}}mF​=-3 is 1.5(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ cm2{\mathrm{cm}}^{2}cm2, and is independent of temperature from 30 to 250 \ensuremath{\mu}K. This determination clarifies the technical requirements for attaining Bose-Einstein condensation in a magnetically trapped Cs vapor. We also study heating due to glancing collisions with 300 K background Cs atoms.