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Low energy elastic scattering of H, D and T on $^{3}$He and $^{4}$He

B. J. P. Jones

TL;DR

This work computes energy-dependent elastic scattering cross sections for H, D, and T on the helium isotopes 3He and 4He across temperatures from 1 mK to 300 K, motivated by atomic tritium sources for neutrino-mass experiments. Using a Born–Oppenheimer framework with ground-state electron potentials and phase-shift analysis for distinguishable atoms, it reveals a near-threshold s-wave bound state that strongly enhances T–He scattering relative to H–He, while all channels converge to a geometric black-disk limit at higher energies. The study analyzes two He–H potentials (Meyer–Frommhold and a modified version), provides extensive low-energy data in tabulated form, and offers open-source code for reproducing the energy-dependent cross sections. The results inform the design and optimization of atomic tritium cooling and source technologies by quantifying how isotope- and potential-dependent scattering shape vapor dynamics and cooling efficiencies.

Abstract

Motivated by the needs of atomic tritium sources for neutrino mass experiments, 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 that 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.

Low energy elastic scattering of H, D and T on $^{3}$He and $^{4}$He

TL;DR

This work computes energy-dependent elastic scattering cross sections for H, D, and T on the helium isotopes 3He and 4He across temperatures from 1 mK to 300 K, motivated by atomic tritium sources for neutrino-mass experiments. Using a Born–Oppenheimer framework with ground-state electron potentials and phase-shift analysis for distinguishable atoms, it reveals a near-threshold s-wave bound state that strongly enhances T–He scattering relative to H–He, while all channels converge to a geometric black-disk limit at higher energies. The study analyzes two He–H potentials (Meyer–Frommhold and a modified version), provides extensive low-energy data in tabulated form, and offers open-source code for reproducing the energy-dependent cross sections. The results inform the design and optimization of atomic tritium cooling and source technologies by quantifying how isotope- and potential-dependent scattering shape vapor dynamics and cooling efficiencies.

Abstract

Motivated by the needs of atomic tritium sources for neutrino mass experiments, we present calculations of energy-dependent elastic scattering cross sections of hydrogen isotopes (H, D and T) on helium isotopes (He and 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 that 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.
Paper Structure (4 sections, 5 equations, 4 figures, 1 table)

This paper contains 4 sections, 5 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Formalism and Potentials
  3. Results
  4. Conclusion

Figures (4)

  • Figure 1: Potentials used in this work. The Meyer Frommhold potential is digitized from Ref. meyer1994long, and the Modified MF potential includes the hard core modification proposed in Ref. chung2002diffusion.
  • Figure 2: Reduced mass dependent s-wave scattering length $a_s$ for the H-He system as a function of reduced mass $\mu$ in units of the H-H reduced mass $\mu_{H-H}$. The low energy scattering lengths for the various isotope combinations of interest are indicated on the curve and reported in Table \ref{['tab:s-wave-scattering-lengths']}
  • Figure 3: Partial wave components of the scattering cross sections for the H-$^4$He (top) and T-$^4$He (bottom) processes. The results are similar over most relative momentum values, with the exception of the resonantly enhanced s-wave amplitude at low energy, as shown on Fig. \ref{['fig:Reduced-mass-dependent']}.
  • Figure 4: Momentum-dependent (top) and energy-dependent (bottom) cross section for each of the processes considered in this paper. The energy reported is the center of mass collision energy in units of Kelvin, $p^2/(2\mu k_B)$. The black X shows the hard-sphere cross prediction based on the Van Der Waals radii of hydrogen and helium. The shaded bands show the difference between the Modified and Unmodified Meyer Frommhold potentials.