Shows Tritium-Helium Scattering Cross Sections Enhanced at Low Energy, below 300 K

Scientists have investigated the subtle yet significant differences in how hydrogen, deuterium and tritium atoms scatter off helium-3 and helium-4, a process crucial for developing efficient atomic tritium sources needed for next-generation neutrino mass experiments. Calculations by B. J. P. Jones, and further work detailed in this paper, reveal that tritium exhibits markedly enhanced scattering cross-sections compared to hydrogen, owing to a near-threshold resonant state at low energies. This resonant behaviour, similar to that previously predicted for tritium-tritium interactions, dramatically influences scattering rates at lower temperatures, though cross-sections converge towards a predictable geometric value at higher energies, offering valuable insights for optimising tritium source design and performance.

Low-energy hydrogen and tritium isotope scattering with helium isotopes reveals interesting quantum effects

Scientists have calculated energy-dependent elastic scattering cross sections for hydrogen and tritium isotopes colliding with helium isotopes, spanning a temperature range of 1 mK to 300 K. This research, motivated by the demands of atomic tritium sources for neutrino mass experiments, provides crucial data for optimising these complex systems.
The team achieved these calculations for collisions between hydrogen (H), deuterium (D), and tritium (T) with helium-3 (3He) and helium-4 (4He), employing a partial-wave phase-shift analysis to model the interactions. The study reveals that tritium-helium cross sections exhibit significant enhancement compared to hydrogen-helium counterparts, due to a near-threshold resonant s-wave bound state at low energies, mirroring predictions for the tritium-tritium system.

Experiments show that while these energy-dependent cross sections vary considerably at low energies because of this s-wave enhancement, they converge towards a common value at higher energies, where scattering becomes predominantly geometric. This behaviour is critical for understanding and predicting the dynamics of cold atomic tritium.

Researchers solved the one-dimensional Schrodinger equation for nuclear motion under the Born-Oppenheimer approximation, utilising a Meyer-Frommhold potential digitised from previous work, with modifications to account for hard-core interactions. The calculations determined partial wave phase shifts, enabling the determination of elastic scattering cross sections via a summation over all relevant angular momentum states.

Specifically, the low energy cross section is determined by the s-wave scattering length, calculated from the limit of the s-wave phase shift. This work establishes a comprehensive dataset of scattering cross sections, not only for tritium-helium interactions but also for all hydrogen isotopes colliding with both helium isotopes.

The findings have direct implications for the design of atomic tritium cooling systems used in neutrino mass experiments like Project 8, KATRIN++, and QTNM, as well as for modelling tritium vapor dynamics within these systems. Furthermore, the research informs the development of supersonic expansion sources and cryogenic dissociation sources utilising tritium and helium, offering insights into energy transfer mechanisms and the accuracy of approximations used in previous studies.

Partial-wave analysis of elastic scattering for tritium and hydrogen on helium isotopes reveals important nuclear interactions

Scientists calculated energy-dependent elastic scattering cross sections of hydrogen and tritium isotopes on helium isotopes, ranging from 1 mK to 300 K, motivated by the requirements of atomic tritium sources for neutrino mass experiments. The research team employed a partial-wave phase-shift analysis to determine the elastic scattering cross section, solving the one-dimensional Schrodinger equation for nuclear motion under the Born-Oppenheimer approximation.

This approach accounted for the ground state electron energy derived from solving for three-electron ground states at fixed nuclear separation, subsequently modelling the dynamical evolution of a nuclear coordinate wave function. Experiments utilized only m=0 partial waves due to axial symmetry, satisfying the central Schrodinger equation to determine the radial wave function for each orbital angular momentum and energy.

The large-distance solution was expressed using partial wave phase shifts, enabling the calculation of the scattering amplitude and ultimately, the cross section via a summation over all angular momentum values. This method differs from previous work by incorporating a pre-factor of 4 and summing over both odd and even values of ‘l’, reflecting the distinguishable nature of the scattered atoms.

Researchers digitized the Meyer Frommhold potential from existing literature and implemented a hard-core modification proposed in a separate reference, refining the inter-atomic potential used in the calculations. At low energies, the cross section was determined solely by the s-wave scattering length, calculated as 4πa²s.

This innovative technique revealed an enhanced tritium-on-helium cross section due to a near-threshold resonant s-bound state at low energy, similar to that predicted for triplet T-T scattering, and provides crucial data for optimizing atomic tritium cooling systems used in projects like Project 8, KATRIN++, and QTNM. The study also provides predictions for all hydrogen isotopes scattering from both helium isotopes, scrutinizing approximations used in prior research.

Tritium-helium scattering reveals resonant enhancement and reduced-mass scaling of s-wave lengths at low energies

Scientists have calculated energy-dependent elastic scattering cross sections of hydrogen and tritium isotopes on helium isotopes, ranging in temperature from 1 mK to 300 K, motivated by the needs of atomic tritium sources for neutrino mass experiments. The research team found that tritium-on-helium cross sections are enhanced compared to hydrogen-on-helium counterparts due to a near-threshold resonant s-bound state at low energy, mirroring predictions for triplet T-T scattering.

These energy-dependent cross sections exhibit a wide range at low energy because of this s-enhancement, but converge towards a common value at higher energies where scattering becomes effectively geometric. Experiments revealed that the low energy limit of the scattering cross section depends solely on the s-wave scattering length, which is a universal function of the reduced mass.

Figure 2 demonstrates the predicted s-wave scattering length as a function of reduced mass μ, relative to the H-H scattering system μH−H = 8.3401 × 10−28kg, with experimentally relevant values marked on the curve. Table I provides the value of μ, the s-wave scattering length, and low-temperature cross section for each two-body process investigated in the study.

Using the modified Meyer Frommhold potential, the team reported an s-wave scattering length of 0.359 Bohr for H-4He, aligning favourably with their calculated value of 0.360 Bohr. For most atom pairs, the modified and unmodified Meyer Frommhold potentials predicted comparable scattering lengths, differing by only a few percent, except for the 3He-H process.

The calculations confirm a clear pole indicating the introduction of a bound state for reduced masses of approximately 3.9 μH−H, higher than the 3.2 μH−H threshold observed in hydrogen-hydrogen scattering. The breakthrough delivers enhancements of the cross sections for heavier isotope combinations, with both T-3He and T-4He scattering significantly stronger than their hydrogen counterparts, by factors of order 102 in scattering length and 104 in cross section.

Figure 3 shows the partial wave decomposition of the H-4He and T-4He processes, highlighting the varying amounts of s-wave enhancement. Measurements confirm that at higher energies, the cross sections converge to a common limiting value consistent with the expected hard-sphere scattering cross section of σ = 2πr2, where r is the summed Van Der Waals radii of hydrogen (rH = 100pm) and helium (rHe = 140pm).

Tritium-helium scattering reveals resonant behaviour crucial for neutrino mass studies and understanding stellar nucleosynthesis

Scientists have calculated energy-dependent elastic scattering cross sections for hydrogen and tritium isotopes interacting with helium isotopes, spanning a temperature range of 1 millikelvin to 300 kelvin. These calculations were motivated by the requirements of atomic tritium sources used in experiments designed to measure neutrino mass.

The research demonstrates that tritium-on-helium cross sections are notably enhanced compared to hydrogen-on-helium interactions, due to a resonant s-wave bound state observed at low energies, mirroring predictions for triplet tritium-tritium scattering. The energy-dependent cross sections exhibit considerable variation at low energies because of this s-wave enhancement, but converge towards a consistent value at higher energies where scattering becomes primarily geometric.

These newly reported cross sections are essential for informing the design and development of atomic sources for neutrino mass experiments, as most had not been previously documented in the literature. The authors acknowledge that the accuracy of their results relies heavily on the treatment of the interaction potential between the colliding particles.

Future work could focus on refining the modelling of this interaction potential to further improve the precision of the calculated cross sections. The complete energy-dependent cross sections are available as supplementary tables, alongside open-source code for reproducing the results, facilitating further investigation by other researchers. This study contributes to a better understanding of low-energy scattering processes relevant to advanced physics experiments, and provides valuable data for optimising tritium source performance.