Abstract The thermophysical properties of spin-polarized atomic tritum (T↓) are calculated in the temperature range 0.01 K–10 K using the Galitskii–Migdal–Feynman (GMF) formalism. The calculations are performed using Silvera and Born–Oppenheimer triplet-state potentials. It is concluded that T↓ may form a liquid at very low temperatures. At low T , the effective s-wave scattering length a 0 < 0, which corresponds to a very weak attractive interaction. There is no bound state for the T↓ dimer, but the negative a 0 indicates that it is only slightly short of binding. The transport properties of T↓ increase with increasing temperature. This behavior shows that T↓ remains as a gas in this T -range. The transport properties of 3 He and 4 He are included for comparison purposes. The difference in the transport properties of T↓ and 3 He is due to the fact that T↓ atoms obey Bose statistics while 3 He atoms obey Fermi statistics, whereas the difference with the 4 He (Boson) is due to the mass difference between T↓ and 4 He.
Abstract The thermophysical properties of spin-polarized atomic tritum (T↓) are calculated in the temperature range 0.01 K–10 K using the Galitskii–Migdal–Feynman (GMF) formalism. The calculations are performed using Silvera and Born–Oppenheimer triplet-state potentials. It is concluded that T↓ may form a liquid at very low temperatures. At low T , the effective s-wave scattering length a 0 < 0, which corresponds to a very weak attractive interaction. There is no bound state for the T↓ dimer, but the negative a 0 indicates that it is only slightly short of binding. The transport properties of T↓ increase with increasing temperature. This behavior shows that T↓ remains as a gas in this T -range. The transport properties of 3 He and 4 He are included for comparison purposes. The difference in the transport properties of T↓ and 3 He is due to the fact that T↓ atoms obey Bose statistics while 3 He atoms obey Fermi statistics, whereas the difference with the 4 He (Boson) is due to the mass difference between T↓ and 4 He.
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.
Abstract The quantum-mechanical formulations for the second virial, and the acoustic virial, coefficients are derived for spin-polarized atomic hydrogen (H↓). The dependence of these coefficients on the temperature T as well as the nuclear polarization ζ is analyzed. This is done for the first time. The main inputs in these computations are the scattering phase shifts, which are obtained using the Lippmann-Schwinger equation, with the Silvera triplet-state potential. Starting with these phase shifts, comprehensive calculations of the thermophysical properties for this system are performed for T ranging from 1µK to 100 K, and ζ varying from 0 to 1. These properties include, in addition to the quantum second virial coefficient and the acoustic virial coefficient: the pressure-polarization-temperature (P-ζ-T) behavior, the entropy (per atom), the speed of sound, the second virial correction (to the total internal energy per atom and unit density), and the specific heat capacity (per atom and unit density). The Boyle temperature and the Joule inversion temperature are determined. The T-dependence of these thermophysical properties, and related quantities, is explored. As expected, this dependence is most evident in the low-T limit, where quantum effects predominate. The corresponding ζ-dependence becomes noticeable at 80 K and below. It is observed that the virial coefficients tend to decrease with increasing ζ. Comparison of the present results to previous results are included whenever possible. The overall agreement is very good. As T is lowered, the disruptive effects of thermal energy are weakened relative to the attractive interactions between the atoms. Consequently, the H↓ gas makes a transition to a state of higher order and lower entropy – Bose-Einstein condensation (BEC). This is explored carefully.
Galitskii–Migdal–Feynman (GMF) model is employed to compute the total scattering cross section [Formula: see text] and the viscosity scattering cross section [Formula: see text] for a mixture of [Formula: see text]Ne and [Formula: see text]Ar atoms over a temperature range 90–120 K and at various number densities. Both [Formula: see text] and [Formula: see text] are determined as a function of relative momentum at different temperatures and densities. It is observed that, at higher density, both cross sections exceed their corresponding values at lower density. The influence of temperature on [Formula: see text] and [Formula: see text] is also examined to investigate the thermal effects on transport properties; no significant temperature-induced variation is detected between 90 and 120 K. Additionally, the contribution of partial scattering waves is analyzed. The results reveal a rich resonance spectrum with multiple sharp peaks corresponding to different partial waves. At low energy, the S-wave dominates the scattering. As the relative momentum increases, a D-wave resonance emerges. With further increase in relative momentum, additional quasi-states corresponding to [Formula: see text], [Formula: see text] and [Formula: see text] are also observed. Finally, the average values of [Formula: see text] and [Formula: see text] are computed as a function of temperature: [Formula: see text] decreases with increasing temperature, whereas [Formula: see text] shows a slight increase.
We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.
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.
The ground-state properties of one-dimensional electron-spin-polarized hydrogen 1 H, deuterium 2 H, and tritium 3 H are obtained by means of quantum Monte Carlo methods. The equations of state of the three isotopes are calculated for a wide range of linear densities. The pair correlation function and the static structure factor are obtained and interpreted within the framework of the Luttinger liquid theory. We report the density dependence of the Luttinger parameter and use it to identify different physical regimes: Bogoliubov Bose gas, super-Tonks–Girardeau gas, and quasi-crystal regimes for bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for fermions. We find that the tritium isotope is the one with the richest behavior. Our results show unambiguously the relevant role of the isotope mass in the properties of this quantum system.