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European Scientific Journal ESJ

SCATTERING PROPERTIES OF SPIN-POLARIZED ATOMIC TRITIUM

Amal F. Al-Maaitah

Published Oct 30, 2012• 0 citations
OpenAlex

Abstract

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.

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Journal of Mathematical Physics•Jun 1, 2017•1 citation
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 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.
The cross sections and the man free path of 3He? atoms in HeII background are calculated. The Ramsauer-Townsend effect in the cross sections is found in these mixtures at low temperatures. In the low energy limit the cross sections are dominated by the S-wave scattering. The influence of S-scattering decreases with increasing magnetic field. With increasing k, S-wave scattering tends to decrease; whereas the contribution of the higher angular-momentum waves (especially P-wave) to the scattering increases. Our results of the mean free path exhibit the 3He? atoms propagate through the HeII background with an exceedingly long mean free path and without friction.
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 .
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.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.
In this work, a system including two neutral atoms confined to an external one-dimensional Morse potential was modelled. The problem can be relevant to cold atom physics, where neutral atoms may be effectively confined in radially tight tubes formed by optical lattices. The atom-atom interaction was considered as a nonlocal separable potential. Analytical expressions for wave-function as well as transition matrix were derived. The contributions of bound states and resonances in the complex energy plane were calculated. For numerical computations, the bound states in a system of argon gas confined in graphite were considered. Since the most important quantity in the low energy quantum scattering problems is “scattering length,” considering various values of Morse parameters, the behavior of this parameter was described versus the reduced energy.