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Europhysics Letters (EPL)

Scattering of hydrogen atoms at low temperature

Anamika Sen, S Chakraborty, Arnab Ghosh

Published Oct 17, 2006• 15 citations
Publisher

Abstract

A non-adiabatic model is employed to investigate the H-H scattering at low temperatures. Unlike molecular-orbital calculation technique, no separate calculations are required to obtain the potential energies of electrons in the field of hadrons. This model generates the non-adiabatic effective potential automatically. The coefficients of van der Waals and higher-order potentials are estimated in the present model and are found to be in very good agreement with the corresponding standard values. The s -wave singlet and triplet scattering lengths and thermal-average total triplet cross-section at 2 K are reported and compared with the existing theoretical and experimental predictions.

DOI
10.1209/epl/i2006-10325-0

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A non-adiabatic model is employed to investigate the H-H scattering at low temperatures. Unlike molecular-orbital calculation technique, no separate calculations are required to obtain the potential energies of electrons in the field of hadrons. This model generates the non-adiabatic effective potential automatically. The coefficients of van der Waals and higher-order potentials are estimated in the present model and are found to be in very good agreement with the corresponding standard values. The s -wave singlet and triplet scattering lengths and thermal-average total triplet cross-section at 2 K are reported and compared with the existing theoretical and experimental predictions.
The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of H2{\mathrm{H}}_{2}H2​. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41a0{\mathit{a}}_{0}a0​ for the singlet case and 1.91a0{\mathit{a}}_{0}a0​ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2 but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2, with a different fit to the triplet potential between 12a0{\mathit{a}}_{0}a0​ and 15a0{\mathit{a}}_{0}a0​. A more accurate triplet-state potential is needed at these separations.
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 .
In view of the recent interest in the trapping of antihydrogen atom $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{},$ at very low temperatures, $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering has been investigated at low incident energies using a close-coupling model with the basis set $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}(1s,2s,2\overline{p})+\mathrm{H}(1s,2s,2\overline{p}).$ The predicted s-wave elastic phase shifts, scattering length, and effective range are in a good agreement with the other recent predictions of Jonsell et al. and of Armour and Chamberlain. The results indicate that the atomic orbital expansion model is suitable to study the $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering at ultracold temperatures.
Calculations are reported for positronium (Ps) scattering by atomic hydrogen (H) in the energy range 0--6.5 eV in a coupled-pseudostate approximation in which excitation and ionization channels of both the Ps and the H are taken into account. The approximation contains an accurate representation of the van der Waals coefficient. Results are presented for phase shifts, scattering lengths, effective ranges, and various cross sections including partial wave, total, and ortho-para conversion cross sections. An analysis of the possible spin transitions is provided and the energy of the positronium hydride (PsH) bound state is determined. Substantial differences are found from earlier work within the frozen target approximation, now clearly confirming the importance of target excitation channels. Good agreement is obtained with recent calculations of S-wave phase shifts and scattering lengths using the stabilization method. Convergence to the exact binding energy for PsH appears to be slow. Resonances corresponding to unstable states of the positron orbiting ${\mathrm{H}}^{\ensuremath{-}}$ are seen in the electronic spin singlet partial waves. The importance of the ${\mathrm{H}}^{\ensuremath{-}}$ formation channel is discussed.
The modified static exchange model (MSEM) recently introduced by Ray [1] to study two-atomic collision processes at low and cold-energies, is used for detailed analysis of the long-range effects due to induced dipole-dipole van der Waals interaction between Ps and H atoms. The MSEM includes the non-adiabatic short-range effect due to electron-exchange and the long-range effect due to induced dynamic dipole polarisabilities of the atoms. The effective interatomic potential is highly sensitive to the minimum distance between the atoms ( ). The s-, p- and d- wave elastic phase shifts, corresponding partial cross sections, the scattering length and effective ranges are calculated and studied with the variation of the chosen least interatomic distance between them. It is found that the scattering length is highly sensitive to the effective interatomic potential that depends on the least interatomic distance. In addition the studies are made in search of Feshbach resonances. The observed interesting feature with the variation of in the triplet channel invites more accurate investigations if new physics.
The effective range in the singlet electron-hydrogen system has been evaluated as 2.646\ifmmode\pm\else\textpm\fi{}0.004 atomic units by using the asymptotic amplitude of the 202-parameter ${\mathrm{H}}^{\ensuremath{-}}$ wave function of Pekeris. This value of the effective range, together with the value of the electron affinity of ${\mathrm{H}}^{\ensuremath{-}}$, determines the scattering length in the singlet system as 6.167 atomic units. The effective range in the triplet system is calculated to be 1.219 atomic units by a Hartree-Fock approximation. It is shown that the effective-range approximation is very good for all energies at which only elastic scattering is allowed. The photo-ionization of ${\mathrm{H}}^{\ensuremath{-}}$ is briefly discussed on the basis of the effective-range theory.