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Journal of Physics B Atomic Molecular and Optical Physics

Investigation of sodium-helium interaction potentials

Paul J. Leo, G. Peach, Ian B. Whittingham

Published Oct 19, 2000• 9 citations

Abstract

We present a detailed theoretical investigation of the sodium-helium interaction and report results of quantum close-coupled calculations for the pressure-broadened widths and shifts of the sodium D lines and the 819.48 nm line over the temperature range 70-500 K, and for the total and fine-structure cross sections in the 3p 2 P level. We also present the first theoretical investigation of the hyperfine pressure shifts using a semiclassical scattering formalism and report results for the hyperfine transition in the 3s 2 S 1/2 ground state over the temperature range 70-1000 K. Finally, we calculate the refractive index of helium for sodium matter waves with velocities up to 2000 m s -1 . Several of the calculations were performed using two versions of the adiabatic molecular potentials of Peach (Peach G 1996 unpublished) and the results compared with those obtained using the l -dependent pseudo-potentials of Pascale (Pascale J 1985 XIII Summer School on Quantum Optics ed J Fiutak and J Mizerski pp 39-91) and Peach (Peach G 1996 unpublished). Detailed comparisons with other theoretical calculations and experimental results are also made.

DOI: 10.1088/0953-4075/33/21/321

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We present a detailed theoretical investigation of the sodium-helium interaction and report results of quantum close-coupled calculations for the pressure-broadened widths and shifts of the sodium D lines and the 819.48 nm line over the temperature range 70-500 K, and for the total and fine-structure cross sections in the 3p 2 P level. We also present the first theoretical investigation of the hyperfine pressure shifts using a semiclassical scattering formalism and report results for the hyperfine transition in the 3s 2 S 1/2 ground state over the temperature range 70-1000 K. Finally, we calculate the refractive index of helium for sodium matter waves with velocities up to 2000 m s -1 . Several of the calculations were performed using two versions of the adiabatic molecular potentials of Peach (Peach G 1996 unpublished) and the results compared with those obtained using the l -dependent pseudo-potentials of Pascale (Pascale J 1985 XIII Summer School on Quantum Optics ed J Fiutak and J Mizerski pp 39-91) and Peach (Peach G 1996 unpublished). Detailed comparisons with other theoretical calculations and experimental results are also made.

The calculations of the elastic scattering properties for collisions between two 23Na atoms at ultra-cold temperatures are reported and compared with experimental and theoretical results in the detail. We present a parametric model potential for the triplet molecular state of the 23Na molecule, and calculate the scattering length ɑ(subscript t) and the effective range r(subscript e) by using the semiclassical and Numerov methods, respectively. The shape resonances occur in the collisions at low energies, and resonance positions and widths are computed by Briet-Wigner formula. In addition, we also present other results that include differential cross sections at zero energy limit.

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium

D

lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation on the sum rule for these cross sections. Good over-all agreement with the existing experimental data is obtained.

Optical pumping of the ground states of sodium can radically alter the shape of the laser-induced fluorescence excitation spectrum, complicating measurements of temperature, pressure, etc., which are based on these spectra. Modeling of the fluorescence using rate equations for the eight hyperfine states of the sodium D manifolds can be used to quantify the contribution to the ground state pumping of transitions among the hyperfine excited states induced by collisions with buffer gas atoms. This model is used here to determine, from the shape of experimental spectra, cross sections for $\ensuremath{\Delta}F$ transitions of the

{P}_{3/2}

state induced by collisions with helium and argon atoms, for a range of values assumed for the ${P}_{1/2}, \ensuremath{\Delta}F$ cross sections. The hyperfine cross sections measured using this method, which to our knowledge is novel, are compared with cross sections for transitions involving polarized magnetic substates

{m}_{F}

measured previously using polarization sensitive absorption. Also, fine-structure transition $(\ensuremath{\Delta}J)$ cross sections were measured in the pumped vapor, giving agreement with previous measurements made in the absence of pumping.

Transitions between hyperfine structure states of antiprotonic

^4 \mathrm{He}

at collisions with medium atoms: interaction \emph{ab initio}

Collisions of metastable antiprotonic helium atoms with atoms of the medium induce, among other processes, transitions between hyperfine structure (HFS) states, as well as shifts and broadening of microwave M1 spectral lines. In order to obtain matrix potential of interaction between

(\mathrm{\bar{p} He} ^+)

and

\mathrm{He}

, we have calculated the potential energy surface (PES) in the framework of unrestricted Hartree-Fock method taking into account electron correlations in the second-order perturbation theory (MP2). With this potential, the system of close-coupling equations for HFS channels is solved numerically. Cross sections and transition rates, shifts and broadening of M1 spectral lines are calculated. They are used to obtain a numerical solution of the master equation that determines the time evolution of the HFS-states density matrix. The results are compared with the experimental data and with the results of model calculation.

Based on the accurate singlet and triplet state interatomic potentials for Na2, a theoretical study of elastic scattering properties of sodium atoms at ultracold temperatures is reported in this paper. The s-wave scattering length, effective range, the p-wave scattering length and the number of bound states are calculated. The singlet and triplet elastic scattering cross section between sodium aotms at ultracold temperatures are dominated by s-wave scattering, and shape resonances occur with collision energy increasing. There exist pronounced f-wave and i-wave shape resonances for the singlet and triplet cross section. In addition, s-wave scattering length is calculated by using the degenerate internet state approximation for selected hyperfine states of sodium atoms. The results are in agreement with calculated values obtained by close-coupling method.