Low-energy scattering properties of ground-state and excited-state positronium collisions

Abstract

Low-energy elastic and inelastic scattering in the Ps(1s)-Ps(2s) channel is treated in a fourbody hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum L = 0 and parity equal to +1. The swave scattering lengths for the asymptotic Ps(1s)-Ps(2s) channel are calculated for each spin configuration. Results obtained for the s-wave scattering lengths are aTT = 7.3(2)a0 − i0.02(1)a0, aSS = 13.2(2)a0 − i0.9(2)a0, and aST = 9.7(2)a0 for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross-sections are carried-out for Ps atoms initially prepared in different uncoupled spin states.

Resonant shifts of positronium energy levels in MgO powder

“…This could be achieved spectroscopically by measuring the collisional frequency (or clock) shift [80], as has been done for trapped hydrogen [34]. The calculation of Higgins et al [35] indicates that for Ps the clock shift will be ≈1×10 −7 Hz cm 3 (for hydrogen this has been measured to be 3.8×10 −10 Hz cm −3 ). Thus, for a Ps density of 10 16 cm 3 (cf.…”

“…Laser cooling of confined Ps would have the advantage that the atoms are localized to a small volume, but in this case line-narrowing effects [29][30][31] due to Ps-surface and Ps-Ps scattering would have to be properly taken into account, for example by using short laser pulses or coherent excitation schemes [32,33]. For cold confined atoms, an optical measurement of the Ps density could be achieved by monitoring the 1 3 S 1 → 2 3 S 1 cold-collision frequency shift [34], which is particularly large in Ps at relevant densities [35]; a direct diagnostic of the Ps density that could be time resolved would be invaluable for target design and optimization.…”

Positronium density measurements using polaritonic effects

“…However, once the Ps gas has become fully spin polarized this method no longer provides any signal [31]. Another way to determine Ps densities would be to measure the density-dependant collisional frequency shift [32] of Ps atomic transitions. This technique has not been demonstrated for confined Ps and may be affected by the detailed interactions between the Ps gas and its environment [33].…”