Effective radius of ground- and excited-state positronium in collisions with hard walls

Abstract

We determine effective collisional radii of positronium (Ps) by considering Ps states in hard-wall spherical cavities. B-spline basis sets of electron and positron states inside the cavity are used to construct the states of Ps. Accurate Ps energy eigenvalues are obtained by extrapolation with respect to the numbers of partial waves and radial states included in the bases. Comparison of the extrapolated energies with those of a pointlike particle provides values of the effective radius ρ nl of Ps(nl) in collisions with a hard wall. We show that for 1s, 2s, and 2p states of Ps, the effective radius decreases with the increasing Ps center-of-mass momentum, and find ρ 1s = 1.65 a.u., ρ 2s = 7.00 a.u., and ρ 2p = 5.35 a.u. in the zero-momentum limit.

Experimental progress in positronium laser physics

“…However, Dicke line narrowing would be expected to produce significantly narrower linewidths. The confined Ps also exhibited a significant shift, generally consistent with expectations [115,403]. However, because the pore structure comprises many interconnected voids, there is likely no singlevalued shift.…”

“…A second, blue-shifted, peak was also observed, which was attributed to Ps excited while still in the porous structure. This shift arises from the effect of confinement on the excited state Ps energy levels: in effect squeezing the atom increases the 1 3 S 1 -2 3 P J energy interval [403]. The cavity Ps did exhibit some degree of line narrowing, in that the inferred linewidth was narrower than the vacuum Ps lineshape, and would represent sub-thermal Ps if it were due to Doppler broadening.…”

“…The assumption of a 5 nm pore size cannot be accurate since the pores are all interconnected, and there must therefore exist a continuum of different mean free paths experienced by the Ps. Brown and co-workers [403] speculate that this disagreement may imply that the radius of confined n = 2 Ps is not much larger than that of the ground state atoms, owing to the nature of Ps-wall interactions. Preliminary experiments designed to study confined Ps have been carried out at UCL using porous films similar to those described above, but made with lower porosity and larger pores [408].…”

“…The cavity shift is non-trivial to calculate [403,407], even for an idealized material. Assuming hard-wall potentials we can, however, make an order of magnitude estimate simply by considering the size of the ground and excited state atoms.…”

“…The effects of confinement on atoms have long been studied as they are relevant to many physical systems, such as many-body physics of atoms in clusters, the behavior of atoms in high pressure environments, and physically confined atoms in buckyballs or other hard-wall potentials [397][398][399][400][401][402]. Ps is a unique system for such studies [403]: spectroscopy of "normal" atoms can be used (e.g. [404,405]), but Ps has some advantages, namely: (1) the atoms can be produced inside isolated voids following positron bombardment, (2) Ps annihilation radiation can be used as a signal and is easily detected outside the material being studied, and (3) Ps atoms are light, and so may have a de Broglie wavelength comparable to the internal spaces being investigated.…”