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

## TL;DR

This paper calculates the effective radii of positronium in various states during collisions with hard walls using a basis set approach, revealing how these radii depend on the center-of-mass momentum.

## Contribution

It introduces a method to determine positronium's effective radii in collisions with hard walls using B-spline basis sets and energy extrapolation techniques.

## Key findings

- Effective radii decrease with increasing center-of-mass momentum.
- Calculated radii for Ps states at zero momentum: 1.65 a.u. (1s), 7.00 a.u. (2s), 5.35 a.u. (2p).
- Method provides accurate estimates of Ps radii in confined geometries.

## 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 $\rho_{nl}$ 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 $\rho_{1s}=1.65$ a.u., $\rho_{2s}=7.00$ a.u., and $\rho_{2p}=5.35$ a.u. in the zero-momentum limit.