Annihilation of positronium atoms in an oscillatory field
Abstract
Annihilation parameters (the angular correlation curve and positronium lifetime) are calculated for annihilation of positronium atoms in a threedimensional oscillatory well. This well can serve as a model of a positron trap in rigid bodies. The model lends itself to exact mathematical analysis, and it admits separation of variables of the centerofmass motion and the relative motion of the particle. A calculation is given for the wave functions of a positronium, which oscillatory field. The wave function of the relative motion of the particles at small distances is similar to the wave function of free positronium, which gives us a basis to speak of the annihilation of an electronpositron pair as the annihilation of a positronium atom in an oscillatory field. With a decrease in the size of the trap, broadening of the correlation curve occurs, which has Gaussian form for the annihilation of positronium from the minimum condition for centerofmass motion. The bound state of the electron and positron exists even in traps of the size of the Bohr radius. The model permits evaluation of the size of traps over an experimentally chosen narrow component of the correlation curve.
 Publication:

Soviet Physics Journal
 Pub Date:
 March 1989
 DOI:
 10.1007/BF00897390
 Bibcode:
 1989SvPhJ..32..226S