Monte Carlo studies of positrons in matter. Temperature and electric field effects on lifetime spectra in low-temperature, high-density helium gas

Lifetime spectra of slow positrons in helium gas at low temperatures and high densities have been calculated using a Monte Carlo technique. Spectra are calculated both with and without applied electric fields using a two-parameter model based on the picture of helium cluster or droplet formation around the positron. The model is remarkably successful in reproducing the observed peak in the low-temperature spectra, the changes in the peak with variation of temperature and electric field, and the behavior of the "equilibrium" decay rate under a variety of conditions. At 5.5°K, the optimal model parameters, independent of electric field, are found to be $E_R=0.005\mathrm{}$ eV for the threshold energy of droplet formation, and $Z_R=18.2\mathrm{}$ for the enhanced decay-rate parameter. The simple slowing-down approximation is relatively successful in explaining the high-temperature spectra and in predicting the position of the peak in the low-temperature spectra when no electric field or only very small fields are present. The approximation breaks down at low temperatures and high electric fields, and consideration of the average positron energy and the width of the energy distribution as functions of time shows why this breakdown occurs.