Dependence of secondary electron emission on the emergent angle of 2.5-MeV protons penetrating a thin carbon foil

Abstract

With 2.5-MeV proton beams incident on a carbon foil of $1.8\ensuremath{\mu}{\mathrm{g}/\mathrm{c}\mathrm{m}}^{2}$ in thickness, the statistical distributions of the number of simultaneously emitted secondary electrons (SEs) have been measured as a function of the emergent angle of ions penetrating the foil in the range from 0.0 mrad to 2.0 mrad for every 0.5-mrad step. The measurement of SEs was carried out at the forward and backward directions of the incident beam separately. For all of the measured angles, the probability of simultaneous n electron emission per projectile, ${W}_{n},$ exhibits roughly an exponential decrease with increasing n. Up to $\ensuremath{\sim}1\mathrm{mrad},$ however, the decreasing rate becomes smaller with an increase in the emergent angle. On the other hand, ${W}_{n}$ reaches saturation at larger angles. This behavior is common to the forward and backward SE emission. In terms of this angular dependence, the average SE yields per projectile at the forward direction, ${\ensuremath{\gamma}}_{\mathrm{F}},$ and at the backward direction, ${\ensuremath{\gamma}}_{\mathrm{B}},$ increase as high as about 50% at 1.0 mrad compared with corresponding ones at 0.0 mrad and saturate at larger angles. As a result of a Monte Carlo simulation taking account of the impact parameter dependent energy loss in a single collision of a proton with a carbon atom, it is found that the calculated energy losses exhibit a quite similar emergent angle dependence to that of the measured SE yields.