Deposited energy density for 100 MeV protons in lithium

Abstract

The density of energy (LET) deposited in a lithium target by 100 MeV protons is estimated by two methods. The protons are slowed down by electronic stopping alone, nuclear stopping being negligible. Multiple scattering and transport of energy by recoil electrons (delta rays) are shown to be negligible. The continuous-slowing-down expression for the range straggling is used in a convolution with the no-straggling distribution in one method; in the other the appropriate transport integral equation is solved to first order in the straggling. (The corresponding solution for the range distribution is also given.) The results are nearly identical, numerically. The multiple-scattering estimate and the transport-equation calculation are thought to be novel. The peak energy density is about 4.8 times the mean, and the fwhm is about 5.4% of the mean range. In the corresponding problem for 200 MeV protons on lead, the numbers are 4.4 and 6.3%, respectively. Simple scaling relations for peak and fwhm are given in terms of a straggling parameter.