The line shape functions for the Doppler-broadened gamma ray spectrum are considered in the $^{10}B(n,{alpha}{gamma})^7Li$ reaction occurring in a surrounding medium where the excited $^7Li$ nucleus is slowed down and stopped before decay. The phenomenological form of the stopping power was used for the broadening effect. Convolution with the detailed response of a germanium detector is taken into consideration for the simplest case of solely electronic stopping. A numerical study for the analysis of $^{10}B$ by thermal neutron capture is conducted by performing a parametric search and fitting the measured spectrum in a least-squares approach. In comparison with the previous numerical approach using the same analysis, the computational speed is increased and reliable information concerning the stopping power of the medium is obtained while estimating the uncertainty. Implementation of the routine analysis of $^{10}B$ is facilitated on a recent version of the gamma ray spectrum analysis package HyperGam.