Abstract: A sort of birth-death process is investigated.We calculate eigenvalue,eigenvectors of the main matrix for the birth-death process differential equation and get a similar decomposition of the main matrix.Using the technique of matrix decomposition,we obtain the solution of the birth-death process differential equation and study the heavy element abundance of the slow neutron capture process(s-process) in the solar system.A full calculation of heavy element abundance of s-process in solar system is carried out.The result agrees well with astrophysical measurement.

Key words: birth-death process, matrix decomposition, nuclear astrophysics, heavy element abundance