A mathematical model and a computer program are developed to calculate the neutron energy spectrum, angular distribution, and integrated yield of the ${}^{9}$Be($d$,$n$) reaction on a thick beryllium target as an accelerator-based neutron source in the incident-deuteron-energy range from 0.5 to 20.0 MeV. The double-differential cross section computed by the talys code and the stopping power derived from the SRIM-2010 code are adopted in the program. Typical computational results are presented, and are compared with the previous experimental data to evaluate the computing model as well as the characteristics of the ${}^{9}$Be($d$,$n$) reaction with a thick Be target. Moreover, the developed theory and calculation methods can also provide a reasonable evaluation for calculating data of double-differential cross sections and stopping power. This model and the program can predict the above characteristics parameters of the ${}^{9}$Be($d$,$n$) reaction for a thick beryllium target as a neutron source in the incident-deuteron-energy range from 0.5 to 20.0 MeV.
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