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In a neutron lifetime measurement at the Japan Proton Accelerator Complex,the neutron lifetime is calculated by the neutron decay rate and the incidentneutron flux. The flux is obtained due to counting the protons emitted from theneutron absorption reaction of ${}^{3}{\rm He}$ gas, which is diluted in amixture of working gas in a detector. Hence, it is crucial to determine theamount of ${}^{3}{\rm He}$ in the mixture. In order to improve the accuracy ofthe number density of the ${}^{3}{\rm He}$ nuclei, we suggested to use the${}^{14}{\rm N}({\rm n},{\rm p}){}^{14}{\rm C}$ reaction as a reference becausethis reaction involves similar kinetic energy as the ${}^{3}{\rm He}({\rmn},{\rm p}){}^{3}{\rm H}$ reaction and a smaller reaction cross section tointroduce reasonable large partial pressure. The uncertainty of the recommendedvalue of the cross section, however, is not satisfied with our requirement.  In this paper, we report the most accurate experimental value of the crosssection of the ${}^{14}{\rm N}({\rm n},{\rm p}){}^{14}{\rm C}$ reaction at aneutron velocity of 2200 m/s, measured relative to the ${}^{3}{\rm He}({\rmn},{\rm p}){}^{3}{\rm H}$ reaction. The result was 1.868 $\pm$ 0.003 (stat.)$\pm$ 0.006 (sys.) b. Additionally, the cross section of the ${}^{17}{\rmO}({\rm n},{\rm \alpha}){}^{14}{\rm C}$ reaction at the neutron velocity isalso redetermined as 249 $\pm$ 6 mb.

Improved determination of thermal cross section of 14N(n,p)14C for the neutron lifetime measurement