1. A neutron ray detecting system that detects neutron rays, the system comprising: a scintillator that generates light when radiant rays enter the scintillator; an optical fiber that allows the light generated in the scintillator to be transmitted therethrough; a discrimination unit that receives the light transmitted through the optical fiber, and discriminates a detection signal relating to the received light from a signal relating to the neutron rays in a case where a wave height of the detection signal exceeds a determination threshold value; and a determination threshold value setting unit that sets the determination threshold value, wherein the determination threshold value setting unit includes a detection signal acquiring unit that acquires a first detection signal that is the detection signal of the radiant rays that have entered the scintillator via a filter that cuts the neutron rays, and a second detection signal that is the detection signal of the radiant rays that have entered the scintillator without the filter, a wave height distribution acquiring unit that acquires a neutron ray wave height distribution of only the neutron rays and a gamma ray wave height distribution of only the gamma rays included in the radiant ray, on the basis of a difference between a wave height distribution based on the first detection signal, and a wave height distribution based on the second detection signal, and a determination threshold value adjusting unit that adjusts the determination threshold value on the basis of the neutron ray wave height distribution and the gamma ray wave height distribution.