Measurement of a Neutron Energy Spectrum by Proton Recoil

5 MEASUREMENT OF A NEUTRON ENERGY SPECTRUM BY PROTON RECOIL 

Detection of neutrons by proton recoil is based on collisions of neutrons with protons and subsequent detection of the moving proton. Since neutrons and protons have approximately the same mass, a neutron may, in one collision, transfer all its kinetic energy to the proton. However, there is a possibility that the struck proton may have any energy between zero and the maximum possible, as a result of which the relationship between a neutron energy spectrum and a pulse-height distribution of the struck protons is not simple. It is the objective of this section to derive a general expression for this relationship. The sections that follow show its application for specific detectors. 

Consider the case of a neutron with kinetic energy colliding with a proton at rest (Fig. 14.8). To calculate the proton kinetic energy after the collision, one must apply the equations of conservation of energy and linear momentum (Eqs. 3.81-3.83) using Q = 0 and M = M. The result for Ep, the proton kinetic energy as a function of the recoil angle d, is 

In a neutron-proton collision, the maximum value of angle 0 is 90°, and the minimum 0° therefore, the limits of the proton energy are 0 Ep E . For neutron energies up to about 14 MeV, the ( — p) collision is isotropic in the center-of-mass system as a consequence, there is an equal probability for the 

The function piE) is shown in Fig. 14.9. What is important for the observer is not p E) but the proton pulse-height distribution produced by the detector. The relationship between the pulse-height distribution and the neutron spectrum is derived as follows. Let 

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