Measurement of the differential and total cross-sections of $\gamma$-ray emission induced by $14.1$ MeV neutrons for C, Al, Si, Ca, Ti, Cr, and Fe using the tagged neutron method

Abstract

In this work, differential cross sections of $\gamma$-ray emission produced in nuclear reactions induced by $14.1$~MeV neutrons are measured for the $4.439$~MeV line from carbon, as well as for $10$ individual $\gamma$-ray lines from aluminum, $6$ from silicon, $8$ from calcium, $16$ from titanium, $6$ from chromium, and $14$ from iron. The measurements were conducted using the tagged neutron method with four LaBr$_3$(Ce) scintillation detectors positioned at angles of $25^{\circ}$, $45^{\circ}$, $60^{\circ}$, and $70^{\circ}$ relative to the generator target -- sample center axis. A neutron generator capable of producing $16$ separate beams of tagged neutrons was employed, which, combined with the detector system, enabled the determination of differential cross-sections for $64$ distinct angle values in the range of $17^{\circ}$ to $89^{\circ}$. To simplify data visualization, the angular distributions were divided into $5^{\circ}$ intervals, with weighted mean values of the angle and differential cross-section calculated for each interval. Corrections for multiple neutron scattering and attenuation, $\gamma$-ray attenuation, and total detection efficiency, computed using GEANT4, were accounted for in the cross-section calculations. Additional measurements were performed to validate the correction calculations. The total $\gamma$-ray emission cross-sections were obtained by approximating the angular distributions with even-order Legendre polynomial expansions up to the $6$th degree, followed by integration over the full solid angle. The total systematic error for the obtained data was estimated as $9$\,\%.