Statistical Theory of Gamma-Ray Spectra Following Nuclear Reactions

Abstract

A theory predicting 7-ray spectra following intermediate or high-energy nuclear reactions is derived on the basis of the statistical theory. The equations take a particularly simple form if the assumption is made that all radiative transitions are of the electric dipole type. The theory is applied to two specific reactions: inelastic neutron scattering and thermal neutron capture. Numerical calculations of spectra arising from thermal neutron capture by two gadolinium isotopes are shown to compare well with experiments.

Modified Methods of Neutron Cross-Section Calculations

“…For the sake of convenience in the formulation, we shall hereafter drop the symbol < ) indicating the energy average. (11) and (12), respectively. Though Eqs.…”

“…(A27) and (A28), we believe that the dependence of the quantities on the spin and parity in Eqs. (11) and (12) may be adequate, as well as in Eqs. (13) and (14).…”

“…9 , ( 11) (12) In both the above expressions, the denominators are the total transmission coefficients given in Eq. ( 5 ) , and not the quantities defined in Eq.…”

“…Though Eqs. (11) and (12) are derived without any proof of their relation to Eqs. (A27) and (A28), we believe that the dependence of the quantities on the spin and parity in Eqs.…”

“…Using Eqs. (11) and (12), the modified transmission coefficients are defined for the neutron and 7-ray channels respectively :…”