Fermi-function integrals for finding relative beta-group intensities

Abstract

Values are presented of the definite integral I(Z, T_max), which is related to the relative number, N, of electrons in a β⁻-group with end point energy T_max by the simple expression N = a²T_max²I(Z, T_max), where a is the y-intercept in the Fermi-Kurie plot, $I(Z,T_{\max })={\int }_0^{T_{max}}f(Z,T)h\left(T\right)dT,$

where f is the Fermi function and $h\left(T\right)=(T+1){(1-T/T_{\max })}^2{\left[T\right(T+2\left)\right]}^{-1/2}{T}_{\max }^{-2}.$

The Z-ranges is 10(1)109; the T_max-range is 0.1(0.05)0.4, 0.5(0.1)5.2.