A parametrization of the phase space factor for allowed β-decay

Abstract

The phase space factor for allowed β-decay is parametrized in the form: ƒ = ƒ Z = 0 exp Σ 3 n = 0 a n (1n E 0) n for | Z| ≦ 101 and for β-particle kinetic energy end points in the range 10 keV to 20 MeV ( ƒ Z = 0 is the usual point nucleus phase space factor for Z = 0). The parametrization uses electron wavefunctions generated in a uniform spherical charge distribution of radius adjusted to fit electron scattering and muonic X-ray data and screened by the atomic electrons; allowance is made for the curvature of the lepton wavefunctions through the nuclear volume, for their convolution with (rectangular) nucleon wavefunctions coterminous with the nuclear charge distribution, for all allowed combinations of l = 0 and l = 1 leptons of j = 1 2 , for the energy-dependent “outer” radiative correction of order α and for the finite mass of the nucleus. Within the context of its definition the parametrization is accurate to better than 0.1 % everywhere.