Physics 135c H. W. Assignment 8 1.) (a.) Use the procedure from HW#7 to calculate the mean lifetime of tritium for β-decay: 3 H → 3 He + e-+ ¯ ν e (i.e. assume massless neutrinos and ignore nuclear recoil and Coulomb distortion). The energy released in the decay is Δ = m e +0 . 0185MeV. Note that 3 H and 3 He both have a ground state spin of 1 2 and in a simple shell model the decay is simply a neutron decaying to a proton with both particles in the 1 s level. Compare your result with the measured lifetime of τ ( 3 H) = 17 . 8 yrs. Comment on possible causes of any discrepancy between the calculated and measured values. (b.) In the non-relativistic approximation (see Bertulani), the Coulomb correction factor to the beta decay spectrum F ( E e , Z ) = a | ψ Coulomb ( r ) | 2 | ψ planewave ( r ) | 2 A assuming that the wave function is evaluated at the origin ( r = 0). Estimate the magnitude of this eFect for tritium β-decay by including this factor into the phase space integral used
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