A positron emitter has a positron endpoint kinetic energy and decays with half-life

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Radioactivity and decay modes · Radioactivity and decay modes

The Nucleus Resolved, Ch Beta decay: Fermi's theory, parity violation and the double beta modes

Problem

A positron emitter has a positron endpoint kinetic energy

Q_{\beta^+} = 4.599\,\mathrm{MeV}

and decays with half-life

T_{1/2} = 1.50\,\mathrm{s}

, entirely (branching fraction

100\%

) to the ground state of the daughter. Using the high-energy approximation for the integrated phase-space factor,

f \approx W_0^5/30

with

W_0 = 1 + Q_{\beta^+}/m_ec^2

and

m_ec^2 = 0.511\,\mathrm{MeV}

(valid because

Q_{\beta^+} \gg m_ec^2

here): ((a)) Calculate

f

. ((b)) Calculate

ft

(with

t

the partial half-life in seconds) and

\log_{10} ft

. ((c)) The corrected superallowed transitions cluster near

\log ft \approx 3.5

. Say whether this transition's

\log ft

is consistent with a favoured (superallowed or strongly allowed) transition.