A hypothetical allowed emitter

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Nuclear Physics · Radioactivity and decay modes

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

Problem

A hypothetical allowed

\beta^-

emitter, with the Coulomb factor of the daughter switched off (as in the model spectrum built for an allowed transition), gives the following counts

N

in four equal-width momentum bins, at kinetic energies

T_e

T_e = 0.1\,\mathrm{MeV}

N = 718

T_e = 0.3\,\mathrm{MeV}

N = 1428

T_e = 0.5\,\mathrm{MeV}

N = 1218

T_e = 0.7\,\mathrm{MeV}

N = 482

((a)) For each bin, compute the electron momentum

p_ec

from

T_e

using

W = 1 + T_e/m_ec^2

and

p_ec = m_ec^2\sqrt{W^2-1}

, with

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

. ((b)) Form the Kurie variable

K = \sqrt{N}/p_ec

at each bin and show the four points lie on a straight line in

T_e

. ((c)) Extrapolate the line to find the endpoint energy

Q