Classical Electrodynamics · Problem 11.21

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · maximum-kinetic-energy-decay

Problem

If a system of mass

M

decays or transforms at rest into a number of particles, the sum of whose masses is less than

M

by an amount

\Delta M

, (a) show that the maximum kinetic energy of the

i

th particle (mass

m_i

) is

(T_i)_{\rm max} = \Delta M\left(1 - \frac{m_i}{M} - \frac{\Delta M}{2M}\right)

(b) determine the maximum kinetic energies in MeV and also the ratios to

\Delta M

for each of the particles in the following decays or transformations of particles at rest:

\begin{aligned} \mu &\to e + \nu + \bar{\nu}\\ K^+ &\to \pi^+ + \pi^- + \pi^+\\ K^\pm &\to e^\pm + \pi^0 + \nu\\ K^\pm &\to \mu^\pm + \pi^0 + \nu\\ p + \bar{p} &\to 2\pi^+ + 2\pi^- + \pi^0\\ p + \bar{p} &\to K^+ + K^- + 3\pi^0 \end{aligned}