Classical Electrodynamics · Problem 15.13

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · bremsstrahlung-virtual-quanta-radiative-beta

Problem

In the decay of a pi meson at rest a mu meson and a neutrino are created. The total kinetic energy available is (mπ−mμ)c2=34(m_\pi - m_\mu)c^2 = 34 MeV. The mu meson has a kinetic energy of 4.1 MeV. Determine the number of quanta emitted per unit energy interval because of the sudden creation of the moving mu meson. Assuming that the photons are emitted perpendicular to the direction of motion of the mu meson (actually it is a sin⁡2θ\sin^2\theta distribution), show that the maximum photon energy is 17 MeV. Find how many quanta are emitted with energies greater than one-tenth of the maximum, and compare your result with the observed ratio of radiative pi-mu decays. [1.24±0.25×10−4[1.24 \pm 0.25 \times 10^{-4} for muons with kinetic energy less than 3.4 MeV. See also H. Primakoff, Phys. Rev., 84, 1255 (1951).]

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