Fermi University Physics

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Isospin as a group: SU(2), Clebsch-Gordan ratios and G-parity

Problem

Take

m_p=938.3\,\mathrm{MeV}

m_d=1875.6\,\mathrm{MeV}

m_{\pi^+}=139.6\,\mathrm{MeV}

. ((a)) Using relativistic kinematics, find the minimum proton beam kinetic energy

T_{\rm lab}

(target proton at rest) for the reaction

pp\to d\pi^+

to occur. ((b)) At a beam energy well above this threshold, a measurement gives

\sigma(pp\to d\pi^+)=2.8\,\mathrm{mb}

. Using the fact that

pp

is a pure isospin-1 state while

np

is an equal mixture of isospin 1 and isospin 0, and that only isospin-1

NN

can produce the isospin-1

d\pi

final state, predict

\sigma(np\to d\pi^0)

at the same energy.