Consider the fusion reaction and its inverse

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear reactions · Nuclear reactions

The Nucleus Resolved, Ch Reactions: four-vectors, amplitudes and partial waves

Problem

Consider the fusion reaction

d+t\to {}^4\mathrm{He}+n

and its inverse

n+{}^4\mathrm{He}\to d+t

, compared at the same centre-of-mass energy. The centre-of-mass momentum in the

d+t

channel is

p_ac = 40.0\,\mathrm{MeV}

and in the

\alpha+n

channel is

p_bc = 166\,\mathrm{MeV}

. The spins are

J_d=1

J_t=1/2

J_\alpha=0

J_n=1/2

. ((a)) Predict which of the two cross sections is larger, then use detailed balance to calculate the ratio

\sigma(dt\to\alpha n)/\sigma(n\alpha\to dt)

. ((b)) In a separate elastic-scattering experiment, a beam of

^4\mathrm{He}

ions (mass number

4

) is fired at a stationary deuterium target (mass number

2

). Predict whether the scattered helium ions have a maximum laboratory angle, and if so calculate it.