A proton beam of kinetic energy strikes a target of areal density at a beam current of

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

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

Problem

A proton beam of kinetic energy

T_p = 5.00\,\mathrm{MeV}

strikes a

^7\mathrm{Li}

target of areal density

n_t = 1.0\times10^{18}\,\mathrm{atoms\,cm^{-2}}

at a beam current of

100\,\mathrm{nA}

, producing neutrons via

^7\mathrm{Li}(p,n)^7\mathrm{Be}

Q = -1.644\,\mathrm{MeV}

. At the forward centre-of-mass angle the reaction amplitude has

|f_{ba}(0)|^2 = 2.50\,\mathrm{fm^2}

in the convention that carries

\sqrt{\mu_a/\mu_b}

. The atomic masses are

m(^1\mathrm{H}) = 1.007825\,\mathrm{u}

m_n = 1.008665\,\mathrm{u}

m(^7\mathrm{Li}) = 7.016004\,\mathrm{u}

m(^7\mathrm{Be}) = 7.016929\,\mathrm{u}

, with

1\,\mathrm{u}c^2 = 931.494\,\mathrm{MeV}

. A neutron counter subtending

\Delta\Omega = 3.0\,\mathrm{msr}

in the centre-of-mass frame is placed at that angle. ((a)) Calculate the centre-of-mass wave numbers

k_a

(proton channel) and

k_b

(neutron channel). ((b)) Calculate the count rate in the detector.