The reaction has

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

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

Problem

The reaction

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

has

Q = -1.644\,\mathrm{MeV}

. 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)) Using the invariant

s

, calculate the exact threshold kinetic energy of the proton beam incident on a stationary

^7\mathrm{Li}

target. ((b)) Calculate the non-relativistic threshold

T_{\rm thr} = -Q(1 + m_1/m_2)

and state the difference from the exact value.