A beam of ions has emittance (rms size times rms angle at a waist

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

The Nucleus Resolved, Ch Beams and the edges of the chart: emittance, heavy ions, high spin and the drip lines

Problem

A beam of

^{12}\mathrm{C}

ions has emittance

\varepsilon = 1.5\,\mathrm{mm\,mrad}

(rms size times rms angle at a waist, an invariant under magnetic transport). ((a)) The beam is focused to a waist of rms size

0.3\,\mathrm{mm}

on a

^{197}\mathrm{Au}

target. Find the rms angular divergence this focus forces on the beam. ((b)) Using the radius convention

R = 1.3(A_1^{1/3}+A_2^{1/3})\,\mathrm{fm}

, compute the Coulomb barrier

B_C

(centre-of-mass frame) for

^{12}\mathrm{C}+^{197}\mathrm{Au}

. ((c)) Find the centre-of-mass energy below which a head-on collision keeps the distance of closest approach at least

5\,\mathrm{fm}

outside touching, i.e.

d_{\min} \ge R+5\,\mathrm{fm}

, guaranteeing pure Coulomb excitation with no nuclear contact.