A beam of ions has emittance .

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

^{40}\mathrm{Ca}

ions has emittance

\varepsilon = 2\,\mathrm{mm\,mrad}

. ((a)) It is focused to a waist of rms size

0.1\,\mathrm{mm}

on a

^{208}\mathrm{Pb}

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

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

, compute the Coulomb barrier

B_C

(centre-of-mass frame) for

^{40}\mathrm{Ca}+^{208}\mathrm{Pb}

. ((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.