A Ni beam bombards a Pb target at a centre-of-mass energy of

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

^{58}

Ni beam bombards a

^{208}

Pb target at a centre-of-mass energy of

300\,\mathrm{MeV}

. Take the sum-of-radii contact condition

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

and treat the trajectories classically (Rutherford orbits bent by the Coulomb field alone until the nuclei touch). ((a)) Compute the Coulomb barrier

B_C

and the grazing impact parameter

b_{\rm gr}

, the largest impact parameter for which the trajectory still reaches contact at

R

. ((b)) Predict which reaction class (elastic/Coulomb excitation, quasi-elastic transfer, deep-inelastic collision, or fusion-evaporation) dominates for collisions at impact parameter

b = 2\,\mathrm{fm}

, at

b = b_{\rm gr}

, and at

b = 8\,\mathrm{fm}

, giving the reasoning for each.

Related theory

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