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

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}\mathrm{Ni}

beam bombards a

^{58}\mathrm{Ni}

target at a centre-of-mass energy

E_{\rm cm} = 200\,\mathrm{MeV}

. Someone argues: 'The Coulomb barrier for this pair is only about

110\,\mathrm{MeV}

, and

200\,\mathrm{MeV}

is well above it, so essentially every collision has enough energy to overcome the barrier and fuse into a single compound nucleus.' ((a)) Using

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

and

\mu_{\rm red}=\dfrac{A_1A_2}{A_1+A_2}\,\mathrm{u}

, compute

B_C

and the grazing angular momentum

\ell_{\rm gr} = R\sqrt{2\mu_{\rm red}(E_{\rm cm}-B_C)}/\hbar

(with

\mu_{\rm red}

expressed as an energy

\mu_{\rm red}c^2

). ((b)) Given that the highest spins seen in any discrete rotational band are of order

60\hbar

, explain why the argument above is wrong, and say which impact parameters (small or large, i.e. small or large orbital angular momentum) actually lead to fusion-evaporation residues at this energy.

Related theory

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