A facility director wants one afternoon's beam time to touch three different edges 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

A facility director wants one afternoon's beam time to touch three different edges of the chart of nuclides. Treat each part independently, using the sharp-radius model

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

for heavy-ion contact,

R = 1.2A^{1/3}\,\mathrm{fm}

for a single nucleus,

\hbar c = 197.327\,\mathrm{MeV\,fm}

and

e^2/4\pi\epsilon_0 = 1.43996\,\mathrm{MeV\,fm}

, and the neutron mass

m_nc^2 = 939.565\,\mathrm{MeV}

. ((a)) A

^{40}

Ca beam fuses with a

^{196}

Pt target at a laboratory energy of

260\,\mathrm{MeV}

. Estimate the grazing angular momentum

\ell_{\rm gr}

this reaction brings in, and compare it with the highest spin seen in any discrete rotational band, about

60\hbar

. What must happen to the angular momentum above that value? ((b))

^{19}

C has a one-neutron separation energy

S_n = 0.53\,\mathrm{MeV}

with the last neutron in a

2s_{1/2}

(

\ell = 0

) orbital outside a

^{18}

C core. Estimate the rms neutron-core separation of the exponential tail alone and compare it with the core's rms radius; does

^{19}

C show halo character? ((c)) A

^{48}

Ca-like light beam of intensity

2.5\times10^{12}\,\mathrm{s^{-1}}

strikes a

0.5\,\mathrm{mg\,cm^{-2}}

target of

^{249}

Cf, and the reaction of interest has a cross section of

0.5\,\mathrm{pb}

. A separator downstream transmits

35\,\mathrm{per\,cent}

of the recoils. Estimate the number of identified atoms produced in a one-week run.

Related theory

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