Repeat the same three estimates for a different set of beams and targets

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

Repeat the same three estimates for a different set of beams and targets, using

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}

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

and

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

. ((a)) A

^{36}

S beam fuses with a

^{208}

Pb target at a laboratory energy of

200\,\mathrm{MeV}

. Estimate the grazing angular momentum and compare it with the highest spin seen in any discrete rotational band, about

60\hbar

. ((b))

^{6}

He has a two-neutron separation energy

S_{2n} = 0.973\,\mathrm{MeV}

; treat its two valence neutrons together as a single particle of mass

2m_n

outside a

^{4}

He core, in a relative

\ell = 0

state. Estimate the rms neutron-pair-to-core separation of the exponential tail and compare it with the core's rms radius. ((c)) A beam of intensity

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

strikes a

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

target of

^{208}

Pb, in a reaction of cross section

200\,\mathrm{pb}

, with a separator downstream transmitting

30\,\mathrm{per\,cent}

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