A laboratory runs two experiments.

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 laboratory runs two experiments. ((a)) A study of two-proton radioactivity needs the decay energy and lifetime of

^{45}\mathrm{Fe}

(

T_{1/2}=1.7\,\mathrm{ms}

), which decays by emitting two protons simultaneously, measured by implanting individual ions in a silicon detector and recording the correlated proton signals afterwards. Iron is a refractory transition metal that adheres to hot surfaces and is chemically difficult to release quickly. State which production route, ISOL or in-flight fragmentation, is used, and justify the choice from the half-life and the chemistry of iron. ((b)) The same laboratory searches for moscovium (element 115) via

^{48}\mathrm{Ca} + {}^{243}\mathrm{Am} \to {}^{288}\mathrm{Mc} + 3n

, for which the measured cross section is

\sigma = 5.0\,\mathrm{pb}

. The calcium beam delivers

I = 1.2\times10^{12}

ions per second onto an americium target of areal density

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

^{243}\mathrm{Am}

(molar mass

243\,\mathrm{g\,mol^{-1}}

), assumed uniform and undamaged throughout the run, and a recoil separator transmits

45\%

of the fusion-evaporation residues to a focal-plane detector. Take

1\,\mathrm{week}=6.048\times10^5\,\mathrm{s}

and Avogadro's number

N_A=6.022\times10^{23}\,\mathrm{mol^{-1}}

. (i) Compute the number of

^{288}\mathrm{Mc}

nuclei produced per week. (ii) Compute the number reaching the focal-plane detector per week. (iii) Describe briefly how the identifications differ from a case where only about one atom a week is expected.

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