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 test of the weak interaction needs the atomic mass of

^{74}\mathrm{Rb}

(

T_{1/2}=64.8\,\mathrm{ms}

), a superallowed

\beta^+

emitter, measured by Penning-trap mass spectrometry, which needs a beam of low emittance and low energy spread, ideally a single isotope rather than a mixed cocktail, delivered within a few half-lives. Rubidium is an alkali metal: it diffuses readily out of a hot target material and ionises with near-unit efficiency by surface ionisation. State which production route, ISOL or in-flight fragmentation, is used, and justify the choice from the half-life, the beam quality the measurement needs, and the chemistry of rubidium. ((b)) The same laboratory later searches for oganesson (element 118) via

^{50}\mathrm{Ti} + {}^{249}\mathrm{Cf} \to {}^{295}\mathrm{Og} + 4n

, for which the measured cross section is

\sigma = 0.50\,\mathrm{pb}

. The titanium beam delivers

I = 2.0\times10^{12}

ions per second onto a californium target of areal density

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

^{249}\mathrm{Cf}

(molar mass

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

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

35\%

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

^{295}\mathrm{Og}

nuclei produced per week. (ii) Compute the number reaching the focal-plane detector per week. (iii) Describe briefly how a single such atom is identified against background.

Related theory

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