A radioactive-ion-beam facility produces

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Nuclear Physics · Nuclear constituents, size and binding

The Nucleus Resolved, Ch Spin, parity and the electromagnetic moments of a nucleus

Problem

^{11}\mathrm{Li}

, half-life

T_{1/2}=8.75\times10^{-3}\,\mathrm{s}

, at a rate of

1.0\times10^{4}

ions s

^{-1}

. Three methods can measure a nuclear spin and moment: bulk NMR, which needs of order

10^{15}

polarised nuclei held in a magnetic field for many precession periods (typically minutes) to build a detectable signal; atomic-beam magnetic resonance, which likewise needs the sample to survive transport and several precession periods, of order seconds; and collinear laser hyperfine spectroscopy performed directly on the flowing beam, which needs only about

10^3

10^4

ions per second passing through the interaction region, as used for

^{31}\mathrm{Mg}

(

T_{1/2}=0.27\,\mathrm{s}

). ((a)) Production and decay run at the same time, so the number of

^{11}\mathrm{Li}

nuclei collected cannot grow without limit. Find the largest number that can be present at once under steady production, and compare it with the

10^{15}

that bulk NMR needs. ((b)) State which of the three methods can measure the spin and moment of

^{11}\mathrm{Li}

, and justify the choice using the numbers given.

Related theory

Nuclear Physics

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