, spin-parity , alpha-decays to two levels of . The atomic mass excesses are , , and…

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The Nucleus Resolved, Ch Decay rates from the golden rule: kinetics closed and alpha decay finished

Problem

^{249}\mathrm{Cf}

, spin-parity

\tfrac{9}{2}^-

, alpha-decays to two levels of

^{245}\mathrm{Cm}

. The atomic mass excesses are

\Delta(^{249}\mathrm{Cf})=48.47\,\mathrm{MeV}

\Delta(^{245}\mathrm{Cm},\text{ground state})=39.75\,\mathrm{MeV}

, and

\Delta(^{4}\mathrm{He})=2.425\,\mathrm{MeV}

. The two branches are: (a) a "favoured" branch (measured intensity

82\%

of all alphas) to a level of

^{245}\mathrm{Cm}

at excitation energy

98\,\mathrm{keV}

, spin-parity

\tfrac{9}{2}^-

, believed to be built on the same deformed single-particle orbital as the

^{249}\mathrm{Cf}

ground state; (b) a ground-state branch (measured intensity

3.0\%

) to the

\tfrac{7}{2}^+

ground state of

^{245}\mathrm{Cm}

, built on a different orbital. Using the two atomic masses, find

Q_\alpha

for the ground-state branch and hence for the favoured branch. State the minimum orbital angular momentum

\ell

the emitted alpha particle can carry in each branch, consistent with conservation of angular momentum and parity (

\pi_\alpha=(-1)^\ell

). Given that the WKB penetrability, computed under the chapter's prescription including this

\ell

, is

2.64

times larger for the ground-state branch than for the favoured branch, compute the hindrance factor of the ground-state branch relative to the favoured branch and state what it indicates about the two nuclear configurations.

Related theory

Nuclear Physics

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