# Prolate nuclear core and rotational bands

1. Consider a deformed prolate nuclear core consisting of an even number of neutrons and one even number of protons outside of this core is a neutron in a d5/2 state

a. What would the degeneracy of the state be if the deformation were zero?

b. What would be in the single particle shell model for deformed nucleim qualitatively plot as a function of the

deformation the energies of the states? Please label them by their mj value.

2. Karne 5-13 book: the levels of 174Hf show two similar rotational bands with energies given as follows in MeV:

E(0+) E(2+) E(4+) E(6+) E(8+) E(10+) E(12+)

Band1 0 0.091 0.297 0.608 1.010 1.486 2.021

Band2 0.287 0.900 1.063 1.307 1.630 2.026 2.489

3. Compare the moments of inertia of these two bands and comment on any difference? (Please see the attached MS Word document for the full question).

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#### Solution Preview

3. Rate dN/dt = -λN where λ = ln2 / t1/2 = 0.693 / 5730 years

Rate = -(0.693 / 5730 y) x 1012 atoms = -0.1224 atoms / year

2. The moment of inertia, IR = [ħ2 /2EJ]x J(J+1)

Sample ...

#### Solution Summary

Degeneracy and moments of inertia are calculated in the following posting.