The ground-state rotational band of has its first excited state at

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · The nuclear force and nuclear models · The nuclear force and nuclear models

The Nucleus Resolved, Ch Collective motion: the deformed nucleus, vibrations, rotations and giant resonances

Problem

The ground-state rotational band of

{}^{160}\mathrm{Dy}

has its first excited state at

E(2^+) = 86.8\,\mathrm{keV}

. Assume a

K=0

even-even band obeying

E(J) = \dfrac{\hbar^2}{2\mathcal{I}}J(J+1)

. ((a)) Find the rotational constant

\hbar^2/2\mathcal{I}

, in keV. ((b)) Predict

E(4^+)

. ((c)) Taking

R_0 = 1.2A^{1/3}\,\mathrm{fm}

and mass

Mc^2 = A\times931.494\,\mathrm{MeV}

, find the ratio

\mathcal{I}/\mathcal{I}_{\rm rigid}

, where

\mathcal{I}_{\rm rigid} = \tfrac{2}{5}MR_0^2

is the moment of inertia of a rigid uniform sphere.