The even-even nuclide ( , ) has these measured levels above its ground 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 even-even nuclide

^{172}\mathrm{Yb}

(

Z=70

A=172

) has these measured levels above its

0^+

ground state:

2^+

78.7\,\mathrm{keV}

4^+

261.0\,\mathrm{keV}

, and

6^+

540.6\,\mathrm{keV}

. ((a)) Compute the ratio

E(4^+)/E(2^+)

and use it to decide whether this sequence is vibrational or rotational. ((b)) Assuming a

K=0

rotational band, extract the rotational constant

\hbar^2/2\mathcal I

from the

2^+

energy. ((c)) Take

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

and the atomic mass unit

931.494\,\mathrm{MeV}/c^2

to compute the rigid-sphere moment of inertia

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

(with

M=Ac^{-2}\times931.494\,\mathrm{MeV}

), and give the ratio

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