# Homework Help: Nuclear Rotational and Vibrational States

1. Jan 22, 2010

### MattLiverpool

1. The problem statement, all variables and given/known data

A nucleus can exhibit vibrational and rotational collective motion. Write down the expression for the energy levels for each type of motion, taking care to explain the symbols used.

Discuss with the aid of calculations how you would decide which collective motion is appropriate to explain experimental energy levels that are measured to be:

Spin/Parity 0+ 2+ 4+ 6+
Energy (keV) 0 180 600 1260

Are these experimental data best explained by vibrational and rotational collective motion?

2. Relevant equations

Given in answer to first part of the solution.

3. The attempt at a solution

Ok so I know the first part I think:

Vibrational:
E=E0+N$$\hbar$$$$\omega$$

Omega is supposed to be in line dont know why it has gone almost superscript!
However I am unsure what $$\omega$$ stands for in this case!

Rotational:
E(I)=$$\frac{I(I+1)\hbar^2}{2\Im}$$

The second part of the question I do not know, I am guessing that you can use the equations some how, but there is no other information about the moment of inertia.

Thanks for any help