Unit 5 : Additional Problems

For those looking for additional problems outside of past exam questions and the worked problems in the lectures please consider the following in the reading list.

• Write the expression for the nuclear magnetic moment in terms of the Nuclear Spin I. How do you calculate the energy of a nuclear magnetic dipole in a B-field?

• Draw the shell filling for oxygen nitrogen isotopes and make predictions for their nuclear spin, parity, magnetic moment, and electric quadrupole moment

• Use the shell model to estimate the magnetic moment of C-13.

• In what circumstances does the shell model result in reasonable predictions of nuclear magnetic moments?

• Look up the proof for classical quadrupole in EM equations.

• If a nuclear has an outer shell one proton short of filled explain what happens to the electric quadrupole moment as protons are added.

• Describe the successes and failings of the shell model.

• Explain the collective model in 4 parts with a sketch. What is important about the volume and density of the nucleus in these models.

• What might a strongly distorted nucleus look like in terms of it’s shape.

• Explain in general terms the origin of the parameters in the formula for the electric quadrupole of a distorted nucleus.

• Sketch the rotating cylindrically deformed nucleus and give it’s (classical) rotational energy.

• Write out the sequence of rotational energy levels relative to the E(2+) level.

• Describe how separation of the basic vibration energy levels differs from that of the rotation energy levels.