7. Non Spherical Nuclei Flashcards
How can you describe classical electric charge distribution
In terms of multipole moments e.g. quadrupole moment
What is the electric quadrupole, Q?
The first non zero moment
- It is 0 for spherical nuclei, and non 0 for non-spherical nuclei
What does a non-spherical nuclei imply?
A non-spherical charge distribution
How do rotations influence spherically symmetric nuclei?
They don’t
Describe how rotations affect an ellipsoid nuclei
Axis of symmetry is the z axis
- Rotations around the z axis don’t change anything
- Rotations around a perpendicular axis introduce additional angular momentum
What is the contribution from the total angular momentum towards to electric quadrupole moment?
Q_j ~ R^2 2j-1 / 2(j+1)
What is the expected electric quadrupole moment for an even-Z even-A nucleus and why?
0 due to the pairing effect and that neutrons have 0 charge
Describe how Rainwater explained the problem with the data of spherical symmetry for odd Z odd A nuclei
He deformed a spherical nucleus to an ellipsoid by a deformation parameter ε
a = R(1+ε)
b = R / sqrt(1+ε)
a is the semi major axis, b is the minor axis and R is the radius of a nucleus, R_0 A^1/3
Describe how Rainwater’s assumption altered the SEMF formula
He altered the coefficients for a_2 and a_3
- This is because of the change in SA of the nucleus and the distances between the protons and neutrons is deformed
What is the electric quadrupole moment equal to for an ellipsoid?
Q = Q_intrinsic * J(2J-1) / [ (J+1) (2J + 3) ]
How do the spectrum of energy levels change for deformed spin-0 nuclei?
They change in steps of 2
E_J = -h bar^2 J(J+1) / 2I
I - Moment of Inertia
What is the Nilsson model?
A single particle model with a different potential complemented by SOC
- Deformed nucleus core induces deformations
How does the deformed nucleus core influence the energies of the different levels
It shifts them, proportionally to the size of the deformation
Describe how the Nilsson model also predicts how the positions of the magic numbers will change
Magic numbers was based on the fact that filled levels were grouped close together, followed by a gap to the next group of levels, so adding a nucleon costs a lot of energy
- Nilsson model shifts these places of significant energy gaps
What is an intrinsic excitation?
When nucleons move to higher energy levels
What are the three types of excitations
Intrinsic excitation, rotations and vibrations
What are shape oscillations?
A form of vibration excitation
- The density of a nucleus remains constant, but the shape changes around equilibrium
Describe the excitations observed when l = 1 and l = 2
When l = 1, the centre of mass is displaced and we get a translation, not a shape change
When l = 2, we get quadrupole deformation
What is the ground state energy?
E_1 = 5/2 h bar w
Describe how the shape oscillations look on a graph
Equilibrium - Circle centered about the origin
Oscillations - Ellipsoids along the x and y axis
What is the energy of the vibrational states?
E_N = (N + 5/2) h bar w
- N determines which excitation we have
What is J^P equal to for one and two phonon excitation?
One phonon: J^P = 2^+
Two phonons: J^P = 0^+, 2^+, 4^+
For two phonons, need to add the spins
How does the energy compare for the one and two phonon 2^+ state?
The one phonon 2^+ state has a smaller energy
