1. The Shell Model of the Nucleus 5. Nuclear moments
The Shell Model of the Nucleus Nuclear moments. The Collective Model of the Nucleus
[Sec. 6.2, 6.4, 6.5, 6.6, 6.7 Dunlap]

2. The Bohr-Mottelson Collective Model of the Nucleus
James Rainwater
(1917 – 1986)
U.S.A
Aage Bohr
(1922 –
Denmark
Ben Mottelson
(1926 –
USA / Denmark
Between about 1950 – 1955, Bohr and Mottelson followed the idea on collective nuclear motion suggested by Rainwater. All three received the 1975 Nobel Prize – “For their work on the connection of collective nuclear motion with single particle motion”

3. Electric nuclear moments
The electrostatic energy associated with charge distribution (r) in electric potential (r) is:
ELECTRIC CHARGE
ELECTRIC DIPOLE
ELECTRIC QUADRUPOLE - +

4. Electric and Magnetic nuclear moments
“For symmetry reasons the electric dipole moment of the nucleus (as well as all other static multipole moments with odd parity; for example – magnetic monopole, magnetic quadrupole or electric octupole) must VANISH.
WHY? Because the both the strong and the electric forces are invarient under the parity operation – which means we should never get different nuclear properties under space inversion

5. The nuclear Quadrupole moment Q
PROLATE “Cigar”
OBLATE “Dou-nut”
Unlike atoms – nuclei can easily distort from spherical state. Unlike atoms the potential the nucleons move in is formed by the nucleons themselves. [In an atom it is the potential coming from the nucleus that dominates]

6. The nuclear Quadrupole moment Q
Quadrupole Moment (Barns)
Magic Numbers

7. The regions of sphericity
Limits of manmade nuclides
QUESTION – will mankind ever make this double magic?

8. Quadrupole moment on the Shell model
An extra proton or neutron added to a closed shell configuration makes an OBLATE ellipsoid
A proton or neutron removed from a closed shell configuration make a PROLATE ellipsoid

9. Quadrupole moment on the Shell model
missing
Odd proton
extra
QM expression
missing
Advanced treatment
Odd neutron
For a uniformly charged sphere:
extra

10. Deformation effects shell states Nilsson Model
In a nonspherical nucleus a definite direction is defined – the direction 3 along the axis. The total angular momentum j is projected along the 3rd axis to give a new quantum no. K. = ± j, ±(j-1), ± (j-2) etc. This phenomenon also splits the degeneracy previously seen for spherical (closed shell) nuclei

11. The Nilsson Shell Model Plot for Deformed Nuclei

12. Irrotational collective rotation of the nucleus
Nuclear collective rotation occurs around an axis perpendicular to the symmetry axis “3”
The rotation is called irrotational because the nucleus is not quite solid – It is largely the “skin” of “outer shape” of the nucles that is rotating

13. Collective rotational motion
Consider energy of a rigid rotator with moment of inertia  J 
and

14. The nucleus can also vibrate
Breathing mode –
First observed in 1977 – very high energy
Requires nuclear fluid compressibility
Quadrupole Deformation
Rotating wave with Sherical Harmonic Wavefunction – circulates – or vibrates the nucleus.
Spin = 2, Parity = +

15. Nuclear vibrations are bosonic

16. The giant dipole resonance
High energy photon  n
PHOTON CROSS SECTION (mb)
PHOTON ENERGY (MeV)

17. Nuclear magnetic momentsj
proton z
The magnetic moment of the nucleus comes about because
We have charged particles – protons moving around the center of the nucleus (i.e. p, d, f, g etc states)
Both protons and neutrons have their own INTRINSIC magnetic moments. s
For the PROTON we must add the mag mom due to ORBITAL motion to get the full mag. Mom.
For the NEUTRON we can write down a similar equation but define that gln=0
After time averaging rapid motion about j then
See SEC 6.6

18. Magnetic dipole moments
MAGNETIC MOMENT (nuc magnetons)
JACKNIFE
ODD NEUTRON
STRETCH
Shown are the “Schmidt lines”
NUCLEAR SPIN J

19. Magnetic dipole moments
Shown are the “Schmidt Lines” named after German physicist T. Schmidt who discovered these lines empirically in 1937.
MAGNETIC MOMENT (nuc magnetons)
ODD PROTON
STRETCH
ODD NEUTRON
JACKNIFE
NUCLEAR SPIN J