Shell model

transcript

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

Shell modelNotes: 1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei. 2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate. 3. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l.4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core.

Shell modelFermi Gas

EF n2/3

Range ?

Shell model

Transition probability?

Nuclear reactions?

Shell model

Ground state: (near closed shells)

1. Angular momentum of odd-A nuclei is determined by the angular momentum of the last nucleon that is odd. 2. Even-even nuclei have zero ground-state spin, because the net angular momentum associated with even N and even Z is zero, and even parity. 3. In odd-odd nuclei the last neutron couples to the last proton with their intrinsic spins in parallel orientation.

Provided that the ordering is known….!!

A < 150190 < A < 220

Shell model

Near valley of

stability

No spin-orbit

coupling

Harmonic oscillator

Near drip line

Shell model

• 17 p, 21 n.• p in 1d3/2 l s = +• n in 1f7/2 l s = -• Rule 3 sp sn lp ln

• ½ + ½ + 3 – 2 = 2

total = -

Shell model

Excited states:

Extreme independent particle model!!! Does the core really remain inert?

Shell model

l pairing

Shell model

• Extreme independent particle model only 23rd neutron.• More complete shell model all three “valence” nucleons.

HW 21HW 21

Discuss the energy levels of nuclei with odd number of nucleons in the 1f7/2 shell.

Shell model

)1()1()1(

sslljjg

sslljjgg lsj

Dipole Magnetic Moment

Nj jg HW 22HW 22 Show that

and examine Eqs. 5.9 in Krane. In addition, work out problem 5.8 in Krane Conclusion?Proton: gs(free) = 5.5856912 ? gl = 1 ?Neutron: gs(free) = -3.8260837 ? gl = 0 ?What about + and -?

Shell model

Electric Quadrupole MomentRefined QM

12 322

<r2> for a uniformly charged sphere

jn 21 Number of protons in

a subshell

ExtremesSingle particle: n = 1 - ive QSingle hole: n = 2j +ive Q

Examine Table 5.1 and Fig.5.10 in

Shell model

ValidityA < 150

190 < A < 220

Nuclide Q (b)2H (D) +0.00288

17O -0.0257859Co +0.4063Cu -0.209133Cs -0.003

161Dy +2.4176Lu +8.0

209Bi -0.37

Collective model• Large quadrupole moments nucleus as a collective body (Liquid drop model).• Interactions between outer nucleons and closed shells cause permanent deformation.• Single-particle state calculated in a non-spherical potential complicated.• Spacing between energy levels depends on size of distortion.• Doubly magic 1st excited state away from GS.• Near closure single-particle states.• Further away from closure collective motion of the core excited states.

Collective model

• A net nuclear potential due to filled core shells exists.

• Collective model combines both liquid drop model and shell model.

• Two major types of collective motion:Vibrations: Surface oscillations.Rotations: Rotation of a deformed shape.

Collective modelSymmetry

Symmetry only even IGS (even-even) 0+

)2/(20)4(

23.152/4.91)2/(6)2(

keVkeVE

Collective model

HW 23HW 23 compare measured energies of the states of the ground state rotational band to the calculations.Rigid body or liquid drop? Intermediate Short range and saturation of nuclear force.

Collective model

Spin parity Emeasured

(keV)E/E(2+) I(I + 1)/6

10+ 1518.00 16.61 18.33

6+ 7.00

4+ 299.44 3.28 3.33

2+ 91.4 1.0 1.0

Higher angular momentum centrifugal stretching higher moment of inertia lower energy than expected.

HW 23 HW 23 (continued)(continued)

nucleonEE 2g2

Collective model

Shell model

Documents