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Shell model. Notes: 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.

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shell model
Shell model

Notes:

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.

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

shell model1
Shell model

Fermi Gas

Range ?

EF n2/3

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

shell model2
Shell model

Nuclear reactions?

Transition probability?

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

shell model3
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 < 150

190 < A < 220

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

shell model4
Shell model

Harmonic oscillator

Near drip line

No spin-orbit coupling

Near valley of  stability

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

shell model5
Shell model

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

shell model6
Shell model
  • 17 p, 21 n.
  • p in 1d3/2l  s   = +
  • n in 1f7/2l  s   = -
  • Rule 3 sp  sn   lp  ln 
  • ½ + ½ + 3 – 2 = 2

 total  = -

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

shell model7
Shell model

Excited states:

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

shell model8
Shell model

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

1d3/2

?

1p1/2

l  pairing 

2s1/2

1d5/2

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

shell model9
Shell model
  • Extreme independent particle model  only 23rd neutron.
  • More complete shell model  all three “valence” nucleons.

HW 21

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

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

shell model10
Shell model

Dipole Magnetic Moment

HW 22Show 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 -?

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

shell model11
Shell model

Electric Quadrupole Moment

Refined QM 

Extremes

Single particle: n = 1  - ive Q

Single hole: n = 2j +ive Q

Number of protons in a subshell

Examine Table 5.1 and Fig.5.10 in Krane

<r2> for a uniformly charged sphere

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

shell model12
Shell model

Validity

A < 150

190 < A < 220

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

collective model
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.

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

collective model1
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 model

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

collective model2
Collective model

Symmetry axis

Rotational

States

Symmetry  only even I

GS (even-even) 0+

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

collective model3
Collective model

HW 23compare 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.

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

collective model4
Collective model

HW 23 (continued)

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

164Er

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

slide19

Collective model

Odd-A

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