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1. Submitted by:
Muhammad Nadeem
Submitted to:
Dr. Naveed Ahmad
University of education ,Lahore

2. Nuclear shell Model
Introduction
⇨The nuclear shell model is a model of the
atomic nucleus. It uses the Pauli exclusion
principle to explain the nucleus structure in
terms of energy levels. In order to study the
complete nucleus structure, various nuclear
shell models were proposed. The first shell
model was introduced in the year 1932 by
Dmitry Ivanenko and later on developed by
various physicists – Maria Goeppert Mayer,
Eugene Paul Wigner, and J.Hans.D. Jensen in
the year 1949.

3. Why there is a need to develop the Shell
Model?
As the Liquid drop model does not explain the
following:
1. It is not able to explain the magic numbers.
2. It is not able to explain quadrupole moment.
3. It is not able to calculate the nuclear spin.

4. Explanation of SM
As is atomic model , the atoms with 2, 10, 18, 36, 54
and 86 electrons have all their electron shell completely
filled.

5. The ionization energy graph for noble gases:

6. Nuclear Shell Model
 In the same way, in 1948 American physicist M G.
Mayor found that nuclei having 2, 8, 20, 28, 50, 82 and
126 neutrons and protons are more abundant than
other nuclei of similar mass numbers, suggesting their
structures are more stable.
 It has been observed that nuclei having either the
number of protons Z or number of neutrons N =A - Z
equal to one of the numbers 2, 8, 20, 50, 82 and 126
are more stable than their neighbours. These numbers
are called magic numbers.

7.  Whereas some nuclei contain magic number of both
protons and neutrons such as Helium-(z=2 , N=2) ,
Oxygen-(z=8 , N=8) Calcium-(z=20 , N=20) . So, these
are called doubly magic numbers and show
exceptionally high stability.

8. Main Assumptions
1. Nucleon forms sub-shells and shells within the nucleus
2. The shell within the nucleus get closed with a suitable
number of nucleons
3. Each nucleon is supposed to possess a spin angular
momentum of ħ/2 and orbital angular momentum Iħ.
4. This theory assumes that LS coupling holds only for the
very lightest nuclei in which the I values are necessarily
small in their normal configuration.

9. 5. The heavier nuclei exhibit j-j coupling. It is assumed
that the nucleons move in its orbit within the nucleus,
independently of all other nucleons as shown in fig

10. Quadrupole Moment
The nuclear electric quadrupole moment is a parameter
which describes the effective shape of the ellipsoid of
nuclear charge distribution. A non-zero quadrupole
moment Q indicates that the charge distribution is not
spherically symmetric.

11. Achievements of Shell Model
 Explains magic numbers
 Explains ground state spin
 Stability and Binding energy
 Phenomenon of nuclear isomerism
 Explain Magnetic moment of some nuclei

12. Limitations:.
 Fails to explain The stability of four stabel nuclei H, Li,
B, N
 It does not predict Correct values of Nuclear spin for
certain nuclei
 The Magnetic moment show deviation From the
observed values.