In the liquid drop model we have emphasized the properties of nuclear matter but in the atomic shell model, we fill the shells with electrons in order of increasing energy consistent with the requirement of the Pauli principle. When we do so, one obtains an inert core of filled shells, containing 2, 10, 18, 36, 54 and 86 electrons and some valence electrons; the atomic properties are determined primarily by the valence electrons.
When we compare some measured properties of atomic system with the predictions of the model, one finds remarkable agreement. The same kind of effect has been observed in nuclei.
In nuclear physics, it was found that nuclei that have 2, 8, 20, 28, 50, 82 and 126 nucleons (protons or neutrons), called magic numbers, are more abundant than other nuclei. The nuclei having any one of the these magic numbers of protons or neutrons or both show more stability than the other nuclei.
Assumptions of the Shell Model
- Nucleons in the nucleus move independently in a common potential determined by the average motion of all other nucleons.
- Proton and neutrons separately fill levels in the nucleus.
- Most of the nucleons are paired and a pair of nucleons contributes zero spin and zero magnetic moment.
- The properties of odd mass number nuclei are characterized by the unpaired nucleon and odd-odd nuclei by the unpaired proton and neutron.
Predictions of the Shell Model
- This scheme clearly reproduce all the magic numbers.
- The shell model has been very successful in predicting the ground state spin of a large number of nuclei.
- The shell model also makes predictions about the electric quadruple moment of the odd A and Z nuclide.
Achievements of the Shell Model
- It explains the ground state spin and parities of all even-even nuclei without any exception.
- It explains the ground state spin and parities of most of odd A (even-odd or odd-even) nuclei.
- It also explains the spin and parities of odd-odd nuclei.
- It explains the extra stability of magic nuclei.
- It is also explains the qualitative features of magnetic dipole and electric quadruple moment of different nuclei.
Failures of Shell Model
- Shell model fails to explain spin values for certain nuclei.
- Shell model is unable to explain the energy of first excited states in even-even nuclei.
- It is unable to explain magnetic moments of some nuclei.
- This model is also unable to explain quadruple moments of many nuclei.