(i) What are the similarities and the differences in the concept of \"Shell Mode
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Question
(i) What are the similarities and the differences in the concept of "Shell Model" between the atoms and in the nuclei. (ii) In the hydrogen atom, what is the size of the spin-orbit splitting (in terms of eV)? (ii) Estimate the size of the spin-orbit energy for the nucleus compared to the energy spacing given by Fermi Gas Theory, by taking the potential to be approximately the Harmonic oscillator potential: V_c(r) = -V_0 (1 - (r/R)^2) where V_0 is 50 MeV, A = 200, Mc^2 = 938 MeV. (iv) Based on (i) and (iii), explain why the "magic numbers" in nuclei is different from that in atoms. Notes the energy level of hydrogen atom is E_n = -13.6/n^2 eV. (v) Draw up a diagram giving the energy level ordering of nucleon orbitals in spherical nuclei up to magic number 32. Using your diagram find the spin and parity of the ground state configurations of the following nuclei:^5_2He, ^37_18Ar. (vi) The following diagram gives the energy levels for three nuclei. In each case, explain the origin of these energy levels.Explanation / Answer
(i) Similarities between Nuclear and atomic shell models:
The nucleons in a nucleus according to nuclear shell model are arranged in various energy levels just like electrons arrange themselves in orbitals around the nucleus.
Protons and neutrons along with electrons have half integral spins, i.e., they are fermions. Hence the electrons in the orbitals as well as protons and neutrons inside the nucleus are filled from lowest to the highest energy states.
Differences between atomic and nuclear shell models:
Spin-orbit interaction is much stronger in nuclei than that of atoms.
The sign of spins in nuclear model is opposite to that of atomic case
Nuclear Spin-orbit interaction is not of magnetic origin but it is a property of nuclear force
Nuclei generally have JJ coupling spin-orbit interaction is much stronger when compared to that of atoms, whereas atoms can have either LS or JJ Coupling.
Transition from higher to lower energy state of a nucleus is accompanied by the emission of gamma radiation whereas the transitions from higher to lower energy state emit a photon.
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