The diagram below shows the sequence of bound single-particle states calculated using the Wood-Saxon potential, and the predicted magic numbers in the absence of the spin-orbit interaction term (numbers shown enclosed in circles, corresponding to closed shells). The predicted magic numbers do not fully agree with the observed values, which are found to be 2, 8, 20, 28, 50 and 82. Using a diagram, show how these energy states evolve with the introduction of the spin- orbit term, and indicate how the magic numbers that are in agreement with experimental observation are obtained. You can stop at magic number 50. The lowest energy levels in the accepted shell model scheme are 1s1/2, 1p3/2, 1p1/2, 1d5/2, 281/2, 1d3/2, 1f7/2, 2p3/2, 1f5/2, 2p1/2, 1g9/2, 1g7/2, 2d5/2, 2d3/2, 381/2 and 1h11/2. (92 1h 38 2d 58 58 1g 40 40 2p 1f 20 2s ld 8 1p 2 1s

The diagram below shows the sequence of bound single-particle states calculated using the Wood-Saxon potential, and the predicted magic numbers in the absence of the spin-orbit interaction term (numbers shown enclosed in circles, corresponding to closed shells). The predicted magic numbers do not fully agree with the observed values, which are found to be 2, 8, 20, 28, 50 and 82. Using a diagram, show how these energy states evolve with the introduction of the spin- orbit term, and indicate how the magic numbers that are in agreement with experimental observation are obtained. You can stop at magic number 50. The lowest energy levels in the accepted shell model scheme are 1s1/2, 1p3/2, 1p1/2, 1d5/2, 281/2, 1d3/2, 1f7/2, 2p3/2, 1f5/2, 2p1/2, 1g9/2, 1g7/2, 2d5/2, 2d3/2, 381/2 and 1h11/2. (92 1h 38 2d 58 58 1g 40 40 2p 1f 20 2s ld 8 1p 2 1s