Digital Nuclear Shell Model

TL;DRAbstract

The subject of this thesis is a digital approach to the investigation of the digital basis of digitalnuclear shell model. The shell model is partly analogous to the atomic shell model which describes thearrangement of electrons in an atom, in that a filled shell results in greater stability. Whenadding nucleons to a nucleus, there are certain points where the binding energy of the next nucleon issignificantly less than the last one. Magic numbers of nucleons: 2, 8, 20, 28, 50, 82, 126 which aremore tightly bound than the next higher number, is the origin of the shell model. “In a threedimensionalharmonic oscillator the total degeneracy at level n is (n+1)(n+2)/2. Due to the spin, thedegeneracy is doubled and is (n+1)(n+2). Thus the magic numbers would be ∑ k n=0 (n+1)(n+2)=(k+1)(k+2)(k+3)/3 for all integer k. This gives the following magic numbers:2,8,20,40,70,112..., which agree with experiment only in the first three entries. These numbers aretwice the tetrahedral numbers (1,4,10,20,

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