To a first approximation, the energy levels of nucleons begin with those of an isotropic three-dimensional harmonic oscillator. A second approximation lowers each level slightly by an amount proportional to , where is the orbital angular momentum quantum number. The code used to designate the values is s, p, d, f, g, h, i, k, … (sober physicists don't find giraffes hiding in kitchens). In contrast to the convention used in atoms, the integer quantum number labels the ordering of levels of a given angular momentum. Thus you will find levels labeled 1, 2, etc. The left side of the graphic gives the designations of the levels. It was suggested by Enrico Fermi that spin-orbit coupling plays an important role in determining nucleon energies. Each -level, except , is accordingly split into two states, with . This leads finally to the spectrum of nucleon energy levels shown on the right, with appropriate gaps determining the magic numbers. Neutrons are represented by blue dots and protons by red dots. The diagram is highly schematic since the magnitudes and even the ordering of the levels differ from nucleus to nucleus.

Following is a partial listing of nuclides with magic numbers and/or :

: ;

: , ;

: , , , , ;

: , , , , ;

: , , , ;

: , , , , , , ;

: .

: , ;

: with ;

: with ;

: with ;

: with ;

: with

Of special interest are the doubly-magic nuclei: , , , , and .