The Science News section of the NY Times (Tuesday, October 17 2006) had an article about the creation of element 118.

The article mentioned “Magic Numbers” of neutrons & protons which result in especially stable nuclei due to the formation of closed or complete shells. I always thought that it was “Magic Totals” of neutrons & protons which resulted in enhanced stability. Now I realize that I do not understand the way protons & neutrons are organized in a nucleus.

To me, the articles implies alternating shells, each consisting exclusively of either protons or neutrons, while I always thought the two types of nuclear particles were intermixed.

Can somebody here give me some clues to the organization of particles in the nucleus?

This area is not well known, and in fact they are not distinct 'particles', but rather 'quark-gluon complexes', which we refer to as bound 'protons' and 'neturons' that convert back and forth, one into the other.

The presumption is that there are 'shells' in the nucleus, similar to 'electron orbital shells' surrounding the nucleus which house standing-waves (the 'electrons', or the 'electric cloud'). The shells can be filled (most stable arrangment, akin to the inert gas electron-orbitals being filled shells) with the proper proton/neutron combination, which leads to the most stable arrangement. Whenever a nuclear 'shell' is filled, that is referred to as an "island of stability". It is theorized that a filled-shell will tend to overcome the destabilizing influence of the coulomb-repulsion of the positive charge of the protons, allowing for the strong-nuclear force to bind the nucleus together for a period of time, instead of instantaneously flying apart upon formation of a large nucleus (by collision of two atoms). Reportedly, they have crept closer to the "island of stability", and now have a measurably long half-life of a millisecond (which, in terms of other ultra-short-lived radioactive materials, is fairly long).

We can measure the energy level of the excited state of some of those shells. For example, Tc-99m is the excited state of Tc-99, and 'decays' to the ground state with a half-life of about 6.02 hours by emitting a gamma photon. The ground state is relatively stable, with a half-life well beyond that of a human lifetime. However, it is still 'unstable' and eventually decays out over millions of years.

Hope this helps

you guys are like one person.

The way I had it explained, was that we can model the nucleons as being analogous to the shells of electrons about the nucleus. Due to the dominant force being the strong force, there are some differences from the electron model, but this model predicts the magic numbers of neutrons and protons very accurately for low end numbers.
This model only works if we assume that the nucleons spend most of their time orbiting without collision, which seems problematic at first, given the relatively small volume of the nucleus. However, because a collision would in general require a change in energy, and the available energy states will generally be filled by other nucleons, the particles can't collide, so the model is accurate.