Physical origin of nucleon pair-breaking energy?

[m.e.t.a.]

I have to give a brief presentation on the evidence for pairing in atomic nuclei. One of the items of evidence I will talk about is the difference in binding energy between even-even and odd-odd isobars. For instance, here I have plotted the atomic masses of a range of even-A isobars A = 40. http://img12.imageshack.us/img12/1419/isobarsmassa40.png" . Starting with Mg (Z = 10) on the left, the nuclei alternate between even-even and odd-odd. The dotted lines indicate the two "mass parabolae", an upper and a lower, which roughly connect the odd-odd and even-even nuclei respectively.

Here is another mass plot, this time for the odd-A isobars A = 41. http://img542.imageshack.us/img542/5127/isobarsmassa41.png" . For odd-A isobars, the nuclei alternate between even-odd and odd-even. There appears to be no zig-zag pattern of high-/low-mass nuclei, and so there is only a single mass parabola.

Various textbook and web sources say that the reason that even-even nuclei sit on a lower mass parabola than odd-odd nuclei is because of the "pairing energy", or "pair-breaking energy". Unfortunately, none of the sources I have read have gone on to explain why there is a pair-breaking energy or what its physical mechanism is.

If I were to hazard an uneducated guess, I would say that maybe a nucleon pair is extra-tightly bound because the two nucleons have identical quantum numbers except for their spin. Perhaps this means that the mean proximity of the two nucleons is very small, and that they are consequently more tightly bound by the strong force? I really don't know. As you can see, I have very little knowledge of nuclear physics (2nd year undergrad.). Any help would be much appreciated!

 

[Bill_K]

The nucleus is a quite complicated system, and many things in nuclear physics are based on ad hoc or partially ad hoc models. The models work, but require you to believe the assumptions that go with them. The best attempt at explaining the pairing energy that I've found is in Preston, "Physics of the Nucleus", sect 9-6.

The simplest nuclear model is the extreme single particle model, in which each nucleon moves independently of the others as a Fermi gas. Next, one considers what effect an attractive force might have, and is led to the idea of pair formation, two nucleons with opposite spins form a quasiparticle. The analogy is with the BCS explanation of superconductivity as due to Cooper pairs. An even-even nucleus is supposed to be in a quasiparticle ground state (no quasiparticles) while its odd-odd neighbor has one quasiparticle excitation. (Yes, I know they don't have the same number of protons and neutrons! But quasiparticle states have the weird property that the number of particles is not well-defined.) Anyway, for more details I'd suggest looking at Preston.

 

[m.e.t.a.]

Thank you, you have been a great help. Your explanation that the pairing energy is a somewhat ad-hoc theory is very helpful to me. This gives me something to say. Beforehand, I was resigned to merely refer to this mysterious thing, "pairing", with no explanation of its physical meaning, or lack of one.