Pairing of nucleons

These are derived frum a. lensui force resulting from a coupling between individual pairs of nucleons and from the coupling between spin and orbital angular moments of the individual nucleus, as described by the shell model of the nucleus. 

We can continue our survey of the lightest nuclei with A = 3. Only the combinations of two protons and one neutron, 3He, and one proton with two neutrons, 3H, are bound, while the combinations of three protons, 3Li, and three neutrons are unbound. Again we see a balance between the numbers of neutrons and protons with the extreme cases being unbound. The nuclear spins of both bound A = 3 nuclei are j indicative of a pair of nucleons plus one unpaired nucleon three unpaired nucleons would have had a total spin of. In the A = 3 system the more neutron-rich nucleus, tritium, 3H, is very slightly less stable than 3He and, it decays by (3 emission with a 12.3-y half-life. 

If the hindrance factor is between 1 and 4, the transition is called a favored transition. In such decays, the emitted a particle is assembled from two low-lying pairs of nucleons in the parent nucleus, leaving the odd nucleon in its initial orbital. 

We assume that each nucleon has a pseudo-spin i and pseudo-orbital angular momentum k. These couple to form the single particle angular momenta J,J (in [j]) of the two interacting nucleons. The wavefunction of a pair of nucleons coupled to a total angular momentum L (and z component p) is then given by ... 

The high energy nuclear photoeffect appears to be dominated by the interaction of photons with a pair of nucleons, and quantitative predictions can be made on the basis of a very simple picture. 

Fig. 14 Moments of inertia for Pu, Cm, Cf, Fm and No nuclei. Upbends around a frequency of 200-300 keV show the alignment of pairs of nucleons with the highest orbital angular momenta (see text). Figure adapted from [27]...

Fig. 27 Schematic illustration of the alpha decay. For an even-even nucleus the least bound pairs of nucleons are combined to form the alpha particle. In an odd-even nucleus the first pairs are usually used to form the alpha (bottom) leaving the daughter nucleus in an excited state, rather than breaking one pair (see text)...

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