Nucleons spin-orbit coupling

Nuclei without nucleon spin-orbit coupling 312... 

Nuclear level scheme with nucleon spin-orbit coupling... 

The shell theory has had great success in accounting for many nuclear properties (3). The principal quantum number n for nucleons is usually taken to be n, + 1, where nr, the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nr + / +1 / is the azimuthal quantum number.) Strong spin-orbit coupling is assumed,... 

Fig. 2. The sequence of nucleonic energy levels with spin-orbit coupling, redrawn, with small changes, from 3, p. 58.

Although the predominant part of the nuclear potential is the part described above that is derived from the central force produced by the average effects of all other nucleons in the system on the individual nucleon under observation, evidence exists that nonsymmetnc tensor and spin-orbit coupling terms must be included in the description of the nuclear potential. 

As shown by Fig. 2.9, with the inclusion of the spin-orbit interaction, the observed magic numbers were properly reproduced. The spin-orbit interaction for atomic electrons is a small quantum-relativistic effect. The nuclear spin-orbit coupling is much stronger and results, in addition to relativistic effects, from the spin dependence of the nucleon-nucleon potential. 

The situation is analogous in the nucleus The pi/2 and p3/2-levels (created from the p-level by the spin-orbit coupling) host six nucleons of the same kind (pi/2 +1/2, —1/2 and P3/2 +3/2, +1/2, —1/2, —3/2). Their energies are the same as long as the nucleus is spherical, but when the nucleus is deformed the degenerate levels split up. 

Some more recent calculations [28], based on careful consideration of the effect of mass asymmetry on the fission barrier and a reduced spin-orbit coupling strength, have indicated that the Z = 114 shell effect is not very large. These calculations do confirm the existence of a shell atN = 184, but also suggest less stability for species with N < 184 that is, the island of stability has a cliff with a sharp drop-off for N < 184. If these considerations are correct, it would become considerably more difficult to synthesize and detect the superheavy elements (defined as those elements stabilized by spherical closed-nucleon shells). A premium would be placed on produdng a nucleus with N = 184 or, very close to this, N = 183, in order that it might have a half-life sufficiently long to make it detectable. 

Presently it is widely accepted that the relativistic mean-field (RMF) model [40] gives a good description of nuclear matter and finite nuclei [41]. Within this approach the nucleons are supposed to obey the Dirac equation coupled to mean meson fields. Large scalar and vector potentials, of the order of 300 MeV, are necessary to explain the strong spin-orbit splitting in nuclei. The most debated... 

Tauber and Wu show that the magnetic moment of Li , calculated with the intermediate coupling parameter which best fits the level spectrum, is in better agreement with observation than that obtained from pure jj coupling. The multiplet splittings in Li can be accounted for, at least qualitatively, by the introduction of a tensor force component into the main interaction between nucleons instead of a spin-orbit force. 

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. 

Due to the large amount of cancellation of the spins and angular momenta due to the strong coupling of nucleons in matching orbitals and pairing of spins, we should... 

To form an a particle within a nucleus, two protons and two neutrons must come together with their spins coupled to zero and with zero orbital angular momentum relative to the center of mass of the a particle. These four nucleons are likely to come from the highest occupied levels of the nucleus. In odd A nuclei, because of the odd particle and the difficulty of getting a partner for it, one pah of nucleons is drawn from a lower lying level, causing the daughter nucleus to be formed in an excited state. 

In this paper, we point out that a somewhat different model, where a Surface Delta Interaction CPLA66D acts between nucleons in degenerate orbits, also makes predictions for these fermion pair amplitudes. For the cases discussed in this paper, the SDI results are mostly intermediate between those for i-i and k-k coupling. For an S-pair, all three models give identical results. Also, for i = 1/2, the results are the same as if i is a conventional intrinsic spin. We then discuss the more realistic case where k = 1 and i = 3/2. This allows for j = 1/2, 3/2, and 5/2, e.g. degenerate s and d shells, or degenerate pl/2, p3/2, and f5/2 shells. 

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 ... 

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