Nuclear pairing and odd-even masses

An attractive pairing interaction often couples time-reversed orbitals into total angular momentum zero. It can mix configurations differing in which pair of orbitals is occupied, lowering the energy of a correlated superposition. This is more than assigning a fixed extra attraction to two labeled particles. All valence identical nucleons participate through antisymmetrized configurations, with proton and neutron pairing commonly treated in separate channels before introducing additional proton-neutron correlations.

In an odd system, an unpaired nucleon can block one orbital from participating in the same pair-scattering pattern. This helps explain why adding the next neutron may bind more strongly when it completes an even neutron population. The effect coexists with ordinary level spacing, deformation, and polarization of the core. Consequently an odd-even pattern is evidence of correlation, but extracting an interaction strength requires calculating those other contributions within the chosen many-body framework.

Use positive total nuclear binding B at fixed proton number. The three-point indicator compares twice the central binding with its two neighbors, then multiplies by a parity-dependent sign. This convention gives a positive indicator for a simple pattern with enhanced even-neutron binding. Authors using negative total energies instead of positive binding reverse the apparent finite-difference sign. Writing the definition before inserting data prevents a purely conventional negative gap.

The filter removes a linear smooth background but retains its curvature. Near a shell closure, a large single-particle gap can therefore contaminate an indicator otherwise interpreted as pairing. Odd-centered and even-centered filters have different sensitivities to such filling effects. Experimental mass uncertainties and correlations also propagate into the difference. A small error bar on each total mass does not automatically establish that every residual fluctuation is a new pairing mechanism.

A Bardeen-Cooper-Schrieffer-type approximation mixes empty and doubly occupied time-reversed pairs. It introduces a chemical potential and a pairing gap that determine quasiparticle excitation energies and occupation probabilities. Orbitals close to the chemical potential acquire fractional mean occupations. These are expectation values in a correlated approximation, not statements that each event contains a fraction of a neutron. The simplest product ansatz does not have an exact particle number.

Number projection, blocking prescriptions, and finite-space treatment matter in real nuclei, especially when correlations are weak. The fitted gap parameter need not equal a three-point mass indicator, and a quasiparticle excitation need not equal a measured odd-nucleus energy without rearrangement effects. Pairing also changes rotational response, connecting odd-even masses with moments of inertia. Agreement with both classes of observables is a stronger test than fitting one indicator and assuming every other consequence follows.