Particle-hole symmetry numbers for nuclei

Two new numbers, v and zeta, inspired by particle-hole symmetry are introduced. These numbers have extreme values at a closed shell and vanish mid-shell. A combination of even powers of these numbers has been used to model experimentally measured quantities such as R-4/2 = E(4(1)(+))/E(2(1)(+)) and the "microscopic'' contribution to binding energies. A binding energy fit consisting of a total of six fit coefficients, including one new shell term, reproduces the experimental binding energies of 2353 nuclei with an r.m.s. standard deviation of 1.55 MeV. The difference between the experimental and fit values of observables, specifically the R-4/2, provides an indication of where shell closure features are less pronounced and where sub-shells closures occur.