Generalized molecule-like structure in atomic nuclei

Starting from a |ϕ|4 field theory with universal pn interacting angular and distance coordinates (θ,r) to depict nuclear long-range correlations, we have derived a cubic Schrödinger equation for NpNn pn interacting virtual bosons, which are believed to dominate the generic evolution of nuclear structure from spherical multi-nucleon shell-model states to deformed collective rotational states. It is shown that two-soliton solution in θ space manifests two opposite pn-type Ising-like chains existing in ground states and their gradual alignment responsible for nuclear rotational excitations. Of particular prominence is two-soliton solution with respect to r: the mutual relative motion of valence protons and neutrons around valence-nucleon mass centers considered as the dynamic equilibrium positions of a non-linear Schrödinger breather. And the resulting non-vanishing root mean square 〈r2〉 divides half the valence nucleons belonging to a chain into four local mass centers and proposes two chain-corresponding molecule-like tetrads outside inert cores pairwise hidden in ground states. Such solitons turn out to be an analogue of opposite axion fluids around a local mass center in the galactic dark-matter halo outside the soliton core (Garnier et al. (2021) [67]) and the present study facilitates making the latter more clear. The generalized molecule-like structure arouses a requisite to the addition of cluster-interior and cluster-to-core electric dipole moments in particular to pear-shaped nuclei, whose variants Schiff moments play an important role in measuring diamagnetic atomic electric dipole moments and therefore understanding CP-violating new physics beyond the standard model. We put additional parts in evidence by befitting the NpNn scheme verified already by electric quadrupole moments in same nuclei.