Year: 2026
Type: preprint
Abstract: Proton and neutron densities can have similar multipole moments while differing locally. We use differential forms to measure and locate such differences between nuclear mean fields. A pair invariant measures the angle between two density gradients, weighted by their magnitudes, and the coarea formula resolves its contribution over level surfaces. A triple invariant factorizes exactly into a weighted pair term and a directional term that measures the variation of a third field along the level-surface intersections. We test these quantities in 98 magnetized Wigner-Seitz solutions, five static Hartree-Fock configurations, an illustrative $^{16}$O + $^{34}$Mg collision, and periodic nuclear pasta (a slab and a connected network). The pair invariant distinguishes cell solutions with comparable proton quadrupole moments and is 253 times larger in $^{34}$Mg than in $^{24}$Mg; refinement to 0.6 fm changes it by at most 1.3% in the four configurations recomputed. The directional factor separates the sampled triaxial configurations from the prolate ones. In the collision, it accounts for the 7.3-fold rise of the triple before the first recorded low-density connection, while the weighted pair term changes by at most 3%. In nuclear pasta, slab and network configurations have similar integrated proton-neutron misalignment but different distributions over density levels; their triple invariants differ by a factor of about 370 on the finer grid, mainly due to the variation of the Coulomb potential along joint density levels. These comparisons require no preferred origin or axis. A resolved nonzero triple excludes a common symmetry axis, but zero does not establish one. The pasta results require further convergence studies.
Source: arXiv (Cornell University)
Author: de Lima, Rafael C. R.
Institution: Universidade do Estado de Santa Catarina
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223203408