# Valence Neutron-Proton Orientation in Atomic Nuclei

## TL;DR

This paper introduces a scaling law linking nuclear deformations and excitation energies to valence neutron-proton orientations, revealing two distinct phases of np pair alignments across a wide mass range.

## Contribution

It presents a novel global scaling law connecting nuclear shape deformations and excitation energies to neutron-proton pair orientations, supported by extensive empirical data.

## Key findings

- Identification of two phases: anti-aligned and fully-aligned np pairs.
- Derivation of partition factors related to np pair orientations.
- Strong correlation between deformation and excitation energy distributions.

## Abstract

It is shown that the renormalized nuclear deformations in different mass regions can be globally scaled by two probability partition factors of Boltzmann-like distribution, which are derived from the competing valence $np$ and like-nucleon interactions. The partition factors are simply related to the probabilities of anti-parallel and fully-aligned orientations of the angular momenta of the neutrons and protons in the valence $np$ pairs, responsible for spherical- and deformed-shape phases, respectively. The partition factors derived from the renormalized deformations are also present in the new scaling law for the energies of the first $2^+$ states. A striking concordance between the distributions of the renormalized deformations and of the newly introduced parameter for the energies of the first $2^+$ states over the extended mass region from Ge to Cf is achieved, giving strong support to the existence of two phases: anti-aligned and fully-aligned subsets of $np$ pairs.