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arXiv:2506.16621

np spin correlations in the deuteron ground state

Singh, Ashutosh, Das, Ankit Kumar, Kumar, Ankit, Arumugam, P.

Published Jun 19, 2025• 0 citations
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Abstract

The deuteron is the simplest atomic nucleus made of two particles - a proton and a neutron. In this work, we study how their spins are quantum entangled with each other. We study two cases: when the deuteron is in a fixed projection of total angular momentum, and when it exists in a superposition of all projections. Our findings show that the spins are most entangled when the total projection is zero, and that strong entanglement still exists even when all spin states are superposed.

DOI
10.48550/arxiv.2506.16621

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The deuteron is the simplest atomic nucleus made of two particles - a proton and a neutron. In this work, we study how their spins are quantum entangled with each other. We study two cases: when the deuteron is in a fixed projection of total angular momentum, and when it exists in a superposition of all projections. Our findings show that the spins are most entangled when the total projection is zero, and that strong entanglement still exists even when all spin states are superposed.
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Abstract We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton–neutron, neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton–neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron–deuteron, proton–deuteron, and deuteron–deuteron scattering.
Background: The nuclear tensor force couples the spin and orbital degrees of freedom, thereby generating spin-orbital (SO) entanglement. This interaction also induces spatial anisotropy of density distributions. While the tensor force underlies both phenomena, the direct connection between them remains unclear. Purpose: We clarify the quantitative relationship between the SO entanglement and spatial anisotropy of the deuteron. This system provides a fully analytical description of both features. Methods: We quantify the SO entanglement by the entanglement entropy and spatial anisotropy by the Kullback-Leibler (KL) divergence. Their evolution is traced by continuously varying the SSS-DDD coupling in the deuteron. Results: We derive analytical expressions for the entanglement entropy and KL divergence, both of which depend on MMM, the projection of the deuteron total angular momentum J=1J=1J=1. The stronger the tensor-force-induced SSS-DDD coupling is, the larger both the entanglement entropy and KL divergence become. Conclusions: The analytical results and the positive correlation between the two quantities clearly demonstrate that the two features stem from the same underlying coupling mechanism governed by the algebraic structure of the deuteron wave function.
Abstract Quantum entanglement in scattering processes has most often been treated in general terms only. A few examples of detailed calculations exist for atomic systems but for nuclear processes it is an almost unexplored area, although it may be important for interpretation of some measured quantities. The present treatment is a study of the time-development of the deuteron-like compound state created in the n – p scattering process. The increase and decay of neutron–proton entanglement in this state is calculated for low transferred momenta over the atto-second range. It is well known that the very high value for the bound proton cross sections ( σ = 81.9 barns) is caused by a specific feature in the deuteron, a virtual 0+ state close to its binding level. In scattering this state causes a negative phase shift δ s in the outgoing neutron wave function, increasing linearly with the transferred momentum. This phase shift is produced during a short-lived virtual energy transfer Δ E in exciting the 0+ state and Δ E is estimated here from the ratio of the phase shift δ observed and the time Δ t it takes to create the entanglement. It is further argued that the nuclear excitation decreases after the n – p encounter in proportion to the degree of n – p entanglement calculated, i.e. as long as the scattering state has deuteron characteristics. This phase shift is neglected in low energy neutron scattering text-books (which are based on the Fermi pseudo potential) and may be negligible for thermal neutron scattering, but will be important already at epithermal energies (0.1–1 eV). The phase shift has measurable consequences in interpretation of INS (inelastic neutron scattering) since its associated energy shift increases quadratically with the transferred momentum. It explains quantitatively certain anomalies found in scattering on water, where water vibration modes are excited far below the expected transferred momentum limit. This paper ends with a short discussion about quantum entanglement in scattering processes in general, with the present example as a starting point.
We examine the mode entanglement and correlation of two fermionic particles. We study the one- and two-mode entropy and a global characteristic, the one-body entanglement entropy. We consider not only angular momentum coupled states with single configuration but use the configuration interaction method. With the help of the Slater decomposition, we derive analytical expressions for the entanglement measures. We show that when the total angular momentum is zero specific single configurations describe maximally entangled states. It turns out that for a finite number of associated modes the one- and two-mode entropies have identical values. In the shell model framework, we numerically study two valence neutrons in the sdsdsd shell. The one-body entanglement entropy of the ground state is close to the maximal value and the associated modes have the largest mutual information.
Several recent experiments on liquid and solid samples containing protons or deuterons show an interesting anomaly, which is a shortfall in the intensity of energetic neutrons scattered by the samples. Previously we demonstrated that quantum correlations in the spatial and spin degrees of freedom of the hydrogen isotopes lead to entanglement in scattering and a reduction in the scattered intensity. The viability of short-lived quantum correlations as the cause of the observed anomalies is further explored and found to be entirely feasible. General features of the basic premiss, that quantum entanglement reduces the scattered signal, are discussed and the interpretation of the neutron scattering experiments is set in context to related work on other systems. For the experiments in question, the duration of a scattering event, τ s , is a fraction of a femtosecond which is extremely short compared to solid-state relaxation times. Increasing τ s , by suitably changing experimental conditions, restores the intensity to the standard value calculated from the single atom cross-section and concentration of particles. Our physical picture of the restoration is evolution with increasing τ s from a pure state of the particles (described by a wavefunction) to a mixed state (described by a density matrix) that is created, through decoherence, by steadily engaging the solid-state environment of the particles.