Entanglement properties of $^4$He and $^6$He are investigated using nuclear many-body calculations, specifically the single-nucleon entanglement entropy, and the two-nucleon mutual information and negativity. Nuclear wavefunctions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases, the harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases, are found to exhibit different degrees of complexity. Entanglement in both nuclei is found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters, and, as anticipated, a core-valence (tensor product) structure emerges from the full six-body calculation of $^{6}$He. The two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. We conclude that measures of one- and two-nucleon entanglement are useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.
In this report we propose that a charge rearrangement within heavy ions may occur during fusion reactions, lowering the Coulomb barrier as the nuclear systems approach each other. In this situation a modified Gamow factor has been calculated, which emphasizes the importance of spatial degrees of freedom in nuclear matter.
We discuss optical potentials for the nuclear elastic scattering from a variational viewpoint. Density-dependence in the effective $N$-$N$ interaction leads to density rearrangement terms, in addition to the conventional folding term. Effects of the rearrangement on the $N$-$A$ optical potential are illustrated in the nuclear-matter limit. Closely relating to consistency with the saturation, the rearrangement appreciably improves the isoscalar optical potential depth over the previous folding model calculations. The rearrangement gives stronger effects as the density grows. We also present rea…
We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero--range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond--mean--field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated to the density--dependent part of the Skyrme fo…
We compute the proton-neutron entanglement entropy in the interacting nuclear shell model for a variety of nuclides and interactions. Some results make intuitive sense, for example that the shell structure, as governed by single-particle and monopole energies, strongly affects the energetically available space and thus the entanglement entropy. We also find a surprising result: that the entanglement entropy at low excitation energy tends to decrease for nuclides when $N \neq Z$. While we provide evidence this arises from the physical nuclear force by contrasting with random two-body interactio…
The Pauli rearrangement potential given by the second-order diagram is evaluated for a nucleon optical model potential (OMP) with $G$ matrices of the nucleon-nucleon interaction in chiral effective field theory. The results obtained in nuclear matter are applied for $^{40}$Ca in a local-density approximation. The repulsive effect is of the order of 5MeV at the normal density. The density dependence indicates that the real part of the microscopic OMP becomes shallower in a central region, but is barely affected in a surface area. This improves the overall resemblance of the microscopic OMP to t…
A quantitative description of the change in ground-state neutron occupancies between $^{136}$Xe and $^{136}$Ba, the initial and final state in the neutrinoless double-$β$ decay of $^{136}$Xe, has been extracted from precision measurements of the cross sections of single-neutron adding and -removing reactions. Comparisons are made to recent theoretical calculations of the same properties using various nuclear-structure models. These are the same calculations used to determine the magnitude of the nuclear matrix elements for the process, which at present disagree with each other by factors of 2 …
An assessment of the magnitude of the rearrangement contribution to the Fermi energy and to the binding energy per particle is carried out in symmetric nuclear matter by extending the G-matrix framework. The restoration of the thermodynamic consistency or, equivalently, the fulfillment of the Hugenholtz-Van Hove theorem, is discussed.
We study systems of three bosons bound by a long-range interaction supplemented by a short-range potential of variable strength. This generalizes the usual two-body exotic atoms where the Coulomb interaction is modified by nuclear forces at short distances. The energy shift due to the short-range part of the interaction combines two-body terms similar to the ones entering the Trueman-Deser formula, and three-body contributions. A sudden variation of the energy levels is observed near the coupling thresholds of the short-range potential. But the patterns of rearrangement are significantly modif…
Chiral effective field theory is a framework to derive systematic nuclear interactions. It is based on the symmetries of quantum chromodynamics and includes long-range pion physics explicitly, while shorter-range physics is expanded in a general operator basis. The number of low-energy couplings at a particular order in the expansion can be reduced by exploiting the fact that nucleons are fermions and therefore obey the Pauli exclusion principle. The antisymmetry permits the selection of a subset of the allowed contact operators at a given order. When local regulators are used for these short-…
We calculated the von Neumann entanglement entropy and the Schmidt number of one dimentional (1D) cluster states and showed that these are useful measures to estimate entanglement caused by delocalization of clusters. We analyze system size dependence of these entanglement measures in the linear-chain $nα$ states given by Tohsaki-Horiuchi-Schuck-Röpke wave functions for 1D cluster gas states. We show that the Schmidt number is an almost equivalent measures to the von Neumann entanglement entropy when the delocalization of clusters occurs in the entire system but it shows different behaviors in…
In order to simulate the relativistic effects of the Dirac Brueckner Hartree Fock approach for finite nuclei the part of the Urbana 3 nucleon (3N) force is considered, which represents the enhancement of the small components of the Dirac spinors for the nucleons in the nuclear medium. This 3N force is included in a Brueckner Hartree Fock calculation with rearrangement terms using a realistic model for the NN interaction. The strength of the 3N force is adjusted to reproduce the empirical saturation point of nuclear matter and then used in corresponding studies of the closed shell nuclei $^{16}…
Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz-van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree-Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To s…
We present a relativistic chiral effective theory for symmetric and asymmetric nuclear matter taken in the Hartree-Fock scheme. The nuclear binding is insured by a background chiral invariant scalar field associated with the radial fluctuations of the chiral quark condensate. Nuclear matter saturation is obtained once the scalar response of the nucleon generating three-body repulsive forces is incorporated. For these parameters related to the scalar sector and quark confinement mechanism inside the nucleon we make use of an analysis of lattice results on the nucleon mass evolution with the qua…
While Josephson-like junctions, transiently established in heavy ion collisions ($τ_{coll}\approx10^{-21}$ s) between superfluid nuclei --through which Cooper pair tunneling ($Q$-value $Q_{2n}$) proceeds mainly in terms of successive transfer of entangled nucleons-- is deprived from the macroscopic aspects of a supercurrent, it displays many of the special effects associated with spontaneous symmetry breaking in gauge space (BCS condensation), which can be studied in terms of individual quantum states and of tunneling of single Cooper pairs. From the results of studies of one- and two- neutron…
We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrang…
The single-nucleon potential in hot nuclear matter is investigated in the framework of the Brueckner theory by adopting the realistic Argonne V18 or Nijmegen 93 two-body nucleon-nucleon interaction supplemented by a microscopic three-body force. The rearrangement contribution to the single-particle potential induced by the ground state correlations is calculated in terms of the hole-line expansion of the mass operator and provides a significant repulsive contribution in the low-momentum region around and below the Fermi surface. Increasing temperature leads to a reduction of the effect, while …
A First Bound on the Moffat Energy and Thorium-229 Clock as a Probe of the Nonlocal Time-Energy Structure and a Proposed Experiment for the use of Nuclear Entanglement and Squeezed States to Test Nonlocal Quantum Field Theory
Wilfrid Laurier University（韦仕兰大学）；University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（基础物理研究所）
The eigenfunctions of the Two-Rotors Model are superpositions of states corresponding to precessions of the rotors around two orthogonal axes. In Nuclear Physics such an entanglement has not been directly confirmed. We discuss how it might be observed and compare with the application of the TRM to single domain nanoparticles. In the latter case, in addition to the present indirect evidence there is the possibility of direct observation in experiments at temperatures of the order of 1 K.
A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A$_1(Z_{A_1}, M_{A_1})$ and A$_2(Z_{A_2}, M_{A_2})$, move along classical trajectories $\vec R_1(t)$ and $\vec R_2(t)$ respectively, while the dynamics of the lighter neutron, n, is considered from a quantum mechanical point of view. Here, $M_i$ are the nucleon masses and $Z_i$ are the Coulomb charges of the heavy nuclei ($i=1,2$). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear p…
