The nuclear spin-orbit force in chiral effective field theories

Furnstahl, R. J.; Rusnak, John; Serot, Brian D.

doi:10.1016/s0375-9474(98)00004-9

Cited by 152 publications

(158 citation statements)

References 36 publications

Supporting

Mentioning

143

Contrasting

Unclassified

Order By: Relevance

“…a large lower component in the Dirac spinor [18]. The spin-orbit splitting is completely correlated with the nucleon effective mass [19]. From Eq.…”

mentioning

confidence: 92%

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

et al. 2001

View full text Add to dashboard Cite

Pseudospin symmetry in nuclei is investigated considering the Dirac equation with a Lorentz structured Woods-Saxon potential. The isospin correlation of the energy splittings of pseudospin partners with the nuclear potential parameters is studied. We show that, in an isotopic chain, the pseudospin symmetry is better realized for neutrons than for protons. This behavior comes from balance effects among the central nuclear potential parameters. In general, we found an isospin asymmetry of the nuclear pseudospin interaction, opposed to the nuclear spin-orbit interaction which is quasi isospin symmetric.PACS numbers: 21.10. Hw, 21.30.Fe, 21.60.Cs In some heavy nuclei a quasi-degeneracy is observed between single-nucleon states with quantum numbers (n, ℓ, j = ℓ + 1/2) and (n − 1, ℓ + 2, j = ℓ + 3/2) where n, ℓ, and j are the radial, the orbital, and the total angular momentum quantum numbers, respectively. This doublet structure is better expressed using a "pseudo" orbital angular momentum quantum number,l = ℓ + 1, and a "pseudo" spin quantum number,s = 1/2. For example, for [ns 1/2 , (n − 1)d 3/2 ] one hasl = 1, for [np 3/2 , (n − 1)f 5/2 ] one hasl = 2, etc. Exact pseudospin symmetry means degeneracy of doublets whose angular momentum quantum numbers are j =l ±s. This symmetry in nuclei was first reported about 30 years ago [1], but only recently has its origin become a topic of intense theoretical research.In recent papers [2,3,4,5,6] possible underlying mechanisms to generate such symmetry have been discussed. We briefly review the main points of these studies.Blokhin et al.[2] performed a helicity unitary transformation in a nonrelativistic single-particle Hamiltonian. They showed that the transformed radial wave functions have a different asymptotic behavior, implying that the helicity transformed mean field acquires a more diffuse surface. Application of the helicity operator to the nonrelativistic single-particle wave function maps the normal state (l, s) onto the "pseudo" state (l,s), while keeping all other global symmetries [2]. The same kind of unitary transformation was also considered earlier by Bahri et al.[3] to discuss the pseudospin symmetry in the nonrelativistic harmonic oscillator. They showed that a particular condition between the coefficients of spin-orbit and orbit-orbit terms, required to have a pseudospin symmetry in that non-relativistic single particle Hamiltonian, was consistent with relativistic mean-field (RMF) estimates.Ginocchio [4], for the first time, identified the pseudospin symmetry as a symmetry of the Dirac Hamiltonian. He pointed out that the pseudo-orbital angular momentum is just the orbital angular momentum of the lower component of the Dirac spinor. Thus, the pseudospin symmetry started to be regarded and understood in a relativistic way. He also showed that the pseudospin symmetry would be exact if the attractive scalar, S, and the repulsive vector, V , components of a Lorentz structured potential were equal in magnitude: S + V = 0. Under this condition, the pseudospi...

show abstract

“…a large lower component in the Dirac spinor [18]. The spin-orbit splitting is completely correlated with the nucleon effective mass [19]. From Eq.…”

mentioning

confidence: 92%

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

et al. 2001

View full text Add to dashboard Cite

show abstract

“…The inclusion of quantum potentials driven by external fields in the Dirac Hamiltonian is relevant for the study of a wide variety of physical systems [10], from the Hydrogen atom [11] to hadronic [15,16] and nuclear physics [17][18][19] models. Such external fields are included into the Dirac equation through the addition of potential matrices to the free Hamiltonian, and the possible terms of such matrices are derived by considering the invariance of the resulting Dirac equation under Poincaré transformations [10].…”

Section: Introductionmentioning

confidence: 99%

Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials

Bittencourt

Bernardini

2016

Annals of Physics

View full text Add to dashboard Cite

A generalized description of entanglement and quantum correlation properties constraining internal degrees of freedom of Dirac(-like) structures driven by arbitrary Poincaré classes of external field potentials is proposed. The role of (pseudo)scalar, (pseudo)vector and tensor interactions in producing/destroying intrinsic quantum correlations for SU(2) ⊗ SU(2) bi-spinor structures is discussed in terms of generic coupling constants. By using a suitable ansatz to obtain the Dirac Hamiltonian eigenspinor structure of time-independent solutions of the associated Liouville equation, the quantum entanglement, via concurrence, and quantum correlations, via geometric discord, are computed for several combinations of well-defined Poincaré classes of Dirac potentials. Besides its inherent formal structure, our results set up a framework which can be enlarged as to include localization effects and to map quantum correlation effects into Dirac-like systems which describe low-energy excitations of graphene and trapped ions.

show abstract

“…This suggests a Dirac structure for the potential with large scalar and vector parts. Regarding the role of ∆ in the nuclear data fittings, it is interesting to point out that recent nuclear matter analysis with many different quantum-hadrodynamics models show a correlation between the finite nuclei spin-orbit energy splitting and the nuclear matter effective nucleon mass m * [19]. The spin-orbit energy splitting increases as m * decreases.…”

Section: Resultsmentioning

confidence: 99%

The Coester line in relativistic mean field nuclear matter

Delfino¹,

Malheiro²,

Timóteo³

et al. 2005

Braz. J. Phys.

View full text Add to dashboard Cite

The Walecka model contains essentially two parameters that are associated with the Lorentz scalar (S) and vector (V ) interactions. These parameters are related to a two-body interaction consisting of S and V , imposing the condition that the two-body binding energy is fixed. We have obtained a set of different values for the nuclear matter binding energies (BN ) at equilibrium densities (ρo). We investigated the existence of a linear correlation between B N and ρ o , claimed to be universal for nonrelativistic systems and usually known as the Coester line, and found an approximate linear correlation only if V − S remains constant. It is shown that the relativistic content of the model, which is related to the strength of V − S , is responsible for the shift of the Coester line to the empirical region of nuclear matter saturation.

show abstract

The nuclear spin-orbit force in chiral effective field theories

Cited by 152 publications

References 36 publications

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials

The Coester line in relativistic mean field nuclear matter

Contact Info

Product

Resources

About