Excited states of mesons and the quark-antiquark interaction

Smith, G.; Tassie, L. J.

doi:10.1016/0003-4916(71)90172-2

Cited by 72 publications

(46 citation statements)

References 4 publications

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“…These symmetries, which have been observed in the hadron and nuclear spectroscopies for a long time [13,14], are derived from the investigation of the dynamics between a quark and an antiquark [15,16]. The very lately studies [9,10] have revealed that, the motion of a spin-1/2 particle with SVPEM satisfies the same differential equation and has the same energy spectrum as a scalar particle.…”

Section: Introductionmentioning

confidence: 97%

Dynamical symmetries of the Klein–Gordon equation

Zhang

Chen

2009

Journal of Mathematical Physics

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The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group corresponding to the Coulomb potential, and the SU (2) group corresponding to the harmonic oscillator potential are derived.Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally.

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Section: Introductionmentioning

confidence: 97%

Dynamical symmetries of the Klein–Gordon equation

Zhang

Chen

2009

Journal of Mathematical Physics

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“…It has been first discovered that the equality of the vector and scalar potentials results in spin symmetry in Ref [9,10] where the authors suggested applications to meson spectra. However, this symmetry was only recently found to be valid for mesons with one heavy quark [11].…”

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confidence: 99%

Spin Symmetry in the Antinucleon Spectrum

2003

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We discuss spin and pseudo-spin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single anti-nucleon spectra. We find a very well developed spin symmetry in single anti-neutron and single anti-proton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in anti-particle spectra and the pseudo-spin symmetry in particle spectra have the same origin. However it turns out that the spin symmetry in anti-nucleon spectra is much better developed than the pseudo-spin symmetry in normal nuclear single particle spectra. 21.10.Hw, 21.10.Pc, 21.60.Jz Symmetries in single particle spectra of atomic nuclei have been discussed extensively in the literature, as the violation of spin-symmetry by the spin-orbit term and approximate pseudo-spin symmetry in nuclear single particle spectra: atomic nuclei are characterized by a very large spin-orbit splitting, i.e. pairs of single particle states with opposite spin (j = l ± 1 2 ) have very different energies. This fact allowed the understanding of magic numbers in nuclei and forms the basis of nuclear shell structure. More than thirty years ago [1, 2] pseudo-spin quantum numbers have been introduced byl = l ± 1 and j = j for j = l ± 1 2 and it has been observed that the splitting between pseudo-spin doublets in nuclear single particle spectra is by an order of magnitude smaller than the normal spin-orbit splitting.After the observation that relativistic mean field models yield spectra with nearly degenerate pseudo spin-orbit partners [3], Ginocchio showed clearly that the origin of pseudo-spin symmetry in nuclei is given by a relativistic symmetry in the Dirac Hamiltonian ([4, 5] and references given therein). He found that pseudo-spin symmetry becomes exact in the limiting case, where the strong scalar and vector potentials have the same size but opposite sign. However, this condition is never fulfilled exactly in real nuclei, because in this limit the average nuclear potential vanishes and nuclei are no longer bound. It has been found that the quality of pseudo-spin symmetry is related to the competition between the centrifugal barrier and the pseudo-spin orbital potential [6].In relativistic investigations a Dirac Hamiltonian is used. In its spectrum one finds single particle levels with positive energies as well as those with negative energies. The latter are interpreted as anti-particles under charge conjugation. This has lead to much efforts to explore configurations with anti-particles and their interaction with nuclei. The possibility of producing a new kind of nuclear system by putting one or more anti-baryons inside ordinary nuclei has recently gained renewed interest [7]. For future studies of anti-particles in nuclei it is therefore of great importance to investigate the symmetries of such configurations.In a relativistic description nuclei are characterized by two strong potentials, an attactive scalar fiel...

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“…Before we present our results, let us briefly discuss how the pseudospin symmetry gets broken. The commutator of the SU(2) generators of pseudospin symmetry with the Hamiltonian (2) is given by [7,11,12,13] [H, Now we turn to the presentation of our results obtained using the Woods-Saxon potentials (1) in eqs. (3) and (4).…”

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confidence: 99%

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

et al. 2001

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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...

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Excited states of mesons and the quark-antiquark interaction

Cited by 72 publications

References 4 publications

Dynamical symmetries of the Klein–Gordon equation

Dynamical symmetries of the Klein–Gordon equation

Spin Symmetry in the Antinucleon Spectrum

Isospin Asymmetry in the Pseudospin Dynamical Symmetry

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