J.N. Urbano

The generalized hedgehog and the projected chiral soliton model

Abstract The linear chiral soliton model with quark fields and elementary pion and sigma fields is solved in order to describe static properties of the nucleon and the delta resonance. To this end a Fock state of the system is constructed which consists of three valence quarks in a 1s orbit with a generalized hedgehog spin-flavour configuration cos η¦u↓〉 − sin η¦d↑〉 . Coherent states are used to provide a quantum description for the mesonic parts of the total wave function. The corresponding classical pion field also exhibits a generalized hedgehog structure. In a pure mean field approximation the variation of the total energy results in the ordinary hedgehog form (η = 45°). In a quantized approach, however, the generalized hedgehog baryon is projected onto states with good spin and isospin and then noticeable deviations from the simple hedgehog form occur (η ≅ 20°), if the relevant degrees of freedom of the wave functions are varied after the projection. Various nucleon properties are calculated. These include proton and neutron charge radii, and the magnetic moment of the proton for which good agreement with experiment is obtained. The absolute value of the neutron magnetic moment comes out too large, similarly as the axial vector coupling constant and the pion-nucleon-nucleon coupling constant. However, due to the generalization of the hedgehog, the Goldberger-Treiman relation and a corresponding virial theorem are fulfilled. Variation of the quark-meson coupling parameter g and the sigma mass mσ shows that the gA is always about 40% too large compared to experiment. The concepts and results of the projections are compared with the semiclassical collective quantization method. It is demonstrated that noticeable deviations occur for the delta-nucleon splitting, the isovector squared charge radius and the axial vector coupling constant.

Nucleon form factors in the projected linear chiral soliton model

Abstract Electromagnetic and axial form factors of the nucleon are evaluated using the lagrangian of the linear chiral soliton model. To this end angular momentum and isospin projected mean field solutions are determined variationally assuming valence quarks and pions in generalized hedgehog configurations. With the proper pion decay constant and after fitting the quark-meson coupling constant to the nucleon energy both proton and neutron charge form factors are reproduced as well as the slope of the magnetic ones. The axial form factor agrees less well with experiment. The pion form factor can be approximated by a monopole with a cut-off mass of 690 MeV.

Nucleon description in a projected chiral soliton model with dynamical confinement

Abstract We present a nucleon description based on a chiral version of a colour-dielectric model with non-strange quarks and scalar-isoscalar (σ) and pseudoscalar-isovector ( π ) meson fields. Approximate solutions of the model are obtained in a beyond-mean-field calculation. Quarks are treated in the valence approximation, occupying the same nodeless s-orbit. Coherent states are used to describe the meson clouds. The total baryon state has a hedgehog shape. A standard projection formalism is used to obtain model states with definite angular momentum and isospin and total linear momentum zero. To a large extent we use a variation-after-projection (VAP) procedure to obtain radial amplitudes for the mesons and quarks. The model state which describes the nucleon is used for evaluating its static properties. The projection on linear momentum causes a major effect on the rest mass of the nucleon. This effect amounts to ~ 30% decrease with respect to the mean-field energy. Except for the charge radius of the proton, the other observables are less affected by the projections. We find sets of parameters for which a reasonable nucleon description is obtained.

The Goldberger-Treiman relation and the chiral soliton model

Abstract The linear chiral soliton model with explicit quark fields and elementary pion- and sigma-fields is solved in order to describes nucleon and delta properties. Special emphasis is put on the axial vector coupling constant g A and on the Goldberger-Treiman relation. To this end baryon Fock states are constructed in a mean field approximation with hedgehog-like configurations from which the physical states are obtained by projection techniques. It is shown that the Goldberger-Treiman relation is only fulfilled if the quark- and pion-hedgehog is generalized and the variation is performed with projected states. Under this condition no parameter set is found which yields a proper g A and a proper pion-nucleon coupling constant g π NN , if the polarization of the Dirac sea is neglected. Other observables are reproduced within 20% limits or less.

On the Hedgehog solution for the chiral bag

Abstract Using the cloudy-bag hamiltonian the nucleon is described by means of a variational quantum field theoretical approach (VQF) involving a coherent state of pions.. In the mean field approximation the well-known hedgehog baryon appears as a variational solution which minimizes the energy. Some properties of this solution are discussed, in particular in view of extracting good spin and isospin quantum numbers.

Canonical quantization of the chiral soliton model with vector mesons and the N-Δ splitting

Abstract We investigate the canonical quantization of the massive Yang-Mills lagrangian including σ , π , ω , ϱ , A mesons as well as valence quarks. After eliminating the time-like component of the vector mesons fields a mean field Fock state is defined as a product of a Slater determinant for the quarks in a 1s state and coherent states for the mesons. This mean field Fock state is projected onto good spin and isospin by means of Peierls-Yoccoz operators and we obtain, after fitting the nucleon mass, a N- Δ splitting which accounts for 80% of the experimental value.

The hedgehog baryon as a variational mean field solution of the spherical linear chiral soliton model

Abstract We prove that the hedgehog baryon arises as a variational solution of the linear σ-model, if this is restricted to the chiral circle and if the boson Fock-states are described by coherent states and the valence quarks by a product of three identical wave functions each consisting of an orbital s-state multiplied with the most general one-quark spin-flavour configuration in the ud-sector. The opposite is shown to be not true, i.e., the assumption of a hedgehog state in the linear σ-model does not lead to fields which obey the requirements of the chiral circle.

Linear and angular momentum projected observables in the chiral chromodielectric model of the nucleon

Abstract Electromagnetic and axial properties of the nucleon are evaluated using the lagrangian of the chiral chromodielectric model. To this end projected mean field states are constructed assuming three valence quarks coupled to σ- and π-fields and a confining chiral invariant scalar field χ, all with hedgehog structure. Peierls-Yoccoz projections are performed simultaneously on angular momentum, isospin, and zero linear momentum. One can find reasonable parameter sets that the nucleon mass, the magnetic moments, the axial vector coupling constant and the proton charge radius are reproduced. The resulting pion field always turns out too weak such that the model fails in describing the delta-nucleon splitting and the neutron charge radius. The nucleon Σ commutator shows about one third of its experimental value.

Dynamical and quantum mechanical corrections to heavy-ion optical potentials

Abstract Low-energy elastic scattering, molecular resonances and barrier penetration properties of the 16 O + 16 O reaction have been investigated microscopically. From a deformed shell model, taking into account nuclear polarization in the overlapping region, we have evaluated a static potential-energy surface V (r) . Dynamic effects are included by evaluating a (variable) collective mass M (r) and a rotational momentum of inertia Θ ( r ). Quantum corrections are included by removing the spurious zero-point energies, Z (r) . An imaginary part is added phenomenologically, where both a surface and a volume absorbing potential are considered. The (collective) scattering equation is solved to obtain the elastic cross section, the position of resonances and barrier penetration parameters. The aim of this work is not to reproduce well experimental data but rather to investigate the importance of the quantum mechanical and dynamical corrections. Therefore no fitting to data has been done. It turns out that the effects of the corrections cannot be neglected for an accurate description of the collision process.

Form factors in the projected chiral soliton model with vector mesons

Abstract Electromagnetic and axial form factors of the nucleon are computed within the framework of a chiral massive Yang-Mills lagrangian including σ, π, ω, ϱ, A mesons as well as valence quarks. For this purpose canonical quantization of all the fields is performed and a hedgehog mean field Fock state is defined as a product of a Slater determinant for the quarks in a 1s-state and coherent states for all the mesons. Using Peierls-Yoccoz projection operators onto spin and isospin quantum numbers the state of the nucleon is determined. Its energy is fitted to the nucleum mass by adjusting the quark-meson coupling constants. Observables and electromagnetic and axial form factors are evaluated. Except for the neutron electric form factor the results agree well with experiment and improve slightly compared to the projected linear σ-model.