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Register a new userOn the Methods for Constructing Meson-Baryon Reaction Models within Relativistic Quantum Field Theory
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Within the relativistic quantum field theory, we analyze the differences between the $pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
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Relativistic quantum molecular dynamics based on the relativistic mean field theory (RQMD.RMF) is extended by including momentum-dependent potential. The equation of state (EoS) dependence of the directed and the elliptic flow of protons in the beam energy range of $2.3 < sqrt{s_{NN}}< 20$ GeV is examined. It is found that the directed flow depends strongly on the optical potential at high energies,$sqrt{s_{NN}} > 3 $ GeV, where no information is available experimentally. The correlation between effective mass at saturation density and the optical potential is found: smaller values of effective mass require smaller strengths of the optical potential to describe the directed flow data.This correlation can also be seen in the beam energy dependence of the elliptic flow at $sqrt{s_{NN}}>3$ GeV, although its effect is rather weak. On the other hand, stiff EoS is required to describe the elliptic flow at lower energies.Experimental constraints on the optical potential from $pA$ collisions will provide important information on the EoS at high energies.The proton directed and the elliptic flow are well described in the RQMD.RMF model from $sqrt{s_{NN}}=2.3$ to 8.8 GeV. In contrast,to reproduce the collapse of the directed flow above 10 GeV, pressure has to be reduced, which indicates a softening of the EoS around $sqrt{s_{NN}} =10 $ GeV.
We report on the recent studies of leading order baryon-baryon interactions in covariant baryon chiral perturbation theory. In the strangeness $S=0$ sector, one can achieve a rather good description of the Nijmegen $np$ phase shifts with angular momenta $Jleq 1$, particularly the $^1S_0$ and $^3P_0$ partial waves, comparable with the next-to-leading order (NLO) heavy baryon approach. In the strangeness $S=-1$ hyperon-nucleon sector, the best fit of the 36 scattering data is similar to the sophisticated phenomenological models and the NLO heavy baryon approach.
We analyze the constraint structure of the interaction of vector mesons with baryons using the classical Dirac constraint analysis. We show that the standard interaction in terms of two independent SU(3) structures is consistent at the classical level. We then require the self-consistency condition of the interacting system in terms of perturbative renormalizability to obtain relations for the renormalized coupling constants at the one-loop level. As a result we find a universal interaction with one coupling constant which is the same as in the massive Yang-Mills Lagrangian of the vector-meson sector.
In this paper, we compare the RMF theory and the model of deformed oscillator shells (DOS) in description of the quantum properties of the bound states of the spherically symmetric light nuclei. We obtain an explicit analytical relation between differential equations for the RMF theory and DOS model, which determine wave functions for nucleons. On such a basis we perform analysis of correspondence of quantum properties of nuclei. We find: (1) Potential $V_{RMF}$ of the RMF theory for nucleons has the wave functions $f$ and $g$ with joint part $h$ coincident exactly with the nucleon wave function of DOS model with potential $V_{rm shell}$. But, a difference between $V_{RMF}$ and $V_{rm shell}$ is essential for any nucleus. (2) The nucleon wave functions and densities obtained by the DOS and RMF theories are essentially different. The nucleon densities of the RMF theory contradict to knowledge about distribution of the proton and neutron densities inside the nuclei obtained from experimental data. This indicates that $g$ and $f$ have no sense of the wave functions of quantum physics. But, $h$ provides proper description of quantum properties of nucleons inside the nucleus. (3) We calculate meson function $w^{0}$ and potential $V_{w}$ in RMF theory based on the found nucleon density. (4) $f$ and $g$ are not solutions of Dirac equation with $V_{w}$. If the meson theory describes quantum properties of nucleus well, then a difference between $V_{w}$ and $V_{RMF}$ should be as small as possible. We introduce new quantum corrections characterizing difference between these potentials. We find that (a) The function $w^{0}$ should be reinforced strongly, (b) The corrections are necessary to describe the quantum properties of the nuclei.
We analyze the localization properties of two-body correlations induced by pairing in the framework of relativistic mean field (RMF) models. The spatial properties of two-body correlations are studied for the pairing tensor in coordinate space and for the Cooper pair wave function. The calculations are performed both with Relativistic-Hatree-Bogoliubov (RHB) and RMF+Projected-BCS (PBCS) models and taking as examples the nuclei $^{66}$Ni, $^{124}$Sn and $^{200}$Pb. It is shown that the coherence length have the same pattern as in previous non-relativistic HFB calculations, i.e., it is maximum in the interior of the nucleus and drops to a minimum in the surface region. In the framework of RMF+PBCS we have also analysed, for the particular case of $^{120}$Sn, the dependence of the coherence length on the intensity of the pairing force. This analysis indicates that pairing is reducing the coherence length by about 25-30 $%$ compared to the RMF limit.
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