The impact of energy conservation in transport models on the π−/π+\pi^-/\pi^+ multiplicity ratio in heavy-ion collisions and the symmetry energy

The charged pion multiplicity ratio in intermediate energy central heavy-ion collisions has been proposed as a suitable observable to constrain the high density dependence of the isovector part of the equation of state, with contradicting results. Using an upgraded version of the T\"ubingen QMD transport model, which allows the conservation of energy at a local or global level by accounting for the potential energy of hadrons in two-body collisions and leading thus to particle production threshold shifts, we demonstrate that compatible constraints for the symmetry energy stiffness can be extracted from pion multiplicity and elliptic flow observables. Nevertheless, pion multiplicities are proven to be highly sensitive to the yet unknown isovector part of the in-medium $\Delta$(1232) potential which hinders presently the extraction of meaningful information on the high density dependence of the symmetry energy. A solution to this problem together with the inclusion of contributions presently neglected, such as in-medium pion potentials and retardation effects, are needed for a final verdict on this topic.Comment: 12 pages, 7 figure

Feasability of constraining the curvature parameter of the symmetry energy using elliptic flow data

A QMD type transport model supplemented by a phase-space coalescence model fitted to FOPI experimental multiplicities of free nucleons and light clusters has been used to study the density dependence of the symmetry energy above the saturation point by a comparison with experimental elliptic flow ratios measured by the FOPI-LAND and ASYEOS collaborations in $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon impact energy. A previous calculation has proven that neutron-to-proton and neutron-to-charged particles elliptic flow ratios probe on average different densities allowing in principle the extraction of both the slope $L$ and curvature $K_{sym}$ parameters of the symmetry energy. Consequently a Gogny interaction inspired potential has been modified to allow independent changes of $L$ and $K_{sym}$. Comparing theoretical predictions with experimental data for neutron-to-proton and neutron-to-charged particles elliptic flow ratios the following constraints have been extracted: $L$=85$\pm$22(exp)$\pm$20(th)$\pm$12(sys) MeV and $K_{sym}$=96$\pm$315(exp)$\pm$170(th)$\pm$166(sys) MeV. Residual model dependence is accounted for in the magnitude of the quoted theoretical error. Systematical uncertainties are generated by the inability of the transport model to reproduce experimental light-cluster-to-proton multiplicity ratios. A value for $L$, free of systematical theoretical uncertainties, can be extracted from the neutron-to-proton elliptic flow ratio alone: $L$=84$\pm$30(exp)$\pm$19(th) MeV. It has also been demonstrated that elliptic flow ratios reach a maximum sensitivity on the $K_{sym}$ parameter in heavy-ion collisions of about 250 MeV/nucleon impact energy, allowing a reduction of the experimental component of uncertainty to about 150 MeV for this parameter.Comment: 22 pages, 13 figure

Dilepton production at HADES: theoretical predictions

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy-ion collisions. They allow to study meson properties, like mass and decay width, at various density and temperature regimes. Present days models allow generally a good description of dilepton spectra in ultra-relativistic heavy ion collision. For the energy regime of a few GeV/nucleon, important discrepancies between theory and experiment, known as the DLS puzzle, have been observed. Various models, including the one developed by the T\"{u}bingen group, have tried to address this problem, but have proven only partially successful. High precision spectra of dilepton emission in heavy-ion reactions at 1 and 2 GeV/nucleon will be released in the near future by the HADES Collaboration at GSI. Here we present the predictions for dilepton spectra in C+C reactions at 1 and 2 GeV/nucleon and investigate up to what degree possible scenarios for the in-medium modification of vector mesons properties are accessible by the HADES experiment.Comment: 12 pages, 4 figures; submitted to Phys.Lett.

Towards a model-independent constraint of the high-density dependence of the symmetry energy

Neutron-proton elliptic flow difference and ratio have been shown to be promising observables in the attempt to constrain the density dependence of the symmetry energy above the saturation point from heavy-ion collision data. Their dependence on model parameters like microscopic nucleon-nucleon cross-sections, compressibility of nuclear matter, optical potential, and symmetry energy parametrization is thoroughly studied. By using a parametrization of the symmetry energy derived from the momentum dependent Gogny force in conjunction with the T\"{u}bingen QMD model and comparing with the experimental FOPI/LAND data for 197Au+197Au collisions at 400 MeV/nucleon, a moderately stiff, x=-1.35 +/- 1.25, symmetry energy is extracted, a result that agrees with that of a similar study that employed the UrQMD transport model and a momentum independent power-law parametrization of the symmetry energy. This contrasts with diverging results extracted from the FOPI $\pi^{-}/\pi^{+}$ ratio available in the literature.Comment: 18 pages, 3 figures, accepted for publication in Phys. Rev.

In-medium Δ(1232)\Delta(1232) potential, pion production in heavy-ion collisions and the symmetry energy

Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the $\Delta$(1232) baryon are studied and information regarding their effective strength is obtained from a comparison to experimental pion production data in heavy-ion collisions below 800 MeV/nucleon impact energy. The best description is achieved for an isoscalar potential moderately more attractive than the nucleon optical potential and a rather small isoscalar relative effective mass m$^*_\Delta \approx$ 0.45. For the isovector component only a constraint between the potential's strength at saturation and the isovector effective mass difference can be extracted, which depends on quantities such as the slope of the symmetry energy and the neutron-proton effective mass difference. These results are incompatible with the usual assumption, in transport models, that the $\Delta$(1232) and nucleon potentials are equal. The density dependence of symmetry energy can be studied using the high transverse momentum tail of pion multiplicity ratio spectra. Results are however correlated with the value of neutron-proton effective mass difference. This region of spectra is shown to be affected by uncertain model ingredients such as the pion potential or in-medium correction to inelastic scattering cross-sections at levels smaller than 10$\%$. Extraction of precise constraints for the density dependence of symmetry energy above saturation will require experimental data for pion production in heavy-ion collisions below 800 MeV/nucleon impact energy and experimental values for the high transverse momentum tail of pion multiplicity ratio spectra accurate to better than 5$\%$.Comment: 22 pages, 13 figure

Flow probe of symmetry energy in relativistic heavy-ion reactions

Flow observables in heavy-ion reactions at incident energies up to about 1 GeV per nucleon have been shown to be very useful for investigating the reaction dynamics and for determining the parameters of reaction models based on transport theory. In particular, the elliptic flow in collisions of neutron-rich heavy-ion systems emerges as an observable sensitive to the strength of the symmetry energy at supra-saturation densities. The comparison of ratios or differences of neutron and proton flows or neutron and hydrogen flows with predictions of transport models favors an approximately linear density dependence, consistent with ab-initio nuclear-matter theories. Extensive parameter searches have shown that the model dependence is comparable to the uncertainties of existing experimental data. Comprehensive new flow data of high accuracy, partly also through providing stronger constraints on model parameters, can thus be expected to improve our knowledge of the equation of state of asymmetric nuclear matter.Comment: 20 pages, 24 figures, review to appear in EPJA special volume on nuclear symmetry energ

Therapeutic alternatives with CPAP in obstructive sleep apnea

Obstructive Sleep Apnea (OSA), characterized by airflow cessation (apnea) or reduction (hypopnea) due to repeated pharyngeal obstructions during sleep, causes frequent disruption of sleep and hypoxic events. The condition is linked to many adverse health related consequences, such as neurocognitive and cardiovascular disorders, and metabolic syndrome. OSA is a chronic condition requiring long-term treatment, so treatment using continuous positive airway pressure (CPAP) has become the gold standard in cases of moderate or severe OSA. However, its effectiveness is influenced by patients’ adherence. Surgery for OSA or treatment with oral appliances can be successful in selected patients, but for the majority, lifestyle changes such as exercise and dietary control may prove useful. However, exercise training remains under-utilized by many clinicians as an alternative treatment for OSA. Other interventions such as oral appliance (OA), upper way stimulation, and oropharyngeal exercises are used in OSA. Because the benefit of all these techniques is heterogeneous, the major challenge is to associate specific OSA therapies with the maximum efficacy and the best patient compliance