.
A QMD transport model that employs a modified momentum dependent interaction (MDI2) potential, supplemented by a phase-space coalescence model fitted to FOPI experimental multiplicities of free ...nucleons and light clusters is 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 using the same model 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
s
y
m
parameters of the symmetry energy. To make use of this result a Gogny interaction inspired potential is modified by the addition of a density dependent, momentum independent term, while enforcing a close description of the empirical nucleon optical potential, allowing independent modifications 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 constraint is extracted:
L
=
85
±
22
(
exp
)
±
20
(
th
)
±
12
(
sys
)
MeV and
K
s
y
m
=
96
±
315
(
exp
)
±
170
(
th
)
±
166
(
sys
)
MeV. Theoretical errors include effects due to uncertainties in the isoscalar part of the equation of state, value of the isovector neutron-proton effective mass splitting, in-medium effects on the elastic nucleon-nucleon cross-sections, Pauli blocking algorithm variants and scenario considered for the conservation of the total energy of the system. 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
±
30
(
exp
)
±
19
(
th
)
MeV. It is demonstrated that elliptic flow ratios reach a maximum sensitivity on the
K
s
y
m
parameter in heavy-ion collisions of about 250 MeV/nucleon impact energy, allowing a reduction of its experimental component of uncertainty to about 150 MeV.
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. A comparison of various transport model predictions with existing experimental data has led, however, to contradictory results. Using an upgraded version of the Tübingen 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. However, pion multiplicities and ratios are proven to be highly sensitive to the yet unknown isovector part of the in-medium Δ(1232) potential which hinders, at present, 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.
We employ an isospin dependent version of the QMD transport model to study the influence of the isospin dependent part of the nuclear matter equation of state and in-medium nucleon–nucleon ...cross-sections on the dynamics of heavy-ion collisions at intermediate energies. We find that the extraction of useful information on the isospin-dependent part of the equation of state of nuclear matter from proton or neutron elliptic flows is obstructed by their sensitivity to model parameters and in-medium values of nucleon–nucleon cross-sections. Opposite to that, neutron–proton elliptic flow difference shows little dependence on those variables while its dependence on the isospin asymmetric EoS is enhanced, making it more suitable for a model independent constraining of the high-density behaviour of asy-EoS. Comparison with existing experimental FOPI-LAND neutron–hydrogen data can be used to set an upper limit to the softness of asy-EoS. Successful constraining of the asy-EoS via neutron–proton elliptic flow difference will require experimental data of higher accuracy than presently available.
Many neutron star properties, such as the proton fraction, reflect the symmetry energy contributions to the equation of state that dominate when neutron and proton densities differ strongly. To ...constrain these contributions at suprasaturation densities, we measure the spectra of charged pions produced by colliding rare isotope tin (Sn) beams with isotopically enriched Sn targets. Using ratios of the charged pion spectra measured at high transverse momenta, we deduce the slope of the symmetry energy to be 42<L<117 MeV. This value is slightly lower but consistent with the L values deduced from a recent measurement of the neutron skin thickness of ^{208}Pb.
Using the dcQMD transport model, the isoscalar and isovector in-medium potentials of the
Δ
(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
Δ
∗
≈
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
Δ
(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%.
Abstract Purpose The aim of the present study was to assess if the combined therapy of intratympanic dexamethasone (ITD) and high dosage of betahistine (HDBH) is able to provide increased vertigo ...control compared to ITD alone in patients suffering from definite unilateral Meniere’s disease (MD). Materials and methods Consecutive MD patients were enrolled and randomly divided in two groups, each comprising 33 cases. Group A received a combination of ITD and identical-appearing placebo pills while Group B received a combination of ITD and HDBH. ITD protocol consisted of three consecutive daily injections. HDBH comprised 144 mg/day (48 mg tid). The main outcome measures were: 1) vertigo class, pure tone average (PTA), speech discrimination score (SDS) and Functional Level Score (FLS) according to the American Academy of Otolaryngology-Head and Neck Surgery criteria; 2) complete and substantial vertigo control according to the Kaplan–Meier survival method. Results Sixty two patients completed the 24-month follow-up. A complete vertigo control was achieved in 14 patients (44%) from Group A and in 22 patients (73.3%) from Group B, statistically significant (p = 0.01). Complete vertigo relief is also significant according to the Kaplan–Meier method: p = 0.027, log rank test. Substantial vertigo control was obtained in 21 patients (65.6%) in Group A and 27 patients (90%) in Group B. The difference is statistically significant, p = 0.02. The difference is significant according to the Kaplan–Meier method: p = 0.035, log rank test. No significant differences between hearing levels and tinnitus scores were demonstrated between the groups. Conclusions Our preliminary results demonstrate that complete and substantial vertigo control is significantly higher in patients treated with a combination of HDBH and ITD.
An upgraded version of the isospin dependent T¨ubingen QMD transport model, which allows the conservation of the total energy, is presented. This is achieved by including in the energy-balance ...equations of the density, isospin asymmetry and momentum dependent inmedium baryon potential energies. It leads to an effective modification of particle production thresholds with respect to the vacuum ones. Compatible constraints for the symmetry energy stiffness from π−/π+ multiplicity ratio and elliptic flow experimental data of Au+Au collisions at 400 MeV/nucleon can be extracted in this case. However, an important dependence of the π−/π+ observable on the strength of the isovector part of the Δ(1232) isobar potential is also demonstrated. The present lack of information on this quantity prevents a precise extraction of the value for the symmetry energy stiffness employing the mentioned observable alone.
.
Flow observables in heavy-ion reactions at incident energies up to about 1GeV 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.
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