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Register a new userSymmetry energy investigation with pion production from Sn+Sn systems
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In the past two decades, pions created in the high density regions of heavy ion collisions have been predicted to be sensitive at high densities to the symmetry energy term in the nuclear equation of state, a property that is key to our understanding of neutron stars. In a new experiment designed to study the symmetry energy, the multiplicities of negatively and positively charged pions have been measured with high accuracy for central $^{132}$Sn+$^{124}$Sn, $^{112}$Sn+$^{124}$Sn, and $^{108}$Sn+$^{112}$Sn collisions at $E/A=270~mathrm{MeV}$ with the S$pi$RIT Time Projection Chamber. While the uncertainties of individual pion multiplicities are measured to 4%, those of the charged pion multiplicity ratios are measured to 2%. We compare these data to predictions from seven major transport models. The calculations reproduce qualitatively the dependence of the multiplicities and their ratios on the total neutron to proton number in the colliding systems. However, the predictions of the transport models from different codes differ too much to allow extraction of reliable constraints on the symmetry energy from the data. This finding may explain previous contradictory conclusions on symmetry energy constraints obtained from pion data in Au+Au system. These new results call for better understanding of the differences among transport codes, and new observables that are more sensitive to the density dependence of the symmetry energy.
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Small angle electron scattering with intense electron beams opens up the possibility of performing almost real photon induced reactions with thin, polarized hydrogen and few body targets, allowing for the detection of low energy charged particles.This promises to be much more effective than conventional photon tagging techniques. For photo-pion reactions some fundamental new possibilities include: tests of charge symmetry in the N-N system by measurement of the neutron-neutron scattering length $a_{nn}$ in the $gamma D rightarrow pi^{+} nn$ reaction; tests of isospin breaking due to the mass difference of the up and down quarks; measurements with polarized targets are sensitive to $pi$N phase shifts and will test the validity of the Fermi-Watson (final state interaction) theorem. All of these experiments will test the accuracy and energy region of validity of chiral effective theories.
The complete and incomplete fusion cross sections for $^{7}$Li+$^{124}$Sn reaction were measured using online and offline characteristic $gamma$-ray detection techniques. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $sim$ 26 % compared to the coupled channel calculations. This suppression observed in complete fusion cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. There is a distinct feature observed in the ICF cross sections, i.e., $textit{t}$-capture is found to be dominant than $alpha$-capture at all the measured energies. A simultaneous explanation of complete, incomplete and total fusion (TF) data was also obtained from the calculations based on Continuum Discretized Coupled Channel method with short range imaginary potentials. The cross section ratios of CF/TF and ICF/TF obtained from the data as well as the calculations showed the dominance of ICF at below barrier energies and CF at above barrier energies.
Symmetry energy, temperature and density at the time of the intermediate mass fragment formation are determined in a self-consistent manner, using the experimentally reconstructed primary hot isotope yields and anti-symmetrized molecular dynamics (AMD) simulations. The yields of primary hot fragments are experimentally reconstructed for multifragmentation events in the reaction system $^{64}$Zn + $^{112}$Sn at 40 MeV/nucleon. Using the reconstructed hot isotope yields and an improved method, based on the modified Fisher model, symmetry energy values relative to the apparent temperature, $a_{sym}/T$, are extracted. The extracted values are compared with those of the AMD simulations, extracted in the same way as that for the experiment, with the Gogny interaction with three different density-dependent symmetry energy terms. $a_{sym}/T$ values change according to the density-dependent symmetry energy terms used. Using this relation, the density of the fragmenting system is extracted first. Then symmetry energy and apparent temperature are determined in a self consistent manner in the AMD model simulations. Comparing the calculated $a_{sym}/T$ values and those of the experimental values from the reconstructed yields, $rho /rho_{0} = 0.65 pm 0.02 $, $a_{sym} = 23.1 pm 0.6$ MeV and $T= 5.0 pm 0.4$ MeV are evaluated for the fragmenting system experimentally observed in the reaction studied.
The $NDeltato NN$ cross sections, which take into account the $Delta$-mass dependence of M-matrix and momentum $p_{NDelta}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $Delta$-mass dependent $NDeltato NN$ cross sections enhance the pion multiplicities and decrease the $pi^-/pi^+$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times normal density. The process of pion production in the reaction is tracked including the loops of $NNleftrightarrow NDelta$ and $Deltaleftrightarrow Npi$, our calculations show that the sensitivity of $pi^-/pi^+$ to symmetry energy is weakened after 4-5 N-$Delta$-$pi$ loops in the pion production path, while the $pi^{-}/pi^{+}$ ratio in reactions at near threshold energies remains its sensitivity to the symmetry energy. By comparing the calculations to the FOPI data, we obtain a model dependent conclusion on the symmetry energy and the symmetry energy at two times normal density is $S(2rho_0)$=38-73 MeV within $1sigma$ uncertainties. Under the constraints of tidal deformability and maximum mass of neutron star, the symmetry energy at two times normal density is reduced to $48-58$ MeV and slope of symmetry energy $L=54-81$ MeV, and it is consistent with the constraints from ASY-EOS flow data.
The LIGO-Virgo collaboration detection of the binary neutron-star merger event, GW170817, has expanded efforts to understand the Equation of State (EoS) of nuclear matter. These measurements provide new constraints on the overall pressure, but do not elucidate its origins, by not distinguishing the contribution to the pressure from symmetry energy which governs much of the internal structure of a neutron star. By combining the neutron star EoS extracted from the GW170817 event and the EoS of symmetric matter from nucleus-nucleus collision experiments, we extract the symmetry pressure, which is the difference in pressure between neutron and nuclear matter over the density region from 1.2$rho_{0}$ to $4.5rho_{0}$. While the uncertainties in the symmetry pressure are large, they can be reduced with new experimental and astrophysical results.
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