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Register a new userThe influence of cluster emission and the symmetry energy on neutron-proton spectral double ratios
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Emissions of free neutrons and protons from the central collisions of 124Sn+124Sn and 112Sn+112Sn reactions are simulated using the Improved Quantum Molecular Dynamics model with two different density dependence of the symmetry energy in the nuclear equation of state. The constructed double ratios of the neutron to proton ratios of the two reaction systems are found to be sensitive to the symmetry terms in the EOS. The effect of cluster formation is examined and found to affect the double ratios mainly in the low energy region. In order to extract better information on symmetry energy with transport models, it is therefore important to have accurate data in the high energy region which also is affected minimally by sequential decays.
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In this work, we firstly investigate how to reproduce and how well one can reproduce the Woods-Saxon density distribution of initial nuclei in the framework of the improved quantum molecular dynamics model. Then, we propose a new treatment for the initialization of nuclei which is correlated with the nucleonic mean-field potential by using the same potential energy density functional. In the mean field potential, the three-body force term is accurately calculated. Based on the new version of the model, the influences of precise calculations of the three-body force term, the slope of symmetry energy, the neutron-proton effective mass splitting, and the width of the wave packet on heavy ion collision observables, such as the neutron to proton yield ratios for emitted free nucleons [$R(n/p)$] and for coalescence invariant nucleons [$R_{ci}(n/p)$] for $^{124}$Sn+$^{112}$Sn at the beam energy of 200 MeV per nucleon, are discussed. Our calculations show that the spectra of neutron to proton yield ratios [$R(n/p)$] can be used to probe the slope of symmetry energy ($L$) and the neutron-proton effective mass splitting. In detail, the $R(n/p)$ in the low kinetic energy region can be used to probe the slope of symmetry energy ($L$). With a given $L$, the inclination of $R(n/p)$ to kinetic energy ($E_k$) can be used to probe the effective mass splitting. In the case where the neutron-proton effective mass splitting is fixed, $R(n/p)$ at high kinetic energy can also be used to learn the symmetry energy at suprasaturation density.
In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, effects of the symmetry energy on the evolutions of free n/p ratio and charged pion ratio in the semi-central collision of $^{197}$Au+$^{197}$Au at an incident beam energy of 400 MeV/nucleon are studied. At the beginning of the reaction (before 11 fm/c) they are both affected by the low-density behavior of the symmetry energy but soon after are affected by the high-density behavior of the symmetry energy after nuclei are compressed (after 11 fm/c) and the effects of the symmetry energy are generally smaller compared with the central collision case. Interestingly, their dependences on the symmetry energy are shown to arise with increase of cone-azimuthal angle of the emitted particles. In the direction perpendicular to the reaction plane, the $pi^{-}/pi ^{+}$ ratio or free n/p ratio especially at high kinetic energies exhibits significant sensitivity to the symmetry energy.
The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number $A=48-60$ is considered. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of $A$ for a family of mirror pairs from selected chains of nuclei with $Z=20$, $N=14$, and $N=50$. The evolution curves show a similar behavior crossing at the $N=Z$ nucleus in each chain and a smooth growing deviation when $N eq Z$ starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made.
Model-independent constraints for the neutron-triton and proton-Helium-3 scattering lengths are calculated with a leading-order interaction derived from an effective field theory without explicit pions. Using the singlet neutron-proton scattering length, the deuteron, and the triton binding energy as input, the predictions $ants=9.2pm2.6 $fm, $antt=7.6pm1.6 $fm, $aphes=3.6pm0.32 $fm, and $aphet=3.1pm 0.23 $fm are obtained. The calculations employ the resonating group method and include the Coulomb interaction when appropriate. The theoretical uncertainty is assessed via a variation of the regulator parameter of the short-distance interaction from $400 $MeV to $1.6 $GeV. The phase-shift and scattering-length results for the proton-Helium-3 system are consistent with a recent phase shift analysis and with model calculations. For neutron-triton, the results for the scattering lengths in both singlet and triplet channels are significantly smaller than suggested by R-matrix and partial-wave-analysis extractions from data. For a better understanding of this discrepancy, the sensitivity of the low-energy four-body scattering system to variations in the neutron-neutron and proton-proton two-nucleon scattering lengths is calculated. Induced by strong charge-symmetry-breaking contact interactions, this dependence is found insignificant. In contrast, a strong correlation between the neutron-triton scattering length and the triton binding energy analogous to the Phillips line is found.
We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN collision rate. We also explore both $DR(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Zge20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.
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