Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions

The nuclear symmetry energy

The symmetry energy describes how the energy of nuclear matter rises as one goes away from equal numbers of neutrons and protons. This is very important to describe neutron rich matter in astrophysics. This article reviews our knowledge of the symmetry energy from theoretical calculations, nuclear structure measurements, heavy-ion collisions, and astronomical observations. We then present a roadmap to make progress in areas of relevance to the symmetry energy that promotes collaboration between the astrophysics and the nuclear physics communities.

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A way forward in the study of the symmetry energy: experiment, theory, and observation

https://bib.irb.hr/datoteka/735056.1-s2.0-S037026931100178X-main.pdf

Symmetry energy from elliptic flow in 197Au + 197Au

Analytical expressions for the saturation density of asymmetric nuclear matter as well as its binding energy and incompressibility at saturation density are given up to fourth order in the isospin asymmetry $\ensuremath{\delta}=({\ensuremath{\rho}}_{n}\ensuremath{-}{\ensuremath{\rho}}_{p})/\ensuremath{\rho}$ using 11 characteristic parameters defined by the density derivatives of the binding energy per nucleon of symmetric nuclear matter, the symmetry energy ${E}_{\mathrm{sym}} (\ensuremath{\rho})$, and the fourth-order symmetry energy ${E}_{\mathrm{sym},4}(\ensuremath{\rho})$ at normal nuclear density ${\ensuremath{\rho}}_{0}$. Using an isospin- and momentum-dependent modified Gogny interaction (MDI) and the Skyrme-Hartree-Fock (SHF) approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility ${K}_{\mathrm{sat}}(\ensuremath{\delta})={K}_{0}+{K}_{\mathrm{sat},2}{\ensuremath{\delta}}^{2}+{K}_{\mathrm{sat},4}{\ensuremath{\delta}}^{4}+O({\ensuremath{\delta}}^{6})$ at saturation density. Our results show that the magnitude of the higher order ${K}_{\mathrm{sat},4}$ parameter is generally small compared to that of the ${K}_{\mathrm{sat},2}$ parameter. The latter essentially characterizes the isospin dependence of the incompressibility at saturation density and can be expressed as ${K}_{\mathrm{sat},2}={K}_{\mathrm{sym}}\ensuremath{-}6L\ensuremath{-}\frac{{J}_{0}}{{K}_{0}}L$, where $L$ and ${K}_{\mathrm{sym}}$ represent, respectively, the slope and curvature parameters of the symmetry energy at ${\ensuremath{\rho}}_{0}$ and ${J}_{0}$ is the third-order derivative parameter of symmetric nuclear matter at ${\ensuremath{\rho}}_{0}$. Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model that can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the higher order ${J}_{0}$ contribution to ${K}_{\mathrm{sat},2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between ${K}_{\mathrm{sym}}$ and $L$ as well as between ${J}_{0}/{K}_{0}$ and ${K}_{0}$. These correlations together with the empirical constraints on ${K}_{0},L,{E}_{\mathrm{sym}} ({\ensuremath{\rho}}_{0})$, and the nucleon effective mass lead to an estimate of ${K}_{\mathrm{sat},2}=\ensuremath{-}370\ifmmode\pm\else\textpm\fi{}120$ MeV.

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Higher-order effects on the incompressibility of isospin asymmetric nuclear matter

Systematics of pion emission in heavy ion collisions in the 1 A GeV regime

During the development of the Multi-Strip Multi-Gap Resistive Plate Chambers (MMRPCs) for the time-of-flight (ToF) upgrade of the FOPI detector system, we have designed different versions of the front-end electronics (FEE). The signals from a MMRPC are read out on each side of the anode strips by an amplifier followed by a leading-edge discriminator. They are digitized in a time-to-amplitude converter (TAC) followed by a charge-to-digital converter (QDC). These counters are designed to provide a ToF resolution below sigmat les 60 ps requiring an amplifier-diecriminator stage with an intrinsic electronic resolution below sigmat(FEE) les 20 ps. We describe the design steps of the FEE-card from a 4-channel version (FEE1) for the R&D phase to the final 16-channel card (FEE5) for the readout of 4800 channels of the total detector array. Through these design steps we have kept the following key characteristics: low noise sigman les 25 muV RMS (to the amplifier input), high gain (200) and a high bandwidth (1 GHz).

A Front-End Electronics Card Comprising a High Gain/High Bandwidth Amplifier and a Fast Discriminator for Time-of-Flight Measurements

During the development of the Multi Strip Multi Gap Resistive Plate Chambers (MMRPCs) for the FOPI Time of Flight (ToF) upgrade, we designed different versions of the Front End Electronics (FEE). The signals from a MMRPCs, which are typically between 1-30 mV, are read out on each side of the strips by a preamplifier followed by a leading edge discriminator. The signals are digitized in a Time-to-Amplitude Converter (TAC) and a QDC. These counters are designed to provide a ToF measurement below sigmat < 60ps which needs a preamplifier-discriminator stage with an intrinsic electronic resolution below sigmat(FEE) les 20ps. We show the design steps of the FEE-card from a 4 channel (FEE1) design for the R&D phase to the final 16 channel card (FEE5) used for the mass production. Through these design steps, we kept the following key characteristics for the FEE: Low noise sigman les 25 muV RMS (to the preamplifier input), high gain (200) and a high bandwidth (1GHz).

X. Lopez

Papers

Systematics of pion emission in heavy ion collisions in the 1 A GeV regime

A Front-End Electronics Card Comprising a High Gain/High Bandwidth Amplifier and a Fast Discriminator for Time-of-Flight Measurements

A Front End Electronic card using a high gain and high bandwidth preamplifier with a fast discriminator for time of flight measurements