Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI
<p>(<b>a</b>) Layout of the double-focusing magnetic spectrometer KaoS with its detector system: time-of-flight (TOF) start and stop detectors, 3 multi-wire proportional chambers (MWPC), Cherenkov detectors with water, lucite and silica aerogel radiators, two hodoscopes for event characterization at target (for large angles) and 7 m downstream the target (for small angles, not shown) [<a href="#B32-particles-05-00003" class="html-bibr">32</a>]. (<b>b</b>) Photo of the setup.</p> "> Figure 2
<p>Examples of the acceptance of the kaon spectrometer in the plane transverse momentum versus normalized rapidity y/y<sub>beam</sub> for several laboratory angles θ<sub>lab</sub> (as indicated) and for various magnetic field settings at 1.0A GeV, at 1.5A GeV and at 1.93A GeV beam energy. The angular acceptance is ∆θ<sub>lab</sub> = ±4°, corresponding to the width of the pink bands.</p> "> Figure 3
<p>Pion multiplicity per participating nucleon measured in nucleus–nucleus collisions (symbols) and in nucleon–nucleon collisions as a function of available energy in the NN system (taken from [<a href="#B33-particles-05-00003" class="html-bibr">33</a>]).</p> "> Figure 4
<p>Differential pion production cross-sections measured at various polar emission angles in Au+Au collisions at 1.5A GeV (π<sup>+</sup> left panel and π<sup>−</sup> center panel) and in C+C collisions at 1A GeV (π<sup>+</sup> right panel) as a function of the kinetic energy in the c.m. system (black triangles) in comparison to results of URQMD transport calculations (green triangles) [<a href="#B34-particles-05-00003" class="html-bibr">34</a>].</p> "> Figure 5
<p>(<b>a</b>) Three snapshots of a Au+Au collision with a beam kinetic energy of 1A GeV (impact parameter b = 7 fm) calculated with the QMD transport code for 4 fm/c (left), 10 fm/c (center) and 16 fm/c (right). The pions are emitted in the reaction plane at backward angles corresponding to a particular detector position. (<b>b</b>) Pion number ratio N<sup>π</sup><sub>proj</sub>/N<sup>π</sup>t<sub>arg</sub> measured as function of transverse momentum in peripheral Au+Au collisions (b ≥ 5.7 fm) at 1A GeV at target rapidity. N<sup>π</sup><sub>proj</sub> and N<sup>π</sup>t<sub>arg</sub> denote the numbers of pions emitted to the projectile and to the target side, respectively, within a cone of ±45° [<a href="#B35-particles-05-00003" class="html-bibr">35</a>].</p> "> Figure 6
<p>(<b>a</b>) Azimuthal distributions of positively charged pions for peripheral, semi-central and central collisions (from top to bottom) measured in Au+Au collisions at 1A GeV [<a href="#B37-particles-05-00003" class="html-bibr">37</a>]. The ordinate is linear starting at zero. Left column: π<sup>+</sup> in the range 160 < p<sub>T</sub> < 260 MeV/c. Right column: π<sup>+</sup> in the range 260 < p<sub>T</sub> < 600 MeV/c. Solid lines: fits to the data with cos (φ) and cos (2φ) terms. φ = 0° and φ = ±180° represent emission of pions parallel to the reaction plane and φ = ±90° corresponds to emission of pions perpendicular to the reaction plane. (<b>b</b>) Illustration of the particle emission pattern for semi-central collisions at intermediate beam energies perpendicular to the reaction plane (“off-plane squeeze-out”) and parallel to the reaction plane (“bounce off”).</p> "> Figure 7
<p>K<sup>+</sup> and K<sup>−</sup> multiplicity per number of participating nucleons as a function of the available energy above threshold in first-chance collisions for C+C and Ni+Ni collisions (for symbols, see legend) and parameterizations of the kaon production cross sections in nucleon–nucleon collisions (for lines, see insert). Taken from [<a href="#B40-particles-05-00003" class="html-bibr">40</a>].</p> "> Figure 8
<p>Inclusive invariant cross-sections at mid-rapidity as a function of the kinetic energy E<sub>c</sub>.<sub>m</sub>. − m<sub>0</sub>c<sup>2</sup> for K<sup>+</sup> mesons (<b>a</b>) and for K<sup>−</sup> mesons (<b>b</b>) for the various collision systems and beam energies measured. Mid-rapidity data were selected by the condition θ<sub>c</sub>.<sub>m</sub>.= 90° ± 10° from measurements at different polar angles [<a href="#B41-particles-05-00003" class="html-bibr">41</a>]. The lines represent fits to the data (see text).</p> "> Figure 9
<p>Multiplicities of K<sup>+</sup> (full symbols) and of K<sup>−</sup> mesons (open symbols) per mass number A of the collision system as a function of the beam energy. The lines represent fits to the data [<a href="#B41-particles-05-00003" class="html-bibr">41</a>].</p> "> Figure 10
<p>Azimuthal distribution of K<sup>+</sup> mesons measured in semi-central Au+Au collisions at 1A GeV (full dots). The kaons are analyzed for transverse momenta within a range of 0.2 GeV/c ≤ p<sub>t</sub> ≤ 0.8 GeV/c and for the normalized rapidity ranges of 0.4 ≤ y/y<sub>proj</sub> ≤ 0.6 (<b>a</b>) and 0.2 ≤ y/y<sub>proj</sub> ≤ 0.8 (<b>b</b>) [<a href="#B7-particles-05-00003" class="html-bibr">7</a>]. The lines show the results of transport calculations using a RBUU model (left; [<a href="#B42-particles-05-00003" class="html-bibr">42</a>]) and a QMD model (right; [<a href="#B43-particles-05-00003" class="html-bibr">43</a>]), which both take into account rescattering; QMD also calculates Coulomb effects. Solid and dashed lines: calculations with and without in-medium K<sup>+</sup>N potential, respectively. Taken from [<a href="#B40-particles-05-00003" class="html-bibr">40</a>].</p> "> Figure 11
<p>Azimuthal angular distributions of π<sup>+</sup>, K<sup>+</sup> and K<sup>−</sup>mesons (from <b>left</b> to <b>right</b>) measured in semi-central Ni+Ni collisions at 1.93A·GeV [<a href="#B46-particles-05-00003" class="html-bibr">46</a>]. The mesons are measured within a rapidity range of 0.3 < y/y<sub>beam</sub> < 0.7 and a momentum range of 0.2 GeV/c < p<sub>t</sub> < 0.8 GeV/c. The data are fitted using the first two components of a Fourier series dN/dΦ∼2 v<sub>1</sub> cos (φ) + 2 v<sub>2</sub> cos (2φ). The resulting values for v<sub>1</sub> and v<sub>2</sub> are indicated.</p> "> Figure 12
<p>Multiplicity density distributions of K<sup>+</sup> mesons (upper panel), K<sup>−</sup> mesons (center panel) and the K<sup>+</sup>/K<sup>−</sup> ratio (lower panel) for near-central (<span class="html-italic">b</span> < 4.4 fm) Ni+Ni collisions at 1.93A GeV, measured by KaoS (red circles) [<a href="#B47-particles-05-00003" class="html-bibr">47</a>] and FOPI (green squares) [<a href="#B48-particles-05-00003" class="html-bibr">48</a>,<a href="#B49-particles-05-00003" class="html-bibr">49</a>]. The measured data (full symbols) are mirrored at <span class="html-italic">y</span><sub>CM</sub> = 0 (open symbols). The data are compared to BUU transport calculations [<a href="#B50-particles-05-00003" class="html-bibr">50</a>]. Solid lines: with in-medium effects. Dotted lines: without in-medium effects. Taken from [<a href="#B33-particles-05-00003" class="html-bibr">33</a>].</p> "> Figure 13
<p>Upper panel: Density in the reaction volume as function of time for a central Au+Au collision at 1A GeV as calculated by a RBUU transport model. Lower panel: Multiplicities of produced Δ resonances (green dotted line), pions (red dashed line) and K<sup>+</sup> mesons (blue line) as functions of time.</p> "> Figure 14
<p>(<b>a</b>) Production cross-sections of K<sup>+</sup> mesons measured in Au+Au and C+C collisions as functions of the projectile energy per nucleon (black diamonds). The data are compared to QMD calculations with (full symbols) and without (open symbols) kaon in-medium modifications, assuming a soft EOS (K<sub>nm</sub> = 200 MeV; blue dots) or a hard EOS (K<sub>nm</sub> = 380 MeV; cyan squares). (<b>b</b>) Ratio of the K<sup>+</sup> multiplicity per mass number in Au+Au over C+C collisions as a function of beam energy. The data are compared to different QMD calculations assuming a soft EOS (K<sub>nm</sub> = 200 MeV; red symbols) or a hard EOS (K<sub>nm</sub> = 380 MeV; blue symbols). Taken from [<a href="#B57-particles-05-00003" class="html-bibr">57</a>].</p> "> Figure 15
<p>Binding energy as a function of nuclear matter density in units of ρ<sub>0</sub>. The lines represent the results of various calculations for neutron matter (upper curves) and for symmetric matter (lower curves) [<a href="#B62-particles-05-00003" class="html-bibr">62</a>]. Lower green area: EOS for symmetric matter as extracted from data of the KaoS [<a href="#B54-particles-05-00003" class="html-bibr">54</a>,<a href="#B55-particles-05-00003" class="html-bibr">55</a>] and FOPI [<a href="#B59-particles-05-00003" class="html-bibr">59</a>] experiments. Upper green area: Symmetry energy E<sub>sym</sub> as extracted from the data of the ASY–EOS experiment [<a href="#B61-particles-05-00003" class="html-bibr">61</a>] added to the experimental EOS for symmetric matter (see text).</p> "> Figure 16
<p>EOS of symmetric nuclear matter expressed as pressure versus baryon density. Grey hatched area: constraint from proton flow data taken at AGS [<a href="#B11-particles-05-00003" class="html-bibr">11</a>,<a href="#B12-particles-05-00003" class="html-bibr">12</a>]. Yellow area: Constraint from fragment flow and kaon data taken at GSI [<a href="#B54-particles-05-00003" class="html-bibr">54</a>,<a href="#B55-particles-05-00003" class="html-bibr">55</a>,<a href="#B59-particles-05-00003" class="html-bibr">59</a>]. Red line: Hard EOS. Blue line: Soft EOS [<a href="#B12-particles-05-00003" class="html-bibr">12</a>].</p> ">
Abstract
:1. Introduction
2. The Kaon Spectrometer (KaoS) Experiment at GSI/SIS18
3. Experimental Results
3.1. Pion Production
3.2. Kaon Production
4. The High-Density Nuclear Matter Equation-of-State
5. Summary
Funding
Data Availability Statement
Conflicts of Interest
References
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Senger, P. Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI. Particles 2022, 5, 21-39. https://doi.org/10.3390/particles5010003
Senger P. Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI. Particles. 2022; 5(1):21-39. https://doi.org/10.3390/particles5010003
Chicago/Turabian StyleSenger, Peter. 2022. "Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI" Particles 5, no. 1: 21-39. https://doi.org/10.3390/particles5010003