Subthreshold Kaon Production Research Articles

Pioneering the Equation of State of Dense Nuclear Matter with Strange Particles Emitted in Heavy-Ion Collisions: The KaoS Experiment at GSI

High-energy heavy-ion collisions offer the unique possibility to study fundamental properties of nuclear matter in the laboratory, which are relevant for our understanding of the structure of compact stellar objects and the dynamics of neutron star mergers. Of particular interest are the nuclear matter equation of state (EOS), the in-medium modifications of hadrons and the degrees of freedom of matter at high densities and temperatures. Pioneering experiments exploring the EOS for symmetric matter were performed at the SIS18 accelerator of GSI, measuring, as function of beam energy, the collective flow of protons and of light fragments and subthreshold strangeness production. These data were reproduced by various microscopic transport model calculations, providing, up to date, the best constraint for the EOS of symmetric matter with an incompressibility of about 200 MeV for densities up to twice the saturation density. This article reviews the experimental results on subthreshold kaon production together with the theoretical interpretation and gives a brief outlook towards future experiments at higher densities.

Nuclear in-medium and isospin effects on subthreshold kaon production in heavy-ion collisions

Subthreshold kaon (K$^{0}$ and K$^{+}$) production in neutron-rich nuclear reactions to probe the kaon-nucleon interaction in nuclear medium and to extract the isospin dependent part of the nuclear equation of state at high-baryon densities, is investigated within an isospin and momentum dependent transport model. A repulsive kaon-nucleon potential is implemented in the model through fitting the flow data and inclusive spectra in heavy-ion collisions, which enhances the energetic kaon emission squeezed out in the reaction zone and leads to a variation of the high-momentum spectrum of the K$^{0}$/K$^{+}$ yields. It is found that the stiffness of nuclear symmetry energy plays a significant role on the isospin ratio with decreasing the incident energy and a hard symmetry energy has a larger value of the K$^{0}$/K$^{+}$ ratio in the domain of subthreshold energies.

Strangeness in astrophysics and cosmology

Some recent developments concerning the role of strange quark matter for astrophysical systems and the QCD phase transition in the early universe are addressed. Causality constraints of the soft nuclear equation of state as extracted from subthreshold kaon production in heavy-ion collisions are used to derive an upper mass limit for compact stars. The interplay between the viscosity of strange quark matter and the gravitational wave emission from rotation-powered pulsars are outlined. The flux of strange quark matter nuggets in cosmic rays is put into perspective with a detailed numerical investigation of the merger of two strange stars. Finally, we discuss a novel scenario for the QCD phase transition in the early universe, which allows for a small inflationary period due to a pronounced first-order phase transition at large baryochemical potential.

Strangeness in Compact Stars

We discuss the impact of strange hadrons, in particular hyperons, on the gross features of compact stars and on core-collapse supernovae. Hyperons are likely to be the first exotic species which appears around twice normal nuclear matter density in the core of neutron stars. Their presence largely influences the mass-radius relation of compact stars, the maximum mass, the cooling of neutron stars, the stability with regard to the emission of gravitational waves from rotation-powered neutron stars and the possible early onset of the QCD phase transition in core-collapse supernovae. We outline also the constraints from subthreshold kaon production in heavy-ion collisions for the maximum possible mass of neutron stars.

Isospin Effects on Subthreshold Kaon Production at Intermediate Energies

We show that in collisions with neutron-rich heavy ions at energies around the production threshold K0 and K+ yields probe the isospin-dependent part of the nuclear equation of state at high baryon densities. In particular, we suggest the K0/K+ ratio as a promising observable. Results obtained in a covariant relativistic transport approach are presented for Au+Au collisions at 0.8-1.8A GeV. The focus is put on the equation of state influence which goes beyond the collision-cascade picture. The isovector part of the in-medium interaction affects the kaon multiplicities via two mechanisms: (i) a symmetry potential effect, i.e., a larger neutron repulsion in n-rich systems, and (ii) a threshold effect, due to the change in the self-energies of the particles involved in inelastic processes. Genuine relativistic contributions are revealed that could allow one to directly "measure" the Lorentz structure of the effective isovector interaction.

Threshold meson production and cosmic ray transport

An interesting accident of nature is that the peak of the cosmic ray spectrum, for both protons and heavier nuclei, occurs near the pion production threshold. The Boltzmann transport equation contains a term which is the cosmic ray flux multiplied by the cross section. Therefore when considering pion and kaon production from proton–proton reactions, small cross sections at low energy can be as important as larger cross sections at higher energy. This is also true for subthreshold kaon production in nuclear collisions, but not for subthreshold pion production.

Subthreshold Kaon and Antikaon Production and Medium Effects in Nucleus–Nucleus Collisions

Production of K±-mesons and antiprotons in heavy ion collisions is considered at energies below the production threshold in free nucleon–nucleon collisions. A simple nuclear fluid dynamics model was used to describe the experimental data. For strange particles and antiparticles the associative character of the production was taken into account, which reduced considerably the absolute value of the production cross-section. The medium effects for K± were taken into account.

K+production in baryon-baryon and heavy-ion collisions

Kaon production cross sections in nucleon-nucleon, nucleon-$\ensuremath{\Delta}$, and $\ensuremath{\Delta}$-$\ensuremath{\Delta}$ interactions are studied in a boson exchange model. For the latter two interactions, the exchanged pion can be on-mass shell; only contributions due to a virtual pion are included via the Peierls method by taking into account the finite $\ensuremath{\Delta}$ width. With these cross sections and also those for pion-baryon interactions, subthreshold kaon production from heavy-ion collisions is studied in the relativistic transport model.

Anisotropy of SubthresholdK+Emission in Heavy Ion Reactions

The origin of the forward-backward enhancement of K{sup +} emission observed in symmetric nucleus-nucleus collisions at 1GeV/nucleon has been explored. The nonisotropic pion-baryon reaction leading to K{sup +} production has been found to play a substantial role in creating the forward-backward peak of the kaon angular distribution. By an analysis including also the effects from relevant final-state interactions on kaons, we can reproduce the experimental kaon angular distribution. We argue that the observed nonisotropic kaon emission may provide a support to the pion-induced channel for subthreshold kaon production in heavy ion reactions. {copyright} {ital 1997} {ital The American Physical Society}

Resonance model study of strangeness production in pp collisions

Results for the energy dependence of the elementary kaon production cross sections in proton-proton collisions are reported. Calculations are performed within an extended version of the resonance model which was used for the previous studies of elementary kaon production in pion-nucleon and pion-Δ collisions. Although the model treatment is within the empirical tree level (observed widths for the resonances are used), it is fully relativistic, and includes all relevant baryon resonances up to 2 GeV. One of the purposes of this study is to provide the results for the simulation codes of subthreshold kaon production in heavy ion collisions. This is the first, consistent study of the elementary kaon production reactions including both πB and BB ( B = N, Δ) collisions on the same footing. Comparisons are made between the calculated results and the existing semi-empirical parametrizations which are widely used for the simulation codes, as well as the experimental data.

Kaon production in hadronic matter

Subthreshold kaon production has been studied in symmetric nucleus-nucleus collisions as a function of the nucleus mass, beam energy and centrality. In Au+Au collsions at 1 AGeV theK+ multiplicity increases more than linearly with increasing number of participating nucleons. Transport calculations have to assume a soft equation of state in order to reproduce the data. The in-mediumK− cross section measured in Ni+Ni collisions is enhanced by about a factor of 7 as compared to the free cross section when using theK+ cross section at equivalent beam energies as a normalization.

SubthresholdK + production in proton-nucleus collisions as a probe for short range nucleon correlations

Double differential cross sections for nearthreshold and subthreshold production ofK + with momentum 1.28 GeV/c at 10.5 degree on Be, Al and Cu targets had been measured. The experiment was performed with FH Spectrometer at ITEP PS in projectile proton kinetic energy range 2.9 – 1.65 GeV. The performed analysis of the excitation functions and target atomic mass dependencies evidences for high order multinucleon correlations are involved in deep subthreshold kaon production.

Internal nuclear momentum and subthreshold kaon production

The role of the high momentum component of the nuclear spectral function in subthreshold K + meson production in proton-nucleus collisions is studied. We use the parametrization of the elementary NN → NYK cross section, which is based on the calculations performed with the boson exchange model. The experimental data on quasi-elastic electron and gamma scattering and backward proton production are analyzed in order to extract the high momentum component in nuclei. It is shown that the contribution from the high momentum component to the kaon production is negligible.

Subthreshold kaon production and the nuclear equation of state

We reexamine in the relativistic transport model the dependence of kaon yield on the nuclear equation of state in heavy ion collisions at energies that are below the threshold for kaon production from the nucleon-nucleon interaction in free space. For Au+Au collisions at GeV/nucleon, we find that the kaon yield measured by the Kaos collaboration at GSI can be accounted for if a soft nuclear equation of state is used. We also confirm the results obtained in non-relativistic transport models that the dependence of kaon yield on the nuclear equation of state is more appreciable in heavy ion collisions at lower incident energies. We further clarify the difference between the predictions from the relativistic transport model and the non-relativistic transport model with a momentum-dependent potential.

The relativistic transport model description of subthreshold kaon production in heavy-ion collisions

The relativistic transport model, in which the nucleon effective mass is connected to the scalar field while its energy is shifted by the vector potential, is extended to include the kaon degree of freedom. We further take into account the medium modification of the kaon mass due to explicit chiral symmetry breaking. Both the propagation of kaons in the mean-field potential and the kaon-baryon elastic scattering are explicitly treated in our study. We find that the attractive kaon scalar mean-field potential in the dense matter leads to an enhanced kaon yield in heavy-ion collisions at energies of about 1 GeV/nucleon that are below the threshold for kaon production from the nucleon-nucleon interaction in free space. The final-state kaon-baryon scattering is seen to affect significantly the kaon momentum spectra, leading to an enhanced yield of kaons with large momenta or at large laboratory angles. With a soft nuclear equation of state and including the attractive kaon scalar potential, the calculated kaon energy spectra agree with the preliminary data on subthreshold kaon production from the heavy-ion synchrotron at GSI.

Subthreshold kaons would reveal density isomers.

If density isomers exist they can be detected by measuring the excitation function of subthreshold kaon production. When the system reaches the density where the density isomer has influence on the equation of state (which depends on the beam energy and on the optical potential), we observe a jump in the cross section of the kaons whereas other observables change little. Above threshold \ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{}'s or p\ifmmode\bar\else\textasciimacron\fi{}'s may be used to continue the search. This is the result of microscopic Boltzman-Uehling-Uhlenbeck calculations.

Medium effects on subthreshold kaon production in heavy-ion collisions.

The relativistic transport model is extended to include the kaon degree of freedom. We also take into account the density dependence of the kaon effective mass in nuclear matter and the rescattering of kaons by nucleons. We find that the inclusion of kaon self-energy due to the attractive scalar mean field leads to an enhanced kaon yield in heavy-ion collisions at subthreshold energies. Also, kaon rescatterings are found to affect significantly the final kaon momentum spectra. We compare the theoretical results with recent experimental data from the Heavy-Ion Synchrotron (SIS) at GSI.

Effect of N-body collisions on subthreshold kaon production in high-energy nuclear reactions

We recently generalized the standard BUU transport model to incorporate N-body collisions. This model has now been further developed so as to allow the calculation of the energy spectra of kaons produced in nuclear reactions at relativistic energies. Applications to the systems Ca+Ca, Nb+Nb, and Au+Au at bombarding energies of 600 and 1000 MeV per nucleon suggest that the effect of N-body collisions on the kaon spectra is relatively minor.

Subthreshold kaon production in Au on Au collisions at 1 GeV/u

Subthreshold kaon production in197 Au+197 Au collisions at 1.0 GeV/u has been investigated with the Kaon Spectrometer at SIS. At Θ lab =44±4∘ we found aK +/p ratio of>3 · 10−4 for the momentum range 650 MeV/c to 1150 MeV/c.

SUBTHRESHOLD KAON- AND PION PRODUCTION IN HEAVY ION COLLISIONS: SIMILARITIFS AND DIFFERENCES

Particle inclusive yields from heavy ion reactions are described by a closed form expression which is not limited to a particular type of particle as long as this is produced in individual baryon-baryon encounters with a small probability. This criterion is satisfied for subthreshold pion and kaon production on which we concentrate. Even though the elementary pion and kaon production cross sections can both be described well by three-particle phase space considerations, the final inclusive production rates differ qualitatively from one another. The reasons for this are discussed.