Disertatie Draft2 [309661]

[anonimizat] – [anonimizat]:

PROF. UNIV. DR. [anonimizat]:

LECT. UNIV. DR. OANA RISTEA

BUCHAREST

2017

[anonimizat] (Lamdau model)

Full transparency (Bjorken model)

Accelerator systems at FAIR and GSI

GSI Helmholtzzentrum für [anonimizat]. Predictions for A-A and p-A collisions

Conclusions

List of figures

Figure 1.1 Participants – spectators region

Figure1.2. Collision geometry for firestreaks model

Figure 1.3 [anonimizat] 1.4 Inelastic pp cross section as a function of

Figure 1.5 Values of the pp and pp¯ total cross section as a

Figure 1.6 Charm quark differential cross as a function of pt

Figure 1.7 Stopping and transparency depending on energy

Figure 1.8 [anonimizat]−Au collisions at different RHIC energies and Pb−Pb at LHC energy

Figure 1.9 The collision geometry

Figure 1.10 Number of partons as a function of collision parameter

Figure 1.11[anonimizat]+Au (AGS) and Pb+Pb (SPS)

Figure 1.12 Full stopping

Figure 1.13 Transparency

Figure 2.1 GSI

Figure 2.2 Accelerator facility

Figure 2.3: FAIR

Figure 3.1 Electronic and muonic configuration

Figure 3.2 CBM – electronic configuration

Figure 3.3 muonic configuration

Figure 3.4 The dipolar magnet of the detection system and the complex chart of its magnetic field

Figure 3.5 STS detector

Figure 3.6 RICH detector

Figure 3.8: Muon detector

Figure 3.9 Identification of particles with TRD detector

Figure 3.11 [anonimizat] 4.1 Evolution of a relativistic nuclear collision

Figure 4.2

Figure 4.3

Figure 4.4

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8

Figure 6.9

Figure 6.10

List of abbreviations

ALICE – A Large Ion Collider Experiment

ATLAS – A [anonimizat] – [anonimizat] – [anonimizat] – [anonimizat] für [anonimizat] – [anonimizat]parator

SIS – Super Ion Synchrotron

CBM – Condensed Baryonic Matter

MVD – Micro Vertex Detector

STS – Silicon Tracking System

TRD – Transition Radiation Detector

TOF – Time Of Flight

PSD – Projectile Spectator Detector

RICH – Ring Imaging Cerenkov Detector

MUCH – Muon Detection System

UrQMD – Ultra relativistic Quantum Molecular Dynamics

AMPT –

Introduction

Since 1948, when Freier discovered the heavy ion component in cosmic rays and founded this new branch of physics, relativistic nuclear physics is in continuous development. The first stage of this new subject is the cosmic rays phase, but the researchers found it very difficult to establish the fundamental characteristics of cosmic ray beams, one of the lack of experimental data. Starting with 1970, when the first accelerating system was made, the second stage of relativistic nuclear psychics, accelerators phase, begun. In the next 20 years after Freier discovered the heavy ion component in cosmic rays, remarkable scientific progresses and technological developments were made. “Relativistic nuclear physics is a connection between classical nuclear physics, particle psychics and cosmology” [1].

Multiple particle production is a quantity of interest in the majority of physical processes and phenomena which appear in relativistic nuclear collisions. Therefore, the first chapter takes into account the properties of variables that contain information about the dynamics of the collision. Knowing the fundamental characteristics of the relativistic nuclear collisions and the importance of the geometry collision, in the first chapter I will talk about: multiplicities and multiplicity distributions, cross section, number of participants and spectators, rapidity and pseudo rapidity, momentum distributions and angular distributions.

Scientific research has provided an increasingly comprehensive insight into the structure of matter and of the development of the universe. At the same time, the new insights generated many technical developments and applications. The bigger part of the insights attained we owe to experiments at accelerator facilities. Scientists from all over the world use the accelerated ions for experiments in various fields of research ranging from particle, nuclear and atomic physics via plasma physics and materials research up to biophysics and tumor therapy. The evolution of the universe also confronts us with many open questions. GSI physicists together with scientists from universities and research institutes, both in Germany and abroad, and also the future international accelerator center FAIR (Facility for Antiproton and Ion Research) for intense, high-energy beams of ions and antiprotons try to answer these fascinating questions. Therefore, the main subject of the second chapter is about GSI and FAIR.

The third chapter is about the CBM experiment (Compressed baryonic Matter) at FAIR, which is a fixed target experiment with the purpose of researching the behavior of nuclear matter in the region of high net-baryon densities and relatively low energies. The CBM detection system will receive beams from the SIS100 and SIS300 superconducting synchrotrons. This experiment’s purpose is to measure the multiplicities, spatial distributions and the flow of protons, pions, kaons, hyperons, hadronic resonant, mesons formed by quark-antiquark bound states (charkmonium, J/psi).

Analyzing the collective features of experimental data, high and ultra high energy nuclear collisions can be better described. The fourth chapter is a short presentation of the hydrodynamic modeling of relativistic nuclear collisions and also of the investigation methods for high energy nuclear matter properties. It is a fact that these models describe most of the phenomena and processes that occur inside this hot and dense matter. Using hydrodynamic modeling, some of the signals for a phase transition inside the nuclear matter can be found.

Quantum molecular dynamics models for high energy nuclear collisions brings us a wide range of information concerning the dynamics of the collision. The quantity and the quality of these information depends on the primary hypotheses, the considered energy domain, the collision geometry and of course it depends in the quality of the simulation environment. In order to obtain data for flow investigation in nucleus – nucleus and proton – nucleus collisions at the available energy from FAIR – GSI I used UrQMD and AMPT simulation codes from YAPT simulation bundle. The fifth chapter is a description of the used simulation environments.

CAPITOLUL 6 – rezultate

Chapter 1

The dynamics of relativistic nuclear collisions

Figure 1.1 Participants – spectators region [1]

The thermodynamic models for relativistic heavy ion collisions are based on the participants – spectators image (Figure 1). Therefore, the geometry of the collision, described by the collision parameter, b, and the asymmetry degree between the colliding nuclei (determined by the ratio between their mass numbers) , plays a very important role in describing the collision dynamics [1].

It is known that, in the center of mass frame, the spectator regions have almost the same velocity as the velocity of the incident nucleus, therefore the velocity of the nuclei inside the spectator region can be described by the Fermi movement of nucleons inside the nucleus [2]. In the laboratory frame, spectators and spectator regions can have different origins. Thereby, the ones with small energies and different emission angles have the origin in the target nucleus, while the ones with high energies, comparable with the nucleon energy of the incident nucleus, emitted forward with small deviations, have the origin in the incident nucleus. When talking about thermodynamic models, participants are important. It is very important to manage to highlight the cinematic separation between the two types of regions, participants and spectators.

The thermodynamic models used to characterize the dynamics of relativistic nuclear collisions are phenomenological models based on the “thermodynamic aspects” known form experimental data. Because of the significant energy transfer (energy transfer much higher than the binding energy per nucleon), in the participant region are observed high densities and temperatures for a very short amount of time. Therefore one can affirm that the majority of the particles detected in the final state are produced here.

Using the energy spectrum and momenta spectrum of several types of particles (pions and protons, at 90 degree angle, in the system of mass) the analysis of the participant region dynamics formed in the relativistic nuclear collisions can be done [1]. This is possible because at 90 degrees angle the contribution from participant region reaches its minimum. To lower the participant region contribution, same mass number nuclei are used.

Angular and multiplicity distributions may contain information about the thermodynamic behavior of hot and dense nuclear matter crated in the participant region. The achievement of the global thermodynamic equilibrium would determine the angular distribution of the particles generated in the participant region to be isotope, and the multiplicity distribution to be fully described by a Poisson distribution function.

Thermodynamic modeling of heavy ion collisions

To describe the dynamic of relativistic nuclear collisions, many thermodynamic models [3] were proposed, the most important being: “fireball model”, “firestreaks model”, “two fireballs model”, “modified thermal model”.

Fireball model

The initial fireball model [4] considered only processes specific to participant region. To describe the geometry of the collision, in the superposition region it is formed a cylinder and the participant nucleons from the incident nucleus transfer all their momenta to the mass system of the nucleons that belong to the fireball. The fireball moves forward with a velocity between the velocity of the target nucleus (in rest in the laboratory frame) and the velocity of the incident nucleus. It is assumed that in the center of mass frame, the fireball expands isotropic, with a Maxwell energy distribution.

Fireball model implies that the primary stage of the collision unfolds in a very short amount of time and in this stage the interaction is localized in the superposition region of the colliding nuclei. Subsequent, the gathered energy in the in the compression process due to the superposition of the nucleons and also the surface energy are dissipated. The dissipation of the energy and the emission of particles from the fireball determine interactions with the spectator region of the colliding nuclei.

All the thermodynamic models assume that the nucleons suffer multiple collisions, and the fireball “loses its memory”, having no information about the way in which it was formed. Thus, all the parts (cells) of the phase space have equal probability. All the particles obey the charge conservation, energy conservation and baryonic number conservation. The usage of a specific type of thermodynamic system (micro – canonic, canonic, macro – canonic) depends on the type of the experiment and the quantity of interest. One example of quantity of interest is the multiplicity distribution [5]. With any thermodynamic model [6], one can calculate the multiplicity of any type of particle.

The main deficiencies of the thermodynamic fireball model are based on the its inability in describing the “shoulder” observed in the protons momentum spectra and because it predicts the same temperature for all particles produced in the fireball – disapproving with experimental data [1]. It also provides, in the center of mass frame, an isotropic angular distribution of particles emitted from the fireball, which also disapproves with experimental data. For further corrections to this first thermodynamic model, scientists proposed more models who use the initial idea of the fireball model (same thermodynamic considerations), but the cinematic is different.

Firestreaks model

Firestreaks model is the first model proposed after the fireball model [7]. This model tries to explain the experimentally observed anisotropy of the angular distribution, suggesting a new collision geometry (Figure 2).

Figure1.2. Collision geometry for firestreaks model [1]

In this model, the colliding nuclei superposition is composed of continuous distribution of parallel tubes. A tube from the incident nucleus overlaps a tube from the target nucleus, and because of the interactions inside the tube, they form a “hot tube”. Nucleus – nucleus collision can be described now by a tube – tube collision and the thermodynamic equilibrium is formed inside each hot tube (is not global equilibrium anymore) [1]. It is taken in account the hypothesis that nucleus – nucleus collision at high energy is determined by deep inelastic scattering inside the superpositioning region of the colliding nuclei. Moreover, it is assumed that the tubes do not interact with each other on the transverse direction.

In order to explain the anisotropy of the experimentally observed angular distribution in the center of mass frame, firestreaks model takes in account the fact that in each tube the number of nucleons coming from the incident nucleus is different that the number of nucleons coming from the target nucleus, this being the reason why in the center of mass frame, an longitudinal movement is noticed. Even if in relation to each tube the particle emission is isotropic, the total particle emission shows maxims on the forward and backward direction [7].

Firestreaks model explains the experimentally observed anisotropy of angular distribution, but has difficulties in explaining the “shoulder” observed in the protons momentum spectra. It also supra estimates the physical quantities such as pion production and it predicts the same temperature for all particles produced in the fireball – disapproving with experimental data.

Two fireballs model

Previous thermodynamic models assumed that in a symmetric nucleus – nucleus collision the center of mass of the system is the same with the center of mass of the fireball, therefore the cross section of the emitted particles (including the cross section of the protons) should be identical. Experimental data suggest the presence of an asymmetry in the proton cross section. To explain this asymmetry, the two fireball model was introduced [8]. The relatively small number of participating nucleons led to the idea that a partial transparency of the colliding nuclei appears. Because the interaction mechanism is not only stopping, the super positioned parts of the colliding nuclei do not lose all their initial momenta (do not lose completely their “memory”), which leads to forming two fireballs. Particle emission is isotropic inside the two fireballs, but overall, in the mass center frame, the angular distribution is anisotropic.

Among the outcomes of the two fireballs model there is also the ratio between the secondary emitted particles multiplicity acquired in nucleus – nucleus collision and the secondary emitted particles multiplicity acquired in nucleon – nucleon, at the same energy. This model, as the firestreaks model, explains the angular distribution anisotropy, furthermore, it explains the proton cross section asymmetry in the center of mass frame. Likewise, as fireball model, it can’t explain the “shoulder” observed in the protons momentum spectra.

Rows on rows model

Rows on rows model [9] uses specific thermodynamic, internuclear cascade concepts and the geometry of collision used in the firestreaks model. In order to obtain the required spectra, this model is based on Glauber theory [10] with the following hypothesis: individual nucleons are moving in straight trajectories. The use of Glauber theory and of participant – spectator image of relativistic nuclear collisions leads to the idea that all the nucleons in the participating region interacts with each other. The assumption made is that only nucleons found on the same straight trajectory interact, therefore, it is introduce a new collision geometry. A row of nucleons found in a tube from the incident nucleus scatters only on the exact row of nucleons in a tube from the target nucleus that is placed on its straight trajectory [1].

Rows on rows model allows a better correlation between the theory and the experimental data and also shows the importance of the stopping length in describing the relativistic nuclear collisions.

Thermodynamic models are used to calculate physical quantities based on a well defined collision geometry (the collision geometry it is usually based on the participants – spectators image) and some mutual hypothesis [1]:

all hadrons are in thermal equilibrium

when hadronic density reaches a critical value, also called freezing density, all hard interactions stop

when the critical density is reached, specific equations for a non interacting gas can be used

baryonic resonances are introduced in order to describe pion and light nuclei production.

1.2 Multiplicity and multiplicity distributions

Multiplicity of different type of particles generated in relativistic nuclear collisions and the associated multiplicity distributions is one of the quantities of interest for the dynamics of relativistic nuclear collisions and also using multiplicity and multiplicity distributions it is possible to highlight “exotic” phenomena and phase transitions.

Multiplicity is defined as the number of same type of secondary particles produced in an well known event. The repartition of secondary particles produced in events that satisfy well known conditions is given by the multiplicity distribution. Usually, the multiplicity distribution reflects the collisions geometry and its associated moments reflects collisions dynamics [11]. This is the reason why multiplicity, multiplicity distribution and its associated moments are very important in studying the relativistic nuclear collisions, collisions in which the dynamics and the geometry are related [12].

Figure 1.3 The charged particle multiplicity density distributions of Au – Au collisions [13]

Multiplicity distribution can be defined in terms of probabilities theory:

If we transit to probability distributions, there is no loss of information concerning multiplicity [1]. In terms of probability theory, to multiplicity distribution can be assigned different phenomenological parameters, namely: moments and cumulates. Using this parameters leads to useful information concerning relativistic nuclear collision dynamics and also it disclose new phenomena in the nuclear matter formed in this collisions.

One of the moments of interest is the order I moment, known as mean multiplicity. Another useful moment is the order 0 moment. It represents the area below the curve and it is used for normalization. Among mean multiplicity, in studying the dynamics of relativistic nuclear collisions , there are modal multiplicity (gives the position of the maximum of the distribution) and median multiplicity (one value for odd numbers and 2 values for even numbers, it is chosen so that the area between the curve is equal in both, left and right, sides). Total multiplicity takes into consideration all charged and neutral particles from a given collision at a known energy. Total multiplicity is not very used in experimental data analysis because of major difficulties in detecting particles, especially the neutral ones.

Multiplicity distributions can be characterized with the aid of some parameters and form indicators. This parameters and form indicators are defined using different type of moments and cumulate [14]. Two of the most used parameters in describing the multiplicity distributions are β 1 , the asymmetry parameter (skewness) and β 2 ,the peaking parameter [1].

Experimental data analysis on negative pion and charged particles multiplicity, obtained in central and non central collision lead to the following conclusions [15]:

in central and non central collisions, for a target nucleus with a higher mass number the mean multiplicity is higher

in central and non central collisions, for a incident nucleus with a higher mass number the mean multiplicity is higher

in central collision, mean multiplicity is higher than in non central collisions

1.3 Cross section

In order to obtain information about the dynamics of relativistic nuclear collisions, an important quantity is cross section. The concept of cross section is correlated with the characterization of interaction processes between different nuclear systems with various properties. Generally, cross section is the interaction probability, its value depending on the nature of the colliding systems and the incident energy. This is the reason why the unit for cross section is related with the geometrical cross section of the interaction process between two spheres.

Cross section can also be considered as a coefficient specific to the interaction. Thereby, the cross section of the target, for an interaction produced by an incident nuclear system, with or without charge, is defined as the ratio between the probability of interaction for the considered target and the incident nuclear system fluency [1].

The definition of cross section is given by the following relation and it is valid only if P << 1.

Φ is the fluency and it represents the number of incident particles on a given area.

Total cross section, σt ,is defined as the probability of appearance of all particles produced in agreement with the conservation laws, in a known collision, at the available energy. This type of cross section increases slowly with the increase of energy for the colliding nuclear systems.

Figure 1.4 Inelastic pp cross section as a function of : the ALICE

measurements are compared with theoretical predictions and data from

other pp and p experiments [16]

Figure 1.5 Values of the pp and pp¯ total cross section as a [17]

Partial cross section offers us the number of a specific type of particles, produced at a given energy. Therefore, this type of cross section shows a dependency of particles type and the number of particles. Partial cross section has a maximum value near the threshold energy of the considered particle type.

Total cross section is given by the sum of partial cross sections [1]:

The production of a specific type of charged particle in the final state of the collision is described by charged cross section. In this particular case, the number of charged particles is a random value and the production of the charged particles in the final state is also a random event. Therefore, for small multiplicities, the charged cross section can be described by a Poisson probability distribution and for large multiplicities it can be described by a gauss probability distribution. If the number of charged particles is fixed in the final state and the collision energy varies, then the charged cross section grows with the energy until it reaches a critical value and slowly decreases.

To fully describe the interaction process it is important to know information about the cross section distribution in terms of the energy and momenta of any nuclear system (particle, nucleus) that exists after the interaction or the solid emission angle foe the considered nuclear system. This type of distribution is called differential cross sections.

Figure 1.6 Charm quark differential cross section per nucleon-nucleon

collision as a function of pt in p + Pb and Pb + Pb collisions [18].

Looking at the physical quantities from this point of view, a great number of dynamical characteristics of nuclear collisions are obtained using the differential cross sections. The most important are: angular distribution (in this case, the variable is the emission angle of the particle in the final state; the common notation for angular distribution are: rapidity distribution and pseudorapidity distribution), momentum distribution and energy distribution, also known as momentum spectra and energy spectra.

Figure 1.7 Stopping and transparency depending on energy [19]

The number of antibaryons at AGS is very small so the baryon distribution looks a lot like the proton distribution. The rapidity distribution of protons is narrow and centered around y=0. The energy available at CERN – SPS is converted into particles, therefore the form of the rapidity distribution is changed especially at y=0. This image suggest that at the available energy at CERN – SPS the nuclei are starting to become transparent (because the number of baryons in mid rapidity area is smaller).

Figure 1.8 Charged hadrons pseudo-rapidity distribution in Au−Au collisions

at different RHIC energies and Pb−Pb at LHC energy along with

comparison of different model results [20]

From this type of distributions we extract important information for describing the relativistic nuclear collision interaction mechanisms and also to establish the influence of the collision geometry on the collision dynamics. in a given collision, in order to obtain the experimental cross section, the following one has to know physical quantities: the number of interactions of the incident nucleus in the target and the number of incident nuclei on the target. The ration between this two quantities has to be multiplied with the cross section for nucleon-nucleon collision, at the same energy, cross section that is well known [21], so, in this way, the cross section of the considered nucleus-nucleus is known [22].

The experimental results obtain in this way to determine the cross section of relativistic nuclear collisions shows a series of dependencies of interest:

the dependency on the mass number of the target nucleus

the dependency on the mass number of the incident nucleus

the dependency on the collision centrality

The experimental results obtained in nucleus-nucleus collisions, at higher energies than 1 AGeV indicates some common dependencies [23]:

for central and non central collisions, for the same incident nucleus, the cross section is higher for higher mass numbers of the target nucleus

for peripheral collisions, for the same target nucleus, the cross section is higher for higher mass number of the incident nucleus

for central collisions, for the same target nucleus, the cross section is lower for higher mass number of the incident nucleus

for a given collision, the cross section is lower if the centrality of the collision is higher and this is better seen at light and symmetric systems

for a given collision, the cross section is higher for higher energy

The experimentally determined cross section in relativistic nuclear collisions is affected by several sources of error. Generally, those errors are related with the technical characteristics of the detection system and with the raw data analysis. The necessary corrections for the cross section vary from 2% to 4% for the first case and from 1% to 2% for the second.

1.4 Participants and spectators

Figure 1.9 The collision geometry [1]

For high energies, energies where pNN is the nucleon momentum from the incident nucleus and m is the resting mass of the free nucleon. Taking into account that the Broglie wavelength smaller than the medium internuclear distance in the nucleus and the mean free path is smaller the radius of the considered nucleus, in the center of mass frame, the two nuclei can be considered „clouds” of nucleons and their collision determines sequential nucleon-nucleon collisions in the superposition region. Thus, two different region, with different dynamical characteristics are formed [24].

Figure 1.10 Number of partons as a function of collision parameter [59]

The overlapping region of the two colliding nuclei is also known as the participating region. Many of the interesting physical phenomena occur in the participant region. The spectator region is formed because of the parts of the nuclei that are not overlapped.

The number of participating protons is given by the following relation:

Where:

– the total multiplicity of charged particles

– the negative pions multiplicity

– the number of participant fragments of the nucleus

– the number of spectator fragments form the target

A better way to calculate the number of participating protons is with the following relation:

Where:

QN – number of participating nucleons

Q – number of participating protons

Ap – mass number of incident nucleus

AT -mass number of target nucleus

Zp – charge of incident nucleus

ZT – charge of target nucleus

This geometrical image of high energy nuclear collisions is known as participants – spectator’s image. The collision geometry implies both collision parameter and the symmetry degree of the two colliding nuclei. According to the collision geometry, the size of the overlapped region of the two colliding nuclei is established and it can contain different numbers of nucleons. Generally, the participant nucleons are defined as the nucleons outside of the fragmentation Fermi spheres of the incident and target nuclei [25].

The studied made on the participating protons and nucleons are correlated with the multiplicity in relativistic nuclear collisions [26] and they can also exhibit important information about some parameters of interest in describing the particle source and its evolution and dynamics [27].

It is expected that the behavior of the participant and spectator region to reflect collision geometry. There are specific interaction mechanisms for each region, this being the reason why we see different behaviors in central and peripheral collisions. Also, an important factor which can influence, after it was created, the evolution of the participant region is the number of participants. As a conclusion, this study can be important for obtaining the interest quantities in order to characterize the system from a dynamical point of view.

In the participating region, medium multiplicities are a lot higher than those from the spectator region and for some collisions, especially for those with a raised asymmetry degree, the multiplicity exceeds the mean multiplicity.

The growth of the absorption process in the in spectator region because of its spatial growth is suggested by this.

Figure 1.11 Rapidity spectra of protons for AGS energies

(upper raw of panel) and net-protons SPS energies (lower raw of panels) from central collisions of Au+Au (AGS) and Pb+Pb (SPS) [28]

Depending on the incident energy of the collisions, there are two extreme possible scenarios on how the system formed in the collision will evolve: complete stopping and full transparency.

1.4.1 Complete stopping (Lamdau model)

For < 10 GeV, the two nuclei are Lotentz contracted with the thickness 2R/γ. In this situation the nuclei will stop each other, generating in the center of mass frame, a dense fireball [69]. In this region nuclear matter can reach energy density a few GeV/fm3 and baryonic density 10 times higher than the density of normal nuclear matter. It is considered that all the available energy from the center of mass frame and the total baryonic number is being balanced in all the volume of the fireball.

Figure 1.12 Complete stopping [57]

1.4.2 Full transparency (Bjorken model)

If > 100 GeV, then the two colliding nuclei instead of stopping, pass through each other and the effects of nuclear transparency are seen.

Based on the following assumptions, in 1983 Bjorken suggested the idea of transparent ultra relativistic nuclear collisions:

at mid rapidity, rapidity densities does not depend on rapidity (the tray seen in the rapidity distribution)

if the collision is transparent, the net baryons shift to higher rapidities

Because of available energy in the collision is very high, the two nuclei are Lorentz contracted and the time they need in order to pass through each other is smaller than the time required for a particle to form. Therefore new particles are created after the nuclei pass through each other, leading to transparency and creating a tray at mid rapidity in the rapidity distribution.

This scenario presents a high interest because the early Universe was characterized by high energy densities and low baryonic densities, exactly like a transparent collision.

Figure 1.13 Transparency [57]

Chapter 2

Accelerator systems at FAIR and GSI

2.1 GSI Helmholtzzentrum für Schwerionenforschung

In order to each a better understanding of the structure of the world that surrounds and its behavior, GSI Helmholtzzentrum für Schwerionenforschung scientific research was created. Currently, GSI employs about 1300 researches and also more than 1000 researchers from universities and the facility is used by other research institutes around the world [29].

2.1.1 History

Figure 2.1 GSI [2]

Under the name Gesellschaft für Schwerionenforschung mbH (GSI), the GSI Helmholtz Center for Heavy Ion Research was founded in 1969 and then renamed in 2008 [30].

Since the beginning of the 1960s Professor Dr. Christoph Schmelzer from the University of Heidelberg worked on a concept of a linear accelerator for heavy ions, UNILAC, for projectiles of all elements up to uranium. The ministry agreed on funding the concept, the instrumentation and the location of the new facility in 1969. In 1975 the first heavy ions were accelerated by UNILAC and the experiments quickly started their operation. Soon a desire for ion beams with significantly higher energies arose. On the one hand these high energies were essential for a tumor therapy; on the other hand they offered new perspectives for the physics of nuclear matter, its equation of state and possible phase transitions.

In 1974 a collaboration with the research facility LBNL in Berkeley, California, was established where GSI scientists conducted similar experiments at the BEVALAC accelerator. After this collaboration, GSI at the beginning of the 1980s to build an additional ring accelerator, the heavy ion synchrotron SIS-18. Additionally a fragment separator and the storage ring ESR for heavy ions were constructed [30]. To probe quark gluon plasma, GSI initiated the heavy ion program at the European nuclear research facility CERN. They aided in the construction of a heavy ion injector offering a unique experimental program till this day. GSI played a leading part in the ALICE experiment at the new CERN accelerator LHC from the beginning.

But also in Darmstadt the developments continue: Soon the new international accelerator facility FAIR will be build next to GSI in cooperation with 16 partner countries [30]. FAIR will deliver beams of anti-protons and ions with so far unparalleled intensities. Scientists from all over the world expect new insights into the building blocks of matter and the evolution of the universe, from the big bang till today.

2.1.2 Research

Scientific research has provided an increasingly comprehensive insight into the structure of matter and of the development of the universe. A key instrument for research at GSI is such an accelerator facility. In a combination of linear accelerator and synchrotron, it is possible to make experiments that provide new insights and findings about the structure of the investigated systems and the powers holding them together. The main focus of the GSI research program is the basic investigation of the field of nuclear physics and atomic physics. In parallel, application-oriented research activities in materials research, plasma physics, biophysics and nuclear medicine were developed. To supply state-of-the-art facilities for science, the accelerator facilities and the experiment facilities are permanently being enhanced and improved [31].

2.1.3 Accelerator facility

Figure 2.2 Accelerator facility [32]

In order to provide the heavy ion experiments at GSI, six main devices are indispensable [32]:

1. The ion sources:

By stripping electrons off the shell of the atom are gained the positively charged ions used at GSI. GSI is able to produce ions of many different kinds of elements, more than any other laboratory in the world. Depending on the element different types of ion sources are used [33].

2. The linear accelerator UNILAC

The linear accelerator UNILAC (Universal Linear Accelerator) is the starting point of acceleration of ions. On a length of 120 meters ions of all kinds can be accelerated up to 20 percent speed of light. The ions are used for experiments in experimental hall, e. g. to create new heavy elements, or injected into the ring accelerator SIS18 for further acceleration [34].

3. Ring accelerator SIS18

Ions coming from the linear accelerator UNILAC are injected into the ring accelerator SIS18 (Schwerionensynchrotron 18). Here they can be accelerated to even higher speed. They circulate in the ring and pass the acceleration structures. Their high voltage accelerates them on every circulation. Magnets keep the ions on their circular path. Once they have reached the desired speed, they are transfered to the experiments to hit a material sample, or directed into the experimental storage ring ESR for storage and further analysis. With the beam coming from the SIS18 up to four experiments can be supplied parallely—from biophysics via exotic matter in planets and neutron stars up to the production of rare nuclei that are formed in supernovae [35].

4. Storage Ring ESR

The experimental storage ring ESR has a circumference of 108 meters. Ions accelerated before by the linear accelerator UNILAC and the ring accelerator SIS18 can circulate in the ESR at high speeds performing several millions of circulations per second. They are stored and used for experiments. Cooling systems allow high precision experiments. By using the fragment separator FRS also new particles like new isotopes can be stored and measured in the ESR [36].

5. Fragment Separator FRS

The fragment separator FRS allows experiments with new particles, especially with new and extremely rare isotopes. They are created by certain reactions of the ions previously accelerated in the ring accelerator SIS18. With the FRS the interesting isotopes can be separated from other reaction products. They are then directed to the storage ring ESR or to further experiments [37].

6. Main control room

The accelerator system at GSI consists of 2,500 individual electrically controllable components such as magnets, vacuum pumps and measuring instruments. It would simply not be possible for the engineers at the facility to individually adjust all of these components by hand. That’s why the signals from all of the instruments are brought together in the main control room. All of the systems are controlled from here — in other words, everything from the ion sources, the linear accelerator UNILAC and the ring accelerator SIS to the experimental storage ring (ESR) and the magnets, strippers and electrodes that guide the ion beam to the correct experiment [38].

2.2 FAIR – facility for antiproton and ion research

FAIR, Facility for Antiproton and Ion Research is a new international accelerator facility for the research with antiprotons and ions. It will be built in cooperation of an international community of countries and scientists. The facility will be financed by a joint international effort of so far ten member states. The Federal Republic of Germany together with the State of Hesse is the major contributor to the construction, the current nine international partners – Finland, France, India, Poland, Romania, Russia, Slovenia, Sweden and the United Kingdom – bear ca. 30% of the construction cost. FAIR will be a host laboratory for basic research for about 3000 scientists from about 50 countries [39].

2.2.1 Accelerators

FAIR will be an international accelerator facility of the next generation. The techniques and developments will be built on the existing GSI facility. The GSI facility – once upgraded and together with a new proton linear accelerator – will serve as pre-accelerator and injector for the new complex [40].

Latest technological concepts will enable the construction of a state-of-the-art, multipurpose accelerator facility. Its core, a double-ring accelerator (SIS100 heavy ion synchrotron) with a circumference of 1100 meters, will be associated with a complex system of cooler and storage rings and experimental setups. The synchrotron will deliver ion beams of unprecedented intensities and energies. Thus also intensive secondary beams can be produced, providing antiprotons and exotic nuclei for groundbreaking experiments [40].

Figure 2.3: FAIR [40]

The system of storage and cooler rings allows to drastically improving the quality – e. g. energy spread and emittance – of the secondary beams in order to use them for high precision experiments. Moreover, in connection with the SIS100 synchrotron an efficient parallel operation of all four scientific programs can be realized.

The whole project is characterized by many technological innovations. This justifies expectations for brilliant beam properties with [40]:

highest beam intensities

brilliant beam quality

highest beam energies

highest beam power

parallel operation

Fundamental questions of the evolution of the universe, the structure of matter and its building blocks will be approached with the physics at FAIR. Over the past century, scientists have built up a deep understanding of the subatomic constituents of matter in the Universe and the fundamental forces binding them. More recently, they have developed compelling theories of how those building blocks came into being [41]. Nevertheless, there are still significant gaps in our knowledge of the nature and evolution of matter on both a cosmic and microscopic scale and there are many questions to explore.

2.2.2 Applications of ion beam research

Research with heavy ions has led to diverse applications and technological innovations in the past. The most spectacular example is the development of a new tumor therapy employing precision ion beams at GSI. This therapy is is used for example in the Heidelberg Ion-Beam Therapy Center (HIT) since early 2010 [42].

As in the past, the proposed facility, too, will push forward new developments, some of which will eventually lead to specific applications. At present one can discern several areas for such applications [43]:

New probes and techniques for Solid State Physics and Materials Research

Radiobiological risk assessments for manned space missions

Test equipment for satellites or spacecraft components

Studies on the creation of fusion plasmas through inertial confinement

2.2.3 Experiment Program

About 3000 scientists from around the world will carry out experiments to understand the fundamental structure of matter, to explore exotic forms of it and to find final answers of how the universe evolved from its primordial state into what we see today.

FAIR allows carrying out several physics programs in parallel, covering four major fields [44]:

1. APPA Physics – Atomic, Plasma Physics and Applications

BIOMAT – Biology and Material Science

FLAIR – Facility for Low-Energy Antiproton and Heavy Ion Research

HEDgeHOB- High Energy Density Matter generated by Heavy Ion Beams

SPARC – Stored Particles Atomic Research Collaboration

WDM- Warm Dense Matter collaboration

APPA R&D

2. CBM – Compressed Baryonic Matter

3. NUSTAR Physics – Nuclear Structure, Astrophysics and Reactions

DESPEC/HISPEC- Decay Spectroscopy/High-Resolution Spectroscopy

ELISe- Electron-Ion Scattering in a Storage Ring

EXL – Exotic nuclei studied in light-ion induced reactions at the NESR storage ring experiment

ILIMA – Isomeric Beams, Lifetimes and Masses

LaSpec – Laser Spectroscopy

MATS – Precision Measurements of very short-lived nuclei with Advanced Trapping System

R3B- Reactions with Relativistic Radioactive Beams

SuperFRS – Super Fragment Separator project

4. PANDA – Antiproton Annihilation at Darmstadt

Chapter 3

CBM detection system

3.1 The CBM experiment

The CBM experiment (Compressed baryonic Matter) at FAIR (Facility for Antiproton and Ion Research) is a fixed target experiment with the purpose of researching the behavior of nuclear matter in the region of high net-baryon densities and relatively low energies. The CBM detection system will receive beams from the SIS100 and SIS300 superconducting synchrotrons. In order to detect and identify some rare particles, created in the early phase of the fireball evolution, it is designed to have interaction rates of up to 107 Hz [50].

This experiment’s purpose is to measure the multiplicities, spatial distributions and the flow of protons, peons, kaons, hyperons, hadronic resonant, mesons formed by quark-antiquark bound states (charkmonium, J/psi). The great technical challenge of the experiment so far has been identifying both the hadrons and the leptons, separating the rare cases, all at interaction rates of approximately 10^7 Hz, the particle multiplicities reaching 1000 per event. At those interaction rates the measurements cannot be performed with slow detectors such as TPC (Time Projection Chamber), but instead need extremely fast detectors. More so the CBM experiment needs a very fast trigger and acquisition system. [49]

The CBM detector will have both an electronic detection system and a muonic one. This proximity combines the advantages of the two methods and ensures trustworthy results, while in the end the two sets of data should correspond, even if they were taken separately.

Figure 3.1 Electronic (left) and muonic (right) configuration [45, 46]

3.2 Electronic and muonic configuration

The CBM detector system has an acceptance of 2 π for azimuth and from 2.5 to 25 degrees for the polar angle in order to meet the requirements. In the electron configuration the following detectors are used: MVD (Micro-vertex Detector), STS (Silicon Tracking System), both placed in the middle of a 1T superconducting magnet, RICH (Ring Imaging Cerenkov Detector), TRD (Transition Radiation Detector), TOF (Resistive Plate Chamber for time-of-flight measurements), ECAL (Electromagnetic Calorimeter) and PSD (Projectile Spectator Detector) as hadronic calorimeter. In the muon configuration the RICH detector will be replaced by MUCH (Muon Detection System) and the ECAL will be removed.

Figure 3.2 CBM – electronic configuration [52]

Figure 3.3 muonic configuration [52]

Dipolar magnet: the CBM detection system will use a superconducting magnet with a large aperture, while the coils (each with 1749 turns, cooled with liquid helium) will provide a magnetic field with a total bending power of 1Tm. The total weight of the magnet will be 160 tons. The MVD and STS detectors will be placed inside it.

Figure 3.4 The dipolar magnet (left) of the detection system and the complex chart (right) of its magnetic field [48]

Micro Vertex Detector (MVD): the MVD will be made from Monolithic Active Pixel Sensors (MAPS), with pixel sizes of 1818 micrometers and 2040 micrometers. Depending on pixel sizes the resolution of the hit position varies from 3.5 to 6 micrometers. The detector will have 3 parts positioned at 5, 10 and 15 cm away from the target contained in a vacuum box [49]. Time resolution of the sensor is expected to be less than 30 microseconds. The MIMOSA-26 chip is an option, having already been tested, with most of the requirements met.

Silicon Tracking System (STS): placed behind the MVD, also inside the dipole magnet is designed for the reconstruction of the trajectories and momentum determination of the charged particles. It will be built out of 8 tracking layers made from silicon sensors with double-sided micro-strips, placed from 30 to 100 cm away from the target. The electronic part is placed outside the active part of the STS, the sensors being connected to the chip via cables as short as possible [54].

Figure 3.5 STS detector [53]

Ring Imaging Cerenkov Detector (Rich): when the CBM detector will operate in the electron configuration this detector will follow the STS. It will be used to identify and suppress peons in the momentum range below 10GeV/c [45]. The gas radiator is 1.7 meters long and is made of CO2, with the Cerenkov radiation threshold for pions of 4.65GeV/c. Gas is used because the particles have very high beta, and by modifying the pressure of the gas different thresholds can be reached, corresponding to different types of particles. The Cerenkov radiation will be reflected by mirrors made of 72 tiles with a curvature radius of 3 meters and a reflecting coating made from Al+MgF2. The photons will be reflected on a photo-detector made from Multi-Andone Photo Multiplier Tubes (MAPMT)[46]. This is made of a particle interaction medium where Cerenkov radiation will appear and a photon detector. The number of photons detected:

Where L is the length of the radiator.

Figure 3.6 RICH detector [45]

Measuring the angle and the momentum, we can determine the particles mass:

Muon Chamber System (MUCH): when the CBM detector will be operating in muonic configuration the STS detector will be followed by the MUCH detector. It’s main purpose is to detect muons from J/psi particle disintegration. MUCH will provide information about the particles trajectories and will identify the muons depending on their momenta [46].

Figure 3.7 MUCH detector (left), its efficiency as a function of hit rate (middle) [48]

Given that the muons interact just by ionizing the medium they pass through, the distances covered are great, so the MUCH detector comes after a filter which stops all the other particles. Once the muons are the only ones left, with a magnetic field and a position sensor, the momentum and trajectory of the muons is calculated.

Figure 3.8: Muon detector

Transition Radiation Detector (TRD): the TRD will be used for identifying electrons and pions with momentum greater than 1 GeV/c [1]. Va fi alcatuit din trei detectori de radiatie de tranzitie, cu o rezolutie de 300 – 500 micrometri de-a latul si de 3-30 milimetri de-a lungul detectorului. Factorul de supresie a pionilor va fi mai mare decat 100, iar eficienta identificarii electronilor va fi peste 90%. In setup-ul in care jetul vine de la SIS100, detectorul TRD va fi folosit doar pentru a reconstrui traiectoria particulelor intre detectorii STS si TOF.

TRD-ul este facut din mai multe foite cu Z cat mai mic deoarece sectiunea eficace a fotoabsorbtiei depinde de Z^5, iar cu cat Z-ul materialului este mai mare, cu atat fotonilor le este mai greu sa iasa din radiator. Aceasta radiatie de tranzitie este apoi detectata. Radiatia de tranzitie este importnta dar in cazul particulelor ultra rekativiste, de obicei pentru identificarea electronului avem devoie de o energie mai mare de 1 GeV, a pionului mai mare de 800 de GeV, iar a kaonului mai mare de 2000 GeV

Figure 3.9 Identification of particles with TRD detector

Time Of Floght wall (TOF): pentru identificare hadronilor si pentru masuratorile de timp de zbor va fi folosit us sir de Timing Multi-gap Resistive Plate Chambers [45], sir care va acoperi o suprafata de 120 de metri patrati. Rezolutia temporala dorita este de 80 de picosecunde [46].

Ideea de baza a acestui detector este de a masura diferenta de timp de zbor dintre doi detectori cu rezolutie temporala foarte buna.

Figure 3.10 Time of flight detector

Figure 3.11 Parallel plate chamber, used at TOF detector

Amestecul de gaze: gaze care sa absoarba fotonii ca ei sa nu mai declanseze avalanse secundare in alte regiuni departe de ionizarea primara. O particula care traverseaza gazul interactioneaza cu acesta si creaza pereche electron – ion. Perderea de energie pe unitatea de parcurs in gaz este data de foermula Bete-Bloch. In acest proces, electronii sunt mai importanti deoarece acestia au mobiliate mult mai mare decat ionii si ajung mult mai repede la anod, dand semnal in detector.

Calorimetrele detectorului CBM: calorimetrul electromagnetic (ECAL) va fi folosit pentru a masura fotonii si mezonii neutri. Projectile Specatator Detector (PDS) va face masuratori de centralitate si plan de ractie. Este facut pentru a determina numarul de nuceoni din proiectil care nu au interactionat intr-o ciocnire nucleu-nucleu. Ambele calorimetre sunt facute din straturi de plumb si scintilator. ECAL este un calorimetru compact, rapid, cu o rezolutie energetica foarte buna.

Chapter 4

Hydrodynamic modeling of the relativistic nuclear

collisions dynamics

Analyzing the collective features (collectivity is a common feature of the particles emitted in a collision) of experimental data, high and ultra high energy nuclear collisions can be better described. Maybe the most studied common feature is collective flow. It describes the movement of a high number of particles emitted in the same direction, with the same speed.

In 1953, Lamdau came with the idea that there is a correlation between collective behavior of the nuclear system and its fundamental properties, and in order to fully describe the relativistic nuclear collisions, he proposed the first hydrodynamic model. Lamdau assumed in his model that in the initial state of the collision, the thermodynamic equilibrium of the system is local and instantaneous (assumption that is made in all hydrodynamic models), and that the created particles strongly interact with each other. He also assumed that the system expands in the beam axis direction and that the particle emission can be described by a fluid flow, which can be described by Navier – Stokes equations and introduced a state equation to link together pressure with density.

Hydrodynamic model for high energy hadronic collisions correctly describes particles multiplicity, can explain angular distributions and regarding transversal momenta of particles produced in the collision gives the same values as experimental results. The “blast wave” concept was also introduced by this model. It is considered that the particles inside the blast wave were emitted with a common speed in the same direction, this being seen in the angular distribution.

Together with intra nuclear cascade model and many other models based on Boltzmann equation or Vlasov equation, hydrodynamic models are included in transport models category.

In order to describe the macroscopic properties of the nuclear matter, some collective features must be defined:

longitudinal flow describes the collective movement of the particles in the initial direction given by the incident beam

radial flow describes the collective movement of the particles emitted at the same speed, in all directions

transversal flow describes the collective movement of the particles for which the speed front independent of azimuthal angle

side splash is related with the orientation of the vector associated with the collision parameter, b, which defines a specific azimuthal direction. A particularity of side splash is elliptic flow, which describes particles emitted with a “back to back” symmetry [56].

All types of flow are correlated and represent different parts of a global image [57].

4.1 Temporal evolution of flow

Using hydrodynamic models to describe the collision between two heavy ions also introduce the concept of reaction plane. The reaction plane is defined by the spatial orientation of the two colliding nuclei and the beam axis, the collision parameter, b, is located in it [1].

In the initial state of the collision (open space), the surface nucleons will reflect direct nucleon – nucleon interaction (Lotentz force type behavior), they will be deviated outward and will determine a particle emission growth in the reaction plane.

When the superposition of the two nuclei is reached, the interaction properties cannot be considered same as in open space. Depending on the collision energy, we can describe the processes that take place in this region (quark gluon plasma is formed or not). Particles which can bring useful information about the global properties of the environment are created in this region. It is also very important to see what happens with the spectator nucleons because they can bring useful information about the behavior of the participating region. Almost all hydrodynamic models assume that spectator nucleons travel along the beam axis because they are influenced only by the two mother nuclei field.

When the maximum compressibility and temperature is reached and the system expands, process that determines a drop in the nuclear density, energy density and temperature. The most important role in describing the way it expands is played by the collision geometry (symmetry degree between the mass numbers of the colliding nuclei and collision parameter, b). Usually, for a central collision of two symmetric nuclei, the expansion is expected to be azimuthal, but in other conditions, it is very difficult to assume a type of symmetry of the expansion. It is expected the expansion to occur in the direction where the gradient of nuclear density, energy density and temperature is highest [58].

Depending on the expansion speed, the hot nuclear matter form the center of the collision (participating region) can interact with the cold spectator region trough elastic (scattering) and inelastic (absorption of particles in spectator region) collisions, this leading to the modification of azimuthal angular distribution. The expansion speed is determined by different parameters of the system and it implies a timescale that is comparable with the timescale given by the kinetic energy of the incident beam:

Where:

Rp is the radius of the incident nucleus

Rt is the radius of the target nucleus

vbeam is the beam speed

is Lorentz contraction factor

When there are no interactions and the system reached freeze-out phase, collective features disappear. Because the baryonic density is small enough, at this point the mean free path is longer than the systems dimensions and the interaction between particles is made only trough elastic collisions.

Figure 4.1 Evolution of a relativistic nuclear collision [60]

An important feature of the observables based on the collective flow is that unlike many hadronic observables (including particle ratios) do not lose their initial memory because the flow is defined taking into account the whole history of the collision [61].

Because nuclear matter flow is present on all energy domains specific for high and ultra high nuclear physics (different temperatures and densities if the matter) [61], many timescales are used in order to correctly evaluate nuclear matter flow phenomena and phase transitions:

time in which the two nuclei pass through each other

time in which the equilibrium is established in the superposition of the two nuclei is reached

expansion time.

As we can see, only the time in which the two nuclei pass through each other does not depend on the properties of the nuclear matter which was formed in the collision. It depends only on the incident beam energy and the dimensions of the system. The other two timescales depend on the properties of the nuclear matter which was formed in the collision [62].

4.2 Types of hydrodynamic models

When talking about the models used in order to study the dynamics of relativistic nuclear collisions, it is very important that the fundamental hypotheses to be in agreement with the experiment. Many of the models that were discussed so far use the thermodynamic equilibrium hypothesis and, of course, adequate timescales. Because in most of the experiments the conditions are difficult to fulfill, applying the statistic- thermodynamic concepts is very difficult, probably impossible, in most of the experiments, so one of the problems of interest is the collision time and its associated timescales. This problem was partially solved when Lamdau introduced the first hydrodynamic model of high energy nuclear collisions in 1953.

In order to have a better understanding of nucleon – nucleon and proton – nucleon intermediate and high energy collisions, different hydrodynamic models were proposed among time. One of the classifications that can be made is depending on the way the hydrodynamic equations were obtained [1] and in both situations it is assumed that the local equilibrium is reached instantaneously in order to fulfill the hydrodynamic conditions:

models which use the Boltzmann equation in order to obtain the hydrodynamic equations

models which use the time dependent Hartee – Fock theory in order to obtain the hydrodynamic equations. Even if hydrodynamic models that are based on time dependent Hartree – Fock theory imply a considerably more difficult calculations, using the probability density function from quantum mechanics it allows the assumption of a continuous nuclear medium.

Hydrodynamic equations obtained with both of the models presented above together with the equation of state gives us information about the considered nuclear system. Usually, the equation of state is based on the dependency of the binding energy per nucleon on the system density and entropy [1]. In order to fully describe the experimental data, the model must also consider nuclear matter viscosity and its thermal conductivity.

Hydrodynamic description of high energy nuclear collisions implies instantaneous local thermal equilibrium, this being possible only if there are enough collisions between the particles (in this way thermal equilibrium is reached). As a conclusion, hydrodynamic models have the best efficiency when there is a large number of participating nucleons [64].

4.3 Global analysis

Using hydrodynamic models, global analysis was introduced to fully describe the dynamics of high energy nuclear collisions. For each independent event, trough global analysis are introduced quantities that describe the mean movement of the particles in the final state [63]. Taking into account all the particles emitted in one event, global quantities can be determined calculating the global variables of the considered event. These global variables are used to build tensors which later on will be diagonalised and the physical quantities of interest are exactly these diagonal components of the tensors. In order to study the dynamics of the collision, many types of tensors were proposed [65].

Flow tensor:

Where:

i, j are the directions x, y, z

n is the track number

w(n) is the weight of the considered particle or fragment.

In the momentum space, the components of the flow tensor form a rotation ellipsoid whose axis are determined by the eigenvalues of the tensor. Some global quantities such as flow ratio (the ratio between the long axis and the short axis of the ellipsoid) and flow angle (the angle between the long axis of the ellipsoid and the incident nucleus direction) can be defined in this way. It was noticed an growth of the flow ratio with the growth of the collision parameter, while in the same conditions, the flow angle decreases.

The most likely initial flow direction of the nuclear matter formed in the overlapping region of the two nuclei can be determined using the thrust tensor [66]:

Where is the direction versor.

The direction of the versor for which this relation reaches a maximum is the most probable flow direction of the hot and dense nuclear matter formed in the overlapping region of the colliding nuclei. Thrust angle distributions are different for different collision parameters [67].

Using the spericity tensor two important quantities can be determined:

sphericity :

Where:

are the eigenvalues of the spericity tensor.

S can take values from 0 (when two jets are produced in the hot and dense nuclear matter) to 1 (when the emission is isotropic)

flatness:

As a conclusion, the flow distribution can bring useful information about the dynamics of relativistic nuclear collisions.

4.4 Event plane method

Am scris pe foi, trebuie sa completez aici

Chapter 5

Simulation environments for relativistic nuclear collisions

5.1 Ultra relativistic Quantum Molecular Dynamics

One of the microscopic models with the purpose of describing the dynamics of high energy nuclear collisions is the molecular dynamics model. This model blends together the classical propagation of hadrons with some quantum effects. Because it is very difficult to build a research facility, the need to predict what will happen in the experiment is very important. A major trend within the pale of molecular dynamics models is to include computing codes that allow the obtaining of abundant information.

One of the most important computing code is UrQMD (Ultra relativistic Quantum Molecular Dynamics) [68]. The most common hadron – hadron collisions are: , this being only 50% of all hadron – hadron collisions that can occur. UrQMD takes into account 120 hadron – hadron interactions, describing only 90% of the collisions that take place in high energy nuclear collisions. In order to describe 99% of the interactions it is necessary thousands of combinations of hadron – hadron interactions, but because of the small amount of knowledge we have on the cross section of these processes, they are not taken into account.

Modelele de dinamică moleculară cuantică pentru energii relatativiste și ultrarelativiste – ca modelel microscopice de transport – folosesc propagarea covariantă a tuturor hadronilor pe traiectorii clasice în combinație cu împrăștieri binare stocastice, formarea “corzilor” de culoare și dezintegrarea rezonanțelor. Codul de calcul asociat este o soluție Monte Carlo la un set larg de de ecuații integro-diferențiale parțial cuplate pentru evoluțiile în timp a diferitelor densități în spațiul fazelor, f i (x,p), ale particulelor prezente la ciocniri

Toate particulele care sunt produse în ciocniri hadron-hadron pot interacționa ulterior unele cu altele. În codurile de calcul asociate sunt implementate diferitele canale de dezintegrare ale nucleonilor, rezonanțele nucleonice (în principal, rezonanța  ) și modurile lor de dezintegrare, hiperonii, precum și alte rezonanțe cu mase de repaus până la 2.25 GeV/c 2 . Sunt incluși, de asemenea, mezonii și modurile lor de dezintegrare. La energii mai mari se ține seama de proprietatea de universalitate a hadronilor. Se introduce un model de “corzi” (“string”-uri) pentru studierea dezintegrării stărilor intermediare .

La folosirea codurilor de simulare secțiunile eficace totale sunt interpretate geoimetric. O ciocnire între doi hadroni se realizează dacă distanța minimă dintre cele două particule, d, este în următoarea relație de legătură cu secțiunea eficace totală pentru interacția considerată,  tot , anume: d   tot . În codurile de simulare UrQMD secțiunea efucace totală,  tot , depinde de izospinii particulelor care senciocnesc, de aromele lor și de energia disponibilă în sistemul centrului de masă. Secțiunile eficace parțiale pot fi utilizate pentru a calcula ponderile relative pentru diferite canale de reacție care se pot deschide în ciocnirea considerată, la o anumită energie. În aceste calcule trebuie avut în vedere că numai o mică parte din toate secțiunile eficace hadronice a fost măsurată în experimente.

Datorită codurilor de simulare asociate modelele de acest tip se apropie cel mai mult de ceea ce se invoca la începutul acestei părți a cursului, anume o teoreie de mai multe corpuri, cuantică, relativistă, cu luarea în considerare a gradelor de liberatate subnucelonice. De aceea, în prezent, acest cod de simulare este unul dintre cele mai folosite pentru studierea dinamicii ciocirilor nucleare relativiste și ultrarelativiste.

Bibliography

1. Jipa FNR, capitolul 2

2. 111, 62, 64, 67

3. 2,4,6,13,14,16,112,113

4. 37, 38

5. 4,118,119

6. 13-16,120,121

7. 122, 140

8. 125,126

9. 129

10. 130

11. 4,5,20,21

12. 1-5,20-25

13.https://www.researchgate.net/figure/265052090_fig24_The-charged-particle-multiplicity-density-distributions-of-AuAu-collisions-at-three

14. 20,21,23-29

15. 3-5,17-19,32-34

16. Measurement of reference cross sections in pp and Pb-Pb collisions at the LHC in van der Meer scans with the ALICE detector – ALICE Collaboration (Gagliardi, Martino for the collaboration) AIP Conf.Proc. 1422 (2012) 110-116 arXiv:1109.5369 [hep-ex]

17. Measurement of the proton-proton total, elastic, inelastic and diffractive cross sections at 2, 7, 8 and 57 TeV – Cartiglia, Nicolò arXiv:1305.6131 [hep-ex]

18. Prospects for Open Heavy Flavor Measurements in Heavy Ion and p + A Collisions in a Fixed-Target Experiment at the LHC , Article · Oct 2015 · Advances in High Energy Physics

19. Brazilian Journal of Physics, Braz. J. Phys. vol.37 no.2c São Paulo June 2007, From RHIC to LHC: a relativistic diffusion approach

20. Charged Hadron Multiplicity Distribution at Relativistic Heavy Ion Colliders – Kumar, Ashwini et al. Adv.High Energy Phys. 2013 (2013) 352180 arXiv:1306.4185 [hep-ph]

21. 53

22. 3-5,54,55

23. 1-5,8-11,54-56

24. 1,4,20,45,60

25. 61,62

26. 45,60-64

27. 1,3-5,17,22,45,48,60-64

28.  Baryon stopping signal for mixed phase formation in HIC – Ivanov, Yu. B. J.Phys.Conf.Ser. 668 (2016) no.1, 012061 arXiv:1509.06944 [nucl-th]

29. https://www.gsi.de/en/about_us.htm

30. https://www.gsi.de/en/about_us/history.htm

31. https://www.gsi.de/en/researchaccelerators/research_an_overview.htm

32.https://www.gsi.de/en/researchaccelerators/accelerator_facility.htm

33. https://www.gsi.de/en/researchaccelerators/accelerator_facility/ion_sources.htm

34. https://www.gsi.de/en/researchaccelerators/accelerator_facility/linear_accelerator.htm

35. https://www.gsi.de/en/researchaccelerators/accelerator_facility/ring_accelerator.htm

36. https://www.gsi.de/en/researchaccelerators/accelerator_facility/storage_ring.htm

37. https://www.gsi.de/en/researchaccelerators/accelerator_facility/fragment_separator.htm

38. https://www.gsi.de/en/researchaccelerators/accelerator_facility/main_control_room.htm

39. http://www.fair-center.eu/public/what-is-fair.html

40. http://www.fair-center.eu/public/what-is-fair/accelerators.html

41. http://www.fair-center.eu/public/what-happens-at-fair.html

42. http://www.fair-center.eu/public/what-happens-at-fair/basic-science.html

43. http://www.fair-center.eu/en/public/what-happens-at-fair/applications.html

44. http://www.fair-center.eu/en/public/experiment-program.html

45. B. Friman et al. (Eds.), The CBM Physics Book, Lect. Notes Phys. 814, Springer-Verlag, 2011

46. GSI Report 2013-4, Technical Design Report for the CBM Silicon Tracking System (STS), October 2013, http://repository.gsi.de/record/54798

47. GSI Report 2013-1, May 2013, GSI Scientific Report 2012, http://repository.gsi.de/record/52876

48. CBM Progress Report 2012, April 2013, https://www-alt.gsi.de/documents/DOC-2013-Mar-49.html

49. The CBM Physics Book: Compressed Baryonic Matter in Laboratory Experiments edited by Bengt Friman, Claudia Höhne, Jörn Knoll, Stefan Leupold, Jorgen Randrup, Ralf Rapp, Peter Senger

50.http://www.fair-center.eu/for-users/experiments/cbm.html

51. Claudia Höhne WEHS: Quarks and Hadrons in strong QCD, St. Goar, March 2008

52.http://slideplayer.com/slide/7639916/

53. Overview of the Silicon Tracking System for the CBM experiment, 2015 J. Phys.: Conf. Ser. 599 012025 (http://iopscience.iop.org/1742-6596/599/1/012025)

54. CBM collaboration, Technical Design report for the CBM Silicon Tracking System, GSI Report 2013-4

55. Curs detectori (I. Lazanu, O.Ristea, M.Calin)

56. [4,6,14-16,35]

57. teza drt oana ristea

58. 135

59. Decorrelation of anisotropic flow along the longitudinal direction – Pang, Long-Gang et al. Eur.Phys.J. A52 (2016) no.4, 97 arXiv:1511.04131 [nucl-th]

60. http://na49info.web.cern.ch/na49info/Public/Press/findings.html

61. 142].

62. [136- 141]

63. 14–16,113,146

64. 149,150

65. 14,15,149-151

66. 139,140,150

67. [143,144,151

68.[171,172].

69. [37]. – phd oana

70.

71.

72.

73,

74,

75,