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Discriminant Analysis and Secondary-Beam Charge Recognition
Abstract
The discriminant-analysis method has been applied to optimize the exotic-beam charge recognition in a projectile fragmentation experiment. The experiment was carried out at the GSI using the fragment separator (FRS) to produce and select the relativistic secondary beams, and the ALADIN setup to measure their fragmentation products following collisions with Sn target nuclei. The beams of neutron poor isotopes around 124La and 107Sn were selected to study the isospin dependence of the limiting temperature of heavy nuclei by comparing with results for stable 124Sn projectiles. A dedicated detector to measure the projectile charge upstream of the reaction target was not used, and alternative methods had to be developed. The presented method, based on the multivariate discriminant analysis, allowed to increase the efficacy of charge recognition up to about 90%, which was about 20% more than achieved with the simple scalar methods. Comment: 6 pages, 7 eps figures, elsart, submitted to Nucl. Instr. and Meth. A
... The fragmentation of 107 Sn on natural Sn targets at this energy was studied by the ALADIN Collabora- tion with radioactive beams produced by the fragmentation of a primary 142 Nd beam [53]. The isotopic composition of the ob- tained secondary beams is presented and discussed in Ref. [59]. In Fig. 10, the mean multiplicity of IMFs is normalized with respect to the mass numbers of the projectiles. ...
The formation of the projectile spectator and the fragmentation processes in 107,124Sn + 120Sn collisions at 600 MeV/nucleon are studied with the isospin-dependent quantum molecular dynamics (IQMD) model. The minimum spanning tree algorithm and the ratio of parallel to transverse kinetic quantities are applied to identify the equilibrated projectile spectator during the dynamical evolution. The influence of secondary decay on fragmentation observables is investigated by performing calculations with and without the statistical code GEMINI. The validity of the theoretical approach is examined by comparing the calculated product yields and correlations with the experimental results of the ALADIN Collaboration for the studied reactions.
... The fragmentation of 107 Sn on natural Sn targets at this energy was studied by the ALADIN Collaboration with radioactive beams produced by the fragmentation of a primary 142 Nd beam [53]. The isotopic composition of the obtained secondary beams is presented and discussed in Ref. [59]. In Fig. 10, the mean multiplicity of IMFs is normalized with respect to the mass numbers of the projectiles. ...
Background: Projectile fragmentation is a well-established technique to produce rare isotope beams, but its underlying physical processes are not fully known. Purpose: We devote ourselves to studying the dynamical properties and secondary decay effects of projectile fragmentations in Sn124, Sn107+Sn120 collisions at 600 MeV/nucleon. Method: The formation of the projectile spectator and the fragmentation process are studied with the isospin-dependent quantum molecular dynamics (IQMD) model. The minimum spanning tree algorithm and the ratio of parallel to transverse quantities are applied to distinguish the equilibrated projectile spectator during the dynamics evolution. The influence of secondary decay on fragmentation observables is investigated by comparing the calculations with and without the statistical code gemini. The validity of the theoretical approach is tested by comparing the calculated product yields with the experimental results of the ALADIN Collaboration for the studied reactions. Results: The general correlation of an increasing excitation energy with a decreasing mass of the spectator system is found for collisions with impact parameter of b=5-10 fm. The nucleon evaporation of the prefragments reduces the multiplicity of intermediate-mass fragments, but does not change their dependence on the isospin of the projectile. The sequential decay also leads to narrower isotope distributions. Switching to gemini at a higher excitation energy results in slightly narrower isotope distributions. With the gemini code, in which the nuclear masses with shell and pairing corrections are adopted, the calculations can rather generally reproduce the data of the isotope distributions and mean neutron-to-proton ratios of the light fragments. Conclusion: By permitting only evaporation in gemini, the IQMD+gemini model is able to reproduce the main features of projectile fragmentation in the studied Sn+Sn reactions.
The neutron emission in projectile fragmentation at relativistic energies was studied with the Large-Area-Neutron-Detector LAND coupled to the ALADIN forward spectrometer at the GSI Schwerionen-Synchrotron (SIS). Stable Sn124 and radioactive Sn107 and La124 beams with an incident energy of 600 MeV/nucleon were used to explore the N/Z dependence of the identified neutron source. A cluster-recognition algorithm is applied for identifying individual particles within the hit distributions registered with LAND. The obtained momentum distributions are extrapolated over the full phase space occupied by the neutrons from the projectile-spectator source. The mean multiplicities of spectator neutrons reach values of up to about 11 and depend strongly on the isotopic composition of the projectile. An effective source temperature of T≈2–5 MeV, monotonically increasing with decreasing impact parameter, is deduced from the transverse momentum distributions. For the interpretation of the data, calculations with the statistical multifragmentation model were performed. The variety of excited projectile spectators assumed to decay statistically is represented by an ensemble of excited sources with parameters determined previously from the fragment production observed in the same experiments. The obtained agreement is very satisfactory for more peripheral collisions where, according to the model, neutrons are mainly emitted during the secondary decays of excited fragments. The neutron multiplicity in more central collisions is underestimated, indicating that other sources besides the modeled statistical breakup contribute to the observed neutron yield. The choice made for the symmetry-term coefficient of the liquid-drop description of produced fragments has a weak effect on the predicted neutron multiplicities.
Isotopic yield distributions of nuclei produced in peripheral collisions of Kr80+Ca40,48 at 35 MeV/nucleon are studied. Experimental results obtained by the FAZIA Collaboration at the LNS facility in Catania are compared with calculations performed with the statistical multifragmentation model (SMM). The fragments with atomic number Z=19–24 observed at forward angles are successfully described with the ensemble method previously established for reactions at higher energy. Using the SMM results, the isotopic compositions of the projectile residues are reconstructed. The results indicate a significant isospin exchange between the projectile and target nuclei, not far from isospin equilibrium, during the initial phase of the reaction. The two groups of light fragments with Z=1–4, experimentally distinguished by their velocities relative to coincident heavy projectile fragments, are found to originate from different sources. The isotopic composition of the slower group is consistent with emission from a low-density neck, enriched in neutrons, and satisfactorily reproduced with SMM calculations for a corresponding neck source of small mass.
The N/Z dependence of projectile fragmentation at relativistic energies has
been studied with the ALADIN forward spectrometer at the GSI Schwerionen
Synchrotron (SIS). Stable and radioactive Sn and La beams with an incident
energy of 600 MeV per nucleon have been used in order to explore a wide range
of isotopic compositions. For the interpretation of the data, calculations with
the statistical multifragmentation model for a properly chosen ensemble of
excited sources were performed. The parameters of the ensemble, representing
the variety of excited spectator nuclei expected in a participant-spectator
scenario, are determined empirically by searching for an optimum reproduction
of the measured fragment-charge distributions and correlations. An overall very
good agreement is obtained. The possible modification of the liquid-drop
parameters of the fragment description in the hot freeze-out environment is
studied, and a significant reduction of the symmetry-term coefficient is found
necessary to reproduce the mean neutron-to-proton ratios /Z and the
isoscaling parameters of Z<=10 fragments. The calculations are, furthermore,
used to address open questions regarding the modification of the surface-term
coefficient at freeze-out, the N/Z dependence of the nuclear caloric curve, and
the isotopic evolution of the spectator system between its formation during the
initial cascade stage of the reaction and its subsequent breakup.
New results for the strength of the symmetry energy are presented which
illustrate the complementary aspects encountered in reactions probing nuclear
densities below and above saturation. A systematic study of isotopic effects in
spectator fragmentation was performed at the ALADIN spectrometer with 124Sn
primary and 107Sn and 124La secondary beams of 600 MeV/nucleon incident energy.
The analysis within the Statistical Fragmentation Model shows that the
symmetry-term coefficient entering the liquid-drop description of the emerging
fragments decreases significantly as the multiplicity of fragments and light
particles from the disintegration of the produced spectator systems increases.
Higher densities were probed in the FOPI/LAND study of nucleon and
light-particle flows in central and mid-peripheral collisions of 197Au+197Au
nuclei at 400 MeV/nucleon incident energy. From the comparison of the measured
neutron and hydrogen squeeze-out ratios with predictions of the UrQMD model a
moderately soft symmetry term with a density dependence of the potential term
proportional to (rho/rho_0)^{gamma} with gamma = 0.9 +- 0.3 is favored.
Isotopic effects in projectile fragmentation at relativistic energies have been studied with the ALADIN forward spectrometer at SIS. Stable and radioactive Sn and La beams with an incident energy of 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. Chemical freeze-out temperatures are found to be nearly invariant with respect to the A/Z ratio of the produced spectator sources, consistent with predictions for expanded systems. Consequences for the proposed interpretation of chemical breakup temperatures as representing the limiting temperatures predicted by microscopic models are discussed. Comment: 7 pages, 4 figures, contribution to proceedings of International School of Nuclear Physics, 30th Course, Heavy-Ion Collisions from the Coulomb Barrier to the Quark-Gluon Plasma, Erice-Sicily: 16 - 24 September 2008
The A/Z dependence of projectile fragmentation at relativistic energies has been studied with the ALADIN forward spectrometer at SIS. A stable beam of (124)Sn and radioactive beams of (124)La and (107)Sn at 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. Chemical freeze-out temperatures are found to be nearly invariant with respect to the A/Z of the produced spectator sources, consistent with predictions for expanded systems. Small Coulomb effects (DeltaT approximately 0.6 MeV) appear for residue production near the onset of multifragmentation.
Isotope temperatures from double ratios of hydrogen, helium, lithium, beryllium, and carbon isotopic yields, and excited-state temperatures from yield ratios of particle-unstable resonances in 4He, 5Li, and 8Be, were determined for spectator fragmentation, following collisions of 197Au with targets ranging from C to Au at incident energies of 600 and 1000 MeV per nucleon. A deviation of the isotopic from the excited-state temperatures is observed which coincides with the transition from residue formation to multi-fragment production, suggesting a chemical freeze-out prior to thermal freeze-out in bulk disintegrations.
This paper introduces a new method for the selection of central single-source events, based on classical multivariate techniques. The resulting discriminating variable is shown to be valid for different hypotheses on the nuclear source deexcitation mechanism. It enables the selection of events which are representative of the whole set of single-source events. Application to the Ni+Ni at 32A MeV system measured with the INDRA multidetector has allowed the determination of the fusion probability as a function of the impact parameter and the evaluation of the corresponding cross section.
Nuclear physics deals more and more with experiments involving a large number of parameters. The analysis of such experiments requires well adapted statistical techniques. The multivariate analysis techniques consist in the representation of the experimental events as points in the multidimensional space of the physical variables. One aim will be to treat experimental information as a whole. This formalism permits the simultaneous studies of the structures of the event cloud and of the correlations between the variables. Principal Component Analysis is concerned with the determination of the so-called principal variables, linear combinations of the primary physical variables, which represent the maximum information. Correspondence Analysis visualises, on a 2D diagram, the correlations between the modalities of qualitative variables. The goal of the Discriminant Analysis is to discriminate different types of events, that is to affect them to a familly. The last part of the work is devoted to a global protocol, involving the PCA, for the comparison of experimental data with data generated by a simulation code. Lecture given at the Joliot-Curie summer school on nuclear physics (Maubuisson France, sept. 1994)
The projectile fragment separator FRS designed for research and applied studies with relativistic heavy ions was installed at GSI as a part of the new high-energy SIS/ESR accelerator facility. This high-resolution forward spectrometer has been successfully used in first atomic and nuclear physics experiments using neon, argon, krypton, xenon, and gold beams in the energy range from 500 to 2000 MeV/u. For the first time relativistic xenon and gold fragments have been isotopically separated. In this contribution we describe first experiments characterizing the performance of this spectrometer.
A systematic study of isospin effects in the breakup of projectile spectators at relativistic energies has been performed with the ALADiN spectrometer at the GSI laboratory (Darmstadt). Four different projectiles 197Au, 124La, 124Sn and 107Sn, all with an incident energy of 600 AMeV, have been used, thus allowing a study of various combinations of masses and N/Z ratios in the entrance channel.The measurement of the momentum vector and of the charge of all projectile fragments with Z > 1 entering the acceptance of the ALADiN magnet has been performed with the high efficiency and resolution achieved with the TP-MUSIC IV detector.The Rise and Fall behavior of the mean multiplicity of IMFs as a function of Zbound and its dependence on the isotopic composition has been determined for the studied systems. Other observables investigated so far include mean N/Z values of the emitted light fragments and neutron multiplicities. Qualitative agreement has been obtained between the observed gross properties and the predictions of the Statistical Multifragmentation Model.
Isotopic effects in spectator fragmentations following heavy-ion collisions at relativistic energies are investigated using data from recent exclusive experiments with SIS beams at GSI. Reactions of 12C on 112,124Sn at incident energies 300 and 600 MeV per nucleon were studied with the INDRA multidetector while the fragmentation of stable 124Sn and radioactive 107Sn and 124La projectiles was studied with the ALADIN spectrometer.The global characteristics of the reactions are very similar. This includes the rise and fall of fragment production and deduced observables as, e.g., the breakup temperature obtained from double ratios of isotope yields. The mass distributions depend strongly on the neutron-to-proton ratio of the decaying system, as expected for a simultaneous statistical breakup. The ratios of light-isotope yields from neutron-rich and neutron-poor systems follow the law of isoscaling. The deduced scaling parameters decrease strongly with increasing centrality to values smaller than 50% of those obtained for the peripheral event groups. This is not compensated by an equivalent rise of the breakup temperatures which suggests a reduction of the symmetry term required in a liquid-drop description of the fragments at freeze-out.
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