We here study fragmentation using a simulated annealing clusterization algorithm (SACA) with binding energy at a microscopic level. In an earlier version, a constant binding energy (4 MeV/nucleon) was used. We improve this binding energy criterion by calculating the binding energy of different clusters using a modified Bethe–Weizsacker mass (BWM) formula. We also compare our calculations with experimental data of the ALADiN group. Nearly no effect of this modification is visible.

Study of fragmentation using clusterization algorithm with realistic binding energies

Momenta and masses of heavy projectile fragments (Z greater than or equal to 8), produced in collisions of (197)AU With C, Al, Cu, and Pb targets at EIA = 600 MeV, were determined with the ALADIN magnetic spectrometer at SIS. Using this information, an analysis of kinematic correlations between the two and three heaviest projectile fragments in their rest frame was performed. The sensitivity of these correlations to the conditions at breakup was verified within the schematic sos model. For a quantitative investigation, the data were compared to calculations with statistical multifragmentation models and to classical three-body calculations. With classical trajectory calculations, where the charges and masses of the fragments are taken from a Monte Carlo sampling of the experimental events, the dynamical observables can be reproduced. The deduced breakup parameters, however, differ considerably from those assumed in the statistical multifragmentation models which describe the charge correlations. If, on the other hand, the analysis of kinematic and charge correlations is performed for events with two and three heavy fragments produced by statistical multifragmentation codes, good agreement with the data is found with the exception that the fluctuation widths of the intrinsic fragment energies are significantly underestimated. A new Version of the multifragmentation code MCFRAG was therefore used to investigate the potential role of angular momentum at the breakup stage. If a mean angular momentum of 0.75(h)over bar>/nucleon is added to the system, the energy fluctuations can be reproduced, but at the same time the charge partitions are modified and deviate from the data.

/pdf/breakup-conditions-of-projectile-spectators-from-dynamical-1cq61gh4ki.pdf

Breakup Conditions of Projectile Spectators from Dynamical Observables

Realistic caloric curves are obtained for the {sup 197}Au+{sup 197}Au reaction with incident energy ranging from 35 to 130 MeV/nucleon in the dynamic statistical multifragmentation model. It is shown that for the excitation energy 3 to 8 MeV/nucleon, the temperature remains constant in the range 5 to 6 MeV, which is close to the experiment. The mechanism of energy deposition through the tripartition of the colliding system envisaged in this model together with interfragment nuclear interaction are found to play important roles. A possible signature of a liquid-gas phase transition is seen in the specific heat distribution calculated from these caloric curves, and the critical temperature is found to be {approximately}6 to 6.5 MeV. {copyright} {ital 1998} {ital The American Physical Society}

Caloric curve in Au+Au collisions

Ground state stable nuclei typically have near-spherical geometries but may exhibit exotic shapes and form $\ensuremath{\alpha}$-particle clusters within their bulk if given excitation energy and/or angular momentum. It is predicted that such clustering can promote the production of angular-momentum stabilized toroidal nuclei. Previous experiment and theory suggest that such states may be evidenced by narrow resonances at high excitation energy in peripheral intermediate energy heavy-ion collisions. There has been recent focus on potential evidence for toroidal states in the $\ensuremath{\alpha}$-particle disassembly of $^{28}\mathrm{Si}$ in collisions of $^{28}\mathrm{Si}+^{12}\mathrm{C}$ at 35 MeV/nucleon; however, prior evidence is limited by the angular resolution and statistical uncertainties that exist in the measurement. The present work aims to measure the excitation energy distribution for these disassembly events with improved angular resolution and reduced statistical uncertainty using the Forward Array Using Silicon Technology (FAUST). FAUST is equipped with resistive dual-axis duolateral (DADL) position-sensitive silicon detectors capable of submillimeter position resolution. The performance and response of the array was previously characterized in detail to accurately predict the expected resolution of measuring narrow resonances. The measured excitation energy distributions for 7- and 8-$\ensuremath{\alpha}$ disassembly events showed no strong evidence for highly excited states at the cross section and widths suggested by previous experiment. Further investigation of collision properties that lead to these exit channels revealed challenges in isolating clean projectile-mass decays, where many 7-$\ensuremath{\alpha}$ events do not originate from a single $^{28}\mathrm{Si}$ source. A statistical likelihood analysis was performed to determine the sensitivity of the present measurement for confidently determining resonant yield, providing an upper limit to toroidal high-spin isomer cross section as a function of the excitation energy and width of potential states. 

Experimental search for toroidal high-spin isomers in collisions of 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>Si</mml:mi><mml:mprescripts/><mml:none/><mml:mn>28</mml:mn></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mi mathvariant="

/pdf/algebraicheskii-metod-tochnogo-resheniia-statisticheskoi-td3s6w048f.pdf

Алгебраический метод точного решения статистической суммы для канонического ансамбля в ядерной мультифрагментации@@@An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

Based on the fireball model and the spectator-participant picture, a statistical simultaneous multifragmentation model is developed for heavy ion induced reactions, with the entrance channel characteristics taken into account. This model has the density as the only parameter and it predicts the excitation energy, the temperature, and the frgmentation cross section, etc., once the incident energy, the projectile, and the target nuclei are specified. As a first application, it has been applied to the central collision data taken at National Superconducting Cyclotron Laboratory on the {sup 40}Ar+{sup 45}Sc reaction at incident energies ranging from 35 to 115 MeV/{ital A}. The study brings out the similarity in the characteristics of high energy proton induced and medium energy heavy ion induced reactions. It is observed that with rise of bombarding energy, the onset of simultaneous multifragmentation occurs at some energy between 50 and 60 MeV/{ital A}. {copyright} {ital 1996 The American Physical Society.}

Statistical simultaneous multifragmentation model for heavy ion collisions with entrance channel characteristics

We study the mechanism of intermediate energy heavy-ion collisions in a picture of tripartition of the total system, using the framework of statistical simultaneous multifragmentation model taking into account the entrance channel characteristics, with no other parameter except density. The relative excitations of the three parts and their contributions to the physical observables such as mean multiplicity for different fragments and total fragment multiplicity are shown as functions of entrance channel properties; namely, the impact parameter, the bombarding energy, and the mass of projectile and target nuclei. As an application we apply the model to describe the data on {sup 40}Ar+{sup 40}Ca and {sup 40}Ar+{sup 197}Au reaction with incident energy varying from 42 to 137 MeV/nucleon, and the intermediate mass fragment production in the {sup 197}Au+{sup 197}Au reaction with incident energies 100 and 400 MeV/nucleon. The importance of the contributions from the spectator parts is clearly demonstrated. It is also shown that the role of the interfragment interaction is important up to bombarding energy 100 MeV/nucleon and a temperature of about 10 MeV. {copyright} {ital 1997} {ital The American Physical Society}

Entrance channel dependence of fragmentation dynamics in heavy-ion collisions

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Statistical simultaneous multifragmentation model for heavy ion collisions with entrance channel characteristics

Caloric curve in Au+Au collisions

Entrance channel dependence of fragmentation dynamics in heavy-ion collisions