Isotope distribution in nuclear multifragmentation

doi:10.1016/0370-2693(87)90245-0

Physics Letters B

Volume 191, Issue 3, 11 June 1987, Pages 232-236

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Abstract

A statistical multifragmentation model is used to analyze the isotope distribution of medium sized nuclei produced in p + Kr reactions at high bombarding energies. The results show that the evaporation processes narrow significantly the primordial hot fragment distributions and washes out almost completely the patterns associated with the isotope distributions in the primary fragments. Thus the calculation supports a scenario in which the formation of hot primary fragments is assumed. From adjustments to the experimental data an excitation energy per nucleon of the initial system is found to range from 3.5 to 7 MeV.

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Cited by (9)

Conditions for equivalence of statistical ensembles in nuclear multifragmentation
2012, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Citation Excerpt :
Even when the number of particles is fixed one can replace a canonical model by a grand canonical model where the particle number fluctuates but the average number is constrained to a given value [4,5]. Both canonical and grand canonical models have been extensively used to study the physics of intermediate energy heavy-ion collisions [1,2,6,7] and results for different observables have been routinely compared to experimental data [8–12]. It is well known that results from different statistical ensembles agree in the thermodynamical limit [5], that is, when the number of particles become infinite.
Statistical models based on canonical and grand canonical ensembles are extensively used to study intermediate energy heavy-ion collisions. The underlying physical assumption behind canonical and grand canonical models is fundamentally different, and in principle agree only in the thermodynamical limit when the number of particles become infinite. Nevertheless, we show that these models are equivalent in the sense that they predict similar results if certain conditions are met even for finite nuclei. In particular, the results converge when nuclear multifragmentation leads to the formation of predominantly nucleons and low mass clusters. The conditions under which the equivalence holds are amenable to present day experiments.
Microcanonical thermodynamics and statistical fragmentation of dissipative systems. The topological structure of the N-body phase space
1997, Physics Report
This review is addressed to colleagues working in different fields of physics who are interested in the concepts of microcanonical thermodynamics, its relation and contrast to ordinary, canonical or grandcanonical thermodynamics, and to get a first taste of the wide area of new applications of thermodynamical concepts like hot nuclei, hot atomic clusters and gravitating systems.
Microcanonical thermodynamics describes how the volume of the N-body phase space depends on the globally conserved quantities like energy, angular momentum, mass, charge, etc. Due to these constraints the microcanonical ensemble can behave quite differently from the conventional, canonical or grandcanonical ensemble in many important physical systems.
Microcanonical systems become inhomogeneous at first-order phase transitions, or with rising energy, or with external or internal long-range forces like Coulomb, centrifugal or gravitational forces. Thus, fragmentation of the system into a spatially inhomogeneous distribution of various regions of different densities and/or of different phases is a genuine characteristic of the microcanonical ensemble. In these cases which are realized by the majority of realistic systems in nature, the microcanonical approach is the natural statistical description.
We investigate this most fundamental form of thermodynamics in four different nontrivial physical cases:
- 1.
  (I) Microcanonical phase transitions of first and second order are studied within the Potts model. The total energy per particle is a nonfluctuating order parameter which controls the phase which the system is in. In contrast to the canonical form the microcanonical ensemble allows to tune the system continuously from one phase to the other through the region of coexisting phases by changing the energy smoothly. The configurations of coexisting phases carry important informations about the nature of the phase transition. This is more remarkable as the canonical ensemble is blind against these configurations. It is shown that the three basic quantities which specify a phase transition of first order — Transition temperature, latent heat, and interphase surface entropy — can be well determined for finite systems from the caloric equation of state T(E) in the coexistence region. Their values are already for a lattice of only $~ 30 ∗ 30 spins$ close to the ones of the corresponding infinite system. The significance of the backbending of the caloric equation of state T(E) is clarified. It is the signal for a phase transition of first order in a finite isolated system.
- 2.
  (II) Fragmentation is shown to be a specific and generic phase transition of finite systems. The caloric equation of state T(E) for hot nuclei is calculated. The phase transition towards fragmentation can unambiguously be identified by the anomalies in T(E). As microcanonical thermodynamics is a full N-body theory it determines all many-body correlations as well. Consequently, various statistical multi-fragment correlations are investigated which give insight into the details of the equilibration mechanism.
- 3.
  (III) Fragmentation of neutral and multiply charged atomic clusters is the next example of a realistic application of microcanonical thermodynamics. Our simulation method, microcanonical Metropolis Monte Carlo, combines the explicit microscopic treatment of the fragmentational degrees of freedom with the implicit treatment of the internal degrees of freedom of the fragments described by the experimental bulk specific heat. This micro-macro approach allows us to study the fragmentation of also larger fragments. Characteristic details of the fission of multiply charged metal clusters find their explanation by the different bulk properties.
- 4.
  (IV) Finally, the fragmentation of strongly rotating nuclei is discussed as an example for a microcanonical ensemble under the action of a two-dimensional repulsive force.
Statistical multifragmentation of nuclei
1995, Physics Reports
This review is devoted to the Statistical Multifragmentation Model (SMFM) developed in Copenhagen more than 10 years ago and widely used now for interpreting experimental data on multiple fragment production in different nuclear reactions. The model is based on the assumption of simultaneous break-up of a thermalized nuclear system. Basic principles and different realizations of the statistical approach to the nuclear multifragmentation are described in detail. Special emphasis is put on the implementation of specific nuclear features such as finite size effects, internal excitation of fragments, their strong and Coulomb interaction. Hot primary fragments are treated within the liquid-drop approximation. An efficient Monte Carlo method is proposed for generating microcanonical ensembles of break-up channels. Deexcitation of hot fragments via evaporation and Fermi break-up is also included in the numerical code. The evolution of nuclear disintegration mechanisms with increasing excitation energy, from compound nucleus to multifragmentation and vaporization, follows naturally from the model. Observable signals of multifragmentation are discussed and numerous applications of the model for analyzing experimental data are demonstrated. In particular, hybrid models, combining dynamical simulations of non-equilibrium stages of the reaction with statistical break-up of thermalized intermediate systems, are described. The “backtracing” method of reconstructing parameters of decaying sources from experimental data is also presented.
Statistical multifragmentation: Comparison of two quite successful models
1994, Nuclear Physics, Section A
We compare the outcome of the Copenhagen and the Berlin statistical multifragmentation models. The two models both start from the assumption of an ensemble of various excited fragments at thermal and chemical equilibrium for an expanded nuclear system at a certain stage, the freeze-out configuration. Details as the volume of this source, the intrinsic excitation of the fragments, and the secondary decays are treated quite differently. Also the technical level of the Monte Carlo sampling differs.
Main characteristics such as total charged multiplicity, IMF multiplicity, and total neutron yield are in reasonable agreement. Thus the overall predictions are quite robust against details in the description. Deviations are however seen for high energies (E★ > 6A MeV) where fewer IMF's, fewer neutrons, and much more α's are seen in the Copenhagen model. The isotopic distribution of the very light fragments is more narrow than in the Berlin model.
Energy levels of light nuclei A = 16-17
1993, Nuclear Physics, Section A
Energy levels of light nuclei A = 11-12
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Isotope distribution in nuclear multifragmentation

Abstract

Phys. Rev. C

Nucl. Phys. A

Nucl. Phys. A

Phys. Lett. B

Nucl. Phys. A

Nucl. Phys. A

Phys. Scr. T

Phys. Rev. Lett.

Phys. Lett. B

Nucl. Phys. A

Nucl. Phys. A

Nucl. Phys. A

Phys. Lett. B

Phys. Lett. B

NBI-preprint NBI-86-44

Phys. Rep.

Phys. Rev. C

Phys. Rev. C

Phys. Rep.