Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

Carmona, J. M.; Richert, J.; Wagner, P.

doi:10.1007/s100500170098

Cited by 14 publications

(18 citation statements)

References 22 publications

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“…Figure 31(b) shows the extraction of β using Eq. (27). An excellent fit was obtained in the region away from the critical point, which indicates a critical exponent β = 0.33 ± 0.01.…”

Section: Determination Of Critical Exponentsmentioning

confidence: 95%

“…Further, applications of -scaling analysis indicate that the observation of power-law mass distributions [23,24], although necessary, is not sufficient to identify the true critical point of the system. We note also that although the role of the long-range Coulomb interaction in determining the transition point has received considerable theoretical and experimental attention [20,[25][26][27][28][29], a number of questions remain as to the appropriate way to deal with the complications it introduces.…”

Section: Introductionmentioning

confidence: 98%

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Critical behavior in light nuclear systems: Experimental aspects

G.¹,

Natowitz²,

Wada³

et al. 2005

Phys. Rev. C

102

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An extensive experimental survey of the features of the disassembly of a small quasiprojectile system with A ∼ 36, produced in the reactions of 47 MeV/nucleon 40 Ar + 27 Al, 48 Ti, and 58 Ni, has been carried out. Nuclei in the excitation energy range of 1-9 MeV/nucleon have been investigated employing a new method to reconstruct the quasiprojectile source. At an excitation energy ∼5.6 MeV/nucleon many observables indicate the presence of maximal fluctuations in the deexcitation processes. These include the normalized second moments of the Campi plot and normalized variances of the distributions of order parameters such as the atomic number of the heaviest fragment Z max and the total kinetic energy. The evolution of the correlation of the atomic number of the heaviest fragment with that of the second heaviest fragment and a bimodality test are also consistent with a transition in the same excitation energy region. The related phase separation parameter, S p , shows a significant change of slope at the same excitation energy. In the same region a -scaling analysis for of the heaviest fragments exhibits a transition to = 1 scaling, which is predicted to characterize a disordered phase. The fragment topological structure shows that the rank-sorted fragments obey Zipf's law at the point of largest fluctuations, providing another indication of a liquid gas phase transition. The Fisher droplet model critical exponent τ ∼ 2.3 obtained from the charge distribution at the same excitation energy is close to the critical exponent of the liquid gas phase transition universality class. The caloric curve for this system shows a monotonic increase of temperature with excitation energy and no apparent plateau. The temperature at the point of maximal fluctuations is 8.3 ± 0.5 MeV. Taking this temperature as the critical temperature and employing the caloric curve information we have extracted the critical exponents β, γ , and σ from the data. Their values are also consistent with the values of the universality class of the liquid gas phase transition. Taken together, this body of evidence strongly suggests a phase change in an equilibrated mesoscopic system at, or extremely close to, the critical point.

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“…Figure 31(b) shows the extraction of β using Eq. (27). An excellent fit was obtained in the region away from the critical point, which indicates a critical exponent β = 0.33 ± 0.01.…”

Section: Determination Of Critical Exponentsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 98%

Critical behavior in light nuclear systems: Experimental aspects

G.¹,

Natowitz²,

Wada³

et al. 2005

Phys. Rev. C

102

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“…[1]. Only a slight effect of the Coulomb interaction has also been reported in the isochore framework [15].…”

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confidence: 91%

Comment on “Negative heat capacities and first order phase transitions in nuclei”

Gulminelli

Chomaz

2004

Phys. Rev. C

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In a recent paper L.G. Moretto et al [1] claim that the negative heat capacities presented in our previously published paper [2] are "artifacts" coming from the use of periodic boundary conditions in the Lattice-Gas calculations. We stress in this comment that this claim is wrong: in ref.[2] we did not use periodic boundary conditions and anyhow the boundary conditions are irrelevant for the statistical ensemble used in [2]. The second claim of [1] is that, because of the Coulomb repulsion, systems "with A > 60 should present no anomalous negative heat capacities". We show that this conclusion is contradicted by exact Lattice-gas simulations including Coulomb forces which present negative heat capacities even for A > 200.Let us start with the discussion about the boundary conditions. It is clearly stated in ref.[2] that"L 3 [the lattice size] is large enough (typically greater than 20 3 lattice sites) so that the boundary conditions do not affect the calculations with a constraining λ." This means that the results of ref.[2] do not depend upon the conditions used at the boundary, and in fact the calculations were made without periodic boundary conditions. At that time we checked the independence of the boundaries comparing N = 8000 and N = 27000 lattices. To see a sizeable effect of the boundary, we have decreased the size of the lattice. A fast calculation of 50000 events for 216 particles in a N = 5832 lattice at an energy E = 0.4ǫ confined by a Lagrange multiplier log λ = −8 , gives a temperature T = (0.687 ± 0.004)ǫ, a heat capacity C = −16.3 ± 0.2, and a kinetic energy fluctuation σ 2 k /T 2 = 1.64 ± 0.03. If periodic boundary conditions are imposed, the temperature becomes T = (0.682 ± 0.004)ǫ, the heat capacity C = −16.9 ± 0.4 and the fluctuation σ 2 k /T 2 = 1.63 ± 0.07. The temperature decrease in the phase transition region is ∆T = (7.6 ± 0.4)10 −3 ǫ (∆T = (6.7 ± 0.6)10 −3 ǫ) with (without) periodic boundary conditions. This shows that the boundary conditions do not affect the thermodynamics. Indeed, in ref.[2] we have analyzed an ensemble of particles in the vacuum for which only the average spatial extension of the system is defined (isobar ensemble). Then, provided that the lattice in which the system has still to be discretized for technical reasons is big enough, boundary conditions are irrelevant since the particles never explore the outer region.In a previous paper [3] we have considered a canonical Lattice Gas model in a box of constant volume (isochore ensemble), and there we have used periodic boundary conditions. In these calculations negative compressibilities are reported but the heat capacity is always positive. In fact, in the canonical ensemble the heat capacity is proportional to the energy variance and can never be negative [4].Concerning the isochore microcanonical ensemble, the published results [5] show that the heat capacity at constant volume C V is always positive. Therefore, contrary to what is claimed in ref.[1], published results dealing with Lattice Gas calculations with typ...

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“…Consequently phase transitions should be reconsidered from a more general point of view. An important theoretical effort started a few years ago to propose and discuss signatures of phase transitions in small systems [137,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227]. "Small" systems have been defined in reference [205] as systems where the linear dimension is of the same order of magnitude as the characteristic range of the interaction.…”

Section: Finite Systems and Phase Transitionsmentioning

confidence: 99%

Nuclear multifragmentation and phase transition for hot nuclei

Borderie

Rivet

2008

Progress in Particle and Nuclear Physics

202

174

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That review article is focused on the tremendous progresses realized during the last fifteen years in the understanding of multifragmentation and its relationship to the liquid-gas phase diagram of nuclei and nuclear matter. The explosion of the whole nucleus, early predicted by Niels Bohr [1], is a very complex and rich subject which continues to fascinate nuclear physicists as well as theoreticians who extend the thermodynamics of phase transitions to finite systems.

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Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

Cited by 14 publications

References 22 publications

Critical behavior in light nuclear systems: Experimental aspects

Critical behavior in light nuclear systems: Experimental aspects

Comment on “Negative heat capacities and first order phase transitions in nuclei”

Nuclear multifragmentation and phase transition for hot nuclei

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