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Experimental nuclear level densities at excitation energies below the neutron threshold follow closely a constant-temperature shape. This dependence is unexpected and poorly understood. In this work, a fundamental explanation of the observed constant-temperature behavior in atomic nuclei is presented for the first time. It is shown that the experimental data portray a first-order phase transition from a superfluid to an ideal gas of non-interacting quasiparticles. Even-even, odd-$A$, and odd-odd level densities show in detail the behavior of gap- and gapless superconductors also observed in solid-state physics. These results and analysis should find a direct application to mesoscopic systems such as superconducting clusters., Comment: 7 pages, 6 figures

Infinite, neutron-proton symmetric, neutral nuclear matter has a critical temperature of 17.9+-0.4 MeV, a critical density of 0.06+-0.01 nucleons per cubic fermi and a critical pressure of 0.31+-0.07 MeV per cubic fermi. These values have been obtained from our analysis of data from six different reactions studied in three different experiments: two "compound nuclear" reactions: 58Ni+12C-->70Se and 64Ni+12C-->76Se (both performed at the LBNL 88" Cyclotron) and four "multifragmentation" reactions: 1 GeV/c pi+197Au (performed by the ISiS collaboration), 1 AGeV 197Au+C, 1 AGeV 139La+12C and 1 AGeV 84Kr+12C (all performed by the EOS collaboration). The charge yields of all reactions as a function of excitation energy were fit with a version of Fisher's droplet model modified to account for the dual components of the fluid (i.e. protons and neutrons), Coulomb effects, finite size effects and angular momentum arising from the nuclear collisions., Comment: 17 pages, 19 figures, 2 tables, 92 references, submitted to Physical Review C

This is a note intended to complement our paper (nucl-th/0504010) and addressed to the attention of QGP workers interested in bag models, Hagedorn spectra, and the like. It tries to show that with a Hagedorn-like experimental spectrum the partition function can not be calculated and that a canonical description derived for the microcanonical ensemble exists only for a single, fixed temperature., Comment: 4 pages

A system H with a Hagedorn-like mass spectrum imparts its unique temperature T_H to any other system coupled to it. An H system radiates particles in preexisting physical and chemical equilibrium. These particles form a saturated vapor at temperature T_H. This coexistence describes a first order phase transition. An H system is nearly indifferent to fragmentation into smaller H systems. A lower mass cut-off in the spectrum does not significantly alter the general picture. These properties of the Hagedorn thermostats naturally explain a single value of hadronization temperature observed in elementary particle collisions at high energies and lead to some experimental predictions., Comment: Contribution to the ``World Consensus Initiative III, Texas A & M University, College Station, Texas, USA, February 11-17, 2005, 15p

Analyses of multifragmentation in terms of the Fisher droplet model (FDM) and the associated construction of a nuclear phase diagram bring forth the problem of the actual existence of the nuclear vapor phase and the meaning of its associated pressure. We present here a physical picture of fragment production from excited nuclei that solves this problem and establishes the relationship between the FDM and the standard compound nucleus decay rate for rare particles emitted in first-chance decay. The compound thermal emission picture is formally equivalent to a FDM-like equilibrium description and avoids the problem of the vapor while also explaining the observation of Boltzmann-like distribution of emission times. In this picture a simple Fermi gas thermometric relation is naturally justified and verified in the fragment yields and time scales. Low energy compound nucleus fragment yields scale according to the FDM and lead to an estimate of the infinite symmetric nuclear matter critical temperature between 18 and 27 MeV depending on the choice of the surface energy coefficient of nuclear matter., Comment: Five page two column pages, four figures, submitted to Phys. Rev. C

A system H with a Hagedorn-like mass spectrum imparts its unique temperature TH to any other system coupled to it. An H system radiates particles in preexisting physical and chemical equilibrium. These particles form a saturated vapor at temperature TH. This coexistence describes a first order phase transition. An H system is nearly indifferent to fragmentation into smaller H systems. A lower mass cut-off in the spectrum does not significantly alter the general picture, Comment: Four pages, one figure

A microcanonical treatment of Hagedorn systems, i.e. finite mass hadronic resonances with an exponential mass spectrum controlled by the Hagedorn temperature $T_H$, is performed. We show that, in the absence of any restrictions, a Hagedorn system is a perfect thermostat, i.e. it imparts its temperature $T_H$ to any other system in thermal contact with it. We study the thermodynamic effects of the lower mass cut-off in the Hagedorn mass spectrum. We show that in the presence of a single Hagedorn resonance the temperature of any number of $N_B$ Boltzmann particles differs only slightly from $T_H$ up to the kinematically allowed limit $N_B^{kin}$. For $N_B > N_B^{kin}$ however, the low mass cut-off leads to a decrease of the temperature as $N_B$ grows. The properties of Hagedorn thermostats naturally explain a single value of hadronization temperature observed in elementary particle collisions at high energies and lead to some experimental predictions., Comment: 5 pages, 1 figure

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but still mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure and density from fixed mean density lattice gas (Ising) model calculations are explained in terms of the complement. Accounting for this finite size effect is key to determining the infinite nuclear matter phase diagram from experimental data., Comment: Four two column pages, four figures, two tables; accepted for publication in PRL

The surface partition of large fragments is derived analytically within a simple statistical model by the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested Hills and Dales Model reproduces the leading term of the famous Fisher result for the surface entropy with an accuracy of a few percent. The surface partition of finite fragments is discussed as well., Comment: 4 pages, 1 figure

A detailed study of the lattice gas (Ising) model shows that the correct definition of cluster concentration in the vapor at coexistence with the liquid leads to Fisher plots that are unique, independent of fixed particle number density $\rho_{\text{fixed}}$, and completely reliable for the characterization of the liquid-vapor phase diagram of any van der Waals systems including nuclear matter., Comment: Five pages, two columns, six figures, one table, submitted to Phys. Rev. C

We explore the effects of Coulomb interaction upon the nuclear liquid vapor phase transition. Because large nuclei (A>60) are metastable objects, phases, phase coexistence, and phase transitions cannot be defined with any generality and the analogy to liquid vapor is ill-posed for these heavy systems. However, it is possible to account for the Coulomb interaction in the decay rates and obtain the coexistence phase diagram for the corresponding uncharged system., Comment: 5 pages, 5 figures

Fission excitation functions have been measured for a chain of neighboring compound nuclei, from 207Po to 212Po. We present a new analysis which provides a determination of the fission barriers and ground state shell effects with nearly spectroscopic accuracy. The improved accuracy achieved in this analysis may lead to a future detailed exploration of the saddle mass surface and its spectroscopy. The sensitivity of the fission probabilities on shell effects extends to excitation energies of 150 MeV and negates recent claims for the disappearance of shell corrections due to collective effects., Comment: 10 pages, 3 figures

A recent paper has reported the observation of the rotational band of 254No for spins up to I=20, showing that the compound nucleus was formed and survived fission decay at angular momenta I >= 20. We show that this survival is consistent with the leading effects of angular momentum on the barrier height., Comment: 1 page, 1 figure

Recent analyses of multifragmentation in terms of Fisher's model and the related construction of a phase diagram brings forth the problem of the true existence of the vapor phase and the meaning of its associated pressure. Our analysis shows that a thermal emission picture is equivalent to a Fisher-like equilibrium description which avoids the problem of the vapor and explains the recently observed Boltzmann-like distribution of the emission times. In this picture a simple Fermi gas thermometric relation is naturally justified. Low energy compound nucleus emission of intermediate mass fragments is shown to scale according to Fisher's formula and can be simultaneously fit with the much higher energy ISiS multifragmentation data., Comment: 10 pages, 4 figures

Anomalous negative heat capacities have been claimed as indicators of first order phase transitions in finite systems in general, and fornuclear systems in particular. A thermodynamic approach allowing for all Q value terms is used to evaluate heat capacities in finitevan der Waals fluids and finite lattice systems in the coexistence region. Fictitious large effects and negative heat capacities are observed in lattice systems when periodic boundary conditions are introduced. Small anomalous effects are predicted for small drops and for finite lattice systems. A straightforward application of the analysis to nuclei shows that negative heat capacities cannot be observed for A>60., Comment: 5 pages, 5 figures, submitted to Phys. Rev. C

The fragment yields from the multifragmentation of gold, lanthanum and krypton nuclei obtained by the EOS Collaboration are examined in terms of Fisher's droplet formalism modifed to account for Coulomb energy. The critical exponents sigma and tau and the surface energy coefficient c0 are obtained. Estimates are made of the pressure-temperature and temperature-density coexistence curves of finite neutral nuclear matter as well as the location of the critical point., Comment: 14 pages, 13 figures, 6 tables, submitted to Phys. Rev. C

For many years it has been speculated that excited nuclei would undergo a liquid to vapor phase transition. For even longer, it has been known that clusterization in a vapor carries direct information on the liquid- vapor equilibrium according to Fisher's droplet model. Now the thermal component of the 8 GeV/c pion + 197Au multifragmentation data of the ISiS Collaboration is shown to follow the scaling predicted by Fisher's model, thus providing the strongest evidence yet of the liquid to vapor phase transition., Comment: four pages, four figures, first two in color (corrected typo in Ref. [26], corrected error in Fig. 4)

Clusters in the three-dimensional Ising model rigorously obey reducibility and thermal scaling up to the critical temperature. The barriers extracted from Arrhenius plots depend on the cluster size as $B \propto A^{\sigma}$ where $\sigma$ is a critical exponent relating the cluster size to the cluster surface. All the Arrhenius plots collapse into a single Fisher-like scaling function indicating liquid-vapor-like phase coexistence and the univariant equilibrium between percolating clusters and finite clusters. The compelling similarity with nuclear multifragmentation is discussed., Comment: (4 pages, 4 figures)

The origin of predicted and observed anomalies in caloric curves of nuclei and other mesoscopic systems is investigated. It is shown that a straightforward thermodynamical treatment of an evaporating liquid drop leads to a backbending in the caloric curve and to negative specific heats in the two phase coexistence region. The cause is found not in the generation of additional surface, but in the progressive reduction of the drop's radius, and surface, with evaporation., Comment: five pages, two columns, four figures, added references

It is shown that the Fisher Droplet Model (FDM), percolation and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42 +- 0.02. The EOS Au multifragmentation data yield barriers with a power-law exponent of 0.68 +- 0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted., Comment: four pages and five figures

Multifragment emission following Xe+Au collisions at 30, 40, 50 and 60 AMeV has been studied with multidetector systems covering nearly 4-pi in solid angle. The correlations of both the intermediate mass fragment and light charged particle multiplicities with the transverse energy are explored. A comparison is made with results from a similar system, Xe+Bi at 28 AMeV. The experimental trends are compared to statistical model predictions., Comment: 7 pages, submitted to Phys. Rev. C

The resilience to averaging over an initial energy distribution of reducibility and thermal scaling observed in nuclear multifragmentation is studied. Poissonian reducibility and the associated thermal scaling of the mean are shown to be robust. Binomial reducibility and thermal scaling of the elementary probability are robust under a broad range of conditions. The experimental data do not show any indication of deviation due to averaging., Comment: 5 pages, 6 figures, submitted to Physical Review C

The multiplicity distributions for individual fragment Z values in nuclear multifragmentation are binomial. The extracted maximum value of the multiplicity is found to depend on Z according to m=Z_0/Z, where Z_0 is the source size. This is shown to be a strong indication of statistical coverage of fragmentation phase space. The inferred source sizes coincide with those extracted from the analysis of fixed multiplicity charge distributions., Comment: 13 pages, 4 revised figures, some revised text

To make a statement about the nature and mechanism of fragmentation, it is necessary to probe directly any competition, or lack thereof, between the emission of various particle species as a function of excitation energy. The task is then to find a global observable that best follows the increase in excitation energy or dissipated energy. In the following, we will consider two contradictory claims that have been advanced recently: 1) the claim for a predominantly dynamical fragment production mechanism; and 2) the claim for a dominant statistical and thermal process. We will present a new analysis in terms of Poissonian reducibility and thermal scaling, which addresses some of the criticisms of the binomial analysis., Comment: 10 pages, 6 figures. Presented the 14th Winter Workshop on Nuclear Dynamics, Snowbird, Utah, January 31- February 7, 1998 (Also available at http://csa5.lbl.gov/moretto/)

We explore the natural limit of binomial reducibility in nuclear multifragmentation by constructing excitation functions for intermediate mass fragments (IMF) of a given element Z. The resulting multiplicity distributions for each window of transverse energy are Poissonian. Thermal scaling is observed in the linear Arrhenius plots made from the average multiplicity of each element. ``Emission barriers'' are extracted from the slopes of the Arrhenius plots and their possible origin is discussed., Comment: 15 pages including 4 .ps figures. Submitted to Phys. Rev. Letters. Also available at http://csa5.lbl.gov/moretto/

In a recent preprint by Tsang and Danielewicz, the authors attempt to give alternative or trivial explanations for the reducible and "thermal" nature of the intermediate mass fragment excitation functions reported previously (Phys. Rev. Lett. 74, 1530 (1995), Phys. Lett B 361, 25 (1995), Phys. Rep. 287, 249 (1997)). We demonstrate that their proposed "self-correlation" explanation for linear Arrhenius plots is based upon a flawed autocorrelation analysis involving circular reasoning., Comment: 11 pages, LaTeX, psfig, also available at http://csa5.lbl.gov/moretto/ps/betty_v3.ps

Fission in 3He and 4He induced reactions at excitation energies between the fission barrier and 140 MeV has been investigated. Twentythree fission excitation functions of various compound nuclei in different mass regions are shown to scale exactly according to the transition state prediction once the shell effects are accounted for. New precise measurements of excitation functions in a mass region where shell effects are very strong, allow one to test the predictions with an even higher accuracy. The fact that no deviations from the transition state method have been observed within the experimentally investigated excitation energy regime allows one to assign limits for the fission transient time. The precise measurement of fission excitation functions of neighboring isotopes enables us to experimentally estimate the first chance fission probability. Even if only first chance fission is investigated, no evidence for fission transient times larger than 30 zs can be found., Comment: 14 pages, TeX, psfig, also available at http://csa5.lbl.gov/moretto/ps/rubehn_lbnl39895.ps, Proc. of the XXXV. International Winter Meeting on Nuclear Physics, Bormio, Italy (1997)

Coulomb bubbles, though stable against monopole displacement, are unstable at least with respect to quadrupole and octupole distortions. We show that there exists a temperature at which the pressure of the vapor filling the bubble stabilizes all the radial modes. In extremely thin bubbles, the crispation modes become unstable due to the surface-surface interaction., Comment: 4 pages, TeX, epsfig, also available at http://csa5.lbl.gov/moretto/ps/bubble.ps, submitted to Phys. Rev. Lett

Rutherford backscattering and particle induced x-ray emission have been utilized to precisely characterize targets used in nuclear fission experiments. The method allows for a fast and non destructive determination of target thickness, homogeneity and element composition., Comment: 11 pages, TeX (elsart.sty), psfig, also available at http://csa5.lbl.gov/moretto/ps/rbs_paper.ps, submitted to Nucl. Instr. Meth. A

The experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and atomic number are compared to the transition state rates. Intermediate-mass-fragment multiplicity distributions for a variety of reactions at intermediate energies are shown to be binomial and thus reducible at all measured transverse energies. From these distributions a single binary event probability can be extracted which has a thermal dependence. A strong thermal signature is also found in the charge distributions. The n-fold charge distributions are reducible to the 1-fold charge distributions through a simple scaling dictated by fold number and charge conservation., Comment: 15 pages, TeX type, psfig, also available at http://csa5.lbl.gov/moretto/ps/brazil.ps, to appear in Proceedings of the 1st International Conference on Nuclear Dynamics at Long and Short Distances, April 8-12, 1996, Angra dos Reis, Brazil

First order phase transitions are described in terms of the microcanonical and canonical ensemble, with special attention to finite size effects. Difficulties in interpreting a "caloric curve" are discussed. A robust parameter indicating phase coexistence (univariance) or single phase (bivariance) is extracted for charge distributions., Comment: 10 pages, TeX type, psfig, also available at http://csa5.lbl.gov/moretto/ps/lgm.ps, to appear in the Proceedings of the 1st Catania Relativistic Ion Studies: Critical Phenomena and Collective Observables, Acicastello, May 27-31, 1996

Fission excitation functions of He-3 and He-4 induced compound nuclei are shown to scale exactly according to the Bohr-Wheeler transition state prediction once the shell effects are accounted for. The presented method furthermore allows one to model-independently extract values for the shell effects which are in good agreement to those obtained from liquid-drop model calculations. The fact that no deviations from the transition state method have been observed within the experimentally investigated excitation energy regime allows one to assign an upper limit for the transient time of 10 zs., Comment: 8 page, TeX type, psfig, to be published in the proccedings of the XII Winter Workshop on Nuclear Dynamics, Snowbird, Utah, February 4-10, 1996, ed. by W. Bauer and G. Westfall

Mastinu et al. recently reported the observation of several positive signals possibly indicating critical behavior in peripheral collisions of Au+Au at $E/A$=35 MeV. In our comment, we examine the choice of variables used to determine the presence (or absence) of critical behavior. We do this by repeating the analysis the work of Mastinu et al. on "data" from a simulation with no critical behavior., Comment: 1 page, TeX type, psfig, also available at http://csa5.lbl.gov/moretto/ps/comment_no_bc.ps, submitted to Phys. Rev. Lett.

A new, sensitive method allows one to search for the enhancement of events with nearly equal-sized fragments as predicted by theoretical calculations based on volume or surface instabilities. Simulations have been performed to investigate the sensitivity of the procedure. Experimentally, charge correlations of intermediate mass fragments emitted from heavy ion reactions at intermediate energies have been studied. No evidence for a preferred breakup into equal-sized fragments has been found., Comment: 12 pages, TeX type, psfig, submitted to Phys. Rev. Lett, also available at http://csa5.lbl.gov/moretto/ps/zcor_pp.ps

Fission excitation functions of compound nuclei in a mass region where shell effects are expected to be very strong are shown to scale exactly according to the transition state prediction once these shell effects are accounted for. The fact that no deviations from the transition state method have been observed within the experimentally investigated excitation energy regime allows one to assign an upper limit for the transient time of 10 zs., Comment: 7 pages, TeX type, psfig, submitted to Phys. Rev. C, also available at http://csa5.lbl.gov/moretto/ps/he3_paper.ps