Search Results (87 total)

We investigate the average sizes of the n largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte Carlo simulations of the percolation type. We find that previous claims of manifestations of Zipf's Law in the rank-ordered fragment size distributions are not borne out in our result, in neither finite nor infinite systems. Instead, we find that Zipf-Mandelbrot distributions are needed to describe the results, and we show how one can derive them in the infinite size limit. However, we agree with previous authors that the investigation of rank-ordered fragment size distributions is an alternative way of looking for the critical point in the nuclear matter diagram.

A method describing NMR-signal formation in inhomogeneous tissue is presented which covers all diffusion regimes. For this purpose, the frequency distribution inside the voxel is described. Generalizing the results of the well-known static dephasing regime, we derive a formalism to describe the frequency distribution that is valid over the whole dynamic range. The expressions obtained are in agreement with the results obtained from Kubos line-shape theory. To examine the diffusion effects, we utilize a strong collision approximation, which replaces the original diffusion process by a simpler stochastic dynamics. We provide a generally valid relation between the frequency distribution and the local Larmor frequency inside the voxel. To demonstrate the formalism we give analytical expressions for the frequency distribution and the free induction decay in the case of cylindrical and spherical magnetic inhomogeneities. For experimental verification, we performed measurements using a single-voxel spectroscopy method. The data obtained for the frequency distribution, as well as the magnetization decay, are in good agreement with the analytic results, although experiments were limited by magnetic field gradients caused by an imperfect shim and low signal-to-noise ratio.

We address spin dephasing induced by stochastic transitions between different precession frequencies. A very famous analytical approximation is the Gaussian approximation presented by [Anderson and Weiss, Rev. Mod. Phys. 25, 269 (1953)]. It states that independent from the transition dynamics, a Gaussian frequency distribution implies a Gaussian distribution of the phase angles, which provides a simple analytical result for the transverse magnetization decay. In contrast we find that (i) the assumption of Gaussian dephasing restricts the stochastic dynamics to a very limited class, (ii) the Anderson-Weiss model is applicable only in a special case of fluctuations, i.e., if and only if the Green’s function G(ω₂,ω₁,Δt) describing the transition probability between two frequencies ω₁→ω₂ is Gaussian, and (iii) the exact time course of magnetization decay is dependent on the relaxation time in the motional narrowing limit and the correlation time describing the correlation function of the local frequencies. In contrast to previous publications, we conclude that a Gaussian equilibrium distribution of local frequencies does not imply a Gaussian-distributed phase angle. The general theory is illustrated by calculating the Green’s function of the transition dynamics for a stochastic process in the strong collision approximation. The result is highly relevant for describing relaxation processes in the presence of local field inhomogeneities.

Recent measurements of the π⁺π⁻ invariant-mass distribution at RHIC show a shifted peak for the ρ meson in 100A  GeV in peripheral Au+Au and even in p+p collisions. A recent theoretical study based on a picture of in-medium production rates of pions showed that a large shift could result from a combination of the Boltzmann factor and the collisional broadening of the ρ. Here we argue that the two-pion density of states is the appropriate quantity if one assumes a sudden breakup of the system. Methods for calculating the density of states which include Bose effects are derived. The resulting invariant-mass distributions are significantly enhanced at lower masses and the ρ peak is shifted downward by ∼35  MeV.

For Markovian dynamics of field fluctuations we present here an extended strong collision approximation, thereby putting our previous strong collision approach [Phys. Rev. Lett. 83, 4215 (1999)]) into a systematic framework. Our approach provides expressions for the free induction and spin-echo magnetization decays that may be solved analytically or at least numerically. It is tested for the generic cases of dephasing due to an Anderson-Weiss process and due to restricted diffusion in a linear field gradient.

A percolation model of nuclear fragmentation is used to interpret 10.2 GeV/c p+¹⁹⁷Au multifragmentation data. Emphasis is put on finding signatures of a continuous nuclear matter phase transition in finite nuclear systems. Based on model calculations, corrections accounting for physical constraints of the fragment detection and sequential decay processes are derived. Strong circumstantial evidence for a continuous phase transition is found, and the values of two critical exponents, σ  =  0.5±0.1 and τ  =  2.35±0.05, are extracted from the data. A critical temperature of T_c  =  8.3±0.2 MeV is found.

Producing rare isotopes through statistical multifragmentation is investigated using the Mekjian method for exact solutions of the canonical ensemble. Both the initial fragmentation and the sequential decay are modeled in such a way as to avoid Monte Carlo and thus provide yields for arbitrarily scarce fragments. The importance of sequential decay, exact particle-number conservation and the sensitivities to parameters such as density and temperature are explored. Recent measurements of isotope ratios from the fragmentation of different Sn isotopes are interpreted within this picture.

Emission of intermediate mass fragments (IMFs) (Z>~3) from central collisions of ⁴⁰Ar+⁴⁵Sc  (E/A=35–115 MeV), ⁵⁸Ni+⁵⁸Ni (E/A=35–105 MeV), and ⁸⁶Kr+⁹³Nb (E/A=35–95 MeV) was studied. For each system, the average number of IMFs per event increased with beam energy, reached a maximum, and then decreased. The beam energy of peak IMF production increased linearly with the combined mass of the system. The number of IMFs emitted at the peak also increased with the system mass. Percolation calculations showed a weaker dependence of the peak beam energy and the number of IMFs on the total mass of the system.

A method for analyzing a N-component percolation model in terms of one parameter p₊ is presented. In Monte Carlo simulations on 16³, 32³, 64³, and 128³ simple cubic lattices the percolation threshold p₊^c is determined for N=2. Continuous transitions of p₊^c are reported in two limits for the bond existence probabilities p₌ and p_≠. In the same limits, empirical formulas for the percolation threshold p₊^c as a function of one-component concentration f_b are proposed and links to existing percolation models are established. In the limit p₌=0 a different site percolation model is proposed and its threshold, f_b^c≃0.145, is reported.

Previous theoretical studies of the disappearance of directed transverse flow showed a dual dependence on the equation of state (EOS) and the in-medium cross section (σ_nn) for light systems. Also, the balance energy was shown to increase as a function of the impact parameter. However, Boltzmann-Uehling-Uhlenbeck (BUU) model calculations show that the dependence on σ_nn weakens for heavy systems such as Au+Au, and data presented here show that the impact parameter dependence nearly vanishes for Au+Au. Therefore, the EOS parameter K can be isolated using the balance energy, and BUU calculations show good agreement for a soft EOS. The reduction in σ_nn is then investigated using the experimental mass dependence of the balance energy.

The balance energy at which repulsive nucleon-nucleon scattering balances the attractive force due to the nuclear mean field is measured for the first time for the Au+Au reaction. The observed balance energy of 42±3_stat±1_sys MeV/nucleon agrees with the previously established power law dependence of E_bal on system mass, providing evidence that the Coulomb interaction does not suppress the attractive mean field near the balance energy, in contrast to recent theoretical predictions.

We present an analytical theory of susceptibility induced nuclear spin dephasing in the capillary network of myocardium. Using a strong collision approach, equations are obtained for the relaxation rate of the free induction and the spin echo decay. Simulation and experimental data are well predicted by the theory. Since paramagnetic deoxyhemoglobin as the origin of nuclear spin dephasing has a higher tissue concentration in myocardium supplied by a stenotic, i.e., significantly narrowed, coronary artery, spin dephasing might serve as a diagnostic tool. Our approach can be modified for capillary networks in other tissues than myocardium and may be applied in material science.

We confirm the importance of standard medium effects (hadronic rescattering) in heavy-ion collisions by using a perturbative-QCD-motivated hadronic model to investigate the dilepton spectra from Pb+Au collisions at 158 GeV/nucleon. These same effects, namely, prompt πρ→πe⁺e^-, have been studied in several CERN SPS systems [J. Murray, W. Bauer, and K. Haglin, Phys. Rev. C 57, 882 (1998)]. The results presented here are consistent with previous studies stating that this type of rescattering effect explains a portion of the “excess” lepton pairs seen by the CERES experiment, but not the entire effect.

The relationship between measured transverse energy, total charge recovered in the detector, and size of the emitting system is investigated. Using only very simple assumptions, we are able to reproduce the observed binomial emission probabilities and their dependences on the transverse energy. Our results show that the observed scaling can arise due to a combination of finite-size effects and detector acceptance effects.

We use a simple QCD-based model to study particle production in S+Au collisions at 200 GeV/nucleon. A requisite consistency is met for the hadronic observables (π⁰ and π^- spectra) while pursuing estimates for e⁺e^- production. Since radiative decays of initially produced hadrons has accounted for only a portion of the observed dileptons at the CERN SPS, we search for additional mechanisms. By including contributions from prompt secondary hadronic scatterings, πρ→πe⁺e^-, and adding to π⁺π^- annihilation and hadronic decays, part of the “excess” dilepton signal can possibly be interpreted.

Significant differences in the relationships between fragment, neutron, and charged particle multiplicities were found between ¹¹²Sn+¹¹²Sn and ¹²⁴Sn+¹²⁴Sn collisions at 40 MeV/A. In this paper we explore the possibility to explain this phenomenon in the framework of percolation models, and find that the results are only reproducible in part.

We reply to the preceding comment.

We introduce an additional method to solve Schrödinger’s equation for a free particle in an infinite well of arbitrary shape (the Helmholtz equation with Dirichlet boundary conditions), a problem of interest in the area of quantum chaos. We expand the wave function in a basis of products of sine functions, then use the constraint operator to contain the wave function to a region within the domain of the basis functions. In this manner, a quantum billiard problem of arbitrary shape can be solved. Several methods exist to solve problems of this sort, but as recent work reviewing these methods has shown, all have shortcomings. Our work represents a different direction in the solution of these problems. Our method is different in that it provides a means of computing an eigenbasis. It is also interesting from a physical standpoint in that it can represent the Hamiltonian of a classically chaotic system in the basis of a classically regular system. © 1996 The American Physical Society.

Sidewards directed fragment flow has been extracted for ⁸⁴Kr+¹⁹⁷Au collisions at E/A  =  200 MeV, using techniques that are free of reaction plane dispersion. The fragment flow per nucleon increases with mass, following a thermal or coalescencelike behavior, and attains roughly constant limiting values at 4≤A≤12. Comparisons of the impact parameter dependences of the measured coalescence-invariant proton flow to Boltzmann-Uehling-Uhlenbeck calculations clearly favor a momentum dependent nuclear mean field.

C₆₀ vapor was bombarded by ¹³⁶Xe³⁵⁺ and ¹³⁶Xe¹⁸⁺ ions in the energy range 420–625 MeV to study the various ionization and fragmentation processes that occur. Since the center-of-mass energies used in this work exceeded those of previous studies by several orders of magnitude, new excitation and dissociation modes were expected and indeed found. Positive ions were extracted from the interaction region and their times of flight were measured both singly and in coincidence with other ionic fragments. A wide range of stable charge states and cluster sizes from monatomic carbon up to C₆₀ was observed. Even-numbered carbon fragments dominated the heavier mass range but both even and odd carbon numbers occurred at lower masses. Evidence was found for three qualitatively different ionization and fragmentation channels suggesting different ranges of collision impact parameters: ionization of the parent C₆₀ molecule, loss of even numbers of carbon atoms, and ‘‘multifragmentation’’ into many small fragments. This latter mode included the production of singly charged C_n⁺ fragments with all values of n being observed from n=1 up to at least n=19. We interpret our results in terms of a theoretical model that indicates that the total interaction cross section contains comparable contributions from (a) excitation of the giant dipole plasmon resonance, and (b) large-energy-transfer processes that lead to multiple fragmentation of the molecule. The distribution of fragment cluster masses for n≲20 is reproduced by a ‘‘percolation theory’’ description analogous to that used to describe multifragmentation of nuclei by high-energy protons. © 1996 The American Physical Society.

A nonthermal expansive component has recently been interpreted from the observed light fragment spectra in Au + Au collisions. We have used the BUU transport model to generate several different freezeout surfaces and applied a coalescence algorithm to approximate the complete final state. We vary the microscopic details leading to specific equations of state, reduce cross sections, and isolate the effect of compression on the spectra for protons and helium isotopes. We find a radial flow signal consistent with experiment in the energy range 0.25A to 1.15A GeV, but find it to be rather insensitive to the microscopic details of the model calculations. © 1996 The American Physical Society.

We examine the line-wrap feature of text processors. We show that adding characters to previously formatted lines leads to the cascading of words to subsequent lines. The length of these cascades shows a power-law distribution. We show that this system is in a state of self-organized criticality. The connection to one-dimensional random walks and diffusion problems is demonstrated. Of particular interest is the exponential cutoff of the power-law distribution occurring for finite line lengths. Finally we examine the predictability of large cascades.

The dynamical evolution of central collisions induced by GeV light-ion projectiles is examined with two different Boltzmann-Uehling-Uhlenbeck (BUU) calculations. For projectile energies above 1 GeV incident on heavy target nuclei, a region of depleted density develops in the core of the nucleus at times of the order of 30 fm/c, producing hot residues with significantly depleted density at longer times. The simulations predict penetration of the target by the projectile momentum front at incident energies near 4–6 GeV, leading to a saturation of deposition energy. These results are examined in the context of marked changes in reaction observables reported for light-ion-induced collisions. © 1996 The American Physical Society.

Recently reported measurements of hard photon correlations in the reactions ³⁶Ar on ²⁷Al at 95A MeV, ⁸⁶Kr on ^natNi at 60A MeV, and ¹⁸¹Ta on ¹⁹⁷Au at 39.5A MeV are analyzed. A Boltzmann-Ühling-Uhlenbeck transport model is used to describe the photon production by individual nucleon-nucleon collisions. In the lighter systems we find the best agreement with data when taking into account only photons from first-chance collisions of nucleons or photons produced during the passage of the nuclei, while the model predicts also a considerable late-time emission of photons, which leads to a depletion of the calculated correlation function. The accuracy of the present data does not allow firm conclusions on the reliability of this late-time evolution. Our investigations do not support a recently reported interference pattern in the heavy Ta + Au system.

Two-proton correlation functions are measured for inclusive collisions of ¹⁶O + ¹⁹⁷Au at E/A=200 MeV. Calculations with the Boltzmann-Uehling-Uhlenbeck transport theory overpredict the dependence of the correlation function on the total momentum of the coincident proton pair, but correctly reproduce the energy-integrated correlation function.