W. F. J. Müller

Universality of spectator fragmentation at relativistic bombarding energies

Abstract Multi-fragment decays of 129Xe, 197Au and 238U projectiles in collisions with Be, C, Al, Cu, In, Au and U targets at energies between E A = 400 and 1000 MeV have been studied with the ALADIN forward-spectrometer at SIS. By adding an array of 84 SiCsI(Tl) telescopes the solid-angle coverage of the setup was extended to θlab = 16°. This permitted the complete detection of fragments from the projectile-spectator source. The dominant feature of the systematic set of data is the Zbound universality that is obeyed by the fragment multiplicities and correlations. These observables are invariant with respect to the entrance channel if plotted as a function of Zbound, where Zbound is the sum of the atomic numbers Zi of all projectile fragments with Zi ⩾ 2. No significant dependence on the bombarding energy nor on the target mass is observed. The dependence of the fragment multiplicity on the projectile mass follows a linear scaling law. The reasons for and the limits of the observed universality of spectator fragmentation are explored within the realm of the available data and with model studies. It is found that the universal properties should persist up to much higher bombarding energies than explored in this work and that they are consistent with universal features exhibited by the intranuclear cascade and statistical multifragmentation models.

Multifragmentation of spectators in relativistic heavy ion reactions

Abstract Using the ALADIN forward-spectrometer at SIS we have studied multi-fragment decays of 197 Au projectiles after collisions with C, Al, Cu and Pb targets at a bombarding energy of E A = 600 MeV . The new data presented in this work comprise the measured cross sections of multifragment processes, the N Z ratios of the produced fragments, and the differential distributions of fragment multiplicities and of observables built on the charge correlations within the event. The 197 Au+Cu data are analyzed with the statistical multifragmentation model. It is shown that all observables can be simultaneously reproduced on an absolute scale, apart from an overall normalization constant which relates the number of model events to the measured cross section. A continuous distribution of excited residual nuclei, used as input for the calculations, was derived from the criterion of a best fit to the data. It exhibits a correlation between decreasing mass number A and increasing excitation energy E x A and a saturation of the excitation energy at E x A ≈ 8 MeV .

Charge correlations as a probe of nuclear disassembly

Abstract We have studied multi-fragment decays of Au projectiles after collisions with C, Al, Cu and Pb targets at a bombarding energy of 600 MeV/nucleon. We examine the correlations between the charges emitted in these reactions. These correlations are given as a function of the total charge in bound fragments, Z bound , at forward angles, which is a measure of the violence of the collision and can be related to the impact parameter. The charge distributions have been fitted by a power law and the extracted τ parameter exhibits a minimum as a function of Z bound . We observe a strong reduction in the maximum charge, Z max , of the event with decreasing Z bound . For those events where Z max is less than half Z bound , the relative sizes of the two largest charges within the event cover the full spectrum of possibilities. The charge-Dalitz plots indicate that the multi-fragmentation events are not an extension of symmetric fission reactions. The event-by-event charge moments are examined to measure the size of the charge fluctuations. All of the charge correlations are independent of the target when plotted as a function of Z bound . The results are compared to both nuclear statistical and percolation calculations. The model predictions differ from each other, establishing that the observables are sensitive to how the available phase space is populated. The sequential nuclear model predicts too asymmetric a decay, while the simultaneous model predicts too symmetric a break-up. The percolation model, which was adjusted to reproduce the size of Z max , correctly predicts the mean behaviour and the fluctuations of the lighter fragments.

Statistical signatures of critical behavior in small systems

The cluster distributions of three different systems are examined to search for signatures of a continuous phase transition. In a system known to possess such a phase transition, both sensitive and insensitive signatures are present; while in systems known not to possess such a phase transition, only insensitive signatures are present. It is shown that nuclear multifragmentation results in cluster distributions belonging to the former category, suggesting that the fragments are the result of a continuous phase transition.

Constructing the phase diagram of finite neutral nuclear matter

Author(s): Elliott, J.B.; Moretto, L.G.; Phair, L.; Wozniak, G.L.; Albergo, S.; Bieser, F.; Brady, F.P.; Caccia, Z.; Cebra, D.A.; Chacon, A.D.; Chance, J.L.; Choi, Y.; Costa, S.; Gilkes, M.L.; Hauger, J.A.; Hirsch, A.S.; Hjort, E.L.; Insolia, A.; Justice, M.; Keane, D.; Kintner, J.C.; Lindenstruth, V.; Lisa, M.A.; Matis, H.S.; McMahan, M.; McParland, C.; Muller, W.F.J.; Olson, D.L.; Partlan, M.D.; Porile, N.T.; Potenza, R.; Rai, G.; Rasmussen, J.; Ritter, H.G.; Romanski, J.; Romero, J.L.; Russo, G.V.; Sann, H.; Scharenberg, R.P.; Scott, A.; Shao, Y.; Srivastava, B.K.; Symons, T.J.M.; Tincknell, M.; Tuve, C.; Wang, S.; Warren, P.; Wieman, H.H.; Wienold, T.; Wolf, K.

Isotopic dependence of the nuclear caloric curve

The A/Z dependence of projectile fragmentation at relativistic energies has been studied with the ALADIN forward spectrometer at SIS. A stable beam of (124)Sn and radioactive beams of (124)La and (107)Sn at 600 MeV per nucleon have been used in order to explore a wide range of isotopic compositions. Chemical freeze-out temperatures are found to be nearly invariant with respect to the A/Z of the produced spectator sources, consistent with predictions for expanded systems. Small Coulomb effects (DeltaT approximately 0.6 MeV) appear for residue production near the onset of multifragmentation.

Coincidence measurement of residues and light particles in the reaction Fe-56+p at 1 GeV per nucleon with the spallation reactions setup SPALADIN

The spallation of 56Fe in collisions with hydrogen at 1A GeV has been studied in inverse kinematics with the large-aperture setup SPALADIN at GSI. Coincidences of residues with low-center-of-mass kinetic energy light particles and fragments have been measured allowing the decomposition of the total reaction cross section into the different possible deexcitation channels. Detailed information on the evolution of these deexcitation channels with excitation energy has also been obtained. The comparison of the data with predictions of several deexcitation models coupled to the INCL4 intranuclear cascade model shows that only GEMINI can reasonably account for the bulk of collected results, indicating that in a light system with no compression and little angular momentum, multifragmentation might not be necessary to explain the data.

Nuclear multifragmentation, percolation and the Fisher Droplet model: common features of reducibility and thermal scaling

It is shown that the Fisher droplet model, 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 Collaboration 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.

Thermal and chemical freeze-out in spectator fragmentation

Isotope temperatures from double ratios of hydrogen, helium, lithium, beryllium, and carbon isotopic yields, and excited-state temperatures from yield ratios of particle-unstable resonances in {sup 4}He, {sup 5}Li, and {sup 8}Be, were determined for spectator fragmentation, following collisions of {sup 197}Au with targets ranging from C to Au at incident energies of 600 and 1000 MeV per nucleon. A deviation of the isotopic from the excited-state temperatures is observed which coincides with the transition from residue formation to multi-fragment production, suggesting a chemical freeze-out prior to thermal freeze-out in bulk disintegrations.

The search for the scaling function in the multifragmentation of gold nuclei

Abstract It is shown that thermodynamic scaling when applied to systems with few (∼150) constituents, in accordance with the theory of critical phenomena, is observed in nuclear multifragmentation. Yields of different nuclear fragments, obtained over a wide range of excitation energies, collapse with some scatter onto a universal curve. This curve is the nuclear scaling function, which is intimately related to the free energy of the system. The determination of the scaling function forms the basis for quantitatively predicting the critical behavior in nuclei.