W. A. Friedman

Isotopic Scaling in Nuclear Reactions

A three parameter scaling relationship between isotopic distributions for elements with Z< or =8 has been observed. This allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed isoscaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation, and deeply inelastic scattering. The origins of this scaling behavior for the various reaction mechanisms are explained. For multifragmentation processes, the systematics is influenced by the density dependence of the asymmetry term of the equation of state.

Isospin fractionation and isoscaling in dynamical simulations of nuclear collisions

Isoscaling is found to hold for fragment yields in the antisymmetrized molecular dynamics (AMD) simulations for collisions of calcium isotopes at 35 MeV/nucleon. This suggests the applicability of statistical considerations to the dynamical fragment emission. The observed linear relationship between the isoscaling parameters and the isospin asymmetry of fragments supports the above suggestion. The slope of this linear function yields information about the symmetry energy in low density region where multifragmentation occurs.

Multifragment Emission in the Reaction 36Ar + 197Au at E/A = 35, 50, 80, and 110 MeV

Abstract Multifragment emission in the reaction 36 Ar + 197 Au at E A =35, 80, and 110 MeV has been measured with a low-threshold 4π detector array. Over this broad range of incident energies, the mean values and variances of the intermediate mass fragment (IMF: 3 ⩽ Z ⩽ 20) multiplicity distributions exhibit an approximate scaling with the total charged particle multiplicity. The measured multiplicities of light charged particles and intermediate mass fragments are compared with both a model involving statistical decay of an expanding compound nucleus, and with a model involving microscopic quasi-particle dynamics. The statistical decay model predictions are sensitive to the low-density nuclear equation of state.

Conditions for isoscaling in nuclear reactions

With the availability of rare isotope beams as well as detection systems that can resolve the masses and charges of the detected particles, isotope yields become an important observable for studying nuclear collisions of heavy ions @1,2#. This additional freedom on isospin asymmetry allows one to study the properties of bulk nuclear matter that are affected by the nucleon composition of the nuclei such as the isospin dependence of the liquid gas phase transition of nuclear matter @3‐5# and the asymmetry term @ 6‐9 # in the nuclear equation of state. To minimize undesirable complications stemming from the sequential decays of primary unstable fragments, it has been proposed that isospin effects can best be studied by comparing the same observables in two similar reactions that differ mainly in isospin asymmetry @5,7,9#. If two reactions, 1 and 2, have the same temperature but different isospin asymmetry, for example, the ratios of a specific isotope yield with neutron and proton numberN and Z obtained from system 2 and system 1 have been observed to exhibit isoscaling, i.e., exponential dependence of the form @5,7# R21~ N,Z!5Y 2~ N,Z!/Y 1~ N,Z!5C exp~ Na1Zb!, ~1!

Barrier-top resonances and heavy ion reactions☆

Abstract In reactions involving strong absorption, we show that the narrowest potential (two body) resonances may be of a novel type, barrier-top (or “orbiting”) resonances whose ReE are at the centrifugal-Coulomb barrier top and whose wave functions are localized at the barrier radius. These resonances provide the link between semiclassical orbiting and quantal Regge poles and establish the close relationship between these concepts. We exploit the dominance and simplicity of barrier-top scattering in a model in which direct reaction amplitudes for heavy ion particle transfers can be calculated analytically. The model assumes complete absorption at small r of inward propagating waves, and a parabolic barrier potential which approximates the optical potential in the barrier region; the wave functions of the model (Weber functions) correspondingly approximate the optical potential wave functions (distoreed waves) in the barrier region. The results of this model reproduce many of the features present in more detailed DWBA computations, and provide simple physical explanations for these features.

Information theory and statistical nuclear reactions II. Many-channel case and Hauser-Feshbach formula☆

Abstract The information approach developed in paper I is applied to the case of systems having a large number of channels (n ⪢ 1) and arbitrary optical matrices S . The fluctutation cross section is explicitly evaluated using the maximum information-entropy S-matrix distribution constructed to reproduce S and constrained solely by flux conservation, time reversal invariance, causality, and ergodicity. The resulting expression is found to be the well-known Hauser-Feshbach formula. The evaluation of the cross section is performed with the aid of an auxiliary S-matrix (obtained by a specific mapping from the physical one) which is distributed according to the invariant volume element. The joint distribution for the elements of the physical S-matrix is evaluated in the limit n ⪢ 1 and found to be Gaussian.

Preequilibrium reactions: Statistical fluctuations and doorways

Abstract An important type of statistical reaction is one that has recently been described as “multistep compound”, because it proceeds through successive classes of doorways. That is, it is a reaction that proceeds through resonances which overlap, and whose partial widths are enhanced by doorways which themselves overlap, with the partial widths of the doorways themselves enhanced by even broader overlapping doorways, etc. A particularly concise theoretical description of such a reaction can be achieved by the use of a nested sequence of energy-averaging intervals I 1 > I 2 ⋯> I N , where each I n is intermediate between the widths of two successive classes of doorways. The present Repor t provides the full details of this approach and employs it to obtain the multidoorway generalizations, first, of the Hauser-Feshbach expression for σ fl and, more important ly, of the Ericson expression for the autocorrelation function, which is found to exhibit several correlation widths, one for each class of doorways. The results are derived in the Feshbach projection-operator formalism. A comparison with the approaches of Agassi, Weidenmuller and Mantzouranis, and of Feshbach, Kerman and Koonin, shows that all three share the features of being (1) probability-conserving and (2) Markovian in their description of the percolation of flux through the doorway classes.

Heating nuclear matter with GeV 3He beams

Abstract The heating curve for hot nuclei formed in the 4.8 GeV 3 He+ nat Ag, 197 Au reactions has been derived from reconstructed excitation-energy distributions and temperatures based on 2,3 H/ 3,4 He isotope ratios. Intranuclear-cascade predictions over-estimate the excitation-energy distributions for hot thermal-like residues, but are in general agreement with the data when contributions from preequilibrium emission are included. Both targets exhibit nearly an identical temperature vs. excitation energy dependence. The heating curve initially increases rapidly, undergoes a slope change near E ∗ /A = 2–3 MeV, and then follows a gradual monotonic increase up to E ∗ /A = 10 MeV. The results are in qualitative agreement with predictions of EES and SMM multifragmentation models.

Mass parametrizations and predictions of isotopic observables

We discuss the accuracy of mass models for extrapolating to very asymmetric nuclei and the impact of such extrapolations on the predictions of isotopic observables in multifragmentation. We obtain improved mass predictions by incorporating measured masses and extrapolating to unmeasured masses with a mass formula that includes surface symmetry and Coulomb terms. We find that using accurate masses has a significant impact on the predicted isotopic observables.

Expansion effects in intermediate energy heavy-ion reactions

Abstract Transverse kinetic energy spectra of fragments in the reaction 36 Ar + 197 Au are used to probe the multifragmentation mechanism at intermediate energies. The mass dependence of the average transverse kinetic energy is examined in the context of the statistical decay of an expanding, emitting source. The role of source expansion during emission is explored. Results suggest the onset of volume emission at the highest incident energy.