arXiv subjects

W. A. Friedman

Publications and source records attributed to W. A. Friedman.

18 recordsLinked to original sources

arXiv2009

Odd-even staggering in nuclear binding and the liquid-drop model

The trends with mass number are examined for the odd-even-staggering (OES) in nuclear binding of neutrons and protons through the conventional measures $Δ^{(3)}$. The large differences previously observed between these trends for even and odd values of these measures is found to arise, in part, from the slow variation of binding energies with mass and charge which provides a background contribution. This background is estimated with the liquid-drop model, and accounts for the greater difference found in proton removal relative to neutron removal. The differences which persist after backgrounds are removed can not be treated in the conventional liquid-drop model but require the addition of a new term. Such a term is investigated, and its effect on specific values of the OES is calcutated. The liquid-drop fitting is also applied to a set of separation energies constrained to match the specific set of nuclei used to determine the observed values for the odd $Δ^{(3)}$. The resulting fit for the pairing term is compared to the average value of even and odd measures. The effect on this value of the new liquid-drop term is observed, and the change in background when the new term is included is also used as an alternate method for determining the difference between trends of the even and odd values of the OES.

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arXiv2008

Whence the odd-even staggering in nuclear binding?

We explore the systematics of odd-even mass staggering with a view to identifying the physical mechanisms responsible. The BCS pairing and mean field contributions have A- and number parity dependencies which can help disentangle the different contributions. This motivates the two-term parametrization c_1 + c_2/A as a theoretically based alternative to the inverse power form traditionally used to fit odd-even mass differences. Assuming that the A-dependence of the BCS pairing is weak, we find that mean-field contributions are dominant below mass number A~40 while BCS pairing dominates in heavier nuclei.

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arXiv2007

Fragmentation cross-sections and binding energies of neutron-rich nuclei

An exponential dependence of the fragmentation cross-section on the average binding energy is observed and reproduced with a statistical model. The observed functional dependence is robust and allows the extraction of binding energies from measured cross-sections. From the systematics of 75,77,78,79Cu isotope cross-sections have been extracted. They are 636.94 +/- 0.40 MeV, 647.1 +/- 0.4 MeV, 651.6 +/- 0.4 MeV and 657.8 +/- 0.5 MeV, respectively. Specifically, the uncertainty of the binding energy of 75Cu is reduced from 980 keV (listed value in the 2003 mass table of Audi and Wapstra) to 400 keV. The predicted cross-sections of two near drip-line nuclei, 39Na and 40Mg, from the fragmentation of 48Ca are discussed.

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arXiv2007

Extrapolation of neutron-rich isotope cross-sections from projectile fragmentation

Using the measured fragmentation cross sections produced from the 48Ca and 64Ni beams at 140 MeV per nucleon on 9Be and 181Ta targets, we find that the cross sections of unmeasured neutron rich nuclei can be extrapolated using a systematic trend involving the average binding energy. The extrapolated cross-sections will be very useful in planning experiments with neutron rich isotopes produced from projectile fragmentation. The proposed method is general and could be applied to other fragmentation systems including those used in other radioactive ion beam facilities.

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arXiv2007

Neutron-Proton pairing revisited

We reexamine neutron-proton pairing as a phenomenon that should be explanable in a microscopic theory of nuclear binding energies. Empirically, there is an increased separation energy when both neutron and proton numbers are even or if they are both odd. The enhancement is present at some level in nearly all nuclei: the separation energy difference has the opposite sign in less than 1% of the cases in which sufficient data exist. We discuss the possible origin of the effect in the context of density functional theory (DFT) and its extensions. Neutron-proton pairing from the Hartree-Fock-Bogoliubov theory does not seem promising to explain the effect. We demonstrate that much of the increased binding in the odd-odd system might be understood as a recoupling energy. This suggests that the DFT should be extended by angular momentum projection to describe the effect.

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arXiv2006

Comparisons of Statistical Multifragmentation and Evaporation Models for Heavy Ion Collisions

The results from ten statistical multifragmentation models have been compared with each other using selected experimental observables. Even though details in any single observable may differ, the general trends among models are similar. Thus these models and similar ones are very good in providing important physics insights especially for general properties of the primary fragments and the multifragmentation process. Mean values and ratios of observables are also less sensitive to individual differences in the models. In addition to multifragmentation models, we have compared results from five commonly used evaporation codes. The fluctuations in isotope yield ratios are found to be a good indicator to evaluate the sequential decay implementation in the code. The systems and the observables studied here can be used as benchmarks for the development of statistical multifragmentation models and evaporation codes.

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arXiv2006

Comment on "Symmetry energy and the isospin dependent equation of state"

In a recent paper, Shetty et al [Phys. Rev. C 70, 011601R (2004)] reported that the experimental isoscaling parameters aexp from several reactions favor the Gogny-AS effective nucleon-nucleon interaction over Gogny interaction. This conclusion is reached by comparing data to Antisymmetrized Molecular Dynamics (AMD) predictions for collisions of calcium isotopes. The specific simulations produce excited fragments at t=300 fm/c before they decay. Sequential decay calculations of the excited fragments suggest that the isoscaling parameter apri from the AMD calculations could be reduced by as much as 50%. We also explore the linear equation used to relate other reactions to the AMD calculations for Ca+Ca collisions. The uncertainty in the relation is larger than the differences between the predicted apri when using Gogny and Gogny-AS interactions.

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arXiv2006

Cooling Dynamics in Multi-fragmentation processes

Fragment energy spectra of neutron deficient isotopes are significantly more energetic than those of neutron rich isotopes of the same element. This trend is well beyond what can be expected for the bulk multi-fragmentation of an equilibrated system. It can be explained, however, if some of these fragments are emitted earlier through the surface of the system while it is expanding and cooling.

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arXiv2004

Symmetry energy for fragmentation in dynamical nuclear collisions

We extract values for the free symmetry energy as a function of the fragment size (the proton number Z) from antisymmetrized molecular dynamics (AMD) calculations of calcium collisions. Simple statistical physics describe well the distribution of hot nuclei at breakup, provided the surface symmetry term in the free energy is much smaller at high excitation than in ground state nuclei. This result may reflect the condition of low density and finite temperature when these systems disassemble.

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arXiv2003

Isotopic Yields and Isoscaling in Fission

A simple model is proposed to examine the isotopic yields of the fragments from binary fission. For a given charge partition the peaks and widths in the isotope distributions are studied both with the liquid-drop model and with shell modifications. The basis for isoscaling is also explored. The symmetry energy plays a dominant role in both the distributions and the isoscaling behavior. A systematic increase in the isoscaling parameter, $α$, with the proton number of the fragment element is predicted in the context of the liquid-drop model. Deviations arising from shell corrections are explored.

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arXiv2003

Isospin Diffusion in Heavy Ion Reactions

Using symmetric 112Sn+112Sn, 124Sn+124Sn collisions as references, we probe isospin diffusion in peripheral asymmetric 112Sn+124Sn, 124Sn+112Sn systems at incident energy of E/A=50 MeV. Isoscaling analyses imply that the quasi-projectile and quasi-target in these collisions do not achieve isospin equilibrium, permitting an assessment of the isospin transport rates. We find that comparisons between isospin sensitive experimental and theoretical observables, using suitably chosen scaled ratios, permit investigation of the density dependence of the asymmetry term of the nuclear equation of state.

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arXiv2003

Isospin fractionation and isoscaling in dynamical 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.

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arXiv2003

Mass Parameterizations 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.

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arXiv2003

Measuring Neutron Separation Energies Far from Stability

A method is proposed for the experimental measurement of neutron separation energies for nuclei far from stability. The procedure is based on determining cross sections for the production of nuclei, by projectile fragmentation, for which only protons are removed but for which the number of neutrons is left unchanged. A simple Abrasion-Ablation analysis leads to a cross section prediction which is sensitive to the neutron separation energy after a single parameter is adjusted in comparison with data. Examples which illustrate the method are presented.

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arXiv2002

Generalized Isoscaling of Isotopic Distributions

Generalized isoscaling relationships are proposed that may permit one to relate the isotopic distributions of systems that may not be at the same temperature. The proposed relationships are applied to multifragmentation excitation functions for central Kr+Nb and Ar+Sc collisions.

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arXiv2001

Conditions for Isoscaling in Nuclear Reactions

Isoscaling, where ratios of isotopes emitted from two reactions exhibit an exponential dependence on the neutron and proton number of the isotope, has been observed over a variety of reactions including evaporation, strongly damped binary collision, and multifragmentation. The conditions for isoscaling to occur as well as the conditions when isoscaling fails are investigated.

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arXiv2001

Study of Isoscaling with Statistical Multifragmentation Models

Different statistical multifragmentation models have been used to study isoscaling, i.e. the factorization of the isotope ratios from two reactions, into fugacity terms of proton and neutron number, R21(N,Z)=Y2(N,Z)/Y1(N,Z)=C*exp(a*N+b*Z). Even though the primary isotope distributions are quite different from the final distributions due to evaporation from the excited fragments, the values of a and b are not much affected by sequential decays. a is shown to be mainly sensitive to the proton and neutron composition of the emitting source and may be used to study isospin-dependent properties in nuclear collisions such as the symmetry energy in the equation of state of asymmetric nuclear matter.

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arXiv2001

Isotopic Scaling in Nuclear Reactions

A three parameter scaling relationship between isotopic distributions for elements with Z$\leq 8$ has been observed that allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed iso-scaling) 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.

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