Compressibility and equation of state of finite nuclei
We present a new approach for calculating the nuclear equation of state and compressibility for finite nuclei using the density-constrained Hartree-Fock method.
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arXiv subjects
A. S. Umar
Publications and source records attributed to A. S. Umar.
Study of $^{64}$Ni+$^{132}$Sn Fusion with Density Constrained TDHF Formalism
We study fusion reactions of the $^{64}$Ni+$^{132}$Sn system using the recently introduced density constrained time-dependent Hartree-Fock formalism. In this formalism the fusion barriers are directly obtained from TDHF dynamics. In addition, we incorporate the entrance channel alignment of the deformed (oblate) $^{64}$Ni nucleus due to dynamical Coulomb excitation. We discuss the influence of particle transfer and other dynamical effects on the fusion cross sections. Calculated cross sections are in very good agreement with data and other calculations.
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Skyrme-HFB Calculations in Coordinate Space for the Krypton Isotopes Up to the Two-Neutron Dripline
For axially symmetric even-even nuclei, we solve the Hartree-Fock-Bogoliubov (HFB) equations on a 2-D grid in cylindrical coordinates. The Skyrme SLy4 interaction is used for the mean field and a zero-range interaction for the pairing field. After decoupling the HFB lattice equations, we obtain quasiparticle states with equivalent single-particle energies up to 100 MeV or more. We present results for the Krypton isotope chain up to the two-neutron dripline, including two-neutron separation energies, pairing gaps, and quadrupole deformations for the ground states and isomeric minima.
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Dynamical deformation effects in subbarrier fusion of $^{64}$Ni+$^{132}$Sn
We show that dynamical deformation effects play an important role in fusion reactions involving the $^{64}$Ni nucleus, in particular the $^{64}$Ni+$^{132}$Sn system. We calculate fully microscopic interaction potentials and the corresponding subbarrier fusion cross sections.
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Heavy-ion interaction potential deduced from density-constrained TDHF calculation
We present a new method for calculating the heavy-ion interaction potential from a density-constrained time-dependent Hartree-Fock calculation.
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TDHF fusion calculations for spherical+deformed systems
We outline a formalism to carry out TDHF calculations of fusion cross sections for spherical + deformed nuclei. The procedure incorporates the dynamic alignment of the deformed nucleus into the calculation of the fusion cross section. The alignment results from multiple E2/E4 Coulomb excitation of the ground state rotational band. Implications for TDHF fusion calculations are discussed. TDHF calculations are done in an unrestricted three-dimensional geometry using modern Skyrme force parametrizations.
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3-D unrestricted TDHF fusion calculations using the full Skyrme interaction
We present a study of fusion cross sections using a new generation Time-Dependent Hartree-Fock (TDHF) code which contains no approximations regarding collision geometry and uses the full Skyrme interaction, including all of the time-odd terms. In addition, the code uses the Basis-Spline collocation method for improved numerical accuracy. A comparative study of fusion cross sections for $^{16}O + ^{16,28}O$ is made with the older TDHF results and experiments. We present results using the modern Skyrme forces and discuss the influence of the new terms present in the interaction.
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Coordinate Space HFB Calculations for the Zirconium Isotope Chain up to the Two-Neutron Dripline
We solve the Hartree-Fock-Bogoliubov (HFB) equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice utilizing the Basis-Spline expansion method. Results are presented for the neutron-rich zirconium isotopes up to the two-neutron dripline. In particular, we calculate binding energies, two-neutron separation energies, normal densities and pairing densities, mean square radii, quadrupole moments, and pairing gaps. Very large prolate quadrupole deformations (beta2=0.42,0.43,0.47) are found for the (102,104,112)Zr isotopes, in agreement with recent experimental data. We compare 2-D Basis-Spline lattice results with the results from a 2-D HFB code which uses a transformed harmonic oscillator basis.
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Time-Dependent Response Calculations of Nuclear Resonances
A new alternate method for evaluating linear response theory is formally developed, and results are presented. This method involves the time-evolution of the system using TDHF and is constructed directly on top of a static Hartree-Fock calculation. By Fourier transforming the time-dependent result the response function and the total probability amplitude are extracted. This method allows for a coherent description of static properties of nuclei, such as binding energies and deformations, while also providing a method for calculating collective modes and reaction rates. A full 3-D Cartesian Basis-Spline collocation representation is used with several Skyrme interactions. Sample results are presented for the giant multipole resonances of 16O, 40Ca, and 32S and compared to other calculations.
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Hartree-Fock-Bogoliubov Calculations in Coordinate Space: Neutron-Rich Sulfur, Zirconium, Cerium, and Samarium Isotopes
Using the Hartree-Fock-Bogoliubov (HFB) mean field theory in coordinate space, we investigate ground state properties of the sulfur isotopes from the line of stability up to the two-neutron dripline ($^{34-52}S$). In particular, we calculate two-neutron separation energies, quadrupole moments, and rms-radii for protons and neutrons. Evidence for shape coexistence is found in the very neutron-rich sulfur isotopes. We compare our calculations with results from relativistic mean field theory and with available experimental data. We also study the properties of neutron-rich zirconium ($^{102,104}Zr$), cerium ($^{152}Ce$), and samarium ($^{158,160}Sm$) isotopes which exhibit very large prolate quadrupole deformations.
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Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines
Nuclei far from stability are studied by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on two-dimensional axially symmetric lattice, in coordinate space. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. The detailed representation of the HFB equations in cylindrical coordinates is discussed. Calculations of observables for nuclei near the neutron drip line are presented to demonstrate the reliability of the method.
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Nuclear structure near the neutron dripline: lattice HFB calculations with high-energy continuum coupling
We have developed a new Hartree-Fock-Bogoliubov (HFB) code which has been specifically designed to study ground state properties of nuclei near the neutron and proton drip lines. The unique feature of our code is that it takes into account the strong coupling to high-energy continuum states, up to an equivalent single-particle energy of 60 MeV. We solve the HFB equations for deformed, axially symmetric even-even nuclei in coordinate space on a 2-D lattice with Basis-Spline methods. For the p-h channel, the Skyrme (SLy4) effective N-N interaction is utilized, and for the p-p and h-h channel we use a delta interaction. We present results for binding energies, deformations, normal densities and pairing densities, Fermi levels, and pairing gaps. In particular, we will discuss neutron-rich isotopes of oxygen (O-22) and tin (Sn-150).
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Quadrupole resonances in unstable oxygen isotopes in time-dependent density-matrix formalism
The strength functions of quadrupole modes in the unstable oxygen isotopes 22O and 24O are calculated using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). It is found that TDDM gives the lowest quadrupole states which are energetically shifted upward and become significantly collective due to the coupling to two-body configurations. It is pointed out that these features of the lowest quadrupole states are similar to those obtained in the quasi-particle random phase approximation.
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HFB Calculations Near the Drip Lines
We present the first set of results of solving the Hartree-Fock-Bogoliubov equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on a two-dimensional axially symmetric lattice, in coordinate space. An important aspect of our method is the proper representation of the quasi-particle continuum wavefunctions, which are considered for energies up to 60 MeV. This stage is essential for a proper description of nuclei near the drip lines, due to the strong coupling between weakly bound states and the particle continuum for such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. Calculations for Sn isotopes are presented to demonstrate the reliability of the method.
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Dipole resonances in oxygen isotopes in time-dependent density-matrix theory
The strength functions of isovector dipole resonances in the even oxygen isotopes $^{18\sim24}$O are calculated by using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). The results are compared with recent experimental data and also with a shell-model calculation. It is found that the observed isotope dependence of low-lying dipole strength is reproduced in TDDM when the strength of the residual interaction is properly chosen. It is also found that there is a difference between the TDDM prediction and the shell-model calculation for $^{24}$O.
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HFB theory for nuclei near the drip-lines: continuum coupling
We have developed a new HFB code that specifically addresses nuclear structure physics near the driplines. The HFB equations are solved on a two-dimensional lattice for axially symmetric even-even nuclei using B-Spline techniques. The quasiparticle energy spectrum is obtained by direct diagonalization of the HFB lattice Hamiltonian with LAPACK. The energy spectrum extends high into the continuum, up to several thousand MeV. Calculations with Skyrme forces and (density-dependent) delta pairing interactions are now underway.
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Relativistic Heavy--Ion Collisions in the Dynamical String--Parton Model
We develop and extend the dynamical string parton model. This model, which is based on the salient features of QCD, uses classical Nambu-Gotō strings with the endpoints identified as partons, an invariant string breaking model of the hadronization process, and interactions described as quark-quark interactions. In this work, the original model is extended to include a phenomenological quantization of the mass of the strings, an analytical technique for treating the incident nucleons as a distribution of string configurations determined by the experimentally measured structure function, the inclusion of the gluonic content of the nucleon through the introduction of purely gluonic strings, and the use of a hard parton-parton interaction taken from perturbative QCD combined with a phenomenological soft interaction. The limited number of parameters in the model are adjusted to $e^+e^-$ and $p $--$p$ data. Utilizing these parameters, the first calculations of the model for $p $--$A$ and $A$--$A$ collisions are presented and found to be in reasonable agreement with a broad set of data.
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The Interplay Between Protoneutron Star Convection and Neutrino Transport in Core Collapse Supernovae
We couple two-dimensional hydrodynamics to realistic one-dimensional multigroup flux-limited diffusion neutrino transport to investigate protoneutron star convection in core collapse supernovae, and more specifically, the interplay between its development and neutrino transport, for both 15 and 25 solar mass models. In the presence of neutrino transport, protoneutron star convection velocities are too small relative to bulk inflow velocities to result in any significant convective transport of entropy and leptons. A simple analytical model supports our numerical results, indicating that the inclusion of neutrino transport reduces the entropy-driven (lepton-driven) convection growth rates and asymptotic velocities by a factor of 3 (50) at the neutrinosphere and a factor 250 (1000) at a density of 10^{12} g/cm^{3}, for both our 15 and 25 solar mass models. Moreover, when transport is included, the initial postbounce entropy gradient is smoothed out by neutrino diffusion, whereas the initial lepton gradient is maintained by electron capture and neutrino escape near the neutrinosphere. Despite the maintenance of the lepton gradient, protoneutron star convection does not develop over the 100 ms duration typical of all our simulations, except in the instance where ``low-test'' initial conditions are used, which are generated by core collapse and bounce simulations that neglect neutrino-electron scattering and ion-ion screening corrections to neutrino- nucleus elastic scattering.
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