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N. Schunck

Publications and source records attributed to N. Schunck.

At least 55 records · Page 3Linked to original sources

Computing Heavy Elements

Reliable calculations of the structure of heavy elements are crucial to address fundamental science questions such as the origin of the elements in the universe. Applications relevant for energy production, medicine, or national security also rely on theoretical predictions of basic properties of atomic nuclei. Heavy elements are best described within the nuclear density functional theory (DFT) and its various extensions. While relatively mature, DFT has never been implemented in its full power, as it relies on a very large number (~ 10^9-10^12) of expensive calculations (~ day). The advent of leadership-class computers, as well as dedicated large-scale collaborative efforts such as the SciDAC 2 UNEDF project, have dramatically changed the field. This article gives an overview of the various computational challenges related to the nuclear DFT, as well as some of the recent achievements.

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Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): a new version of the program

We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite temperature formalism for the HFB and HF+BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected.

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Surface Symmetry Energy of Nuclear Energy Density Functionals

We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron- rich matter and description of fission rates for r-process nucleosynthesis.

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Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization

In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test $χ^2$ function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.

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Nuclear Energy Density Optimization

We carry out state-of-the-art optimization of a nuclear energy density of Skyrme type in the framework of the Hartree-Fock-Bogoliubov (HFB) theory. The particle-hole and particle-particle channels are optimized simultaneously, and the experimental data set includes both spherical and deformed nuclei. The new model-based, derivative-free optimization algorithm used in this work has been found to be significantly better than standard optimization methods in terms of reliability, speed, accuracy, and precision. The resulting parameter set UNEDFpre results in good agreement with experimental masses, radii, and deformations and seems to be free of finite-size instabilities. An estimate of the reliability of the obtained parameterization is given, based on standard statistical methods. We discuss new physics insights offered by the advanced covariance analysis.

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One-quasiparticle States in the Nuclear Energy Density Functional Theory

We study one-quasiproton excitations in the rare-earth region in the framework of the nuclear Density Functional Theory in the Skyrme-Hartree-Fock-Bogoliubov variant. The blocking prescription is implemented exactly, with the time-odd mean field fully taken into account. The equal filling approximation is compared with the exact blocking procedure. We show that both procedures are strictly equivalent when the time-odd channel is neglected, and discuss how nuclear alignment properties affect the time-odd fields. The impact of time-odd fields on calculated one-quasiproton bandhead energies is found to be rather small, of the order of 100-200 keV; hence, the equal filling approximation is sufficiently precise for most practical applications. The triaxial polarization of the core induced by the odd particle is studied. We also briefly discuss the occurrence of finite-size spin instabilities that are present in calculations for odd-mass nuclei when certain Skyrme functionals are employed.

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HFODD (v2.40h) User's Guide

We describe the input data and installation procedures of the code HFODD (v2.40h). The present write-up contains complete and comprehensive information that has originally been given in six independent publications. It is enhanced by the subject index and indexes of variables, input-data keywords, subroutines, and files that are used in this user guide.

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Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) HFODD (v2.38j): a new version of the program

We describe the new version (v2.38j) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for state-dependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D2h transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected two insignificant errors.

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Odd-even mass differences from self-consistent mean-field theory

We survey odd-even nuclear binding energy staggering using density functional theory with several treatments of the pairing interaction including the BCS, Hartree-Fock-Bogoliubov, and the Hartree-Fock-Bogoliubov with the Lipkin-Nogami approximation. We calculate the second difference of binding energies and compare with 443 measured neutron energy differences in isotope chains and 418 measured proton energy differences in isotone chains. The particle-hole part of the energy functional is taken as the SLy4 Skyrme parametrization and the pairing part of the functional is based on a contact interaction with possible density dependence. An important feature of the data, reproduced by the theory, is the sharp gap quenching at magic numbers. With the strength of the interaction as a free parameter, the theory can reproduce the data to an rms accuracy of about 0.25 MeV. This is slightly better than a single-parameter phenomenological description but slightly poorer than the usual two-parameter phenomenological form C/A^alpha . The following conclusions can be made about the performance of common parametrization of the pairing interaction: (i) there is a weak preference for a surface-peaked neutron-neutron pairing, which might be attributable to many-body effects; (ii) a larger strength is required in the proton pairing channel than in the neutron pairing channel; (iii) pairing strengths adjusted to the well-known spherical isotope chains are too weak to give a good overall fit to the mass differences.

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Search for Fingerprints of Tetrahedral Symmetry in $^{156}Gd$

Theoretical predictions suggest the presence of tetrahedral symmetry as an explanation for the vanishing intra-band E2-transitions at the bottom of the odd-spin negative parity band in $^{156}Gd$. The present study reports on experiment performed to address this phenomenon. It allowed to determine the intra-band E2 transitions and branching ratios B(E2)/B(E1) of two of the negative-parity bands in $^{156}Gd$.

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Nuclear Halos and Drip Lines in Symmetry-Conserving Continuum HFB Theory

We review the properties of nuclear halos and nuclear skins in drip line nuclei in the framework of the spherical Hartree-Fock-Bogoliubov theory with continuum effects and projection on good particle number with the Gogny force. We first establish the position of the un-projected HFB drip lines for the two most employed parametrizations of the Gogny force and show that the use of finite-range interactions leads almost always to small-sized halos, even in the least bound nuclei, which is in agreement with most mean-field predictions. We also discuss the size of the neutron skin at the drip line and its relation to neutron asymmetry. The impact of particle-number projection and its conceptual consequences near the drip line are analyzed in detail. In particular, we discuss the role of the chemical potential in a projected theory and the criteria required to define the drip line. We show that including particle number projection can shift the latter, in particular near closed shells. We notice that, as a result, the size of the halo can be increased due to larger pairing correlations. However, combining the most realistic pairing interaction, a proper treatment of the continuum and particle number projection does not permit to reproduce the very large halos observed in very light nuclei.

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Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations

The coordinate space formulation of the Hartree-Fock-Bogoliubov (HFB) method enables self-consistent treatment of mean-field and pairing in weakly bound systems whose properties are affected by the particle continuum space. Of particular interest are neutron-rich, deformed drip-line nuclei which can exhibit novel properties associated with neutron skin. To describe such systems theoretically, we developed an accurate 2D lattice Skyrme-HFB solver {\hfbax} based on B-splines. Compared to previous implementations, we made a number of improvements aimed at boosting the solver's performance. These include: explicit imposition of axiality and space inversion, use of the modified Broyden's method to solve self-consistent equations, and a partial parallelization of the code. {\hfbax} has been benchmarked against other HFB solvers, both spherical and deformed, and the accuracy of the B-spline expansion was tested by employing the multiresolution wavelet method. Illustrative calculations are carried out for stable and weakly bound nuclei at spherical and very deformed shapes, including constrained fission pathways. In addition to providing new physics insights, {\hfbax} can serve as a useful tool to assess the reliability and applicability of coordinate-space and configuration-space HFB solvers, both existing and in development.

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Continuum and Symmetry-Conserving Effects in Drip-line Nuclei Using Finite-range Forces

We report the first calculations of nuclear properties near the drip-lines using the spherical Hartree-Fock-Bogoliubov mean-field theory with a finite-range force supplemented by continuum and particle number projection effects. Calculations were carried out in a basis made of the eigenstates of a Woods-Saxon potential computed in a box, thereby garanteeing that continuum effects were properly taken into account. Projection of the self-consistent solutions on good particle number was carried out after variation, and an approximation of the variation after projection result was used. We give the position of the drip-lines and examine neutron densities in neutron-rich nuclei. We discuss the sensitivity of nuclear observables upon continuum and particle-number restoration effects.

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Strong Deformation Effects in Hot Rotating 46Ti

Exotic-deformation effects in 46Ti nucleus were investigated by analysing the high-energy gamma-ray and the alpha-particle energy spectra. One of the experiments was performed using the charged-particle multi-detector array ICARE together with a large volume (4"x4") BGO detector. The study focused on simultaneous measurement of light charged particles and gamma-rays in coincidence with the evaporation residues. The experimental data show a signature of very large deformations of the compound nucleus in the Jacobi transition region at the highest spins. These results are compared to data from previous experiments performed with the HECTOR array coupled to the EUROBALL array, where it was found that the GDR strength function is highly fragmented, strongly indicating a presence of nuclei with very large deformation.

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Tetrahedral correlations in $^{80}$Zr and $^{98}$Zr

Axial octupole and tetrahedral correlations in $^{80}$Zr and $^{98}$Zr have been investigated using the generator coordinate method, applied to a basis generated by Skyrme HF+BCS calculations. We focus on the possible presence of states with tetrahedral symmetry and their stability with respect to octupole vibrations. We show that pairing significantly reduces the stability of the tetrahedral configuration and that a shallow mean-field tetrahedral minimum coexists with an axial octupole minimum. The contributions to the correlation energies coming from the tetrahedral degree of freedom and octupole axial deformation are discussed.

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Nuclei with Tetrahedral Symmetry

We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.

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Quantum fluctuations and stability of tetrahedral deformations in atomic nuclei

The possible existence of stable axial octupole and tetrahedral deformations is investigated in $^{80}$Zr and $^{98}$Zr. HFBCS calculations with parity projection have been performed for various parametrizations of the Skyrme energy functional. The correlation and excitation energies of negative parity states associated with shape fluctuations have been obtained using the generator coordinate method (GCM). The results indicate that in these nuclei both the axial octupole and tetrahedral deformations are of dynamic character and possess similar characteristics. Various Skyrme forces give consistent results as a function of these two octupole degrees of freedom both at the mean-field level as well as for configuration mixing calculations.

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Deformation Effects in Hot Rotating 46Ti Probed by the Charged Particle Emission and GDR gamma-Decay

The 46Ti* compound nucleus, as populated by the fusion-evaporation reaction 27Al+19F at the bombarding energy of E_lab=144 MeV, has been investigated by charged particle spectroscopy using the multidetector array ICARE at the VIVITRON tandem facility of the IReS (Strasbourg). The light charged particles and high-energy gamma-rays from the GDR decay have been measured in coincidence with selected evaporation residues. The CACARIZO code, a Monte Carlo implementation of the statistical-model code CASCADE, has been used to calculate the spectral shapes of evaporated alpha-particles which are compared with the experimental coincident spectra. This comparison indicates the signature of large deformations (possibly superdeformed and hyperdeformed shapes) present in the compound nucleus decay. The occurrence of the Jacobi shape transition is also discussed in the framework of a newly developed rotating liquid drop model.

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