arXiv subjects

J. Dobaczewski

Publications and source records attributed to J. Dobaczewski.

At least 73 records · Page 4Linked to original sources

arXiv2012

Effective theory for low-energy nuclear energy density functionals

We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology to low-energy phenomena in nuclei. They allow for defining the order of expansion in terms of the order of derivatives acting on the finite-range potential. Numerical calculations show a rapid convergence of the expansion and independence of results of the regularization scale.

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arXiv2012

Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular-momentum-projected nuclear Density Functional Theory

Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I=0+,T=1 --> I=0+,T=1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T=1/2 --> I,T=1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.

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arXiv2012

Giant Monopole Resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than 208Pb. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semi-magic nuclei. Methods: We employ self-consistently the Quasiparticle Random Phase Approximation on top of spherical Hartree-Fock-Bogolyubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the difference between centroids of Giant Monopole Resonances measured in lead and tin (about 1 MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility. Conclusions: The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data.

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arXiv2012

Hartree-Fock-Bogoliubov solution of the pairing Hamiltonian in finite nuclei

We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the HFB wave function. Thereafter, we present derivation and structure of the HFB equations within the superfluid nuclear density functional formalism and discuss several aspects of the theory, including the unitarity of the Bogoliubov transformation in truncated single-particle and quasiparticle spaces, form of the pairing functional, structure of the HFB continuum, regularization and renormalization of pairing fields, and treatment of pairing in systems with odd particle numbers.

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arXiv2012

Precision Mass Measurements beyond $^{132}$Sn: Anomalous behaviour of odd-even staggering of binding energies

Atomic masses of the neutron-rich isotopes $^{121-128}$Cd, $^{129,131}$In, $^{130-135}$Sn, $^{131-136}$Sb, and $^{132-140}$Te have been measured with high precision (10 ppb) using the Penning trap mass spectrometer JYFLTRAP. Among these, the masses of four r-process nuclei $^{135}$Sn, $^{136}$Sb, and $^{139,140}$Te were measured for the first time. The data reveals a strong $N$=82 shell gap at $Z$=50 but indicates the importance of correlations for $Z>50$. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across $N$=82 for Sn, with the $Z$-dependence that is unexplainable by the current theoretical models.

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arXiv2011

Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in $^{158}$Er at ultrahigh spin

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}$Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes -- as done in previous cranking calculations -- two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $γ$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment $Q_t \approx 10.5$\,eb is close to the measured value of $\sim$11\,eb; hence, it is a candidate for the structure observed in experiment.

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arXiv2011

Continuity equation and local gauge invariance for the N3LO nuclear Energy Density Functionals

Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invariance of the functional under gauge transformations. Methods: Derive conditions for the validity of the continuity equation in the framework of time-dependent density functional theory. The conditions apply separately to the four spin-isospin channels of the one-body density matrix. Results: We obtained four sets of constraints on the coupling constants of the N3LO energy density functional that guarantee the validity of the continuity equation in all spin-isospin channels. In particular, for the scalar-isoscalar channel, the constraints are the same as those resulting from imposing the standard U(1) local-gauge-invariance conditions. Conclusions: Validity of the continuity equation in the four spin-isospin channels is equivalent to the local-gauge invariance of the energy density functional. For vector and isovector channels, such validity requires the invariance of the functional under local rotations in the spin and isospin spaces.

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arXiv2011

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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arXiv2011

Effective pseudopotential for energy density functionals with higher order derivatives

We derive a zero-range pseudopotential that includes all possible terms up to sixth order in derivatives. Within the Hartree-Fock approximation, it gives the average energy that corresponds to a quasi-local nuclear Energy Density Functional (EDF) built of derivatives of the one-body density matrix up to sixth order. The direct reference of the EDF to the pseudopotential acts as a constraint that divides the number of independent coupling constants of the EDF by two. This allows, e.g., for expressing the isovector part of the functional in terms of the isoscalar part, or vice versa. We also derive the analogous set of constraints for the coupling constants of the EDF that is restricted by spherical, space-inversion, and time-reversal symmetries.

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arXiv2011

Microscopic calculations of isospin-breaking corrections to superallowed beta-decay

The superallowed beta-decay rates that provide stringent constraints on physics beyond the Standard Model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the CKM matrix, |V_{ud}|= 0.97447(23), agrees well with the recent result by Towner and Hardy [Phys. Rev. C {\bf 77}, 025501 (2008)].

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arXiv2010

Isospin mixing in the vicinity of the N=Z line

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed beta-decay rates in the vicinity of the N=Z line. A preliminary value obtained for the Cabbibo-Kobayashi-Maskawa matrix element, |V_{ud}|=0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev. C{\bf 77}, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.

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arXiv2010

Isospin mixing in nuclei around N=Z and the superallowed beta-decay

Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N~Z nuclei. By including simultaneous isospin and angular-momentum projection, we compute the isospin-breaking corrections to the 0+ --> 0+ superallowed beta-decay.

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arXiv2010

Current Developments in Nuclear Density Functional Methods

Density functional theory (DFT) became a universal approach to compute ground-state and excited configurations of many-electron systems held together by an external one-body potential in condensed-matter, atomic, and molecular physics. At present, the DFT strategy is also intensely studied and applied in the area of nuclear structure. The nuclear DFT, a natural extension of the self-consistent mean-field theory, is a tool of choice for computations of ground-state properties and low-lying excitations of medium-mass and heavy nuclei. Over the past thirty-odd years, a lot of experience was accumulated in implementing, adjusting, and using the density-functional methods in nuclei. This research direction is still extremely actively pursued. In particular, current developments concentrate on (i) attempts to improve the performance and precision delivered by the nuclear density-functional methods, (ii) derivations of density functionals from first principles rooted in the low-energy chromodynamics and effective theories, and (iii) including effects of low-energy correlations and symmetry restoration. In this study, we present an overview of recent results and achievements gained in nuclear density-functional methods.

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arXiv2010

Title: Quadrupole collective inertia in nuclear fission: cranking approximation

Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

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arXiv2010

Convergence of density-matrix expansions for nuclear interactions

We extend density-matrix expansions in nuclei to higher orders in derivatives of densities and test their convergence properties. The expansions allow for converting the interaction energies characteristic to finite- and short-range nuclear effective forces into quasi-local density functionals. We also propose a new type of expansion that has excellent convergence properties when benchmarked against the binding energies obtained for the Gogny interaction.

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arXiv2010

The Negele-Vautherin density matrix expansion applied to the Gogny force

We use the Negele-Vautherin density matrix expansion to derive a quasi-local density functional for the description of systems of fermions interacting with short-ranged interactions composed of arbitrary finite-range central, spin-orbit, and tensor components. Terms that are absent in the original Negele-Vautherin approach owing to the angle averaging of the density matrix are fixed by employing a gauge invariance condition. We obtain the Kohn-Sham interaction energies in all spin-isospin channels, including the exchange terms, expressed as functions of the local densities and their derivatives up to second (next to leading) order. We illustrate the method by determining the coupling constants of the Skyrme functional or Skyrme force that correspond to the finite-range Gogny central force. The resulting self-consistent solutions reproduce the Gogny-force binding energies and radii within the precision of 1-2%.

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arXiv2010

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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arXiv2010

Spatial symmetries of the local densities

Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.

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