The modeling of nuclear reactions and radioactive decays in astrophysical or earth-based conditions requires detailed knowledge of the masses of essentially all nuclei. Microscopic mass models based on nuclear energy density functionals (EDFs) can be descriptive and used to provide this information. The concept of intrinsic symmetry breaking is central to the predictive power of EDF approaches, yet is generally not exploited to the utmost by mass models because of the computational demands of adjusting up to about two dozen parameters to thousands of nuclear masses. We report on a first step to bridge the gap between what is presently feasible for studies of individual nuclei and large-scale models: we present a new Skyrme-EDF-based model that was adjusted using a three-dimensional coordinate-space representation, for the first time allowing for both axial and triaxial deformations during the adjustment process. To compensate for the substantial increase in computational cost brought by the latter, we have employed a committee of multilayer neural networks to model the objective function in parameter space and guide us towards the overall best fit. The resulting mass model BSkG1 is computed with the EDF model independently of the neural network. It yields a root mean square (rms) deviation on the 2457 known masses of 741 keV and an rms deviation on the 884 measured charge radii of 0.024 fm.
We present a method based on mean-field states generated by triaxial quadrupole constraints which are projected on particle number and angular momentum and mixed by the generator coordinate method on the quadrupole moment. This method is equivalent to a seven-dimensional GCM calculation, mixing all five degrees of freedom of the quadrupole operator and the gauge angles for protons and neutrons. A first application to Mg24 permits to analyze in detail the effects of triaxial deformations and of K-mixing.
After a brief review of the Hartree-Fock-Bogoliubov method with Skyrme effective interactions, we show how it can be applied to the description of various nuclear systems, from finite nuclei to neutron-star crusts.
We calculate positions of one- and two-particle, proton and neutron drip lines within the Hartree-Fock-Bogoliubov theory using Skyrme interaction. We also determine an approximate $r$-process path defined as a line where the neutron binding energy is equal to 2~MeV. A weakening of the nuclear shell structure at drip lines is found and interpreted as resulting from a coupling with continuum states.
We have studied odd-even nuclear mass staggering with the Skyrme-Hartree-Fock-Bogoliubov theory by employing isoscalar and isovector contact pairing interactions. By reproducing the empirical odd-even mass differences of the Sn isotopic chain, the strengths of pairing interactions are determined. The optimal strengths adjusted in this work can give better description of odd-even mass differences than that fitted by reproducing the experimental neutron pairing gap of $^{120}$Sn.
The nuclear time-dependent Hartree-Fock model formulated in the three-dimensional space,based on the full Skyrme energy density functional and complemented with the tensor force,is presented for the first time. Full self-consistency is achieved by the model. The application to the isovector giant dipole resonance is discussed in the linear limit, ranging from spherical nuclei (16O, 120Sn) to systems displaying axial or triaxial deformation (24Mg, 28Si, 178Os, 190W, 238U). Particular attention is paid to the spin-dependent terms from the central sector of the functional, recently included toget…
We analyse deformation mechanism in neutron-rich Cr, Fe and Ti isotopes with N=32-44 by means of a Skyrme-Hartree-Fock-Bogoliubov mean-field code employing a two-dimensional mesh representation in the cylindrical coordinate system. Evaluating systematically the quadrupole deformation energy, we show that the Skyrme parameter set SkM* gives a quadrupole instability around the neutron number N$\sim$38-42 in Cr isotopes, where the deformation energy curve suggests a transitional behavior with a shallow minimum extending to a large prolate deformation. Roles of a deformed N=38 gap and the position…
By performing fully 3D symmetry-unrestricted Skyrme-Hartree-Fock-Bogoliubov calculations, we discuss shape coexistence and possibility of exotic deformations simultaneously breaking the reflection and axial symmetries in proton-rich N=Z nuclei: 64Ge, 68Se, 72Kr, 76Sr, 80Zr and 84Mo. Results of calculation indicate that the oblate ground state of 68Se is extremely soft against the Y33 triangular deformation, and that the low-lying spherical minimum coexisting with the prolate ground state in 80Zr may be unstable against the Y32 tetrahedral deformation.
A study of rotational properties of the ground superdeformed bands in \Hg{0}, \Hg{2}, \Hg{4}, and \Pb{4} is presented. We use the cranked Hartree-Fock-Bogoliubov method with the {\skm} parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of \Hg{2}.
We present the development of the extended Skyrme N2LO pseudo-potential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behaviour of the solutions at the origin. Finally, a fitting procedure for such a N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.
We present a new Skyrme-Hartree-Fock-Bogoliubov nuclear-mass model in which the contact-pairing force is constructed from microscopic pairing gaps of symmetric nuclear matter and neutron matter calculated from realistic two- and three-body forces, with medium-polarization effects included. With the pairing being treated more realistically than in any of our earlier models, the rms deviation with respect to essentially all the available mass data falls to 0.581 MeV, the best value ever found within the mean-field framework. Since our Skyrme force is also constrained by the properties of pure ne…
The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform.…
We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, the SeaLL1 functional was added and the calculation of the Coulomb potential was improved. Finally, the code has been refactored to facilitate maintenance and future developments.
I have investigated the $N$-dependence of the charge radii $r_c$ across $N=126$ in the Pb isotopes and the surface densities of $^{208}$Pb using new Skyrme interactions that contain a density-dependent spin-orbit term, which I have named the Skyrme-ddso interactions. I have compared the results obtained using Skyrme-Hartree-Fock-Bogoliubov calculations that employ the Skyrme-ddso interactions with the original Skyrme results and have discussed the effects of including the density-dependent spin-orbit term. The results for the kink behavior of $r_c$ at $N=126$ in the Pb isotopes were improved b…
The neutron pair correlation in nuclei near the neutron drip-line is investigated using the selfconsistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with the coordinate-space Green's function technique. Numerical analysis is performed for even-even N = 86 isotones in the Mo-Sn region, where the 3p3/2 and 3p1/2 orbits lying near the Fermi energy are either weakly bound or unbound. The quasiparticle states originating from the l = 1 orbits form resonances with large widths, which are due to the low barrier height and the strong continuum coupling caused by the pair potential. An…
The self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique in the coordinate space is developed to investigate odd-$A$ nuclei by incorporating the blocking effect. In a calculation performed with the SLy4 parameter for the neutron-rich Mg isotopes with $A=36-42$ around the neutron shell closure N=28, the odd-even staggering in the neutron rms radius, i.e., a larger value in $^{39}$Mg than those in $^{38}$Mg and $^{40}$Mg, is found. The large neutron radius in $^{39}$Mg is due to the blocking effect on the pair correlation energy, for which th…
We review our recent achievements in the construction of microscopic mass tables based on the Hartree-Fock-Bogoliubov method with Skyrme effective interactions. In the latest of our series of HFB-mass models, we have obtained our best fit ever to essentially all the available mass data, by treating the pairing more realistically than in any of our earlier models. The rms deviation on the 2149 measured masses of nuclei with N and Z>8 has been reduced for the first time in a mean field approach to 0.581 MeV. With the additional constraint on the neutron-matter equation of state, this new force i…
The giant halos predicted in neutron-rich Zr isotopes with $A=124-138$ are investigated by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov approach, in which the asymptotic behavior of continuum quasiparticle states is properly treated by the Green's function method. We study in detail the neutron pair correlation involved in the giant halo by analyzing the asymptotic exponential tail of the neutron pair condensate (pair density) in addition to that of the neutron particle density. The neutron quasiparticle spectra associated with these giant halo nuclei are examined. It is …
To study the exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formula are presented.To perform the integrals of the Green's function properly, the contour paths $C_{\rm b}^{-}$ and $C_{\rm b}^{+}$ introduced for the blocking effects should include the blocked quasi-particle state but can not intrude into the continuum area. By comparing with the box-discretized calculations, the great advantages of the Green's function …
The ground-state deformations of the Ge isotopes are investigated in the framework of Gogny-Hartree-Fock-Bogoliubov (HFB) and Skyrme Hartree-Fock plus pairing in the BCS approximation. Five different Skyrme parametrizations are used to explore the influence of different effective masses and spin-orbit models. There is generally good agreement for binding energies and deformations (total quadrupole moment, triaxiality) with experimental data where available (i.e., in the valley of stability). All calculations agree in predicting a strong tendency for triaxial shapes in the Ge isotopes with only…
Starting from HFB-6, we have constructed a new mass table, referred to as HFB-8, including all the 9200 nuclei lying between the two drip lines over the range of Z and N > 6 and Z < 122. It differs from HFB-6 in that the wave function is projected on the exact particle number. Like HFB-6, the isoscalar effective mass is constrained to the value 0.80 M and the pairing is density independent. The rms errors of the mass-data fit is 0.635 MeV, i.e. better than almost all our previous HFB mass formulas. The extrapolations of this new mass formula out to the drip lines do not differ significantly fr…
Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include correlations associated with the geometrical arrangement of the system's constituents. Such reference states have been used already for a long time within self-consistent methods that are either based on effective valence-space Hamiltonians or energy density functionals, and they are presently also gaining popularity in the design of novel ab-initio methods. A ful…
We construct a new Hartree-Fock-Bogoliubov (HFB) mass model, labeled HFB-18, with a generalized Skyrme force. The additional terms that we have introduced into the force are density-dependent generalizations of the usual $t_1$ and $t_2$ terms, and are chosen in such a way as to avoid the high-density ferromagnetic instability of neutron stars that is a general feature of conventional Skyrme forces, and in particular of the Skyrme forces underlying all the HFB mass models that we have developed in the past. The remaining parameters of the model are then fitted to essentially all the available m…
Background: The symmetry-unrestricted Hartree-Fock-Bogoliubov (HFB) simulation is important for describing various quantum many-body systems. However, the HFB problem in Cartesian coordinate space is numerically challenging. Purpose: For describing ground states without imposing axial symmetry and looking ahead to future extension for dynamics with full time dependence, we present a numerically efficient implementation of the three-dimensional (3D) HFB code. Methods: We develop a 3D Skyrme HFB code based on the mixed-basis representation (HFBmix) which consists of two harmonic-oscillator (HO) …
To study shape fluctuations of nuclei in transitional regions, the collective Hamiltonian method has often been employed. We intend to construct the quadrupole collective Hamiltonian with the collective inertial functions given by the local quasiparticle random-phase approximation (QRPA) based on the Skyrme energy density functional. For this purpose, we first construct a practical framework of Skyrme QRPA for triaxial nuclear shapes with the finite amplitude method (FAM). We show quadrupole strength functions for a triaxial superfluid nucleus $^{188}$Os and the Thouless-Valatin rotational mom…
We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin ($J$), isospin ($T$) and mass number ($A$). Systematic VAP calculations with $JTA$-projection have been performed for the even-even $sd$-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin pro…
The five-dimensional quadrupole collective model based on energy density functionals (EDF) has often been employed to treat long-range correlations associated with shape fluctuations in nuclei. Our goal is to derive the collective inertial functions in the collective Hamiltonian by the local quasiparticle random phase approximation (QRPA) that correctly takes into account time-odd mean-field effects. Currently, practical framework to perform the QRPA calculation with the modern EDFs on the $(β,γ)$ deformation space is not available. Toward this goal, we develop an efficient numerical method to…
In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.
In this latest of our series of Skyrme-HFB mass models, HFB-16, we introduce the new feature of requiring that the contact pairing force reproduce at each density the $^1S_0$ pairing gap of neutron matter as determined in microscopic calculations with realistic nucleon-nucleon forces. We retain the earlier constraints on the Skyrme force of reproducing the energy-density curve of neutron matter, and of having an isoscalar effective mass of $0.8M$ in symmetric infinite nuclear matter at the saturation density; we also keep the recently adopted device of dropping Coulomb exchange. Furthermore, t…
To describe the yrast states in weakly bound nuclei, I directly solve the coordinate-space cranked Skyrme-Hartree-Fock-Bogoliubov equation on a three-dimensional lattice with the continuum states discretized in a box. After the numerical demonstration for the ground-state band in a medium-mass nucleus, I apply the newly-developed method to neutron-rich even-$N$ Mg isotopes. I find that the appearance of the significantly low $I^π=2^+$ state in $^{40}$Mg is mainly due to the suppression of pairing. The calculation predicts that the $2^+$ state in $^{42}$Mg appears as high in energy as in $^{34\…
We consider here variational solutions in the Hartree-Fock approximation upon breaking time reversal and axial symmetries. When decomposed on axial harmonic oscillator functions, the corresponding single particle triaxial eigenstates as functions of the usual cylindrical coordinates (r, $θ$, z) are evaluated on a mesh in r and z to be integrated within Gauss-Hermite and Gauss-Laguerre approaches and as Fourier decompositions in the angular variable $θ$. Using an effective interaction of the Skyrme type, the Hartree-Fock hamiltonian is also obtained as a Fourier series allowing a two dimensiona…
The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Sn isotopes are explored with the continuum Skyrme Hartree-Fock-Bogoliubov theory formulated with the Green's function method. The available experimental two-neutron separation energies $S_{\rm 2n}$ and one-neutron separation energies $S_{\rm n}$ are well reproduced. Much shorter drip lines predicted by $S_{\rm n}$ are obtained compared with those by $S_{\rm 2n}$. The systematic studies of the neutron pairing energies $-E_{\rm pair}$ shown that values of the odd-$A$ nuclei are much smaller in comparison with those of th…
Recently, Allmond and Wood [Phys. Lett. B 767, 226 (2017)] were able to extract the three moments of inertia $I_k$ of a dozen of superfluid triaxial nuclei from experimental data. The observed dependence of the $I_k$ on the deformation parameters is rather smooth. Here we show that these moments of inertia can be surprisingly well explained by a semiclassical cranked Hartree-Fock-Bogoliubov (HFB) calculation in which the velocity field is a simple superposition of rigid and irrotational flows.
Improved microscopic nuclear level densities within the triaxial Hartree-Fock-Bogoliubov plus combinatorial method
Institut d’Astronomie et d’Astrophysique, ULB（布鲁塞尔自由大学天体物理学与天文学研究所）；CEA/DIF, Service de Physique Nucléaire（法国原子能和替代能源委员会DIF核物理处）；Nuclear Data Section, IAEA（国际原子能机构核数据处）
The Skyrme-Hartree-Fock-Bogoliubov code HFBTHO using the axial (2D) Transformed Harmonic Oscillator basis is tested against the HFODD (3D Cartesian HO basis) and HFBRAD (radial coordinate) codes. Results of large-scale ground-state calculations are presented for the SLy4 and SkP interactions.
The ground-state properties of neutron-deficient Hg isotopes have been investigated by the constrained self-consistent Hartree-Fock-Bogoliubov approach with the Skyrme and Gogny effective forces. In the case of the Skyrme interaction we h ave also applied the Hartree-Fock+BCS model with the state-dependent $δ$-pairing interaction. Potential energy surfaces and pairing properties have been compared for the both types of forces.
Models based on nuclear energy density functionals can provide access to a multitude of observables for thousands of nuclei in a single framework with microscopic foundations. Such models can rival the accuracy of more phenomenological approaches, but doing so requires adjusting parameters to thousands of nuclear masses. To keep such large-scale fits feasible, several symmetry restrictions are generally imposed on the nuclear configurations. One such example is time-reversal invariance, which is generally enforced via the Equal Filling Approximation (EFA). Here we lift this assumption, enablin…
We have constructed four new complete mass tables, referred to as HFB-4 to HFB-7, each one including all the 9200 nuclei lying between the two drip lines over the range of Z and N>8 and Z<120. HFB-4 and HFB-5 have the isoscalar effective mass M*_s$ constrained to the value 0.92 M, with the former having a density-independent pairing, and the latter a density-dependent pairing. HFB-6 and HFB-7 are similar, except that M*_s is constrained to 0.8 M. The rms errors of the mass-data fits are 0.680, 0.675, 0.686, and 0.676 MeV, respectively, almost as good as for the HFB-2 mass formula, for which M*…
In a previous work [Int. J. Mod. Phys. E 24, 1550073 (2015)], hereafter referred as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree-Fock-Bogoliubov method with SLy5 skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even-even and odd Mo and Ru isotopes. For this, we have used Hartree- Fock-Bogoliubov method with SLy4 skyrme force, and a new formula of the pairing strength wh…
We construct three new Hartree-Fock-Bogoliubov (HFB) mass models, labeled HFB-19, HFB-20, and HFB-21, with unconventional Skyrme forces containing $t_4$ and $t_5$ terms, i.e., density-dependent generalizations of the usual $t_1$ and $t_2$ terms, respectively. The new forces underlying these models are fitted respectively to three different realistic equations of state of neutron matter for which the density dependence of the symmetry energy ranges from the very soft to the very stiff, reflecting thereby our present lack of complete knowledge of the high-density behavior of nuclear matter. All …
With the self-consistent three-dimensional cranked Hartree-Fock-Bogoliubov (3d-cranked HFB) method, various types of rotational motion near the yrast line are investigated in an even-even nucleus in the $A\simeq 130$ mass region ($^{134}_{58}$Ce$_{76}$). The possibilities of chiral rotations, tilted-rotations, and dynamical aspects of these rotations are discussed through the analysis of the 3d-cranked HFB solutions. Although a stable planar solution of the chiral rotation is obtained, an aplanar chiral configuration is found to be unstable when triaxial deformation is treated self-consistentl…
Large-amplitude dynamics of axial and triaxial quadrupole deformation in 24,26Mg, 24Ne, and 28Si is investigated on the basis of the quadrupole collective Hamiltonian constructed with use of the constrained Hartree-Fock-Bogoliubov plus the local quasiparticle random phase approximation method. The calculation reproduces well properties of the ground rotational bands, and beta and gamma vibrations in 24Mg and 28Si. The gamma-softness in the collective states of 26Mg and 24Ne are discussed. Contributions of the neutrons and protons to the transition properties are also analyzed in connection wit…
Charge radii of Sn, Ba, Yb, and Pb isotopes are calculated within Hartree-Fock-Bogoliubov theory with a Skyrme force and a density-dependent delta-force pairing. We investigate mean field effects of the pairing upon odd-even staggering of isotope shifts. HFB equations are solved in the canonical basis. Odd nuclei are treated in the blocking approximation.
Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: V. The N2LO extension of the Skyrme EDF
Université Libre de Bruxelles（布鲁塞尔自由大学）；Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔自由大学天体物理与天文学研究所）；Brussels Laboratory of the Universe – BLU-ULB（布鲁塞尔宇宙实验室）；Universität Potsdam（波茨坦大学）；Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）
Using the Hartree-Fock-Bogoliubov (HFB) self-consistent mean-field theory with the SkM* Skyrme energy-density functional, we study nuclear structure properties of even-even superheavy nuclei (SHN) of $Z=120$ isotopes and $N=184$ isotones. The shape of the nucleus along the lowest energy curve as a function of the quadrupole moment $Q_{20}$ makes a sudden transition from the oblate spheroids (biconcave discs) to the toroidal shapes, in the region of large oblate quadrupole moments.
We describe the program HFBTHO for axially deformed configurational Hartree-Fock-Bogoliubov calculations with Skyrme-forces and zero-range pairing interaction using Harmonic-Oscillator and/or Transformed Harmonic-Oscillator states. The particle-number symmetry is approximately restored using the Lipkin-Nogami prescription, followed by an exact particle number projection after the variation. The program can be used in a variety of applications, including systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to nucleon drip lines.
We introduce a local-scaling point transformation to allow for modifying the asymptotic properties of the deformed three-dimensional Cartesian harmonic oscillator wave functions. The resulting single-particle bases are very well suited for solving the Hartree-Fock-Bogoliubov equations for deformed drip-line nuclei. We then present results of self-consistent calculations performed for the Mg isotopes and for light nuclei located near the two-neutron drip line. The results suggest that for all even-even elements with $Z$=10--18 the most weakly-bound nucleus has an oblate ground-state shape.
This article extends previous studies on the effect of tensor terms in the Skyrme energy density functional by breaking of time-reversal invariance. We have systematically probed the impact of tensor terms on properties of superdeformed rotational bands calculated within the cranked Hartree-Fock-Bogoliubov approach for different parameterizations covering a wide range of values for the isoscalar and isovector tensor coupling constants. We analyze in detail the contribution of the tensor terms to the energies and dynamical moments of inertia and study their impact on quasi-particle spectra. Spe…
A recently introduced separable pairing force for relativistic Hartree-Bogoliubov (RHB) calculations, adjusted in nuclear matter to the pairing gap of the Gogny force, is employed in the 3D RHB model for triaxial shapes. The pairing force is separable in momentum space but, when transformed to coordinate space in calculations of finite nuclei, it is no longer separable because of translational invariance. The corresponding pairing matrix elements are represented as a sum of a finite number of separable terms in the basis of a 3D harmonic oscillator. The 3D RHB model is applied to the calculati…
Weakly-bound deformed nuclei have been studied by the Skyrme Hartree-Fock-Bogoliubov (HFB) approach in large coordinate-space boxes. In particular, the box-size dependence of the HFB calculations of weakly-bound deformed nuclei are investigated, including the particle density and pairing density distributions at nuclear surfaces, the near-threshold resonant and continuum quasiparticle spectra, and energetic properties. The box size may have larger influences in pairing properties than in other bulk properties. We demonstrate that large-box calculations of weakly-bound nuclei are important to p…
We describe a new version of the EV8 code that solves the nuclear Skyrme-Hartree-Fock+BCS problem using a 3-dimensional cartesian mesh. Several new features have been implemented with respect to the earlier version published in 2005. In particular, the numerical accuracy has been improved for a given mesh size by (i) implementing a new solver to determine the Coulomb potential for protons (ii) implementing a more precise method to calculate the derivatives on a mesh that had already been implemented earlier in our beyond-mean-field codes. The code has been made very flexible to enable the use …
We present exact Hartree-Fock-Bogoliubov calculations with the finite range density dependent Gogny force using a triaxial basis. For the first time, all contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of …
Complex many-body systems, such as triaxial and reflection-asymmetric nuclei, weakly-bound halo states, cluster configurations, nuclear fragments produced in heavy-ion fusion reactions, cold Fermi gases, and pasta phases in neutron star crust, they are all characterized by large sizes and complex topologies, in which many geometrical symmetries characteristic of ground-state configurations are broken. A tool of choice to study such complex forms of matter is an adaptive multi-resolution wavelet analysis. This method has generated much excitement since it provides a common framework linking man…
Systematic investigations of the electric dipole (E1) modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy E1 mode…
