Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculations are performed to study the evolution of shapes with the number of nucleons in various chains of Yb, Hf, W, Os, and Pt isotopes from neutron number N=110 up to N=122. Potential energy curves are analyzed in a search for signatures of oblate-prolate phase shape transitions and results from various Skyrme and pairing forces are considered. Comparisons with results obtained with the Gogny interaction as well as with relativistic mean field calculations are presented. The role of the $γ$ degree of freedom is also discussed.
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.
Self-consistent Skyrme Hartree-Fock plus BCS calculations are performed to generate potential energy curves (PEC) in various chains of Pd, Xe, Ba, Nd, Sm, Gd, and Dy isotopes. The evolution of shapes with the number of nucleons is studied in a search for signatures of E(5) and X(5) critical point symmetries. It is shown that the energy barriers in the PECs are determined to a large extent by the treatment of the pairing correlations.
Spontaneous fission barriers, quadrupole inertia, and zero-point quadrupole-energy corrections are calculated for 252,256,258Fm in the framework of the self-consistent Skyrme-Hartree-Fock+BCS theory. Two ways of computing dynamical inertia are employed: the Gaussian Overlap Approximation to the Generator Coordinate Method and cranking ansatz. The Skyrme results are compared with those of the Gogny-Hartree-Fock-Bogolyubov model.
We describe the new version (v2.07f) 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, all symmetries can be broken, which allows for calculations with angular frequency and angular momentum tilted with respect to the mass distribution. The new version contains an interface to the LAPACK subroutine ZHPEVX.
The properties of kaonic nuclei are studied using a two-dimensional Skyrme-Hartree-Fock model with a $KN$ Skyrme force. We focus in particular on the instability of the solutions for a too strong $KN$ interaction, which determines a maximum value of the kaon binding in this approach. We then analyze the change of the deformation properties of several core-deformed nuclei caused by the added kaon, and find a shrinking of the core and in some cases a complete loss of deformation.
In the present work, we systematically study the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between the Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and macroscopic quantities was analyzed. Moreover, we obtained a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical …
We describe the first version (v1.00) of the code HFBRAD which solves the Skyrme-Hartree-Fock or Skyrme-Hartree-Fock-Bogolyubov equations in the coordinate representation within the spherical symmetry. A realistic representation of the quasiparticle wave functions on the space lattice allows for performing calculations up to the particle drip lines. Zero-range density-dependent interactions are used in the pairing channel. The pairing energy is calculated by either using a cut-off energy in the quasiparticle spectrum or the regularization scheme proposed by A. Bulgac and Y. Yu.
Spontaneous-fission properties of 256Fm, 258Fm, and 260Fm isotopes are studied within the Skyrme-Hartree-Fock+BCS framework. In the particle-hole channel we take the Skyrme SkM* effective force, while in the particle-particle channel we employ the seniority pairing interaction. Three static fission paths for all investigated heavy fermium isotopes are found. The analysis of these fission modes allows to describe observed asymmetric fission of 256Fm, as well as bimodal fission of 258Fm and symmetric fission in 260Fm.
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.
On the basis of the cranked Skyrme-Hartree-Fock calculations in the three-dimensional coordinate-mesh representation, we suggest that, in addition to the well-known candidate 32S, the neutron-rich nucleus 36S and the drip-line nuclei,48S and 50S, are also good candidates for finding superdeformed rotational bands in Sulfur isotopes. Calculated density distributions for the superdeformed states in 48S and 50S exhibit superdeformed neutron skins
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.
We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions.
We describe the new version (v1.75r) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the Cartesian deformed harmonic-oscillator basis. Three minor errors that went undetected in the previous version have been corrected. The new version contains an interface to the LAPACK subroutine ZHPEV. Several methods of terminating the Hartree-Fock iteration procedure, and an algorithm that allows to follow the diabatic configurations, have been implemented.
Hartree-Fock calculations with the SKX Skyrme interaction are carried out to obtain alpha-decay Q values for deformed nuclei above $^{208}$Pb assuming axial symmetry. The results for even-even nuclei are compared with experiment and with previous calculations. Predictions are made for alpha-decay Q values and half-lives of even-even super-heavy nuclei. The results are also compared for the recently discovered odd-even chain starting at Z=112 and N=165.
We reanalyze the results of our extensive Hartree-Fock + BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2 <= Z <= 114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration form…
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.
We address very briefly five critical points in the context of the Skyrme-Hartree-Fock (SHF) scheme: 1) the impossibility to consider it as an interaction, 2) a possible inconsistency of correlation corrections as, e.g., the center-of-mass correction, 3) problems to describe the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, 4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE), and 5) a yet inappropriate trend in fission life-times when going to the heaviest SHE. While the first two points have more a formal bias, the other three points…
There are many complementing strategies to estimate the extrapolation errors of a model which was calibrated in least-squares fits. We consider the Skyrme-Hartree-Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they are: binding energies, charge r.m.s. radii, and charge formfactor. Amongst others, we check in particular the predict…
We report on the first Skyrme-Hartree-Fock calculations with the tilted-axis cranking in the context of magnetic rotation. The mean field symmetries, differences between phenomenological and self-consistent methods and the generation of shears-like structures in the mean field are discussed. Significant role of the time-odd spin-spin effective interaction is pointed out. We reproduce the shears mechanism, but quantitative agreement with experiment is rather poor. It may have to do with too large core polarization, lack of pairing correlations or properties of the Skyrme force.
We investigate the role of odd-odd (with respect to time inversion) couplings in the Skyrme force on collisions of light nuclei, employing a fully three-dimensional numerical treatment without any symmetry restrictions and with modern Skyrme functionals. We demonstrate the necessity of these couplings to suppress spurious spin excitations owing to the spin-orbit force in free translational motion of a nucleus but show that in a collision situation there is a strong spin excitation even in spin-saturated systems which persists in the departing fragments. The energy loss is considerably increase…
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.
The properties of $Ξ^-$ hypernuclei are studied systematically using a two-dimensional Skyrme-Hartree-Fock approach combined with three different $ΞN$ Skyrme forces fitted to reproduce the existing data. We explore the impurity effect of a single $Ξ^-$ hyperon on the radii, deformations, and density distributions of the nuclear core and point out qualitative differences between the different forces. We find that the $Ξ^-$ removal energy of $^{\hskip0.10em13}_{Ξp}$B [$^{12}$C(g.s.)+ $Ξ^-$(1p)] calculated by the SLX3 force is 0.7 MeV, which is in good agreement with a possible value of $0.82\pm0…
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}.
Melting of N=20 shell and development of N = 16 and N = 34 shells for neutron-rich nuclei have been studied extensively through inclusion of tensor interaction in Skyrme Hartree Fock theory optimized to reproduce the splitting neutron 1f states of 40, 48Ca and 56Ni nuclei. Evolution of gap generated by the energy difference of single particle levels neutron 2s1/2 and neutron 1d3/2 state has been found to be responsible for the development of a shell closure at N = 16. The splitting pattern of spin-orbit partners 2p shell model state in Ca, Ti, Cr, Fe and Ni isotopes indicates formation of a 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.…
With the use of the symmetry-unrestricted cranked Skyrme-Hartree-Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30-50 region. Along the N=Z line, we have found superdeformed solutions in 32S, 36Ar, 40Ca, 44Ti, and hyperdeformed solutions in 36Ar, 40Ca, 44Ti, 48Cr. The superdeformed band in 40Ca is found to be extremely soft against both the axially symmteric (Y30) and asymmetric (Y31) octupole deformations. An interesting role of symmetry breaking in …
We present a systematic analysis of the description of odd nuclei by the Skyrme-Hartree-Fock approach augmented with pairing in BCS approximation and blocking of the odd nucleon. Current and spin densities in the Skyrme functional produce time-odd mean fields (TOMF) for odd nuclei. Their effect on basic properties (binding energies, odd-even staggering, separation energies and spectra) is investigated for the three Skyrme parameterizations SkI3, SLy6, and SV-bas. About 1300 spherical and axially-deformed odd nuclei with 16 < Z < 92 are considered. The calculations demonstrate that the TOMF eff…
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…
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.
Fission-related phenomena of heavy $Λ$ hypernuclei are discussed with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method, in which a similar Skyrme-type interaction is employed also for the interaction between a $Λ$ particle and a nucleon. Assuming that the $Λ$ particle adiabatically follows the fission motion, we discuss the fission barrier height of $^{239}_Λ$U. We find that the fission barrier height increases slightly when the $Λ$ particle occupies the lowest level. In this case, the $Λ$ particle is always attached to the heavier fission fragment. This indicates that one may produce h…
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…
We describe the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or non-rotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A~150 nucleus within one CPU hour of the CRAY C-90 supercomputer …
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.
Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of super-heavy elements. For nuclei with a sufficient oblate deformation ($Q_{20}\leq$ -200 b), it becomes energetically favourable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region …
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 have performed a systematic study of the ground state for even-even 1,002 nuclei in which 28 octupole-deformed nuclei are found. The interplay between the spatial deformation and the pairing correlation, plays important roles in nuclear structure. Our model is based on the Skyrme Hartree-Fock plus BCS model represented in the three-dimensional Cartesian coordinate space which can describe any kind of nuclear shape. The quadrupole and octupole deformed nuclei appear in the mass region with characteristic neutron and proton numbers which are consistent with previous studies. In our results, t…
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 Schi…
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 …
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.
Low-energy E1 strength in neutron-rich $^{132-164}$Sn isotopes is analyzed in the framework of the Skyrme random phase approximation (RPA) with different Skyrme forces. A double folding procedure is applied to take into account the energy-dependent width effects beyond RPA. All the considered Skyrme forces indicate a soft prolate deformation in the open shell isotopes $^{142-164}$Sn. The integrated E1 strength in the energy region of the pygmy resonance grows with the neutron number. The influence of deformation on the integrated strength near the particle emission thresholds (which is of a ke…
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…
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic-oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for mu…
A method for incorporating the effect of the resonant continuum into Hartree-Fock+BCS equations is proposed. The method is applied for the case of a neutron-rich nucleus calculated with a Skyrme-type force plus a zero-range pairing interaction and the results are compared with Hartree-Fock-Bogoliubov calculations. It is shown that the widths of resonant states have an important effect on the pairing properties of nuclei close to the drip line.
We perform calculations of the variation after parity projection with Skyrme interaction for ground and excited states of even-even Mg isotopes. Using the 3D real-space representation, we can take into account any kind of deformation; e.g., cluster structure, gamma-deformation. We also perform the full 3D angular momentum projection to obtained rotational spectra and B(E2). In 24Mg, the ground K^pi=0+ and several odd-parity bands are calculated. In 30,32,34Mg, our calculation reproduces a breaking of the N=20 magic number, so-called "Island of inversion" phenomena. Properties of both the groun…
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck (iv) the regularization of zero-range p…
We have performed deformed Hartree-Fock+BCS calculations with the Skyrme SIII force for the ground states of even-even nuclei with 2 <= Z <= 114 and N ranging from outside the proton drip line to beyond the experimental frontier in the neutron-rich side. We obtained spatially localized solutions for 1029 nuclei, together with the second minima for 758 nuclei. The single-particle wavefunctions are expressed in a three-dimensional Cartesian-mesh representation, which is suitable to describe nucleon skins, halos, and exotic shapes as well as properties of ordinary stable nuclei. After explaining …
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…
In the present paper we explore the neutron-drip region of cold non-rotating isolated neutron stars. We have performed extended nuclear-structure calculations for nuclei embedded in the electron gas. For modeling the outer crust we use a set of Wigner-Seitz cells, where every cell contains one nucleus surrounded by a cloud of relativistic electrons. Above the drip point a non-relativistic neutron gas occurs in the cell. These calculations are carried out within the Hartree-Fock approach in combination with Skyrme effective interactions. For every baryon density we have determined the configura…
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…
A study of the charge and matter densities and the corresponding rms radii for even-even isotopes of Ni, Kr, and Sn has been performed in the framework of deformed self-consistent mean field Skyrme HF+BCS method. The resulting charge radii and neutron skin thicknesses of these nuclei are compared with available experimental data, as well as with other theoretical predictions. The formation of a neutron skin, which manifests itself in an excess of neutrons at distances greater than the radius of the proton distribution, is analyzed in terms of various definitions. Formation of a proton skin is …
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 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…
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.
The superdeformation (SD) in non-rotating states is studied with the HF+BCS method using the Skyrme interaction. In applying the BCS theory, the seniority pairing force is employed, of which strengths are determined in order to reproduce the empirical pairing gap formula, $\barΔ = 12 A^{-1/2}$ MeV, through a smooth level density obtained in the Thomas-Fermi approximation. Properties of superdeformation are investigated by calculating potential energy surfaces (PES) for various sets of the pairing force strengths and the Skyrme force parameter for 194Hg and 236,238U. The best results are obtain…
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 …
We describe the new version (v2.73y) 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 the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calc…
A search for the self-consistent solutions for the chiral rotational bands in the N=75 isotones, 130Cs, 132La, 134Pr and 136Pm is performed within the Skyrme-Hartree-Fock cranking approach using SKM* and SLy4 parametrizations. The dependence of the solutions on the time-odd contributions in the energy functional is studied. From among the considered four isotones, self-consistent chiral solutions are obtained only in 132La. The microscopic calculations are compared with the 132La experimental data and with results of a classical model that contains all the mechanisms underlying the chirality o…
In this work, we systematically study the two-proton($2p$) radioactivity half-lives using the two-potential approach while the nuclear potential is obtained by using Skyrme-Hartree-Fock approach with the Skyrme effective interaction of {SLy8}. For true $2p$ radioactivity($Q_{2p}$ $>$ 0 and $Q_p$ $< $0, where the $Q_p$ and $Q_{2p}$ are the released energy of the one-proton and two-proton radioactivity), the standard deviation between the experimental half-lives and our theoretical calculations is {0.701}. In addition, we extend this model to predict the half-lives of 15 possible $2p$ radioactiv…
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.
