Self-consistent Skyrme Hartree-Fock Research Articles

Single-particle properties of the near-threshold proton-emitting resonance in B11

The excitation function of proton elastic scattering from $^{10}\mathrm{Be}$ at keV energy is calculated using the method of self-consistent Skyrme Hartree-Fock in the continuum. The calculation successfully reproduces the narrow near-threshold proton-emitting resonance (${E}_{x}=11.4$ MeV, $\mathrm{\ensuremath{\Gamma}}=6$ keV, and quantum number ${J}^{\ensuremath{\pi}}=1/{2}^{+}$) in $^{11}\mathrm{B}$ relevant to the $\ensuremath{\beta}$-delayed proton emission of $^{11}\mathrm{Be}$. This supports the recent experimental result of Ayyad et al. at the ReA3 reaccelerator facility of the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The resonance is interpreted as the ${s}_{1/2}$ single-proton resonance state in the Skyrme Hartree-Fock mean-field theory.

Self-consistent calculations of electron-capture decays in Z=118, 119, and 120 superheavy isotopes

Weak decays in superheavy nuclei with proton numbers Z=118−120 and neutron numbers N=175−184 are studied within a microscopic formalism based on deformed self-consistent Skyrme Hartree-Fock mean-field calculations with pairing correlations. The half-lives of β+ decay and electron capture are compared with α-decay half-lives obtained from phenomenological formulas. The sensitivity of the half-lives to the unknown Q-energies is studied by comparing the results obtained from different approaches for the masses. It is shown that α-decay is always dominant in this mass region. The competition between α and β+/EC decay modes is studied in seven α-decay chains starting at different isotopes of Z=118, 119, and 120.

Electron-capture decay in isotopic transfermium chains from self-consistent calculations

Weak decays in heavy nuclei with charge numbers Z = 101–109 are studied within a microscopic formalism based on deformed self-consistent Skyrme Hartree–Fock mean-field calculations with pairing correlations. The half-lives of β+ decay and electron capture are compared with α-decay half-lives obtained from phenomenological formulas. Transfermium isotopes of Md, No, Lr, Rf, Db, Sg, Bh, Hs, and Mt that can be produced in the frontier of cold and hot fusion-evaporation channels are considered. Several isotopes are identified whose β+/EC- and α-decay half-lives are comparable. The competition between these decay modes opens the possibility of new pathways towards the islands of stability.

Fully self-consistent calculation of β-decay half-lives within Skyrme energy density functional * *Supported by the National Natural Science Foundation of China (11975096, 11805280, 11775014, 11635003, 11161130520), National Basic Research Program of China (2010CB832903), European Commission's 7th Framework Programme (Fp7-PEOPLE-2010-IRSES) under Grant Agreement Project (269131), and Continuous Basic Scientific Research Project (WDJC-2019-13)

-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA). The self-consistency is addressed, in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states. First, the impact of terms on the -decay half-lives is investigated by using the SGII interaction, revealing a large influence. Subsequently, numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII, LNS, SKX, and SAMi. Finally, comparisons to available experimental data and predictions of different theoretical models are discussed.

Microscopic calculations of weak decays in superheavy nuclei

Half-lives of beta+ decay and electron capture are studied in some selected superheavy nuclei produced in hot fusion reactions, namely, 290Fl, 293Mc, 294Lv, and 295Ts. The nuclear structure is described microscopically from deformed self-consistent Skyrme Hartree-Fock mean-field calculations that include pairing correlations. The sensitivity of the half-lives to deformation and to the QEC energies, which are still not determined experimentally, are studied. The results are compared with phenomenological alpha-decay half-lives, showing that the latter decay mode is dominant in this mass region.

Coulomb exchange functional with generalized gradient approximation for self-consistent Skyrme Hartree-Fock calculations

We perform the self-consistent Skyrme Hartree-Fock calculation with the Coulomb exchange functional in the form of generalized gradient approximation (GGA). It is found that the Perdew-Burke-Ernzerhof GGA (PBE-GGA) Coulomb exchange functional is able to reproduce the exact-Fock energy for the nuclei in a large region of the nuclear chart with one adjustable parameter. The remaining error of Coulomb exchange energy by the GGA with respect to the exact-Fock energy dominantly comes from the functional-driven error.

Giant Monopole Resonance and Nuclear Incompressibility of Hypernuclei**Supported by the National Natural Science Foundation of China under Grant Nos 11575060, 11775014, 11505058 and 11435014.

The isoscalar giant monopole resonances (ISGMRs) of hypernuclei , , and are investigated using a fully self-consistent Skyrme–Hartree–Fock plus random phase approximation method. The Skyrme-type forces, SGII, No.5 and SΛΛ1, are adopted to describe the nucleon–nucleon, Λ hyperon–nucleon and Λ hyperon–Λ hyperon (ΛΛ) interactions, respectively. For a given hyperon fraction, we find that effects of ΛΛ interaction on the properties of infinite symmetric nuclear matter and finite hypernuclei are very small. The ISGMR strengths are shifted to the high energy region when two Λ are added into normal nuclei. The changes are from two parts, one is due to the mean field calculations, and the other is from the residual interaction associated with Λ hyperons. The constrained energies are increased by about 0.5–0.7 MeV, which consequently enhances the effective incompressibility modulus of hypernuclei.

Beta-decay properties of neutron-rich medium-mass nuclei

β-decay properties of even-even and odd-A neutron-rich Ge, Se, Kr, Sr, Zr, Mo, Ru, and Pd isotopes involved in the astrophysical rapid neutron capture process are studied within a microscopic proton-neutron quasiparticle random-phase approximation. The underlying mean field is based on a self-consistent Skyrme Hartree-Fock + BCS calculation that includes deformation as a key ingredient. The isotopic evolution of the various nuclear equilibrium shapes and the corresponding charge radii are investigated in all the isotopic chains. The energy distributions of the Gamow-Teller strength, as well as the β-decay half-lives are discussed and compared with the available experimental information. It is shown that nuclear deformation plays a significant role in the description of the decay properties in this mass region. Reliable predictions of the strength distributions are essential to evaluate decay rates in astrophysical scenarios.

Gamow-Teller response and its spreading mechanism in doubly magic nuclei

The scope of the paper is to apply a state-of-the-art beyond mean-field model to the description of the Gamow-Teller response in atomic nuclei. This topic recently attracted considerable renewed interest, due, in particular, to the possibility of performing experiments in unstable nuclei. We study the cases of $^{48}\mathrm{Ca},\phantom{\rule{0.16em}{0ex}}^{78}\mathrm{Ni},\phantom{\rule{0.16em}{0ex}}^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. Our model is based on a fully self-consistent Skyrme Hartree-Fock plus random phase approximation. The same Skyrme interaction is used to calculate the coupling between particles and vibrations, which leads to the mixing of the Gamow-Teller resonance with a set of doorway states and to its fragmentation. We compare our results with available experimental data. The microscopic coupling mechanism is also discussed in some detail.

Microscopic study of the isoscalar giant monopole resonance in Cd, Sn, and Pb isotopes

The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.

NUCLEAR PHYSICS HAMILTONIANS, INVERSE PROBLEM AND THE RELATED ISSUE OF PREDICTIVE POWER

In this paper we formulate and discuss the strategy of constructing theories capable of providing not only the numerical predictions sensu stricto but also the distributions of probability that such predictions apply in the predefined physics context. Examples of applications of the presented ideas are illustrated using as a choice the nuclear mean-field theory with two realistic realizations of the underlying Hamiltonians: Phenomenological Woods–Saxon and self-consistent Skyrme–Hartree–Fock.

Effect of the Tensor Force on the Charge Exchange Spin-Dipole Excitations ofPb208

The charge exchange spin-dipole (SD) excitations of 208Pb are studied by using a fully self-consistent Skyrme Hartree-Fock plus random phase approximation formalism which includes the tensor interaction. It is found, for the first time, that the tensor correlations have a unique, multipole-dependent effect on the SD excitations; that is, they produce a softening of 1{-} states, but a hardening of 0{-} and 2{-} states. This paves the way to a clear assessment of the strength of the tensor terms. We compare our results with a recent measurement, showing that our choice of tensor terms improves the agreement with experiment. The robustness of our results is supported by the analytic form of the tensor matrix elements.

β-decay properties of neutron-rich Zr and Mo isotopes

Gamow-Teller strength distributions, beta-decay half-lives, and beta-delayed neutron emission are investigated in neutron-rich Zr and Mo isotopes within a deformed quasiparticle random-phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. Comparison with recent measurements of half-lives stresses the important role that nuclear deformation plays in the description of beta-decay properties in this mass region.

Neutrino propagation in the nuclear ‘pasta phase’ of neutron stars

The mean free path of the neutrino in charged and neutral current reactions is calculated for inhomogeneous nuclear matter which is expected to appear in the inner crust of neutron stars. The relevant cross section depends on Fermi and Gamow–Teller strength distributions, which are derived from the self-consistent Skyrme–Hartree–Fock and a relativistic mean-field calculations. The inhomogeneous nuclear matter, which appears at the boundary between the inner crust and outer core, is described in terms of cubic Wigner–Seitz cells. It allows for a microscopic description of the structures in the so-called pasta phase of nuclear configurations and provides a smooth transition to the limit of homogeneous matter. The influence of the pasta phase, its microscopical structure and geometrical shapes on neutrino propagation are considered.

Shape mixing andβ-decay properties of neutron-deficient Kr and Sr isotopes

Gamow-Teller strength distributions and $\ensuremath{\beta}$-decay half-lives in neutron-deficient Kr and Sr isotopes are investigated within a deformed quasiparticle random phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. A simple two-level model is used to mix the nuclear shapes into the physical ground state. Good agreement with experiment is found with shape mixing coefficients which are consistent with those obtained phenomenologically from mixing of rotational bands.

Reflection symmetry instability at high spins in 162,164Yb

A shape evolution of 162,164Yb in yrast states is traced using the self-consistent Skyrme Hartree–Fock calculations. We found that nonaxial octupole deformations (in particular, Y31 term) become favourable at ℏΩ>0.4 MeV in 162Yb, while in 164Yb a nonaxial quadrupole shape is dominant at fast rotation. The cranked Nilsson model and random phase approximation are used to understand the dynamics of octupole correlations in both nuclei. We demonstrate that the disappearance of one of the octupole vibrational modes in the rotating frame gives rise to the nonaxial octupole deformations in 162Yb, while the octupole modes are nonzero in 164Yb.

Charge Exchange Spin-Dipole Excitations of 90Zr and the Neutron Skin Thickness

Charge exchange spin-dipole (SD) excitations of 90 Zr are studied by the 90 Zr(p, n) and 90 Zr(n, p) reactions at 300 MeV. A multipole decomposition technique is employed to obtain the SD strength distributions in the cross section spectra. A model-independent SD sum rule value is obtained: 148 ± 12 fm 2 . The SD strength distributions and the sum rule value are compared with the calculated results of the self-consistent Skyrme Hartree-Fock + Tamm-Dancoff approximation with the coupling to the continuum. The neutron skin thickness of 90 Zr is determined to be 0.07 ± 0.04 fm from the SD sum rule.

SKYRME–HARTREE–FOCK CALCULATIONS OF FISSION BARRIERS OF THE HEAVIEST AND SUPERHEAVY NUCLEI

Self-consistent Skyrme–Hartree–Fock (SHF) calculations of static fission barriers are presented for even-even Fermium isotopes as well as for superheavy even-even N=184 isotones. In the particle-hole channel, we use the SLy4 Skyrme parametrization, while in the particle-particle channel we take a T=1 seniority pairing force treated in the BCS approximation. The influence of reflection-asymmetric and triaxial degrees of freedom on the static fission paths are investigated.

A microscopic investigation of the transition form factor in the region of collective multipole excitations of stable and unstable nuclei

We have used a self-consistent Skyrme–Hartree–Fock plus continuum-RPA model to study the low-multipole response of stable and neutron/proton-rich Ni and Sn isotopes. We focus on the momentum-transfer dependence of the strength distribution, as it provides information on the structure of excited nuclear states and in particular on the variations of the transition form factor (TFF) with the energy. Our results show, among other things, that the TFF may show significant energy dependence in the region of the isoscalar giant monopole resonance and that the TFF corresponding to the threshold strength in the case of neutron-rich nuclei is different compared to that corresponding to the respective giant resonance. Perspectives are given for more detailed future investigations.

Momentum distribution in heavy deformed nuclei: Role of effective mass

The impact of nuclear deformation on the momentum distributions (MD) of occupied proton states in $^{238}$U is studied with a phenomenological Woods-Saxon (WS) shell model and the self-consistent Skyrme-Hartree-Fock (SHF) scheme. Four Skyrme parameterizations (SkT6, SkM*, SLy6, SkI3) with different effective masses are used. The calculations reveal significant deformation effects in the low-momentum domain of $K^{\pi}=1/2^{\pm}$ states, mainly of those lying near the Fermi surface. For other states, the deformation effect on MD is rather small and may be neglected. The most remarkable result is that the very different Skyrme parameterizations and the WS potential give about identical MD. This means that the value of effective mass, being crucial for the description of the spectra, is not important for the spatial shape of the wave functions and thus for the MD. In general, it seems that, for the description of MD at $0\le k \le 300$ MeV/c, one may use any single-particle scheme (phenomenological or self-consistent) fitted properly to the global ground state properties.