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 HartreeFock-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. Special attention is devoted to the time-odd tensor terms, the effect of variations of their coupling constants and finite-size instabilities.

Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals [1,2]. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei.In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.

It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functional form of the EDF and that can be utilized during the adjustment of its coupling constants. Tuning the coupling constant $C^{\rho \Delta\rho}_{1}$ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. The link to instabilities of SNM is made by extracting the lowest density $\rho_{\text{crit}}$ at which a pole appears at zero energy in the RPA response function when employing the critical value of the coupling constant $C^{\rho \Delta\rho}_{1}$ extracted in nuclei. Our analysis suggests a two-fold stability criterion to avoid scalar-isovector instabilities: (i) The density $\rho_{\text{min}}$ corresponding to the lowest pole in the RPA response function should be larger than about 1.2 times the saturation density; (ii) one needs to verify that $\rho_{p}(q_{\text{pq}})$ exhibits a distinct global minimum and is not a decreasing function for large transferred momenta.Comment: 9 pages, 11 figures, submitted to Phys. Rev.

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 of a large variety of Skyrme energy density functionals that have been introduced in the last years. Finally, the treatment of the constraints that can be introduced in the mean-field equations has been improved. The code Ev8 is today the tool of choice to study the variation of the energy of a nucleus from its ground state to very elongated or triaxial deformations with a well-controlled accuracy.Keywords: Self-consistent mean field; Hartree-Fock; Hartree-Fock+BCS; Skyrme interaction; Quadrupole deformation. The program expands the single-particle wave-functions on a 3D Cartesian mesh. The nonlinear mean-field equations are solved by the imaginary time step method. A quadratic constraint is used to obtain states corresponding to given values of the monopole and quadrupole operators. Summary of revisions: PROGRAM SUMMARY/NEW VERSION PROGRAM SUMMARY1. Skyrme energy functionals with tensor terms 2. Improved accuracy for calculating derivatives 3. Improved accuracy for solving Coulomb problem 4. Improvement of the numerics of constraints Restrictions:Ev8 assumes time-reversal invariance and nuclear shapes exhibiting three plane-reflection symmetries. Pairing correlations are treated at the BCS level of approximation. Running time: A few minutes for the examples provided, which concern rather heavy nuclei in modest boxes with an initial guess of Nilsson wavefunctions.

The shape of exotic even-mass [182][183][184][185][186][187][188][189][190] Pb isotopes was probed by measurement of optical isotope shifts providing mean square charge radii (hr 2 i). The experiment was carried out at the ISOLDE (CERN) on-line mass separator, using in-source laser spectroscopy. Small deviations from the spherical droplet model are observed, but when compared to model calculations, those are explained by high sensitivity of hr 2 i to beyond mean-field correlations and small admixtures of intruder configurations in the ground state. The data support the predominantly spherical shape of the ground state of the proton-magic Z 82 lead isotopes near neutron midshell (N 104). The subtle interplay between individual and collective behavior of a finite number of strongly interacting fermions leads to aspects of mesoscopic systems that can only be studied in atomic nuclei [1]. For neutron-deficient nuclides around the closed proton shell at Z 82, this interplay leads to the appearance of states with different shapes at low excitation energy. These so-called shape coexisting states can be interpreted as particle-hole excitations across the closed proton shell gap [2] whereby the interaction of the valence proton particles and holes with the neutrons drives the nucleus into deformation. The phenomenon of shape-coexistence is subject to intensive experimental and theoretical studies [3,4]. Alpha-decay experiments have revealed a triplet of low-lying 0 states in the 186 Pb nucleus, which is located at neutron midshell between N 82 and 126 [1]. Excited bands built on top of the 0 states were observed in [182][183][184][185][186][187][188][189][190], and recent lifetime measurements confirmed the deformed character of the bands [11]. For 186 188 Pb, it was concluded that the ground state and the 2 1 state have a very different structure, the 0 ground state of predominantly spherical and the 2 1 state of predominantly prolate character. Monopole transition strengths between the 0 states were used to estimate the mixing between the normal and intruder configuration [12] and revealed limited configuration mixing in the 190;192;194 Pb ground-state wave function [13,14]. But as the excited 0 states become lower in energy when approaching N 104 ( 186 Pb), the mixing could increase substantially.Several theoretical models have been applied to describe the structure of the neutron-deficient lead isotopes with their coexisting and mixed spherical, prolate, and oblate states, such as phenomenological shape mixing calculations [13,14], symmetry guided shell model and interacting boson model truncations [15,16], and beyond mean-field approaches [4,17,18]. All models that provide a consistent picture of the available data suggest that the ground state of lead isotopes is dominated by spherical configurations, even when the prolate and oblate rotational bands come down very low in energy around N 104, and the barrier that separates the corresponding structures in the total energy surface is very small. But all models also ...

The role of configuration mixing in the Pt region is investigated. For this chain of isotopes, the nature of the ground state changes smoothly, being spherical around mass A ∼ 174 and A ∼ 192 and deformed around the mid-shell N = 104 region. This has a dramatic effect on the systematics of the energy spectra as compared to the systematics in the Pb and Hg nuclei. Interacting Boson Model with configuration mixing calculations are presented for gyromagnetic factors, α-decay hindrance factors, and isotope shifts. The necessity of incorporating intruder configurations to obtain an accurate description of the latter properties becomes evident.PACS numbers: 21.10.-k, 21.60.-n, 21.60.Fw.

In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in 188 Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model.

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