Superfluid properties of the inner crust of neutron stars
We investigated the superfluid properties of the inner crust of neutron stars, solving the Hartree-Fock-Bogoliubov equations in spherical Wigner-Seitz cells. Using realistic two-body interactions in the pairing channel, we studied in detail the Cooper-pair and the pairing-field spatial properties, together with the effect of the proton clusters on the neutron pairing gap. Calculations with effective pairing interactions are also presented, showing significant discrepancies with the results obtained with realistic pairing forces. At variance with recent studies on finite nuclei, the neutron coherence length is found to depend on the strength of the pairing interaction, even inside the nucleu…
Nuclear Energy Density Optimization: UNEDF2
The parameters of the UNEDF2 nuclear energy density functional (EDF) model were obtained in an optimization to experimental data consisting of nuclear binding energies, proton radii, odd-even mass staggering data, fission-isomer excitation energies, and single particle energies. In addition to parameter optimization, sensitivity analysis was done to obtain parameter uncertainties and correlations. The resulting UNEDF2 is an all-around EDF. However, the sensitivity analysis also demonstrated that the limits of current Skyrme-like EDFs have been reached and that novel approaches are called for.
Partial wave decomposition of the N3LO equation of state
By means of a partial wave decomposition, we separate their contributions to the equation of state of symmetric nuclear matter for the N3LO pseudo-potential. In particular, we show that although both the tensor and the spin-orbit terms do not contribute to the equation of state, they give a non-vanishing contribution to the separate (JLS) channels.
The magnet of the scattering and neutrino detector for the SHiP experiment at CERN
The Search for Hidden Particles (SHiP) experiment proposal at CERN demands a dedicated dipole magnet for its scattering and neutrino detector. This requires a very large volume to be uniformly magnetized at B > 1.2 T, with constraints regarding the inner instrumented volume as well as the external region, where no massive structures are allowed and only an extremely low stray field is admitted. In this paper we report the main technical challenges and the relevant design options providing a comprehensive design for the magnet of the SHiP Scattering and Neutrino Detector.
First observation of the doubly charmed baryon decay Ξcc++→Ξc+π+
The doubly charmed baryon decay Ξcc++→Ξc+π+ is observed for the first time, with a statistical significance of 5.9σ, confirming a recent observation of the baryon in the Λc+K−π+π+ final state. The data sample used corresponds to an integrated luminosity of 1.7 fb−1, collected by the LHCb experiment in pp collisions at a center-of-mass energy of 13 TeV. The Ξcc++ mass is measured to be 3620.6±1.5(stat)±0.4(syst)±0.3(Ξc+) MeV/c2 and is consistent with the previous result. The ratio of branching fractions between the decay modes is measured to be [B(Ξcc++→Ξc+π+)×B(Ξc+→pK−π+)]/[B(Ξcc++→Λc+K−π+π+)×B(Λc+→pK−π+)]=0.035±0.009(stat)±0.003(syst).
Extended Skyrme pseudopotential deduced from infinite nuclear matter properties
We discuss the contributions to the equation of state for the NlLO Skyrme pseudopotential (l = 2,3). We show that by adding fourth- and sixth-order gradient terms, it is possible to fairly reproduce the spin/isospin decomposition of an equation of state obtained from ab initio methods. Moreover, by inspecting the partial-wave decomposition of the equation of state, we show for the first time a possible way to add explicit constraints on the sign of the tensor terms of the Skyrme interaction.
Nuclear energy density optimization: Shell structure
Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. In this work, we propose a new parameterization UNEDF2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDerS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parameterization UNEDF1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose c…
Two-body contributions to the effective mass in nuclear effective interactions
Starting from general expressions of well-chosen symmetric nuclear matter quantities derived for both zero- and finite-range effective theories, we derive the contributions to the effective mass. We first show that, independently of the range, the two-body contribution is enough to describe correctly the saturation mechanism but gives an effective mass value around $m^*/m \simeq 0.4$. Then, we show that the full interaction (by instance, an effective two-body density-dependent term on top of the pure two-body term) is needed to reach the accepted value $m^*/m \simeq 0.7-0.8$.
Spurious finite-size instabilities in nuclear energy density functionals
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 functi…
Linear response of homogeneous nuclear matter with energy density functionals
Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions…
Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions
We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with lo…
Finite-size effects and collective vibrations in the inner crust of neutron stars
We study the linear response of the inner crust of neutron stars within the Random Phase Approximation, employing a Skyrme-type interaction as effective interaction. We adopt the Wigner-Seitz approximation, and consider a single unit cell of the Coulomb lattice which constitutes the inner crust, with a nucleus at its center, surrounded by a sea of free neutrons. With the use of an appropriate operator, it is possible to analyze in detail the properties of the vibrations of the surface of the nucleus and their interaction with the modes of the sea of free neutrons, and to investigate the role of shell effects and of resonant states.
Model nuclear energy density functionals derived from ab initio calculations
We present the first application of a new approach, proposed in [Journal of Physics G: Nuclear and Particle Physics, 43, 04LT01 (2016)] to derive coupling constants of the Skyrme energy density functional (EDF) from ab initio Hamiltonian. By perturbing the ab initio Hamiltonian with several functional generators defining the Skyrme EDF, we create a set of metadata that is then used to constrain the coupling constants of the functional. We use statistical analysis to obtain such an ab initio-equivalent Skyrme EDF. We find that the resulting functional describes properties of atomic nuclei and infinite nuclear matter quite poorly. This may point out to the necessity of building up the ab init…
Extended Skyrme Equation of State in asymmetric nuclear matter
We present a new equation of state for infinite systems (symmetric, asymmetric, and neutron matter) based on an extended Skyrme functional that has been constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces the main features of microscopic calculations very accurately and is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest.
Bootstrap Technique to Study Correlation Between Neutron Skin Thickness and the Slope of Symmetry Energy in Atomic Nuclei
We present a new statistical tool based on random sampling to assess the confidence interval of Pearson's and Spearman's correlation coefficients. These estimators are then used to quantify the statistical correlations among the neutron skin thickness of atomic nuclei and the slope of the symmetry energy in the infinite nuclear medium.
WITHDRAWN: Linear Response Theory with finite-range interactions
Shape staggering of midshell mercury isotopes from in-source laser spectroscopy compared with density-functional-theory and Monte Carlo shell-model calculations
Neutron-deficient Hg177-185 isotopes were studied using in-source laser resonance-ionization spectroscopy at the CERN-ISOLDE radioactive ion-beam facility in an experiment combining different detection methods tailored to the studied isotopes. These include either α-decay tagging or multireflection time-of-flight gating for isotope identification. The endpoint of the odd-even nuclear shape staggering in mercury was observed directly by measuring for the first time the isotope shifts and hyperfine structures of Hg177-180. Changes in the mean-square charge radii for all mentioned isotopes, magnetic dipole, and electric quadrupole moments of the odd-A isotopes and arguments in favor of I=7/2 s…
Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals
The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predic…
Linear response of light deformed nuclei investigated by self-consistent quasiparticle random-phase approximation
We present a calculation of the properties of vibrational states in deformed, axially-symmetric even-even nuclei, within the framework of a fully self-consistent quasiparticle random phase approximation (QRPA). The same Skyrme energy density and density-dependent pairing functionals are used to calculate the mean field and the residual interaction in the particle-hole and particle-particle channels. We have tested our software in the case of spherical nuclei against fully self-consistent calculations published in the literature, finding excellent agreement. We investigate the consequences of neglecting the spin-orbit and Coulomb residual interactions in QRPA. Furthermore we discuss the impr…
Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms
The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry, and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.
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 dif…
Tools for incorporating a D-wave contribution in Skyrme energy density functionals
International audience; The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.
Neutron-proton pairing correlations in a single l-shell model
The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.
Linear Response Theory with finite-range interactions
International audience; This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interactio…
Neutrino mean free path in neutron matter with Brussels-Montreal Skyrme functionals
We calculate the neutrino mean free path in cold neutron matter with some modern Brussels-Montreal functionals. The three typical functionals used in this article produce quite different results implying a possible impact on the cooling mechanism of neutron stars.
Measurement of the branching fraction of the decay Bs0→KS0KS0
A measurement of the branching fraction of the decay Bs0→KS0KS0 is performed using proton-proton collision data corresponding to an integrated luminosity of 5 fb-1 collected by the LHCb experiment between 2011 and 2016. The branching fraction is determined to be B(Bs0→KS0KS0)=[8.3±1.6(stat)±0.9(syst)±0.8(norm)±0.3(fs/fd)]×10-6, where the first uncertainty is statistical, the second is systematic, and the third and fourth are due to uncertainties on the branching fraction of the normalization mode B0→φKS0 and the ratio of hadronization fractions fs/fd. This is the most precise measurement of this branching fraction to date. Furthermore, a measurement of the branching fraction of the decay B0…
Dependence of two-proton radioactivity on nuclear pairing models
Sensitivity of two-proton emitting decay to nuclear pairing correlation is discussed within a time-dependent three-body model. We focus on the $^6$Be nucleus assuming $\alpha + p + p$ configuration, and its decay process is described as a time-evolution of the three-body resonance state. For a proton-proton subsystem, a schematic density-dependent contact (SDDC) pairing model is employed. From the time-dependent calculation, we observed the exponential decay rule of a two-proton emission. It is shown that the density dependence does not play a major role in determining the decay width, which can be controlled only by the asymptotic strength of the pairing interaction. This asymptotic pairin…
Spurious finite-size instabilities in nuclear energy density functionals: Spin channel
Background: It has been recently shown that some Skyrme functionals can lead to nonconverging results in the calculation of some properties of atomic nuclei. A previous study has pointed out a possible link between these convergence problems and the appearance of finite-size instabilities in symmetric nuclear matter (SNM) around saturation density. Purpose: We show that the finite-size instabilities not only affect the ground-state properties of atomic nuclei, but they can also influence the calculations of vibrational excited states in finite nuclei. Method: We perform systematic fully-self consistent random phase approximation (RPA) calculations in spherical doubly magic nuclei. We employ…
Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry
International audience; We present the development of the extended Skyrme N2LO pseudopotential 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 behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.
Superfluid properties of the inner crust of neutron stars
We investigated the superfluid properties of the inner crust of neutron stars, solving the Hartree-FockBogoliubov equations in spherical Wigner-Seitz cells. Using realistic two-body interactions in the pairing channel, we studied in detail the Cooper-pair and the pairing-field spatial properties, together with the effect of the proton clusters on the neutron pairing gap. Calculations with effective pairing interactions are also presented, showing significant discrepancies with the results obtained with realistic pairing forces. At variance with recent studies on finite nuclei, the neutron coherence length is found to depend on the strength of the pairing interaction, even inside the nucleus…
Effect of three-body forces on response functions in infinite neutron matter
International audience; We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.
Nuclear matter response function with a central plus tensor Landau interaction
We present a method to obtain response functions in the random phase approximation (RPA) based on a residual interaction described in terms of Landau parameters with central plus tensor contributions. The response functions keep the explicit momentum dependence of the RPA, in contrast with the traditional Landau approximation. Results for symmetric nuclear matter and pure neutron matter are presented using Landau parameters derived from finite-range interactions, both phenomenological and microscopic. We study the convergence of response functions as the number of Landau parameters is increased.
Partial wave decomposition of finite-range effective tensor interaction
We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial-wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the next-to-next-to-next-leading-order (N3LO) Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the te…
Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange
International audience; We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry, and temperature. We evaluate the role of statistical errors related to the uncertainties of the coupling constants of the Skyrme functional and thus determine the confidence interval of the resulting response functi…
Does the Gogny interaction need a third Gaussian?
International audience; By considering infinite matter constraints only, we suggest in this paper that the Gogny interaction should benefit from a third Gaussian in its central part. A statistical analysis is given to select the possible ranges which are compatible with these constraints and which minimize a $\chi^2$ function.
Spatial dependence of the pairing field calculated with bare and induced interactions
The interaction induced by the exchange of low-lying surface vibrations between pairs of orbitals close to the Fermi surface provides an important contribution to pairing correlations in superfluid nuclei. We study the spatial dependence of the pairing field obtained adding the bare and induced interaction in 120Sn.
Characterization of the shape-staggering effect in mercury nuclei
In rare cases, the removal of a single proton (Z) or neutron (N) from an atomic nucleus leads to a dramatic shape change. These instances are crucial for understanding the components of the nuclear interactions that drive deformation. The mercury isotopes (Z = 80) are a striking example1,2: their close neighbours, the lead isotopes (Z = 82), are spherical and steadily shrink with decreasing N. The even-mass (A = N + Z) mercury isotopes follow this trend. The odd-mass mercury isotopes 181,183,185Hg, however, exhibit noticeably larger charge radii. Due to the experimental difficulties of probing extremely neutron-deficient systems, and the computational complexity of modelling such heavy nucl…
Skyrme effective pseudopotential up to next-to-next-to leading order
The explicit form of the next-to-next-to-leading order ((NLO)-L-2) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in a Cartesian basis. It is shown in particular that for such a pseudopotential there is no spin-orbit contribution and that the D-wave term suggested in the original Skyrme formulation does not satisfy the invariance properties. The six new (NLO)-L-2 terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed.
Clinicogenetic Risk Models in Patients Randomized to Receive Consolidative Autologous Stem-Cell Transplantation after Frontline R-CHOP for Advanced Follicular Lymphoma: An Analysis from the GLSG2000 Trial
Abstract Introduction: Advanced follicular lymphoma (FL) is a clinically and molecularly heterogeneous disease. About 20% of patients have early progression of disease (POD) and short overall survival (OS). We have previously shown that integration of lymphoma-specific gene mutations and clinical factors improves pretreatment risk stratification (Pastore, 2015) and prediction of early POD (i.e., within 24 months, POD24; Jurinovic, 2016). Recently, we have shown that high-dose therapy (HDT) followed by autologous stem-cell transplantation (ASCT) is an effective treatment option for eligible patients with high-risk disease as defined by POD24 (Jurinovic, 2018). Here, we aimed to explore wheth…
Fitting N$^{3}$LO pseudopotentials through central plus tensor Landau parameters
Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of next-to-next-to-next-to-leading order ((NLO)-L-3) pseudo-potentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at (NLO)-L-3 is given.