Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions

The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The effects of triaxial deformation and of $K$-mixing is illustrated in a study of spectroscopic properties of low-spin states in $^{24}$Mg.Comment: 15 pages, 11 figures, 4 tables, accepted for publication in Phys. Rev.

Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations

A new strategy of fitting the coupling constants of the nuclear energy density functional is proposed, which shifts attention from ground-state bulk to single-particle properties. The latter are analyzed in terms of the bare single-particle energies and mass, shape, and spin core-polarization effects. Fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants directly to the f5/2-f7/2 spin-orbit splittings in 40Ca, 56Ni, and 48Ca is proposed as a practical realization of this new programme. It is shown that this fit requires drastic changes in the isoscalar spin-orbit strength and the tensor coupling constants as compared to the commonly accepted values but it considerably and systematically improves basic single-particle properties including spin-orbit splittings and magic-gap energies. Impact of these changes on nuclear binding energies is also discussed.Comment: 15 pages, 7 figures, submitted to Physical Review

Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field + Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent $\delta$-interaction in the pairing channel. Illustrative calculations are performed for $^{24}$Mg, $^{32}$S and $^{36}$Ar, and compared with results obtained employing the model developed in the first part of this work, i.e. without particle-number projection, as well as with the corresponding non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 37 pages, 10 figures, submitted to Physical Review

Entanglement generation resonances in XY chains

We examine the maximum entanglement reached by an initially fully aligned state evolving in an XY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of [n/2] peaks in the global entanglement for an $n$-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite n-spin chains obtained through the Jordan-Wigner mapping, are discussed

Beyond the relativistic mean-field approximation: configuration mixing of angular momentum projected wave functions

We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed which uses the generator coordinate method to perform configuration mixing calculations of angular momentum projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic mean-field + BCS equations in an axially deformed oscillator basis. A number of illustrative calculations are performed for the nuclei 194Hg and 32Mg, in comparison with results obtained in non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 32 pages, 14 figures, submitted to Phys. Rev.

Time-dependent Internal DFT formalism and Kohn-Sham scheme

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.Comment: 13 pages. To be published in Phys. Rev.

Microscopic study of 240Pu, mean-field and beyond

The influence of exact angular-momentum projection and configuration mixing on properties of a heavy, well-deformed nucleus is discussed for the example of Pu240. Starting from a self-consistent model using Skyrme interactions, we analyze the resulting modifications of the deformation energy, the fission barrier height, the excitation energy of the superdeformed minimum associated with the fission isomer, the structure of the lowest rotational bands with normal deformation and superdeformation, and the corresponding quadrupole moments and transition moments. We present results obtained with the Skyrme interactions SLy4 and SLy6, which have slightly different surface tensions.Comment: 7 pages REVTEX4, 4 figures. accepted for publication in Phys. Rev.

New analysis method of the halo phenomenon in finite many-fermion systems. First applications to medium-mass atomic nuclei

A new analysis method to investigate halos in finite many-fermion systems is designed, as existing characterization methods are proven to be incomplete/inaccurate. A decomposition of the internal wave-function of the {$N$-body} system in terms of overlap functions allows a model-independent analysis of medium-range and asymptotic properties of the internal one-body density. The existence of a spatially decorrelated region in the density profile is related to the existence of three typical energy scales in the excitation spectrum of the {$(N-1)$-body} system. A series of model-independent measures, taking the internal density as the only input, are introduced. The new measures allow a quantification of the potential halo in terms of the average number of fermions participating to it and of its impact on the system extension. Those new "halo factors" are validated through simulations and applied to results obtained through energy density functional calculations of medium-mass nuclei. Performing spherical Hartree-Fock-Bogoliubov calculations with state-of-the-art Skyrme plus pairing functionals, a collective halo is predicted in drip-line Cr isotopes, whereas no such effect is seen in Sn isotopes.Comment: 27 Pages, 29 Figures. Accepted for publication in Phys. Rev. C back-to-back with second part (arXiv:0711.1275

Horizontal Equity Revisited

From the introduction: No tax policy analysis stands complete without examination of equity implications. But despite its role as a traditional pillar of tax policy analysis, equity itself remains a controversial concept. What is meant by the term equity? How should it be measured? Is there more than one type of equity? What is the relationship of different types of equity to each other? For decades, scholars and policy makers have explored the possibility that equity is best understood as two distinct concepts — vertical equity and horizontal equity — both of which must be evaluated. Horizontal equity (HE) is defined to mean that equals should be treated alike. Vertical equity (VE) is defined to mean that an appropriate distinction should be made in the treatment of people who are not alike. Although disagreement exists, HE in our tax system has generally been thought to require that individuals with the same income should pay the same tax. VE has generally been thought to require a progressive rate structure that imposes progressively higher rates on individuals with higher incomes. Despite frequent reliance on both HE and VE in tax policy analysis over the years, scholars have engaged in an active and vibrant debate about whether HE has any significance independent of VE in designing a tax system. This dispute has been best captured by the debate between two economists, Richard Musgrave and Louis Kaplow

Genome-wide association study identifies common and low-frequency variants at the AMHgene locus that strongly predict serum AMH levels in males

Anti-Müllerian hormone (AMH) is an essential messenger of sexual differentiation in the foetus and is an emerging biomarker of postnatal reproductive function in females. Due to a paucity of adequately sized studies, the genetic determinants of circulating AMH levels are poorly characterized. In samples from 2815 adolescents aged 15 from the ALSPAC study, we performed the first genome-wide association study of serum AMH levels across a set of ∼9 M ‘1000 Genomes Reference Panel’ imputed genetic variants. Genetic variants at the AMH protein-coding gene showed considerable allelic heterogeneity, with both common variants [rs4807216 (PMale = 2 × 10−49, Beta: ∼0.9 SDs per allele), rs8112524 (PMale = 3 × 10−8, Beta: ∼0.25)] and low-frequency variants [rs2385821 (PMale = 6 × 10−31, Beta: ∼1.2, frequency 3.6%)] independently associated with apparently large effect sizes in males, but not females. For all three SNPs, we highlight mechanistic links to AMH gene function and demonstrate highly significant sex interactions (PHet 0.0003–6.3 × 10−12), culminating in contrasting estimates of trait variance explained (24.5% in males versus 0.8% in females). Using these SNPs as a genetic proxy for AMH levels, we found no evidence in additional datasets to support a biological role for AMH in complex traits and diseases in men