60 research outputs found
Magicity of the Ca and Ca isotopes and tensor contribution within a mean--field approach
We investigate the magicity of the isotopes Ca and Ca, that was
recently confirmed by two experimental measurements, and relate it to
like--particle and neutron--proton tensor effects within a mean--field
description. By analyzing Ca isotopes, we show that the like--particle tensor
contribution induces shell effects that render these nuclei more magic than
they would be predicted by neglecting it. In particular, such induced shell
effects are stronger in the nucleus Ca and the single--particle gaps are
increased in both isotopes due to the tensor force. By studying and
isotones, neutron--proton tensor effects may be isolated and their role
analyzed. It is shown that neutron--proton tensor effects lead to increasing
and gaps, when going along isotonic chains, from Fe to
Ca, and from Fe to Ca, respectively.
The mean--field calculations are perfomed by employing one Skyrme parameter
set, that was introduced in a previous work by fitting the tensor parameters
together with the spin--orbit strength. The signs and the values of the tensor
strengths are thus checked within this specific application. The obtained
results indicate that the employed parameter set, even if generated with a
partial adjustment of the parameters of the force, leads to the correct shell
behavior and provides, in particular, a description of the magicity of
Ca and Ca within a pure mean--field picture with the effective
two--body Skyrme interaction.Comment: 7 figure
From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter
We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614
(2016)] where a functional for Fermi systems with anomalously large -wave
scattering length was proposed that has no free parameters. The
functional is designed to correctly reproduce the unitary limit in Fermi gases
together with the leading-order contributions in the s- and p-wave channels at
low density. The functional is shown to be predictive up to densities
fm that is much higher densities compared to the Lee-Yang
functional, valid for fm. The form of the functional
retained in this work is further motivated. It is shown that the new functional
corresponds to an expansion of the energy in and to all
orders, where is the effective range and is the Fermi momentum. One
conclusion from the present work is that, except in the extremely low--density
regime, nuclear systems can be treated perturbatively in with
respect to the unitary limit. Starting from the functional, we introduce
density--dependent scales and show that scales associated to the bare
interaction are strongly renormalized by medium effects. As a consequence, some
of the scales at play around saturation are dominated by the unitary gas
properties and not directly to low-energy constants. For instance, we show that
the scale in the s-wave channel around saturation is proportional to the
so-called Bertsch parameter and becomes independent of . We also
point out that these scales are of the same order of magnitude than those
empirically obtained in the Skyrme energy density functional. We finally
propose a slight modification of the functional such that it becomes accurate
up to the saturation density fm
Tensor and tensor-isospin terms in the effective Gogny interaction
We discuss the need of including tensor terms in the effective Gogny
interaction used in mean-field calculations. We show in one illustrative case
that, with the usual tensor term that is employed in the Skyrme interaction
(and that allows us to separate the like-nucleon and the neutron-proton tensor
contributions), we can describe the evolution of the N=28 neutron gap in
calcium isotopes. We propose to include a tensor and a tensor-isospin term in
finite-range interactions of Gogny type. The parameters of the two tensor terms
allow us to treat separately the like-nucleon and the neutron-proton
contributions. Two parameterizations of the tensor terms have been chosen to
reproduce different neutron single-particle properties in the 48Ca nucleus and
the energy of the first 0- state in the 16O nucleus. By employing these two
parameterizations we analyze the evolution of the N=14, 28, and 90 neutron
energy gaps in oxygen, calcium and tin isotopes, respectively. We show that the
combination of the parameters governing the like-nucleon contribution is
crucial to correctly reproduce the experimental (where available) or
shell-model trends for the evolution of the three neutron gaps under study.Comment: 20 pages, 6 figures. Accepted for publication in Physical Review
Constraining the nuclear pairing gap with pairing vibrations
Pairing interactions with various density dependencies (surface/volume
mixing) are constrained with the two-neutron separation energy in the Tin
isotopic chain. The response associated with pairing vibrations in very
neutron-rich nuclei is sensitive to the density dependence of the pairing
interaction. Using the same pairing interaction in nuclear matter and in Tin
nuclei, the range of densities where the LDA is valid in the pairing channel is
also studied
Towards a power counting in nuclear energyâdensityâfunctional theories through a perturbative analysis
We illustrate a step towards the construction of a power counting in energyâdensityâfunctional (EDF) theories, by analyzing the equations of state (EOSs) of both symmetric and neutron matter. Within the adopted strategy, nextâtoâleading order (NLO) EOSs are introduced which contain renormalized firstâorderâtype terms and an explicit secondâorder finite part. Employing as a guide the asymptotic behavior of the introduced renormalized parameters, we focus our analysis on two aspects: (i) With a minimum number of counterterms introduced at NLO, we show that each energy contribution entering in the EOS has a regular evolution with respect to the momentum cutoff (introduced in the adopted regularization procedure) and is found to converge to a cutoffâindependent curve. The convergence features of each term are related to its Fermiâmomentum dependence. (ii) We find that the asymptotic evolution of the secondâorder finiteâpart coefficients is a strong indication of a perturbative behavior, which in turns confirms that the adopted strategy is coherent with a possible underlying power counting in the chosen Skyrmeâinspired EDF framework
Dimensional regularization applied to nuclear matter with a zero--range interaction
We apply the dimensional regularization procedure to treat an ultraviolet
divergence occurring in the framework of the nuclear many-body problem. We
consider the second--order correction (beyond the mean-field approximation) to
the equation of state of nuclear matter with a zero-range effective
interaction. The unphysical ultraviolet divergence that is generated at second
order by the zero range of the interaction is removed by the regularization
technique and the regularized equation of state (mean-field + second-order
contributions) is adjusted to a reference equation of state. The main practical
advantage of this procedure, with respect to a cutoff regularization, is to
provide a unique set of parameters for the adjusted effective interaction. This
occurs because the regularized second-order correction does not contain any
cutoff dependence. The encouraging results found in this work indicate that
such an elegant technique to generate regularized effective interactions is
likely to be applied in future to finite nuclei in the framework of beyond
mean-field models.Comment: 11 figures. Revised versio
Hartree-Fock-Bogoliubov theory versus local-density approximation for superfluid trapped fermionic atoms
We investigate a gas of superfluid fermionic atoms trapped in two hyperfine
states by a spherical harmonic potential. We propose a new regularization
method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov
equations caused by the use of a zero-range atom-atom interaction. Compared
with a method used in the literature, our method is simpler and has improved
convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations
with the semiclassical local-density approximation. We observe that for systems
containing a small number of atoms shell effects, which cannot be reproduced by
the semiclassical calculation, are very important. For systems with a large
number of atoms at zero temperature the two calculations are in quite good
agreement, which, however, is deteriorated at non-zero temperature, especially
near the critical temperature. In this case the different behavior can be
explained within the Ginzburg-Landau theory.Comment: 12 pages, 8 figures, revtex; v2: references and clarifying remarks
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TRIIAL national reports Belgium, Hungary, Italy, Poland, Portugal, Romania, Slovenia, Spain, The Netherlands
Recent constitutional and legislative changes in several member states are questioning core features of EU rule of law. For the first time ever, the EU institutions have proposed activation of the preventive mechanism in Article 7 TEU against Poland and Hungary, and the European Commission has launched the rule of law conditionality mechanism against Hungary. The jurisprudence of the CJEU finding numerous violations of judicial independence and fundamental rights undermining the rule of law in Europe is growing at a fast pace. Moreover, many preliminary references show the willingness of national courts to engage in judicial dialogue with the CJEU, relying on it to provide harmonised standards and guidelines on the rule of law. However, the future of such interactions is undermined by recent decisions of supreme and constitutional courts limiting the rights of domestic courts to use the preliminary reference procedure and prohibiting their obligation to give effect to EU law based on a tendentious understanding of national constitutional identity. In this context, the TRIIAL project has embarked on an ambitious research quest, which resulted in the present Edited Working Paper. It consists of nine country reports which cover the most relevant issues concerning judicial independence, impartiality, accountability, mutual trust and the rule of law in the jurisdictions of the project partners: Belgium, the Netherlands, Hungary, Romania, Italy, Portugal, Poland, Spain and Slovenia. The country reports primarily build on case law identified and analysed during the TRIIAL project and published in the CJC database. They outline the current state of affairs and challenges the member states face in the topics covered by TRIIAL exposing and analysing specific pressing issues, especially ones that are not yet covered in other reports such as the European Commissionâs Rule of Law report.
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