Towards a new Gogny force parameterization: Impact of the neutron matter equation of state

Chappert, F.; Girod, M.; Hilaire, Stéphane

doi:10.1016/j.physletb.2008.09.017

Cited by 164 publications

(221 citation statements)

References 44 publications

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“…The polaron energy follows from the energy density (3) by E pol = (∂E/∂ρ ↓ ) ρ ↓ =0 . Figure 3 shows the predic-tions for E pol of various state-of-the-art nuclear density functionals: SIII [49], SGII [50], SkM * [51], SLy4 and SLy5 [12], SkO and SkO [52], BSk9 [53], SAMi [54], as well as the Gogny D1N functional [13]. All functionals predict an attractive polaron energy, but E pol varies greatly among the different functionals and is generally underestimated.…”

Section: This Is Equivalent To the Dyson Equationmentioning

confidence: 99%

Neutron polaron as a constraint on nuclear density functionals

et al. 2014

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We study the energy of an impurity (polaron) that interacts strongly in a sea of fermions when the effective range of the impurity-fermion interaction becomes important, thereby mapping the Fermi polaron of condensed matter physics and ultracold atoms to strongly interacting neutrons. We present Quantum Monte Carlo results for this neutron polaron, and compare these with effective field theory calculations that also include contributions beyond the effective range. We show that stateof-the-art nuclear density functionals vary substantially and generally underestimate the neutron polaron energy. Our results thus provide constraints for adjusting the time-odd components of nuclear density functionals to better characterize polarized systems. Energy-density functionals are the only method available to study heavy nuclei and to globally describe the chart of nuclides [1,2]. Due to the need for a precise description of low-energy observables, parameters of these functionals are generally fit to properties of nuclei, including masses and radii. This empirical construction can therefore also benefit from additional input to constrain their properties in exotic, i.e., neutron-rich or spin-polarized systems. Examples of such pseudo-data include calculations of neutron matter [3-9] and neutron drops [10]. This approach has been successfully used to shape new functionals (see, e.g., Refs. [11-16]). In this work, we study the neutron polaron and use its energy as a constraint on nuclear density functionals.The polaron was first introduced in condensed matter physics, and has recently been investigated in strongly interacting ultracold Fermi gases [17] -a system that has many similarities with the physics of low-density neutron matter (see, e.g., Refs. [3,4]). The Fermi polaron is an impurity interacting in a Fermi sea, realized in ultracold atoms and neutron matter as a spin-down fermion in a sea of N ↑ spin-up fermions. The polaron energy E pol = E N ↑ +1 − E N ↑ is defined as the energy difference between the system with the polaron added and the N ↑ (noninteracting) Fermi system. In the thermodynamic limit, this is equivalent to the spin-down chemical potential in the limit of high polarization, and therefore constrains the phase diagram of strongly interacting Fermi systems as a function of spin imbalance [18][19][20][21][22].For attractive interactions, E pol < 0 measures the polaron binding energy in the Fermi sea. In the unitary limit, where the S-wave scattering length |a| → ∞, the polaron energy is universal at low densities and scales as E pol = ηE F where E F = k 2 F /2m is the Fermi energy (with Fermi momentum k F ) and η < 0 is a universal number [18]. Neutrons, whose scattering length is large (a = −18.5 fm), have low-density properties close to the unitary limit. At unitarity, the polaron energy admits a variational bound that sums one-particle-one-hole excitations, η ≤ −0.6066 [18], which is remarkably close to a full manybody treatment [23], η = −0.6158, and agrees with Quantum Monte Carlo (QMC) calculation...

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Section: This Is Equivalent To the Dyson Equationmentioning

confidence: 99%

Neutron polaron as a constraint on nuclear density functionals

et al. 2014

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“…Traditional parameterizations of nuclear EDFs such as Skyrme and Gogny often rely, through the fitting protocol applied, on a combination of carefully selected experimental data as well as pseudo data characterizing properties of nuclear matter (see, e.g., discussion in Refs. [1][2][3][4][5]). Considering the fairly simple forms (and small number of coupling constants) of commonly used nuclear EDFs, the success of the nuclear density functional theory (DFT) to describe a wide range of nuclear properties has been truly remarkable.…”

Section: Introductionmentioning

confidence: 99%

Surface symmetry energy of nuclear energy density functionals

et al. 2011

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We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutronrich matter and description of fission rates for r-process nucleosynthesis.

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“…In that sense, we can say that the tensor has been added perturbatively to the Gogny interaction contrary to the M3Y one for which the tensor parameters enter directly in the fitting procedure. Several parametrizations have also been fitted [5,9,38] aiming at improving the description of finite nuclei energies and sizes, energy levels, pairing properties, nucleon matter, etc. Finally, a new interaction named D2, with a finite-range version of the density dependent term has been presented recently in Ref.…”

Section: Gogny Interactionmentioning

confidence: 99%

“…It is worth remembering that a too soft EoS in PNM, as in the case of Gogny D1S, induces an artificial drift in nuclear binding energies when compared with experimental available masses of neutron rich nuclei. To correct such a behaviour the parametrisation D1N was created [59,38].…”

Section: Equation Of State and Its Decompositionsmentioning

confidence: 99%

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

et al. 2016

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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 local gauge invariance. Finally, we show that the zerorange limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.

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Towards a new Gogny force parameterization: Impact of the neutron matter equation of state

Cited by 164 publications

References 44 publications

Neutron polaron as a constraint on nuclear density functionals

Neutron polaron as a constraint on nuclear density functionals

Surface symmetry energy of nuclear energy density functionals

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

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