arXiv subjects

R. Navarro Perez

Publications and source records attributed to R. Navarro Perez.

At least 19 recordsLinked to original sources

arXiv2026

Coarse graining the Bethe-Goldstone equation: nucleon-nucleon high momentum components

The delta-shell representation of the nuclear force allows a simplified treatment of nuclear correlations. We show how this applies to the Bethe-Goldstone equation as an integral equation in coordinate space with a few mesh points, which is solved by inversion of a 5-dimensional square matrix in the single channel cases and a $10\times10$ matrix for the tensor-coupled channels. This allows us to readily obtain the high momentum distribution, for all partial waves, of a back-to-back correlated nucleon pair in nuclear matter. We find that the probability of finding a high-momentum correlated neutron-proton pair is about 18 times that of a proton-proton one, as a result of the strong tensor force, thus confirming in an independent way previous results and measurements.

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arXiv2019

Propagation of Statistical Uncertainties of Skyrme Mass Models to Simulations of $r$-Process Nucleosynthesis

Uncertainties in nuclear models have a major impact on simulations that aim at understanding the origin of heavy elements in the universe through the rapid neutron capture process ($r$ process) of nucleosynthesis. Within the framework of the nuclear density functional theory, we use results of Bayesian statistical analysis to propagate uncertainties in the parameters of energy density functionals to the predicted $r$-process abundance pattern, by way not only of the nuclear masses but also through the influence of the masses on $β$-decay and neutron capture rates. We additionally make the first identifications of specific parameters of Skyrme-like energy density functionals which are correlated with particular aspects of the $r$-process abundance pattern. While previous studies have explored the reduction in the abundance pattern uncertainties due to anticipated new measurements of neutron-rich nuclei, here we point out that an even larger reduction will occur when these new measurements are used to reduce the uncertainty of model predictions of masses, which are then propagated through to the abundance pattern. We make a quantitative prediction for how large this reduction will be.

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arXiv2018

Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation

We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. The first component of this functional is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. A second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. We obtain a set of microscopically-constrained functionals for local chiral potentials from leading-order up to next-to-next-to-leading order with and without three-body forces and contributions from $Δ$ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei and the fission barrier of $^{240}$Pu. Quantitatively, they perform noticeable better than the more phenomenological Skyrme functionals. The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies. This result is especially promising since all the fits have been performed at the single reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction have not been taken into account yet.

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arXiv2018

Low energy peripheral scaling in Nucleon-Nucleon Scattering and uncertainty quantification

We analyze the peripheral structure of the nucleon-nucleon interaction for LAB energies below 350 MeV. To this end we transform the scattering matrix into the impact parameter representation by analyzing the scaled phase shifts $(L+1/2) δ_{JLS} (p)$ and the scaled mixing parameters $(L+1/2)ε_{JLS}(p)$ in terms of the impact parameter $b=(L+1/2)/p$. According to the eikonal approximation, at large angular momentum $L$ these functions should become an universal function of $b$, {\it independent} on $L$. This allows to discuss in a rather transparent way the role of statistical and systematic uncertainties in the different long range components of the two-body potential. Implications for peripheral waves obtained in chiral perturbation theory interactions to fifth order (N5LO) or from the large body of NN data considered in the SAID partial wave analysis are also drawn from comparing them with other phenomenological high-quality interactions, constructed to fit scattering data as well. We find that both N5LO and SAID peripheral waves disagree more than $5 σ$ with the Granada-2013 statistical analysis, more than $ 2 σ$ with the 6 statistically equivalent potentials fitting the Granada-2013 database and about $1 σ$ with the historical set of 13 high-quality potentials developed since the 1993 Nijmegen analysis.

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arXiv2017

Precise Determination of Charge Dependent Pion-Nucleon-Nucleon Coupling Constants

We undertake a covariance error analysis of the pion-nucleon-nucleon coupling constants from the Granada-2013 np and pp database comprising a total of 6720 scattering data below LAB energy of 350 MeV. Assuming a unique pion-nucleon coupling constant in the One Pion Exchange potential above a boundary radius $r_c=3 {\rm fm}$ we obtain $f^2=0.0763(1)$. The effects of charge symmetry breaking on the $^3P_0$, $^3P_1$ and $^3P_2$ partial waves are analyzed and we find $f_{p}^2 = 0.0761(4)$, $f_{0}^2 = 0.0790(9)$ and $f_{c}^2 = 0.0772(6)$ with a strong anti-correlation between $f_c^2$ and $f_0^2$. We successfully test normality for the residuals of the fit. Potential tails in terms of different boundary radii as well as chiral Two-Pion-Exchange contributions as sources of systematic uncertainty are also investigated.

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arXiv2017

Coarse grained short-range correlations

We develop a scheme to take into account the effects of short-range nucleon-nucleon correlations in the nucleon-pair wave function by solving the Bethe-Goldstone equation for a coarse grained delta shell potential in S-wave configuration. The S-wave delta shell potential has been adjusted to reproduce the $^1$S$_0$ phase shifts of the AV18 potential for this partial wave up to 2 GeV in the laboratory kinetic energy. We show that a coarse grained potential can describe the high momentum tail of the back-to-back correlated pairs and the $G$-matrix in momentum space. We discuss the easiness and robustness of the calculation in coordinate space and the future improvements and utilities of this model. This work suggests the possibility of using perturbation theory for describing the short-range correlations, and related to this, to substitute the $G$-matrix by an appropriate coarse-grained potential.

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arXiv2017

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) hfbtho (v3.00): a new version of the program

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck (iv) the regularization of zero-range pairing forces (v) the calculation of localization functions (vi)MPI interface for large-scale mass table calculations.

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arXiv2016

The falsification of Chiral Nuclear Forces

Predictive power in theoretical nuclear physics has been a major concern in the study of nuclear structure and reactions. The Effective Field Theory (EFT) based on chiral expansions provides a model independent hierarchy for many body forces at long distances but their predictive power may be undermined by the regularization scheme de- pendence induced by the counterterms and encoding the short distances dynamics which seem to dominate the uncertainties. We analyze several examples including zero energy NN scattering or perturbative counterterm-free peripheral scattering where one would ex- pect these methods to work best and unveil relevant systematic discrepancies when a fair comparison to the Granada-2013 NN-database and partial wave analysis is undertaken.

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arXiv2016

Three pion nucleon coupling constants

There exist four pion nucleon coupling constants, $f_{π^0, pp}$, $-f_{π^0, nn}$, $f_{π^+, pn} /\sqrt{2}$ and $ f_{π^-, np} /\sqrt{2}$ which coincide when up and down quark masses are identical and the electron charge is zero. While there is no reason why the pion-nucleon-nucleon coupling constants should be identical in the real world, one expects that the small differences might be pinned down from a sufficiently large number of independent and mutually consistent data. Our discussion provides a rationale for our recent determination $$f_p^2 = 0.0759(4) \, , \quad f_{0}^2 = 0.079(1) \,, \quad f_{c}^2 = 0.0763(6) \, , $$ based on a partial wave analysis of the $3σ$ self-consistent nucleon-nucleon Granada-2013 database comprising 6713 published data in the period 1950-2013.

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arXiv2016

The Low energy structure of the Nucleon-Nucleon interaction: Statistical vs Systematic Uncertainties

We analyze the low energy NN interaction by confronting statistical vs systematic uncertainties. This is carried out with the help of model potentials fitted to the Granada-2013 database where a statistically meaningful partial wave analysis comprising a total of $6713$ np and pp published scattering data from 1950 till 2013 below $350 {\rm MeV}$ has been made. We extract threshold parameters uncertainties from the coupled channel effective range expansion up to $j \le 5$. We find that for threshold parameters systematic uncertainties are generally at least an order of magnitude larger than statistical uncertainties. Similar results are found for np phase-shifts and amplitude parameters.

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arXiv2016

Binding in light nuclei: Statistical NN uncertainties vs Computational accuracy

We analyse the impact of the statistical uncertainties of the the nucleon-nucleon interaction, based on the Granada-2013 np-pp database, on the binding energies of the triton and the alpha particle using a bootstrap method, by solving the Faddeev equations for $^3$H and the Yakubovsky equations for $^4$He respectively. We check that in practice about 30 samples prove enough for a reliable error estimate. An extrapolation of the well fulfilled Tjon-line correlation predicts the experimental binding of the alpha particle within uncertainties.

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arXiv2016

Uncertainty quantification of effective nuclear interactions

We give a brief review on the development of phenomenological NN interactions and the corresponding quantification of statistical uncertainties. We look into the uncertainty of effective interactions broadly used in mean field calculations through the Skyrme parameters and effective field theory counter-terms by estimating both statistical and systematic uncertainties stemming from the NN interaction. We also comment on the role played by different fitting strategies on the light of recent developments.

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arXiv2015

Statistical error propagation in ab initio no-core full configuration calculations of light nuclei

We propagate the statistical uncertainty of experimental NN scattering data into the binding energy of $^3$H and $^4$He. We also study the sensitivity of the magnetic moment and proton radius of the $^3$H to changes in the NN interaction. The calculations are made with the no-core full configuration method in a sufficiently large harmonic oscillator basis. For those light nuclei we obtain $ΔE$($^3$H) = 0.015 MeV and $ΔE$($^4$He) = 0.055 MeV.

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arXiv2015

The Falsification of Nuclear Forces

We review our work on the statistical uncertainty analysis of the NN force. This is based on the Granada-2013 database where a statistically meaningful partial wave analysis comprising a total of 6713 np and pp published scattering data from 1950 till 2013 below pion production threshold has been made. We stress the necessary conditions required for a correct and self-consistent statistical interpretation of the discrepancies between theory and experiment which enable a subsequent statistical error propagation and correlation analysis

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arXiv2015

Low energy chiral two pion exchange potential with statistical uncertainties

We present a new phenomenological Nucleon-Nucleon chiral potential fitted to 925 pp and 1743 np scattering data selected from the Granada-2013 NN-database up to a laboratory energy of $125$ MeV with 20 short distance parameters and three chiral constants $c_1$, $c_3$ and $c_4$ with $χ^2/ν= 1.02$. Special attention is given to testing the normality of the residuals which allows for a sound propagation of statistical errors from the experimental data to the potential parameters, phase-shifts, scattering amplitudes and counter-terms. This fit allows for a new determination of the chiral constants $c_1$, $c_3$ and $c_4$ compatible with previous determinations from NN data. This new interactions is found to be softer than other high quality potentials by undertaking a Weinberg eigenvalue analysis. We further explore the interplay between the error analysis and the assumed form of the short distance interaction. The present work shows that it is possible to fit NN scattering with a TPE chiral potential fulfilling all necessary statistical requirements up to 125 MeV and shows unequivocal non-vanishing D-wave short distance pieces.

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arXiv2014

Error analysis of nuclear forces and effective interactions

The Nucleon-Nucleon interaction is the starting point for ab initio Nuclear Structure and Nuclear reactions calculations. Those are effectively carried out via effective interactions fitting scattering data up to a maximal center of mass momentum. However, NN interactions are subjected to statistical and systematic uncertainties which are expected to propagate and have some impact on the predictive power and accuracy of theoretical calculations, regardless on the numerical accuracy of the method used to solve the many body problem. We stress the necessary conditions required for a correct and self-consistent statistical interpretation of the discrepancies between theory and experiment which enable a subsequent statistical error propagation and correlation analysis. We comprehensively discuss an stringent and recently proposed tail-sensitive normality test and provide a simple recipe to implement it. As an application, we analyze the deduced uncertainties and correlations of effective interactions in terms of Moshinsky-Skyrme parameters and effective field theory counterterms as derived from the bare NN potential containing One-Pion-Exchange and Chiral Two-Pion-Exchange interactions inferred from scattering data.

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arXiv2014

Triton binding energy with realistic precision

We compute the binding energy of triton with realistic statistical errors stemming from NN scattering data uncertainties and the deuteron and obtain $E_t=-7.638(15) \, {\rm MeV}$. Setting the numerical precision as $ΔE_t^{\rm num} \lesssim 1 \, {\rm keV}$ we obtain the statistical error $ΔE_t^{\rm stat}= 15(1) \, {\rm keV}$ which is mainly determined by the channels involving relative S-waves. This figure reflects the uncertainty of the input NN data, more than two orders of magnitude larger than the experimental precision $ΔE_t^{\rm exp}= 0.1 \, {\rm keV}$ and provides a bottleneck in the realistic precision that can be reached. This suggests an important reduction in the numerical precision and hence in the computational effort.

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arXiv2014

Bootstrapping the statistical uncertainties of NN scattering data

We use the Monte Carlo bootstrap as a method to simulate pp and np scattering data below pion production threshold from an initial set of over 6700 experimental mutually $3σ$ consistent data. We compare the results of the bootstrap, with 1020 statistically generated samples of the full database, with the standard covariance matrix method of error propagation. No significant differences in scattering observables and phase shifts are found. This suggests alternative strategies for propagating errors of nuclear forces in nuclear structure calculations.

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