Uncertainty quantification of effective nuclear interactions

Pérez, R. Navarro; Amaro, J. E.; Arriola, E. Ruiz

doi:10.1142/s0218301316410093

Cited by 21 publications

(35 citation statements)

References 72 publications

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“…Following the recent suggestion [67], we find that this happens with the current form of the potential when E lab ≤ 125 MeV. In a companion paper we will analyze the statistical properties of the present fit and how there is a trade-off of different uncertainty sources.…”

Section: Discussionsupporting

confidence: 65%

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

et al. 2015

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We construct a coordinate-space chiral potential, including ∆-isobar intermediate states in its two-pion-exchange component up to order Q 3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q 2 and Q 4 , respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0-300 MeV. For the total 5291 pp and np data in this range, we obtain a χ 2 /datum of roughly 1.3 for a set of three models characterized by long-and short-range cutoffs, RL and RS respectively, ranging from (RL, RS) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

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Section: Discussionsupporting

confidence: 65%

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

et al. 2015

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“…This is usually detected by use of Levinson's theorem, δ l (0) − δ l (∞) = nπ, which requires checking phases at energies much larger than the fitting range. An equivalent way to find spurious bound states is by checking the volume integrals (and high moments) for which a large degree of universality has been found [51]. Too large attractive couplings in the potential permitting a bound state would consequently generate unnaturally large volume integrals of the potentials.…”

Section: B Naturalness Of Fitting Parametersmentioning

confidence: 99%

Precise determination of charge-dependent pion-nucleon-nucleon coupling constants

2017

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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 = 3fm we obtain f 2 = 0.0763(1). The effects of charge symmetry breaking on the 3 P 0 , 3 P 1 and 3 P 2 partial waves are analyzed and we find f 2 p = 0.0761(4), f 2 0 = 0.0790(9) and f 2 c = 0.0772(6) with a strong anti-correlation between f 2 c and f 2 0 . 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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“…Afnan and Tang recognized this for the case of 3 He and 4 He [17] where good binding energies were achieved when S-waves are fitted up to E LAB 100MeV. Using simple coarse grained interactions and mean field wave functions we have verified this feature for nuclei as heavy as 40 Ca [18].…”

Section: Introductionmentioning

confidence: 59%

“…We have recently evaluated them and confronted statistical and systematic errors based on this expansion [61]. Table II shows the low energy threshold parameters of all partial waves with j ≤ 5 for the low energy DS-χTPE potential.…”

Section: F Low Energy Threshold Parametersmentioning

confidence: 99%

“…Once the data base was fixed we modified the DS potential including a chiral two pion exchange χTPE tail starting at 1.8fm and made a new determination of the chiral constants c 1 , c 3 and c 4 with statistical uncertainties [14]. Also a local and smooth potential, that describes the same database [15], has allowed to propagate statistical uncertainties into few body calculations [40]. The basic requirement of normally distributed data for any least squares fit is verified; it has been checked for all three phenomenological potentials previously mentioned [15].…”

Section: Introductionmentioning

confidence: 99%

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Low-energy chiral two-pion exchange potential with statistical uncertainties

2015

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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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Uncertainty quantification of effective nuclear interactions

Cited by 21 publications

References 72 publications

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Minimally nonlocal nucleon-nucleon potentials with chiral two-pion exchange includingΔresonances

Precise determination of charge-dependent pion-nucleon-nucleon coupling constants

Low-energy chiral two-pion exchange potential with statistical uncertainties

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