13,757 research outputs found
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 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.Comment: 19 pages and 10 figure
Coarse grained NN potential with Chiral Two Pion Exchange
We determine the chiral constants of the Nucleon-Nucleon Two Pion Exchange
potential deduced from Chiral Perturbation Theory. By using a coarse grained
representation of the short distance interactions with 30 parameters, the
Partial Wave Analysis fit gives chi^2/dof = 1.1 to a mutually consistent set of
6713 data previously built from all published proton-proton and neutron proton
scattering data from 1950 till 2013 with LAB energy below 350 MeV. We obtain
(c1, c3, c4)=(-0.41+- 1.08,-4.66+- 0.60, 4.31+- 0.17)/GeV with an almost 100%
anti-correlation between c1 and c3. We also provide the errors in the short
distance parameters and propagate them to the deuteron properties and low
partial waves phase shifts.Comment: 11 pages, 7 figures, 11 tables. Enlarged versio
Nuclear Binding Energies and NN uncertainties
There is an increasing interest in quantifying the predictive power in
nuclear structure calculations. We discuss how both experimental and systematic
errors at the NN-level can be used to estimate the theoretical uncertainties by
rather simple means and without solving the full nuclear many body problem. We
emphasize the role of effective interactions defined by coarse graining the NN
potential to length scales of the order of the minimal de Broglie wavelength
probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim
0.1 - 0.4MeV for the binding energy per particle throughout the periodic table
for 2 \leq A \leq 208, and a linear growth of the error with density for
nuclear matter \DeltaB/A \sim 3.75{\rho}n.m. and neutron matter \DeltaB/N \sim
3.5{\rho}n.. This suggests to limit the computational effort in solving the
Nuclear Many Body Problem to such an accuracy.Comment: 6 pages. 2 figures. Presented by RNP at Sixth International
Conference on Quarks and Nuclear Physics, April 16-20, 2012. Ecole
Polytechnique, Palaiseau, Paris, Franc
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 MeV with 20 short distance parameters and
three chiral constants , and with . 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 ,
and 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.Comment: 16 pages, 10 figures, 5 tables. Enlarged version including Weinberg
eigenvalue analysis and cut-off dependenc
Effective interactions in the delta-shells potential
We determine two-body Skyrme force parameters from a Nucleon-Nucleon
interaction as a function of the maximal momentum fitting NN scattering data.
We find general agreement with Vlowk interactions based on high quality
potentials.Comment: 4 page, 1 figure, Presented by R.N.P. at the 20th International IUPAP
Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka,
Japa
Error Analysis of Nuclear Matrix Elements
We estimate the expected errors of nuclear matrix elements coming from the
uncertainty on the NN interaction. We use a coarse grained (GR) interaction
fitted to NN scattering data, with several prescriptions for the long-part of
the interaction, including one pion exchange and chiral two-pion exchange
interactions.Comment: Presented at the 22th European Conference On Few-Body Problems In
Physics: EFB22 9 - 13 Sep 2013, Krakow (Poland
Coarse grained Potential analysis of neutron-proton and proton-proton scattering below pion production threshold
Using the delta-shell representation we present a successful fit to
neutron-proton and proton-proton scattering data below pion production
threshold. A detailed overview of the theory necessary to calculate observables
with this potential is presented. A new data selection process is used to
obtain the largest mutually consistent data base. The analysis includes data
within the years 1950 to 2013. Using 46 parameters we obtain chi^2/Ndata = 1.04
with Ndata = 6713 including normalization data. Phase shifts with error bars
are provided.Comment: 32 pages, 1 figure, 10 table
Statistical Error analysis of Nucleon-Nucleon phenomenological potentials
Nucleon-Nucleon potentials are commonplace in nuclear physics and are
determined from a finite number of experimental data with limited precision
sampling the scattering process. We study the statistical assumptions implicit
in the standard least squares fitting procedure and apply, along with more
conventional tests, a tail sensitive quantile-quantile test as a simple and
confident tool to verify the normality of residuals. We show that the
fulfilment of normality tests is linked to a judicious and consistent selection
of a nucleon-nucleon database. These considerations prove crucial to a proper
statistical error analysis and uncertainty propagation. We illustrate these
issues by analyzing about 8000 proton-proton and neutron-proton scattering
published data. This enables the construction of potentials meeting all
statistical requirements necessary for statistical uncertainty estimates in
nuclear structure calculations.Comment: 20 pages. 13 figures. 10 tables, (minor numerical changes) Physical
Review C (to appear
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
we obtain . The effects of charge symmetry
breaking on the , and partial waves are analyzed and we
find , and
with a strong anti-correlation between and . 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.Comment: 14 pages, 6 figures, 13 tables. Discussion on naturalness, Analysis
of systematic errors, Inclusion of Two Pion Exchange and Tables with
phases-shifts adde
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 np and pp published scattering data
from 1950 till 2013 below has been made. We extract threshold
parameters uncertainties from the coupled channel effective range expansion up
to . 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.Comment: 18 pages. 6 tables. 8 Figures. Includes results presented at Workshop
on Information and Statistics in Nuclear Experiment and Theory (ISNET-3) ECT*
Trento, Italy, 16-20 November 2015. To appear in Jour. Phys.
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