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Register a new userScale Dependence of Nucleon-Nucleon Potentials
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Authors
Omar Benhar
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The scale-dependence of the nucleon-nucleon interaction, which in recent years has been extensively analysed within the context of chiral effective field theory, is, in fact, inherent in any potential models constrained by a fit to scattering data. A comparison between a purely phenomenological potential and local interactions derived from chiral effective field theory suggests that--thanks to the ability to describe nucleon-nucleon scattering at higher energies, as well as the deuteron momentum distribution extracted from electro-disintegration data--phenomenological potentials are best suited for the description of nuclear dynamics at the scale relevant to neutron star matter.
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Recently a new approach to calculate the nuclear potential from lattice QCD has been proposed. In the approach the nuclear potential is constructed from Bethe-Salpeter (BS) wave functons through the Schroedinger equation. The procedure leads to non-local but energy independent potential, which can be expanded in terms of local functions. In several recent applications of this method, local potentials, which correspond to the leading order (LO) terms of the expansion, are calculated from the BS wave function at E~0 MeV, where E is the center of mass energy. It is therefore important to check the validity of the LO approximation obtained at E~0. In this report, in order to check how well the LO approximation for the NN potentials works, we compare the LO potentials determined from the BS wave function at E~45 MeV with those at E~0 MeV in quenched QCD. We find that the difference of the LO potentials between two energies are not found wihin the statistical errors. This shows that the LO approximation for the potential is valid at low energies to describe the NN interactions.
Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e. starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In this work we study the domain of applicability of microscopic two-body chiral potentials in the construction of an optical potential. Methods: We basically follow the KMT approach to build a microscopic complex optical potential and then we perform some test calculations on 16O at different energies. Results: Our conclusion is that a particular set of potentials with a Lippmann-Schwinger cutoff at relatively high energies (above 500 MeV) has the best performances reproducing the scattering observables. Conclusions: Our work shows that building an optical potential within Chiral Perturbation Theory is a promising approach to the description of elastic proton scattering, in particular, in view of the future inclusion of many-body forces that naturally arise in such framework.
We closely investigate NN potentials based upon the Delta-full version of chiral effective field theory. We find that recently constructed NN potentials of this kind, which (when applied together with three-nucleon forces) were presented as predicting accurate binding energies and radii for a range of nuclei from A=16 to A=132 and providing accurate equations of state for nuclear matter, yield a chi^2/datum of 60 for the reproduction of the pp data below 100 MeV laboratory energy. We compare this result with the first semi-quantitative $NN$ potential ever constructed in the history of mankind: the Hamada-Johnston potential of the year of 1962. It turns out that the chi^2 for the new Delta-full potentials is more than three times what was already achieved some 60 years ago. In fact, there has not been any known NN potential during the entire history of nuclear forces with a chi^2 as large as the ones of these recent Delta-full potentials of the Gothenburg-Oak Ridge group of the year of 2020. We perceive this historical fact as highly disturbing in view of the current trend for which the term precision has become the most frequently used label to characterize contemporary advances in microscopic nuclear structure physics. We are able to trace the very large chi^2 as well as the apparent success of the potentials in nuclear structure to unrealistic predictions for P-wave states, in which the Delta-full NNLO potentials are off by up to 40 times the NNLO truncation errors. In fact, we show that, the worse the description of the P-wave states, the better the predictions in nuclear structure. Misleading results of the above kind are unhelpful to the communitys efforts in microscopic nuclear structure, because they obscure a correct understanding of the nature of the remaining problems and, thus, hamper sincere attempts towards genuine solutions.
A linear correlation is found between the magnitude of nucleon-nucleon short-range correlations and the nuclear binding energy per nucleon with pairing energy removed. By using this relation, the strengths of nucleon-nucleon short-range correlations of some unmeasured nuclei are predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon short-range correlations are made. The found nuclear dependence of nucleon-nucleon short-range correlations may shed some lights on the short-range structure of nucleus.
The potentials $V (v)$ in the nonrelativistic (relativistic) nucleon-nucleon (NN) Schroedingerequation are related by a quadratic equation. That equation is numerically solved, thus providing phase equivalent v- potentials related for instance to the high precision NN potentials, which are adjusted to NN phase shift and mixing parameters in a nonrelativistic Schroedinger equation. The relativistic NN potentials embedded in a three-nucleon (3N)system for total NN momenta different from zero are also constructed in a numerically precise manner. They enter into the relativistic interacting 3N mass operator, which is needed for relativistic 3N calculations for bound and scattering states.
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