Coarse graining ofNNinelastic interactions up to 3 GeV: Repulsive versus structural core

Abstract

The repulsive short distance core is one of the main paradigms of nuclear physics which even seems confirmed by QCD lattice calculations. On the other hand nuclear potentials at short distances are motivated by high energy behavior where inelasticities play an important role. We analyze NN interactions up to 3 GeV in terms of simple coarse grained complex and energy dependent interactions. We discuss two possible and conflicting scenarios which share the common feature of a vanishing wave function at the core location in the particular case of Swaves. We find that the optical potential with a repulsive core exhibits a strong energy dependence whereas the optical potential with the structural core is characterized by a rather adiabatic energy dependence which allows to treat inelasticity perturbatively. We discuss the possible implications for nuclear structure calculations of both alternatives.

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

“…This imposes limits for the maximum value of the high momentum components and the meaning of the predictions for high-momentum components above 2-3 k F with a real potential should be taken with care. In a recent paper coarse graining has been shown to work nicely up to scattering LAB energies of 3 GeV [56], in this case including inelasticity effects. However, the analysis of the Bethe-Goldstone equation including inelasticities through a complex potential will be postponed for a future work.…”

Coarse graining hadronic scattering

“…However, the actual number is smaller since for L ≥ 1 some of the points located at r n fall well below the centrifugal barrier, and correspond to the classicaly forbidden region, thus their contribution is suppressed. Taking into account both spin and isospin degrees of freedom the following estimate can be obtained as [17] 8) where N S and N I the number of spin and isospin channels respectively. The number of independent parameters is plotted in Fig.…”

Coarse graining $$\pi \pi $$ π π scattering

“…This corresponds to a coarse graining of the short range piece and, in its simplest realization, the inner potential will be written as a superposition of equidistant delta-shell interactions. A key issue is to confidently determine the numerical value of the separation scale r c , since, as noted in [41,42] and we will see below, the combination pr c , with p the CM momentum, will fix the total number of independent fitting parameters. The longest range interaction corresponds to a 2π -exchange which is O(e −2m π r ), so that a naive estimate suggests r c ∼ 2/(2 m π ) ∼ 1.4 fm, 2 a number which will be corroborated by our numerical analysis.…”

“…While the potential approach has been explained in great detail in previous works within the NN context (see for instance [42]), it is unconventional within the ππ scattering folklore. Thus, we will assume no previous knowledge from the side of the reader and for the sake of completeness we will briefly go through all the important issues along the paper.…”

“…3 In addition, the current extraordinary precision achieved theoretically in extracting the S-waves scattering lengths or the lightest ππ resonance pole parameters [43][44][45][46] provides a great confidence on the theoretical ideas supporting these benchmarking extractions. The fact that the coarse graining approach works for NN scattering in a regime where relativistic and inelastic effects become important, such as pp scattering up to √ s ∼ 2 GeV [42], suggests extending the method to other hadronic reactions under similar operating conditions. 4 Finally, for the sake of completeness let us mention that lattice calculations are naturally formulated in coordinate space.…”