Ay Puzzle Research Articles

Nucleon-Nucleon Scattering Up to N5LO in Chiral Effective Field Theory

During the past few decades a large effort has been made towards describing the NN interaction in the framework of chiral Effective Field Theory (EFT). The main idea is to exploit the symmetries of QCD to obtain an effective theory for low energy nuclear systems. In 2003, the first accurate charge-dependent $NN$ potential in this scheme was developed and it has been applied to many ab-initio calculations, opening the possibility to study nuclear systems in a systematic and accurate way. It was shown that the fourth order (N3LO) was necessary and sufficient to describe the NN scattering data with a $\chi^2/$d.o.f of the order of one. However the systematics of chiral EFT also allow to relate two- and many-body interactions in a well-defined way. Since many-body forces make their first appearance at higher order, they are substantially smaller then their two-body counterparts, but may never-the-less be crucial for some processes. Thus, there are observables where they can have a big impact and they are expected to solve problems like the long standing Ay puzzle of N-d scattering. The last few years, have also seen substantial progress towards higher orders of chiral EFT which was motivated by the fact that only three-body forces of rather high order may solve some outstanding issues in microscopic nuclear structure and reactions. In this chapter we will review the chiral EFT based potentials that have been developed up to N4LO as well as first calculations conducted for NN scattering at N5LO.

Three-nucleon reactions with chiral dynamics

Faddeev calculations using the chiral three-nucleon force at next-to-next-to- next-to-leading-order show that this force is not able to provide an explanation for the low-energy Ay puzzle. Also the large discrepancies between data and theory for the symmetric-space-star and for the neutron-neutron quasi-free-scattering cross sections in low energy neutron-deuteron breakup cannot be explained by that three-nucleon force. The discrepancy for the neutron-neutron quasi-free-scattering cross section seems to re- quire a modification of the 1 S 0 neutron-neutron force.

Few-nucleon systems interacting via non-local quark-model baryon-baryon interaction

Low- and medium-energy nucleon-deuteron scattering less than the incident energy 65 MeV per nucleon is examined by using the quark-model nucleon-nucleon interaction fss2. The off-shell effect of this non-local interaction yields a part of the attractive effect given by the three-nucleon force in the standard description by meson-exchange potentials. The triton binding energy and the spin-doublet scattering length are well described by fss2 without introducing the three-nucleon force. The nucleon analyzing power is slightly improved from the results by the AV18 potential, but the so-called Ay puzzle in the low-energy region still remains. Similar reduction of the peak heights by the Coulomb force is also seen in the vector analyzing power of the deuteron, iT11(θ). Other observables are rather similar to the predictions by meson-exchange potentials, including discrepancies of deuteron breakup differential cross sections from experiment for some particular kinematical configurations. The systematic KVI data of the 1H(d⃗, 2p)n scattering at Ed = 130 MeV are reasonably reproduced for breakup differential cross sections and deuteron analyzing powers.

Off-shell Effect of the Quark-model NN Interaction in the Nd Scattering

Low- and medium-energy nucleon–deuteron (Nd) scattering less than the incident energy 65 MeV per nucleon is examined by using the quark-model nucleon–nucleon (NN) interaction fss2. The off-shell effect of this non-local interaction yields a part of the attractive effect given by the three-nucleon force in the standard description by the meson-exchange potentials. The triton binding energy and the spin-doublet scattering length are well described by fss2 without introducing the three-nucleon force. The nucleon analyzing power is slightly improved from the results by the AV18 potential, but the so-called Ay puzzle in the low-energy region is not essentially solved nor is the similar deficiency of the peak heights seen in the vector analyzing power of the deuteron, iT11(θ). Other observables are rather similar to the predictions by meson-exchange potentials, including disagreements of the deuteron breakup differential cross sections with experiment for some particular kinematical configurations. The space-star anomaly of the nd and pd scattering at EN = 13 MeV is not improved. The accurate and systematic KVI data of the \({^{1}H(\overrightarrow{d}, 2p)n}\) scattering at Ed = 130 MeV are compared with the predictions by fss2 for the breakup differential cross sections and the deuteron analyzing powers.

ChiralNNmodel andAypuzzle

We analyze the results by chiral NN models for the two-nucleon system and calculate the predictions for the nucleon vector analyzing power of elastic nucleon-deuteron (Nd) scattering, Ay, by these models. Our conclusion is that a QUANTITATIVE chiral two-nucleon potential does not resolve the Nd Ay puzzle (when only two-body forces are included).

Low-energy P–D elastic scattering and the “Ay puzzle”

A compilation of experimental and theoretical information is presented on the mass 3 systems 3n, 3H, 3He and 3p. Emphasis is on advances since the previous evaluation Tilley et al. (1987) [1987TI07] such as, (1) detailed calculations of the vector and tensor analyzing powers for neutron and proton scattering by deuterium which led to the discovery of the still unresolved analyzing power puzzle, (2) the wide spread use of polarized 3He targets which allowed for the experimental study of sum rules among other things and (3) the ability to include the Coulomb interaction in three-body calculations. As stated in the 1987 evaluation and is still the case, there is no firm evidence for either excited states of 3H or 3He nuclei or for the existence of the trineutron or triproton.

Ay puzzle at intermediate energy pd elastic scattering

Ay puzzle at intermediate energy pd elastic scattering

Phenomenological spin-orbit three-body force

In order to improve the description of the N-d vector analyzing powers Ay and iT11 (the so-called Ay puzzle) a spin-orbit three-body force has been introduced. The L.S term in the NN potential has been modified including a two-parameter three-body function depending on the hyperradius \rho. The modification has been performed in channels where the pair nucleons (i,j) are coupled to spin Sij=1 and isospin Tij=1. Calculations have been done in the energy region from Elab=648 keV up to Elab=10 MeV. A noticeable improvement in the description of the polarization observables has been obtained