S-wave Optical Potential Research Articles

Chiral dynamics of deeply bound pionic atoms.

We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear s-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the 1s and 2p levels in pionic 205Pb and 207Pb are well reproduced without need for a notorious "missing repulsion" in the pion-nuclear s-wave optical potential. The connection with the in-medium change of the pion decay constant is clarified.

Nonlocalities and Fermi motion corrections in K − atoms

We evaluate the p-wave K −N amplitudes from the chiral Lagrangians and from there construct the p-wave part of the K − nucleus optical potential plus a small s-wave part induced from the elementary p-wave amplitude and the nuclear Fermi motion. Simultaneously, the momentum and energy dependence of the s-wave optical potential, previously developed, are taken into account and shown to generate a small p-wave correction to the optical potential. All the corrections considered are small compared to the leading s-wave potential, and lead to changes in the shifts and widths which are smaller than the experimental errors. A thorough study of the threshold region and low densities is conducted, revealing mathematical problems for which a physical solution is given.

Chiral Lagrangians and quark condensate in nuclei

We study the evolution with density of the quark condensate in the nuclear medium with interacting nucleons and including the short range correlations. We work with two chiral models, the linear sigma model and the non-linear one. For the last one we use two versions, one which does not satisfy PCAC, and another one which does. We show that the quark condensate, as other observables, is independent on the variant selected. The application to physical pions excludes the linear sigma model as a credible one. In the non-linear models our conclusions are: first there is no systematic reaction imposed by chiral symmetry against symmetry restoration, second, if one keeps only the s-wave pion-nucleon interaction, the quark condensate evolves essentially linearly with density, as if the nucleons were non interacting. The main correction arises from the p-wave pion-nucleon interaction. Last, in the s-wave optical potential, chiral symmetry tolerates but does not impose two body terms. On the other hand the effect of correlations linked to the isospin symmetric amplitude is negligible.

Short-range correlations in the pion s-wave self-energy of pionic atoms

We evaluate the contribution of second-order terms to the pion-nucleus s-wave optical potential of pionic atoms generated by short-range nuclear correlations. The corrections are sizeable because they involve the isoscalar s-wave πN amplitude for half off-shell situations where the amplitude is considerably larger than the on-shell one. In addition, the s-wave optical potential is reanalyzed by looking at all the different conventional contributions together: lowest-order, Pauli corrected rescattering term, second-order absorptive effects, terms from the interaction of pions with the virtual pion cloud (chiral corrections) and correlation effects. Different off-shell extrapolations for the πN amplitude are used and it is found that, although some individual terms are sensitive to the extrapolation, the sum of them is rather insensitive. The results are compared with empirical values from best fits to the data and are found to be compatible, within theoretical and empirical uncertainties. The results do not rule out further contributions but they put stringent constraints on their strength.

Microscopic s-wave optical potential for slow pions scattered by a nucleus.

We have done a microscopic calculation of the s-wave optical potential for the pion-nucleus system at low energies, 0\ensuremath{\le}${T}_{\ensuremath{\pi}}$\ensuremath{\le}100 MeV, using a description based on hadronic degrees of freedom. We have obtained, separately, the real and imaginary parts of the optical potential coming from one-body and two-body processes. We have also separated the imaginary part of the potential associated to absorption and to quasielastic channels. We find that the imaginary part of the absorption channel is independent of the energy (within the range of energies considered here) in agreement with a recent empirical determination. We compare our results with phenomenological potentials obtained by fits to the empirical data. The comparison shows a good qualitative agreement. We discuss the dependence of the optical potential on the \ensuremath{\pi}N amplitudes, taken as an input in this model, and we find that a more repulsive isoscalar \ensuremath{\pi}N s-wave amplitude would provide better consistency between the \ensuremath{\pi}-nucleus theoretical results and the \ensuremath{\pi}-nucleus data. New experiments to provide more accurate \ensuremath{\pi}N phase shifts at low energies would be welcome.

Calculation of the first-order s-wave optical potential in pionic atoms.

A microscopic calculation of the first-order s-wave optical potential in pionic atoms which allows the inclusion of the off-shell dependence in momentum of the s-wave \ensuremath{\pi}N amplitude is carried out. Binding effects are also properly taken into account. The results obtained, together with those of the second-order optical potential, are in disagreement with phenomenological optical potentials. The results of the paper suggest the need of new and precise experiments on \ensuremath{\pi}N scattering at low energies and other experiments which can provide precise values of the \ensuremath{\pi}N scattering lengths.

S-wave optical potential in pionic atoms.

We present a new formal approach for the calculation of the s-wave optical potential for pionic atoms which makes extensive use of the Lindhard function, its analytical properties, and its useful low density limit. The conventional parameters ${b}_{0}$ and ${B}_{0}$ are calculated and compared to results from empirical fits to pionic atom data. We show that the virtual excitation of ph-\ensuremath{\Delta}h components by the pion is the main source of the real part of ${B}_{0}$. Higher order effects from the polarization of the pion lead to some enhancement of Im${B}_{0}$, providing values which are compatible with the empirical data. The real part of the potential suffers from larger uncertainties due to the off-shell extrapolation of the \ensuremath{\pi}N scattering amplitude.