Density dependence of the s-wave repulsion in pionic atoms

Abstract

Several mechanisms of density dependence of the s-wave repulsion in pionic atoms, beyond the conventional model, are tested by parameter fits to a large (106 points) set of data from $^{16}$O to $^{238}$U, including `deeply bound' states in $^{205}$Pb. Special attention is paid to the proper choice of nuclear density distributions. A density-dependent isovector scattering amplitude suggested recently by Weise to result from a density dependence of the pion decay constant is introduced and found to account for most of the so-called anomalous repulsion. The presence of such an effect might indicate partial chiral symmetry restoration in dense matter. The anomalous repulsion is fully accounted for when an additional relativistic impulse approximation term is included in the potential.Comment: 18 pages, 5 figures, version 2 (extended

Precision Spectroscopy of Pionic1sStates of Sn Nuclei and Evidence for Partial Restoration of Chiral Symmetry in the Nuclear Medium

“…The combined isoscalar parameter, b 0 + 0.215 ReB 0 = −0.0274 ± 0.0002, is in good agreement with that obtained in the analysis of the 205 Pb [28]. The imaginary part, ImB 0 = 0.0472 ± 0.0013, is consistent with the global-fit value of 0.055 ± 0.003 by Batty et al [26] and Friedman [29,30], considering that they included the angle-transformation (AT) term, which causes an appreciable decrease in the width [27]. In fact, the best-fit value in our analysis with the AT term included is: ImB 0 = 0.058 ± 0.003.…”

“…In recent papers we showed that the density-dependent parameter b * 1 (ρ) can be well represented by a constant parameter b 1 [27], and developed a method to deduce the b 1 parameter [28]. The data of the 1s π − state in 205 Pb [20], π [30], although some ambiguity arising from the p-wave part remains. In order to determine b 1 more reliably and accurately, it is essential to perform high-precision spectroscopy on deeply bound 1s π − states in heavy nuclei.…”

Elastic scattering of low energy pions by nuclei and the in-medium isovectorπNamplitude

“…This model which was shown [14,15] to explain the anomaly in pionic atoms, is denoted here by W. An alternative approach which was also shown to explain the anomaly in pionic atoms [21] is to replace E by E − V c by imposing the minimal substitution requirement [22], which is effective through the energy dependence of the isoscalar parameter b 0 . This model is denoted here by E. Finally, applying both mechanisms we have the EW model.…”

“…Large scale fits to pionic atom data encompassing the whole of the periodic table showed [14,15] that indeed the density-dependence of the pion decay constant [9] which causes the isosvector scattering amplitude to become density dependent, is capable of removing the anomaly. Similar conclusions were also presented [16,4,17,5] on the basis of very restricted data sets, consisting mainly of the recently observed 'deeply bound' states of pionic atoms.…”

Renormalization of the isovector πN amplitude in pionic atoms

“…Smaller values of r n − r p were also used in Ref. [4]. In the present work we vary, among other things, the values of r n −r p and we therefore look for a simple parameterization that will be easy to relate to the RMF results.…”