Studies of mesic atoms and nuclei

TL;DR

This study analyzes kaonic atoms and possible kaon-nuclear quasibound states using six chirally inspired $K^-N$ interaction models to build in-medium $K^-$ optical potentials via self-consistent subthreshold energy shifts. A phenomenological multi-nucleon term is required to fit kaonic-atom data, and only two models (P and KM) reproduce the bubble-chamber single-nucleon absorption fractions, constraining the reliable density range to roughly $0.25\rho_0$ for the real part and $0.5\rho_0$ for the imaginary part. When exploring $K^-$ nuclear quasibound states, the imaginary part is dominated by multi-nucleon absorption, leading to widths well above $100$ MeV across nuclei, making such states unobservable except possibly in very light systems like $K^-pp$. Consequently, despite well-defined deeply bound kaonic atoms, the interior nuclear densities probed remain limited, and the search for narrow, observable kaonic nuclear states in heavier nuclei is unlikely with current models and data.

Abstract

$K^-$ mesons offer a unique setting where mesic atoms have been studied both experimentally and theoretically, thereby placing constraints on the possible existence and properties of meson-nuclear quasibound states. Here we review progress in this field made recently by the Jerusalem--Prague Collaboration using near-threshold $K^-N$ scattering amplitudes generated in several meson--baryon coupled channels models inspired by a chiral EFT approach. Our own procedure of handling subthreshold kinematics self consistently is used to transform these free-space energy dependent amplitudes to in-medium density dependent amplitudes from which $K^-$ optical potentials are derived. To fit the world data of kaonic atoms, these single-nucleon optical potentials are augmented by multi-nucleon terms. It is found that only two of the studied models reproduce also the single-nucleon absorption fractions available from old bubble chamber experiments. These two models are then checked for possible $K^-$ nuclear quasibound states, despite realizing that $K^-$ optical potentials are not constrained by kaonic atom data at densities exceeding half nuclear-matter density. We find that when such states exist, their widths are invariably above 100 MeV, forbiddingly large to allow observation. Multi-nucleon absorption is found to be substantial in this respect. This suggests that observable strongly bound $K^-$ mesons are limited to the very light systems, such as $K^-pp$.

Figures (7)

• Figure 1: Energy dependence of real (left) and imaginary (right) parts of $K^-p$ (top) and $K^-n$ (bottom) scattering amplitudes from six meson-baryon coupled-channel chirally inspired EFT models CMMS16 constrained by threshold and low-energy $K^- N$ data. Threshold energies $E_{\rm th}$ are marked by vertical lines.
• Figure 2: Energy dependence of the free-space (dotted) P-model amplitudes $f_{K^-N}=\frac{1}{2}(f_{K^-p}+f_{K^-n})$, where $f(E)=F(E;\,p=p'=0)$, and of several versions of in-medium P-model amplitudes at nuclear-matter density $\rho_0=0.17$ fm$^{-3}$ (left: real parts, right: imaginary parts). Figure adapted from Ref. HM17b.
• Figure 3: Density dependence of meson-nucleon energy shifts involved in mesic atom calculations. The various KM$\alpha$ branches of model KM in the right panel are defined in Sect. \ref{['sec:atoms']}. Figure adapted from Ref. FG14.
• Figure 4: Calculated SNAF FG17 in models P & KM (left) and in other models (right). For P & KM, solid circles (open squares) stand for 'lower' ('upper') states. For right-panel notations and choice of $\alpha$, see FG17.
• Figure 5: Real part (left) and imaginary part (right) of best-fit $K^-$Ni optical potentials 'KM$\alpha$' based on the KM $1N$ amplitude plus a phenomenological $mN$ amplitude $B\,(\rho/\rho_0)^\alpha$. Shown for comparison in short-dashed lines is a purely phenomenological potential. Figure adapted from Ref. FG17.