Determination of the ${\mathbf{\eta }}^3\mathrm{He}$ threshold structure from the low energy $\mathbf{pd}\to {\mathbf{\eta }}^3\mathrm{He}$ reaction

Abstract

We analyze the data on cross sections and asymmetries for the $pd(dp)\to {\eta }^3\mathrm{He}$ reaction close to threshold and look for bound states of the ${\eta }^3\mathrm{He}$ system. Rather than parameterizing the scattering matrix, as is usually done, we develop a framework in which the ${\eta }^3\mathrm{He}$ optical potential is the key ingredient, and its strength, together with some production parameters, are fitted to the available experimental data. The relationship of the scattering matrix to the optical potential is established using the Bethe-Salpeter equation and the ${\eta }^3\mathrm{He}$ loop function incorporates the range of the interaction given by the empirical ${}^3\mathrm{He}$ density. We find a local Breit Wigner form of the ${\eta }^3$He amplitude $T$ below threshold with a clear peak in $|T{|}^2$, which corresponds to an ${\eta }^3\mathrm{He}$ binding of about 0.3 MeV and a width of about 3 MeV. By fitting the potential we can also evaluate the ${\eta }^3\mathrm{He}$ scattering length, including its sign, thus resolving the ambiguity in the former analyses.

arXiv comment7 pages, 9 figures. Title slightly changed, more considerations added

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• Onset of $\eta$-meson binding in the He isotopes
• Constraining the optical potential in the search for eta-mesic 4He
• $\eta$-nucleus interaction from the $d+d$ reaction around the $\eta$ production threshold
• Resonance-like structure near the $\eta d$ threshold in the $\gamma d${$\to$}${\pi }^0\eta d$ reaction
• Total and differential cross sections of $\eta$-production in proton-deuteron fusion for excess energies between $Q_{\eta }=13\text{MeV}$ and $Q_{\eta }=81\text{MeV}$
• Search for the $\eta$ mesic ${}^3$He in the $pd\to dp{\pi }^0$ reaction with the WASA-at-COSY facility
• Search for eta mesic 3He with the WASA-at-COSY facility in the pd-> 3He 2gamma and pd-> 3He 6gamma reactions
• Structure of double pionic atoms
• Systematic few-body analysis of eta-d, eta-3He and eta-4He interaction at low energies
• Theoretical study of the $\gamma d\to {\pi }^0\eta d$ reaction
• On the determination of the $D$ meson width in the nuclear medium with the transparency ratio
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