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.

7 pages, 9 figures. Title slightly changed, more considerations added

References in corpus (11)

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• Onset of $\eta$-meson binding in the He isotopes
• $\eta$-nucleus interaction from the $d+d$ reaction around the $\eta$ production threshold
• Structure of double pionic atoms
• On the determination of the $D$ meson width in the nuclear medium with the transparency ratio
• Theoretical study of the $\gamma d\to {\pi }^0\eta d$ reaction
• The ${\eta }^{\prime }N$ interaction from the ${\eta }^{\prime }p$ correlation function
• Probing the existence of η^3He mesic nucleus with a few-body approach