$pn\to d\eta$ and then converted them into the rate of (\[2N-absorption\]). In terms of the imaginary part $W_{NN}$ of the optical potential $U$, this rate was found to be proportional to $\rho^2$, being $W_{NN}=3.4$ MeV at central nuclear density. This is only about 15% of $W_N \sim 23$ MeV related with the absorption of $\eta$ by one nucleon. Nevertheless such a small fraction of $NN$ can be quite visible experimentally because of a specific isotopic contents of the $\pi N$ and $NN$ pairs.

The matter is that $\gtrsim 90\%$ of these $NN$ pairs are proton plus neutron because the cross section of $pp\to pp\eta$ (and $nn\to
nn\eta$) is by order or magnitude less than that of $pn\to pn\eta$ (plus $pn\to d\eta$), see Fig. \[fig-etaNN\] where pertinent Uppsala-Celsius [@calen96; @calen97; @calen98a; @calen98b] and COSY [@smyrski00; @moskal09] data are shown (and see also, e.g., [@baru03] for theoretical explanations). This difference can be traced to isospin factors and Fermi statistics signs in the dominating pion-exchange mechanism of the reaction $NN\to NN\eta$ shown in Fig. \[diagrams-NNeta\]. If the experimental setup detects one charged and one neutral particle from the pairs, it detects $\sim90\%$ of $NN$ and only $\sim33\%$ of $\pi N$. Then count rates 