  Let $H_0$ and $V$ be self-adjoint operators, such that $V$ admits a
factorisation $V = F^*JF$ with bounded self-adjoint $J$ and
$|H_0|^{1/2}$-compact $F.$ Coupling resonance functions, $r_j(z),$ of the pair
$H_0$ and $V$ can be defined as $r_j(z) = - \sigma_j(z) ^{-1},$ where
$\sigma_j(z)$ are eigenvalues of the compact-operator valued holomorphic
function $F(H_0-z)^{-1} F^*J.$ Taken together, the functions $r_j(z)$ form an
infinite-valued holomorphic function on the resolvent set of~$H_0.$ These
functions contain a lot of information about the pair $H_0, V$ (this is
well-known in the case of rank one $V$). A point $z_0$ of the resolvent set we
call \emph{absorbing} if some $r_j(z)$ goes to $\infty$ as $z \to z_0$ along
some half-interval.
  In this note I present some partial results concerning absorbing points of
coupling resonances.
