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In the book $R$-Matrix Theory of Atomic Collisions it is defined the $R$-matrix basis \begin{aligned} \psi_{k}^{\Gamma}\left(\mathbf{X}_{N+1}\right)=& \mathcal{A} \sum_{i=1}^{n} \sum_{j=1}^{n_{c}} \bar{\Phi}_{i}^{\Gamma}\left(\mathbf{X}_{N} ; \hat{\mathbf{r}}_{N+1} \sigma_{N+1}\right) r_{N+1}^{-1} u_{i j}^{0}\left(r_{N+1}\right) a_{i j k}^{\Gamma} \\ &+\sum_{i=1}^{m} \chi_{i}^{\Gamma}\left(\mathbf{X}_{N+1}\right) b_{i k}^{\Gamma}, \quad k=1, \ldots, n_{t} \end{aligned} for the process $\mathrm{e}^{-}+A_{i} \rightarrow A_{j}+\mathrm{e}^{-}$, where $n$ is the number of channels retained in the expansion, $n_{c}$ is the number of radial continuum basis orbitals retained in each channel, $m$ is the number of quadratically integrable functions and $n_{t}=n n_{c}+m$ is the total number of linearly independent basis functions in this expansion.

I am not understanding what is the number of radial continuum basis orbitals retained in each channel $n_c$. What I mean is this since we have this process $\mathrm{e}^{-}+A_{i} \rightarrow A_{j}+\mathrm{e}^{-}$ we should have only one continuum basis function for each channel. Why there is more than one continuum basis function for each channel

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