# What is the continuum function in $R$-matrix basis?

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