n}u_{\alpha' n'}(a)(C^{-1})_{\alpha' n', \alpha n}u_{\alpha n}(a),
\\
&&{\cal Z}_{\alpha' \alpha} \equiv I_{\alpha} (k_\alpha a) \delta_{\alpha' \alpha}-
{\cal R}_{\alpha' \alpha}k_\alpha a I'_{\alpha}(k_\alpha a).\end{aligned}$$ The $S$-matrix is finally obtained as $$\begin{aligned}
S^{J\pi}=({\cal Z}^*)^{-1}{\cal Z}.\end{aligned}$$ In this paper we focus on the elastic phase shifts $\delta_{\alpha}^{J\pi}$ that are defined by the diagonal elements of the $S$-matrix, $$\begin{aligned}
S_{\alpha \alpha}^{J\pi}=\eta_\alpha^{J\pi} e^{2i\delta_\alpha^{J\pi}}.\end{aligned}$$

We study four-nucleon scattering involving the $d$+$d$, $t$+$p$ and $h$+$n$ channels in the energy region around and below the $d$+$d$ threshold. In Table \[chan0\] we list all possible labels $^{2I+1}\ell_J$ of physical channels for $J^{\pi}=0^{\pm}$, $1^{\pm}$, and $2^{\pm}$, assuming $\ell \leq 2$. Here “physical” means that the channels involve the cluster bound states that appear in the external region as well. Non-physical channels involving excited pseudo states will also be included in most calculations. Note that the $d$+$d$ channel must satisfy the condition of $I+\ell$ even (see Eq. (\[wf.channel\])). The channel spin $I=0$ or 2 can couple with only even $\ell$, but $I=1$ with only odd $\ell$. It is noted that the relative motion for the $d$+$d$ scattering can have $\ell=0$ only when $J^{\pi}$ is equal to $0^+$ and $2^+$.

                                                                                   0$^+$     1$^+$     2$^+$     0$^-$     1$^-$     2$^-$
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