Representation method (GVR) [@DGVR; @GVR], Green’s function Monte Carlo method [@carlson98], no core shell model [@navratil00], correlated hyperspherical harmonics method [@viviani98r], unitary correlation operator method [@ucom], and so on. Although the application of $ab$-$initio$ reaction calculations with a realistic interaction are restricted so much in comparison with structure calculations, it has been intensively applied to the four-nucleon systems $t$+$n$ and $h$+$p$ [@arai10; @hofmann01; @deltuva07; @navratil09; @viviani98; @lazauskas05; @fisher06]. Especially $d$+$d$ scattering states, which couple to $t$+$p$ and $h$+$n$ channels, have attracted much attention, because the $d$+$d$ radiative capture is one of the mechanisms making $^4$He through electro-magnetic transitions [@arriaga91; @sabourov04] and also have posed intriguing puzzles for analyzing powers [@hofmann08; @hofmann97; @deltuva08; @lazauskas04; @ciesielski99], which are motivated by the famous $A_y$ problem in the three-nucleon system.

Furthermore, the $d$+$d$ elastic-scattering phase shifts are interesting because the astrophysical S-factor of the $d$($d$,$\gamma$)$^4$He reaction is not explained by any calculation using an effective interaction that contains no tensor term, and is expected to be contributed by the $D$-wave components of the clusters through $E2$ transitions [@langanke87; @fowler67].

Also, thanks to recent developments of the microscopic cluster model, the simple model using the (0$s$) harmonic-oscillator wave function with an effective interaction is not 