Description of inclusive $(d,d^{\prime}x)$ reaction with the semiclassical distorted wave model

The description of deuteron-induced inclusive reactions has been an important subject in direct nuclear reaction studies and nuclear data science. For proton-induced inclusive processes, the semiclassical distorted wave model (SCDW) is one of the most successful models based on quantum mechanics. We improve SCDW for deuteron-induced inclusive processes and clarify the importance of the proper treatment of the kinematics of the deuteron inside a nucleus. The double differential cross section (DDX) of the inclusive deuteron-emission process $(d,d^{\prime}x)$ is described by one-step SCDW. The changes in the kinematics due to the distortion effect, the refraction effect, is taken into account by the local semiclassical approximation (LSCA). The calculated DDXs of $(d,d^{\prime}x)$ reasonably reproduce experimental data in the small energy-transfer region and at forward and middle angles with some exceptions. The angular distributions of $(d,d^{\prime}x)$ are improved by including the refraction effect. The proper treatment of the changes in the kinematics of the deuteron inside a nucleus is necessary in describing the ($d$,$d'x$) reaction. The effect of the changes on the DDX of $(d,d^{\prime}x)$ is significant compared to on the proton-induced inclusive process $(p,p^{\prime}x)$ because of the stronger distortion effect on the deuteron.