  Transients powered by interaction with the circumstellar medium (CSM) are
often observed in wavelengths other than optical, and multi-wavelength
modelling can be important when inferring the properties of the explosion and
CSM, or for distinguishing from other powering mechanisms. We develop a model
calculating time dependent emission spectrum of interaction-powered transients.
We solve energy equations of electron-proton plasma in the shocked SN ejecta
and CSM and a radiation transfer equation out to the outer edge of the CSM,
incorporating the collisional relaxation and the comptonization of the
bremsstrahlung radiation. We compare our model to observations of Type IIn
supernovae covering frequency ranges from optical to X-rays. For SN 2010jl the
observed optical and X-ray light curves can be consistently explained if clumpy
or asymmetric structure in the CSM is assumed, in agreement with previous
studies. For SN 2014C our model successfully reproduces the X-ray
bremsstrahlung component and the emergence of H$\alpha$ emission at 400 days
after explosion. Finally we find a parameter space where the supernova is
extremely X-ray bright, reaching $10^{43}$-$10^{44}\ {\rm erg\ s^{-1}}$ for up
to $100$ days. Such X-ray transients are likely detectable with all-sky surveys
by e.g. eROSITA.
