Is the incident X-ray beam, with the original wavelength, detected at different scattering angles in Compton scattering experiment? I was reading about Compton scattering. I have a question I did not find an answer for it in the book (Concepts of Modern Physics, sixth edition, by Arthur Beiser) or with the Internet search. My question is:
Is the incident x-ray beam, with the original wavelength, detected at different scattering angles in the Compton scattering experiment or only at zero scattering angle? If the answer is yes, why?

 A: Photons with almost the original wavelength can be detected at angles other than $\theta=0$, because the beam may be deflected off things other than electrons.  Compton himself observed this.  In a heavy-target Compton scattering experiment, there are both electrons and nuclei in the target, and a photon can be scattered off either a electron or a nucleus.
When a photon is scattered, the particle that it scattered off also recoils, taking up some of the photon's energy.  If the recoiling particle is a free electron (or at least an electron whose atomic binding energy is small compared to the photon beam energy), then you get scattered photons with energies given by Compton's formula.  However, if the photon scatters off the nucleus, the recoil energy is much smaller.  (This is because the recoil momentum is always of the order of the photon momentum $\sim p_{0}=\frac{h}{\lambda_{0}}$, but the energy of the recoiling particle $\frac{p^{2}}{2m}$ depends on the mass of the recoiling charged particle.)  So scattering off a nucleus will transfer a much smaller energy than scattering off an electron.
We usually express the change in photon energy by the wavelength shift
$$\lambda-\lambda_{0}=\frac{h}{mc}(1-\cos\theta),$$
and this formula depends of the mass of the scatterer.  If $m$ is the electron mass, you get the usual Compton effect.  If $m$ is the mass of an atomic nucleus, then the wavelength shift is thousands to hundreds of thousands of times smaller, because of the much larger nuclear mass.  In many experimental setups, the energy shift due to scattering off the nucleus will in fact be too small to be observed; thus it will look like there are deflected photons with the original beam energy.
