Which type of x-ray interaction involves a change in photon energy due to scattering with matter?

The Compton effect is the interaction that specifically involves a change in the energy of an incoming x-ray photon as it scatters off a matter, typically an outer shell electron in an atom. During this interaction, the photon transfers some of its energy to the electron, resulting in a decrease in the energy of the scattered photon. This process not only alters the photon's energy but also changes its direction, which is a hallmark characteristic of Compton scattering.

The other interactions describe different phenomena that do not involve a straightforward scattering effect that results in energy change through interaction with electrons. The photoelectric effect involves the complete absorption of an x-ray photon by an electron, leading to the ejection of the electron from the atom without any residual energy left in the photon. Pair production refers to the conversion of photon energy into matter when the energy exceeds a certain threshold, resulting in the creation of electron-positron pairs rather than scattering. Photodisintegration is a process where a high-energy photon interacts with a nucleus, causing the emission of nucleons or other nuclear particles, rather than scattering. Thus, the Compton effect being associated directly with scattering and energy change makes it the definitive answer to the question.