The Nature of X-Rays and Their Interactions with Matter - Volume II: Beyond Semi-Classical Concepts

Volume II of the second edition, subtitled Beyond Semi-Classical Concepts, expands the description of x-rays into the framework of quantum optics, rooted in the full theory of light and matter: quantum electrodynamics (QED). Following a brief introduction, the book is organized into three parts and an appendix.

Part I explores the description of x-rays and diffraction phenomena within the advanced formalism of quantum optics. The discussion extends conventional quantum mechanics, which treats photons as independent particles, to higher-order quantum states containing multiple photons. A central theme is the emerging paradigm that quantum states with two or more photons can be directly observed in diffraction experiments using multi-photon detection. This makes it possible to overcome constraints of the classical framework, such as the diffraction limit, and to probe novel effects including photon-photon entanglement and interference.

Part II presents the quantum formulation of weak photon-matter interactions using the Kramers-Heisenberg-Dirac perturbation framework. This is applied to polarization-dependent, first-principles descriptions of interaction cross sections for x-ray absorption and dichroism, x-ray emission, Thomson scattering, and both resonant elastic (REXS) and inelastic (RIXS) scattering. A new section introduces the derivation of cross sections for two-photon x-ray absorption and ionization.

Part III extends the discussion from weak to strong interactions of x-rays with atoms and solids. Topics include the time-dependent transfer of x-ray energy to the electronic system and the lattice, the challenges of sample damage, and the intriguing phenomenon of x-ray transparency. Resonant core-to-valence excitations are analyzed using the optical Bloch equations, revealing effects such as Rabi oscillations of electronic populations and the intensity-dependent emergence of stimulated x-ray scattering.

An extensive appendix provides reference materials, including units and physical constants, the calculation of electronic transition matrix elements, and a survey of important quantum states of light and their matrix elements with photon creation and destruction operators encountered in the quantum formulation of diffraction.