*Acta
Cryst.* (1995). A**51**,
590-591

**Pp. xii + 688.
Amsterdam: North-Holland, Elsevier, 1994
Price Dfl 350, US $200. ISBN
0-444-82025-6**

The intention of this book is to review, in a single volume, the present status of theory and experiments in X-ray resonant scattering from gases to solids. The book is a reference work, with 39 articles, on many different fields of research, chosen from contributions presented at the International Conference on Anomalous Scattering held in Malente, Germany, in 1992.

An earlier book on anomalous scattering, edited by S. Ramaseshan and S. C. Abrahams (Munksgaard, 1975) presented what then appeared to be a well understood field of X-ray science. The last twenty years, however, have seen a rapid development of synchrotron X-ray sources, and completely new experimental details can now be observed using the brilliance, wavelength tunability and polarization properties of these new radiation sources. Thus, where the older book summarizes the achievements of the X-ray-tube era in X-ray resonant scattering research, this book illustrates the new experimental possibilities created by the rapid expansion of dedicated synchrotron-radiation facilities and the renewed interest in theoretical details previously beyond experimental verification. The new knowledge will find applications in many fields, as diverse as protein phasing and surface magnetism.

The first part of the book concentrates on the theoretical and experimental aspects of the resonant terms in the X-ray scattering factors. For energies approximately 100 eV below or 500 eV above the absorption edges, the resonant terms calculated for the free atoms agree well with experimental values. However, more sophisticated theoretical models, including electron correlation and the effect of atomic neighbours, are needed around the edges. The state of the art theoretical calculations are reviewed, as well as the methods for experimentally determining the resonant terms. Dipole, quadrupole and polarization effects are discussed.

A second part of the book deals with applications to crystals. One of the classical problems in crystallography, the phase problem, is discussed in detail, showing the potential for phasing using standing-wave or multiple-wavelength anomalous diffraction (MAD) techniques. The MAD technique is rapidly developing into a major tool for macromolecular structure determination. The theoretical and experimental basis for the method is well described. Anomalous-dispersion studies have also proved to be a powerful tool in the study of site distribution of near-neighbour atoms in the Periodic Table. Careful analysis of the resonant terms shows that, in certain cases, they are markedly anisotropic, and a new `tensor' crystallography, probing density of states and transition probabilities, is beginning to emerge.

Another section of the book is devoted to short-range correlation studies, such as the use of resonant scattering in pair-correlation studies, small-angle scattering and in the combination of long-range diffraction and the short-range sensitivities of X-ray absorption techniques.

Several articles are devoted to inelastic X-ray scattering, which, close to the resonant frequencies, is dominated by X-ray Raman scattering. This spectroscopic technique is used to probe unfilled energy states. It is pointed out that these studies can be carried out without being affected by inner-shell lifetimes.

The emergence of dedicated synchrotrons has started a renewed interest
in
the magnetic scattering of X-rays. Magnetic X-ray scattering is
extremely weak away from the resonant edges, but it is shown that
important
enhancement is achieved around the resonant energies, in particular for
the *M*
edges of rare-earth and actinide elements. Magnetic X-ray scattering
promises to give important new information that is not available from
neutron scattering experiments, for instance making it possible to
separate the
contributions from spin and orbital momentum and to approach
the challenging task of studying magnetic surfaces.
The articles in this section give an interesting
insight into the interplay between new experimental tools and the
development of theories.

The final section of the book deals with nuclear resonant scattering. Again, the synchrotron sources have given an opportunity to excite nuclear transitions, producing radiation with extreme longitudinal coherence and energy resolution. The early developments and future applications are discussed in a series of articles.

This book should be seen as a reference book and a status report on the development of the field of resonant X-ray scattering. The review articles have been well written by the leading experts, and thus present the latest in theory and experiments. With more than 1200 references, the book gives rapid access to all aspects of the subject and it is recommended not only for the experts but also for use by students and other nonspecialists.

If I have any criticism of the work, it is that the editors would have been wise to have issued instructions on a common nomenclature, as a nonspecialist may be somewhat confused in going from one article to another. They clearly recognized this after the fact, however, and the book ends with an article sorting out the different crystallographic symbols and definitions.

**Åke
Kvick**

*
Experiments Division
European Synchrotron Radiation Facility
F-38043 Grenoble
France
*

**Copyright © 1997 International Union of Crystallography**