Covering a wide range of topics related to neutron and x-ray optics, this book explores the aspects of neutron and x-ray optics and their associated background and applications in a manner accessible to both lower-level students while retaining the detail necessary to advanced students and researchers. It is a self-contained book with detailed mathematical derivations, background, and physical concepts presented in a linear fashion. A wide variety of sources were consulted and condensed to provide detailed derivations and coverage of the topics of neutron and x-ray optics as well as the background material needed to understand the physical and mathematical reasoning directly related or indirectly related to the theory and practice of neutron and x-ray optics. The book is written in a clear and detailed manner, making it easy to follow for a range of readers from undergraduate and graduate science, engineering, and medicine. It will prove beneficial as a standalone reference or as a complement to textbooks.

Key Features

  • Supplies a historical context of covered topics.
  • Detailed presentation makes information easy to understand for researchers within or outside the field.
  • Incorporates reviews of all relevant literature in one convenient resource.


Advanced students and researchers in x-ray, gamma, and neutron sciences as well as in general physics and astronomy, bioengineering, and biophysics.

Table of Contents

1. Introduction

1.1 Refractive Index for Neutrons and X-rays

1.2 CRLs—Thin-Lens Approximation: Focal Length, Ray Path Lengths, and Attenuation

1.3 CRL Arrays

1.4 Integration on the Complex Plane—Cauchy–Riemann Theorem, Cauchy Integration, and Residues

1.5 Derivation of the Complex Refractive Index of Material Medium (e.g., Lenses) Based on the Rayleigh Scatter of X-rays and Gammas

1.6 Refractive of Gammas via Rayleigh and Delbrück Scatter

1.7 Historical Introduction to Gamma Lenses—The Dirac Equation and the Delbrück Effect


2. Neutron Refractive Index in Materials and Fields

2.1 Calculation of General Refractive Decrement for Material or Magnetic Media

2.2 Comparison of the Electron, Neutron, X-ray, and Light Refractive Index

2.3 Neutron Decrement for Composite Materials, and Neutron Refraction Due to Decrement Gradient

2.4 Neutron Decrement and Refractive Index in a Gravitational Field

2.5 Neutron Spin and Magnetic Dipole Moment Vectors in Applied Magnetic Fields

2.6 Potential Energy, Force, and Decrement for Neutrons in Applied Magnetic Fields

2.7 The Bloch Equation and Neutron Precession in an Applied Magnetic Field

2.8 Temperature Effect on Neutron Spin and Magnetic Dipole Moment Orientation in an Applied Magnetic Field

2.9 The Bloch Equation and the Lorentz Force Equation

2.10 Average Spin Polarization of a Neutron in an Applied Magnetic Field

2.11 Equation of Motion of the Expected Value of the Neutron Spin Vector in an Applied Magnetic Field

2.12 Expected Values of Quantum Mechanical Quantities Follow Classical Trajectories

2.13 Average Spin Polarization of a Beam of Neutrons in an Applied Magnetic Field

2.14 Adiabatic and Nonadiabatic Polarization Rotation About Magnetic Field Lines That Change Direction

2.15 Magnetic Reso


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© 2013
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About the author

Jay Theodore Cremer, Jr.

Affiliations and Expertise

Chief Scientist, Adelphi Technology, Inc.


"Among his topics are neutron refractive index in materials and fields, the magnetic scatter of neutrons in paramagnetic materials, diffractive X-ray and neutron optics, neutron and X-ray optics in general relativity and cosmology, and neutron and charged particle magnetic optics."--Reference & Research Book News, October 2013