Introduction to the Theory of Thermal Neutron Scattering

by Squires, G. L.

• ISBN13: 9780486694474
• ISBN10: 048669447X
• Edition: Reprint
• Format: Paperback
• Copyright: 1997-02-11
• Publisher: Dover Publications

Summary

Graduate-level monograph develops theoretical ideas in a relatively informal manner. Nuclear scattering, nuclear scattering by crystals, scattering by liquids, neutron optics, polarization analysis, much more. Problem examples at chapter ends. Prerequisites are some familiarity with basic concepts of quantum mechanics and solid state physics. Solutions. Bibliography. Appendixes. 1978 edition.

Table of Contents

Preface	ix
1 Introduction	1	(9)
1.1 Basic properties of the neutron	2	(3)
1.2 Numerical values for velocity, energy, wavelength	2	(3)
1.3 Definitions of scatering cross-sections	5	(2)
1.4 Scattering of neutrons by a single fixed nucleus	7	(3)
Nuclear scattering -- basic theory	10	(15)
2.1 Introduction	10	(1)
2.2 Fermi's golden rule	10	(3)
2.3 Expression for	13	(8)
2.4 Coherent and incoherent scattering	21	(4)
3 Nuclear scattering by crystals	25	(36)
3.1 Introduction	25	(1)
3.2 Normal modes	26	(1)
3.3 Probability function for a harmonic oscillator	27	(1)
3.4 Development of (exo U exp V)	28	(2)
3.5 Phonon expansion	30	(2)
3.6 Coherent elastic scattering	32	(11)
3.7 Coherent one-phonon scattering	43	(10)
3.8 Coherent multiphonon scattering	53	(1)
3.9 Incohorent scattering	54	(3)
3.10 Multiphonon cross-sections -- approximation methods	57	(2)
Examples	59	(2)
4 Correlation function in nuclear scattering	61	(25)
4.1 Definitions of I(k,t), G(r,t), and S(k,w)	61	(2)
4.2 Expressions for G(r,t), and G(r,t)	63	(2)
4.3 Analytic properties of the correlation functions	65	(3)
4.4 Principle of detailed balance	68	(2)
4.5 Scattering from a single free nucleus	70	(3)
4.6 Moments of the scattering function	73	(2)
4.7 Relation between elastic scattering and I	75	(3)
4.8 Static approximation	78	(6)
9 Examples	84	(2)
Scattering by liquids	86	(24)
5.1 Introduction	86	(1)
5.2 No elastic scattering	87	(1)
5.3 Coherent scattering	88	(8)
5.4 Incoherent scattering	96	(14)
6 Neutron optics	110	(19)
6.1 Refractive index	110	(4)
6.2 Neutron reflection	114	(2)
6.3 Dynamical theory of scattering	116	(12)
Examples	128	(1)
7 Magnetic scattering -- basic theory	129	(17)
7.1 Preliminary results	129	(2)
7.2 Expression for	131	(6)
7.3 Scattering due to spin only	137	(2)
7.4 Scattering by ions with spin and orbital angular momentum	139	(1)
7.5 Time-dependent operators	139	(4)
7.6 Cross-section for a paramagnet	143	(1)
Examples	144	(2)
8 Scattering from magnetically ordered crystals	146	(25)
8.1 Elastic magnetic scattering	146	(9)
8.2 Scattering by spin waves	155	(14)
Examples	169	(2)
Polarisation analysis	171	(25)
9.1 Introduction	171	(1)
9.2 Nuclear scattering	172	(5)
9.3 Magnetic scattering	177	(4)
9.4 Bragg scattering from magnetically ordered crystals	181	(7)
9.5 Scattering by the atomic field	188	(6)
Examples	194	(2)
Appendices	196	(35)
A The Dirac delta function	196	(5)
B Fourier trasforms	201	(3)
C Some results for linear operators and matrix elements	204	(3)
D Heisenberg operators	207	(3)
E The harmonic oscillator in quantum mechanics	210	(5)
F Angular momentum in quantum mechanics	215	(3)
G Normal modes of crystals	218	(8)
H The proofs of two results for magnetic scattering	226	(3)
I Some mathematical results	229	(2)
Solutions to examples	231	(10)
Bibliography	241	(2)
References	243	(4)
Glossary of symbols	247	(8)
Index	255