Long lived nuclear spin order : theory and applications 2.2.5.3 Hamiltonian Averaging over Internal Motions 2.3 Number of Expected Long lived Orders 2.3.1 Approximations 2.3.2 Number of LLS and Analytical Expression in the Idealized Case 2.3.3 Example for a Two spin System 2.3.4 Example for a Three spin System 2.4 LLS Accessibility via Coherent Incoherent Mechanisms 2.4.1 Example 1 2.4.2 Example 2 2.4.3 Example 3 2.4.4 Example 4 2.5 Conclusions References Chapter 3 Relaxation Theory of Long lived Spin Order 3.1 Introduction 3.2 Longitudinal and Singlet Order 3.3 A Model for Nuclear Spin Relaxation 3.4 Relaxation Decay Rates 3.5 Relaxation of Longitudinal and Singlet Order Under Different Mechanisms 3.5.1 Isolated Singlet Pairs 3.5.1.1 Intra pair Dipole Dipole (ipDD) Mechanism 3.5.1.2 Symmetric Chemical Shift Anisotropy (CSA+) Mechanism 3.5.1.3 Anti symmetric Chemical Shift (CSA−) Mechanism 3.5.1.4 Spin Rotation (SR) Mechanism 3.5.2 Singlet Pairs in the Presence of a 3rd Spin 3.5.2.1 Out of pair Dipole Dipole Mechanism (opDD) 3.5.2.2 Inter molecular Dipole Dipole (imDD) Mechanism 3.5.2.3 Scalar coupling of the 2nd Kind (JSK) Mechanism 1.3.3.2 Symmetric Approximation of the Fluctuating Hamiltonian 1.3.3.3 The Permutation Group of the Symmetric Approximate Hamiltonian 1.3.4 The Number of Long lived States 1.3.5 Long lived State Operators 1.4 Long lived State NMR 1.4.1 Excitation 1.4.1.1 Thermal Magnetization 1.4.1.2 Hyperpolarization 1.4.1.3 Spin isomer Imbalances 1.4.2 Filtering 1.4.3 Evolution 1.4.4 Read out 1.4.5 Detection Acknowledgements References Chapter 2 Symmetry and Long lived Spin Order 2.1 Introduction 2.1.1 The Concept of Symmetry 2.1.2 The Definition of Group Intro Title Copyright Preface Contents Part 1 Singlet Order and Its Properties Chapter 1 Long lived States in Nuclear Magnetic Resonance: An Overview 1.1 Introduction 1.2 What Are Long lived States 1.2.1 Disconnected Eigenstates 1.2.2 Disconnected State Manifolds 1.3 Symmetry Theory of Long lived States 1.3.1 The Coherent Hamiltonian and Its Symmetry 1.3.2 The Fluctuating Hamiltonian and Its Symmetry 1.3.3 The Symmetric Approximate Hamiltonian 1.3.3.1 Symmetric Approximation of the Coherent Hamiltonian 2.1.3 The Group Formed by the Permutation of Three Elements 2.1.4 Representation of Groups Homomorphism and Isomorphism 2.1.5 Reducible and Irreducible Representations 2.1.6 The Vanishing Integral Rule 2.2 Symmetry Conditions for the Existence of Long lived Spin Orders 2.2.1 Spin Eigenstates 2.2.2 Spin Relaxation 2.2.3 Symmetry Classification of Nuclear Spin Operators 2.2.4 Spin System Definition 2.2.5 Symmetry of the Nuclear Spin Hamiltonian 2.2.5.1 Symmetry of the Coherent Hamiltonian 2.2.5.2 Symmetry of the Fluctuating Hamiltonian A long lived form of spin order namely singlet order can be prepared from nuclear spin magnetisation and this first book on the subject gives a thorough description of the various aspects that interfere in the development of the topic and details the interdisciplinary applications