bluuebunny/crossref_metadata_2025_split huggingface dataset:
Dynamic Structure Factor Of Solid Helium
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we set out the dynamic structure factor, S(Q,ω), in solid helium. In the previous chapter we saw that helium atoms interact via a simple two-body potential and form simple lattice structures. However, because of the light mass, the zero point energy in these structures is large and solid helium is highly anharmonic. Helium is therefore a simple solid which dramatically displays anharmonic effects in S(Q, ω;).Our first purpose is to express S(Q,ω) in terms of the characteristic excitations, phonons, and highlight the effects of anharmonic interactions. This is done by expanding S(Q, ω) in the usual way as a sum of terms involving the excitation of single phonons, pairs of phonons, and higher orders plus interference between these orders. We present calculations of these terms to display their character. In this way solid helium displays phonon interactions, damping, and interference effects characteristic of all anharmonic solids.
Self-Consistent Phonon Theory
Authors: Glyde Henry R 
Published: November 2023

Abstract
The self-consistent phonon (SCP) theory is an elegant and pragmatic method for evaluating the dynamics of atoms in anharmonic crystals. In it, anharmonic contributions are summed into a generalized force constant. It is particularly suited to solid helium since, as noted in Chapter 3, the harmonic approximation (HA) is very poor and anharmonic terms are large. Also, the He–He interatomic potential has a steeply repulsive hard core. This makes the quartic and higher even anharmonic terms, that are summed in the lowest order SCP theory, larger than the cubic anharmonic term which appears first in second order. Thus the lowest order SCP theory, denoted the self–consistent harmonic (SCH) approximation, already provides a reasonable description of the phonon energies. This is not the case in alkali metals, for example, where the quartic and cubic anharmonic terms make approximately equal and opposite contributions. The SCH theory applied to solid helium is reviewed by Koehler (1975), Horner (1974a), Varma and Werthamer (1976), Glyde (1976), and Werthamer (1976).
Neutron Studies Of Solid Helium
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we compare the theory and calculations in Chapters 4 and 5 with neutron data in solid helium. Measurements of S(Q, ω) in solid 4He have been made at the volumes and temperatures indicated in Table 3.1. We begin with the bcc phase at V = 21.1 cm3 mol-1 and move to fee 4He at V = 9.03 cm3 mol-1. In this way we move from the largest volume and most quantum, anharmonic example to the smallest volume and least anharmonic case studied to date. We also begin with measurements made at low momentum transfer. At low Q the aim is to determine one- phonon properties. As Q is increased, interference and multiphonon terms become important so that the observed S(Q, ω) is quite different from the one-phonon component, S 1(Q, ω). At Q≳ 4 Å-1 bcc 4He responds like a collection of weakly interacting atoms. At high Q, the goal is to explore the single-atom properties and how the atoms interact with their neighbours.
Theory Of Liquid 4He
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this section we present the dielectric formulation (DF) of the dynamics of a Bose fluid. It is called a dielectric theory because the density and single-particle response of the fluid is expressed in terms of a wavevector and frequency-dependent dielectric function ϵ (Q, ω). It is also an extension of the field theory or response function theory introduced in §§’s 8.2, 8.4, and 9.4. It represents a coherent theory of the density and single-particle response taking explicit account of the condensate.The DF has its origins in the diagrammatic studies of Bose liquids by Gavoret and Nozieres (1964) and by Hohenberg and Martin (1965). The theory may be said to have two basic motivations. Firstly, when a Bose fluid has a condensate, n 0, the density and single-particle response are coupled, via the condensate. This coupling was discussed in §8.2 where we saw that the single-particle Green function, G, appears as a term in the density dynamic susceptibility χ when there is a condensate. Similarly, the self-energy, Σ, has a term containing the dynamic susceptibility χRgiven by (8.26) and (8.58). Via this term, the density response appears in the single-particle G. The first motivation of the DF is to build this coupling of χ sind G directly in the theory. The full χ and G are expressed in terms of simpler, ‘uncoupled’ [ineq] and [ineq] and the structure of the theory will incorporate the coupling via the condensate.
Dynamic Susceptibility Of Liquid 3He
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we derive a general integral equation for the dynamic susceptibilities χc(Q, ω) and xI(Q, ω), defined by (2.31) and (2.41), respectively, and used in (2.24) to evaluate S’(Q, ω). The general equation holds for a strongly interacting Fermi liquid at any temperature. For a gas of non-interacting fermions, the first term of this equation reduces to the Lindhard function, χ0(Q, ω), defined in (2.63). Approximations to the general equation are discussed in Chapter 15 and models of S(Q, ω) for liquid 3He based on it are discussed in Chapter 16.
Approximations To The Dynamic Susceptibility
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we discuss approximations to the dynamic susceptibility used to evaluate χ (Q, ω) in liquid 3He. In the previous chapter we obtained exact equations for χ (Q, ω)- We discuss, firstly, the mean field or random phase approximation (RPA) to these equations. The RPA is obtained from the full equation by approximating the full interaction by a local one and is widely used. In §15.2 we consider the conserving approximations of Baym and Kadanoff (1961). The low Q limit is considered in §15.3 which allows us to relate the interaction to the Landau parameters. Finally, approximations valid at high momentum transfer, Q ≫kF and ω ≃ ωR ≫ ∈ F are presented in §15.4.
Models Of S(Q, ω) In Liquid 3He
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we survey model calculations of the dynamic structure factor, S(Q, ω), in liquid 3He. We consider low Q models based on Landau theory, on the parmagnon theory, and the more complete polarization potential theory initiated by Aldrich and Pines (1978). At intermediate Q, calculations based on microscopic theory are sketched. All the models begin with the general equation for χ (Q, ω) derived in Chapter 14 and employ approximations discussed in Chapter 15. Comparisons with experiment are made in both this chapter and in Chapter 13.
Mori And Kinetic Theories Of Liquid 3He
Authors: Glyde Henry R 
Published: November 2023

Abstract
Lovesey (1975), Yoshida and Takeno (1979), and Pathak and Lücke (1983) have evaluated S(Q, ω) in liquid 3 He using techniques initiated by Mori (1965) and Zwanzig (1966). There are many variants of the Mori method. It was developed initially for classical liquids and its use there is reviewed by Copley and Lovesey (1975). Takeno and Yoshida (1978) and Yoshida and Takeno (1989) have presented a parallel treatment of classical and quantum liquids which provides an excellent introduction to their work. The Mori method is also called the memory function formalism. Here we survey the three applications to 3He emphasizing common features.
Intermediate And High Momentum Transfer
Authors: Glyde Henry R 
Published: November 2023

Abstract
In this chapter we discuss neutron scattering from condensed helium at intermediate and high momentum transfer. The aim is to present the basic physics of high Q scattering, introduce experimental data, and relate this to the theory set out in Chapters 18 and 19. The goal of experiment at high Q is to measure single-particle properties: the momentum distribution, particularly the condensate fraction in superfluid 4He, kinetic energies, and the interaction of the struck particle with its neighbours, the final state effects. At intermediate Q these interactions also lead to interesting oscillations of S(&lt;2,uj) with Q.In §2.5 we introduced the impulse approximation (IA) and the final state broadening function. In Chapter 18 we derived the I A, which holds exactly in helium at Q → ∞. In Chapter 19 we derived expressions for S(Q, ω) at high but finite Q and for the final state broadening function, R (Q, ω).
The Physics of Ultracold Neutrons
Authors: Ignatovich V K , Pontecorvo G B 
Published: November 2023

Abstract
Neutrons provide an important tool for investigations in physics. Ultracold neutrons (UCN) belong to the extremely low energy range (10 -7 eV to 10-8 eV), have velocities in the range 1-10 m s-1 and wavelengths of 100-1000 A. Ultracold neutrons can be kept in hermetically sealed vessels for up to 15 minutes until they decay. This time is sufficient to observe the action of very weak fields and gives an insight into the properties of neutrons and their environment. Capture and heating by wall nuclei reduce the storage time of neutrons to below 15 minutes. Present research areas include attempts to understand and prevent the large losses of UCN, improve storage time, and to obtain fundamental results such as an upper limit to the electric dipole moment of neutrons and improved measurements of decay time. These studies have also led to a new approach to diffraction and diffusion theory, which is applicable to any radiation: waves or corpuscles. The book explains how physicists should cope with the problems of UCN research, how UCN can be used for fundamental and applied research, and summarizes the results which have been published.
The interaction of UCN with a magnetic field
Authors: Ignatovich V K , Pontecorvo G B 
Published: November 2023

Abstract
In this chapter the storage of neutrons in magnetic traps will be considered, as well as issues of UCN polarization and methods of analysing it, and also methods of UCN spin reversal. Magnetic traps have the advantage that no absorption or inelastic scattering exists in them within the range of thermal energies. There are, however, certain peculiarities that must be taken into account in estimating the UCN storage time in these traps. The magnetic field in a trap is extremely inhomogeneous and can confine neutrons within a restricted region of space only in the case of a certain neutron spin projection on to the field direction. When the spin direction changes, and in an inhomogeneous field it is sure to undergo changes, the magnetic ‘walls’ win stop being walls and a neutron will leave the trap with ease. It is noteworthy that a spin flip is most probable when the neutron is as far as possible from the ‘magnetic wall’, and not when it impinges upon the ‘wall’.
Dilute ferromagnetic alloys
Authors: Hicks Trevor J 
Published: November 2023

Abstract
Dilute ferromagnetic alloys are an important class of disordered magnetic materials. Because of the dilution, simple models may be employed when discussing the spatial variation of moment. The most important simplifying feature is the independence of the impurity centres so that the description of the scattering can be interpreted in terms of the effect of a single defect on the magnetism of the host. Thus the data from dilute ferromagnetic alloys is a rich source of information about the electronic state of the impurity atoms and their affect on the electronic state of the surrounding host and its spin polarization. However, before describing models particularly for dilute ferromagnetic alloys, we outline some general equations for the neutron scattering, in various situations of experimental importance, from ferromagnetic alloys in general and take a look at a classic diffractometer built especially for the small diffuse cross sections expected from dilute alloys.
Defect scattering from antiferromagnetic alloys
Authors: Hicks Trevor J 
Published: November 2023

Abstract
Antiferromagnetic alloys of the 3d transition series are interesting for the same reason as their ferromagnetic cousins. The problems of measurement of the magnetic defect cross section is, however, quite different. Whereas for the ferromagnetic systems it was possible to separate out the magnetic defect cross section either by manipulating the ferromagnetic direction with a field or by measuring total cross sections for incident polarized neutrons with the polarization along or opposite to the ferromagnetic direction, antiferromagnetic alloys in general do not have such a direction.
Excitations
Authors: Hicks Trevor J 
Published: November 2023

Abstract
Atomic randomness makes a qualitative difference to the excitations in materials with long range magnetic order. Even to predict the correct number of modes, full account must be taken of the range of atomic environments for most materials. This is quite difficult and has only been done for a limited number of materials within the coherent potential approximation. Excitations near the critical temperature for some types of random systems can show very complicated behaviour even to time-dependent effects measurable on laboratory time scales. This chapter explores some of the experiments in which the excitations in magnetically ordered alloys have been measured and the diverse constructs for their analysis.
Nonresonant inelastic X-ray scattering; regime of characteristic valence electron excitations
Authors: Schülke Winfried 
Published: November 2023

Abstract
Nonresonant inelastic X-ray scattering is a photon-in photon-out process and based on that part of the photon–electron interaction which is expressed in the Aterm of the corresponding interaction Hamiltonian. In this chapter we shall deal with scattering processes, which are connected with a momentum transfer q characterized by 2π/q l c , where l c is the mean electron–electron distance, and with an energy transfer, or energy loss, characteristic for excitations of the scattering valence electron system. We designate this special type of scattering process the “regime of characteristic energy losses”.
The Tangent Map of Real Cartesian Spaces
Authors: Wasserman Robert H 
Published: November 2023

Abstract
Up to now we have been discussing certain abstract vector spaces, namely, tensor product spaces. These will be important in the context of our objective of modeling physical phenomena by various mathematical spaces with mappings between them. Tensor product spaces will be part of the structure of the image spaces of our mappings. For now we will focus on their domains.
Pseudo-Riemannian Geometry
Authors: Wasserman Robert H 
Published: November 2023

Abstract
In order to have “geometrical” concepts in a manifold, M, such as lengths of curves, surface area, or curvatures of curves or surfaces, we have to impose an additional “structure” on M. Here we assign a metric tensor, g, to Min terms of which we define the length of a curve and the distance between two points. We then examine the important special case when M has an atlas on each coordinate neighborhood of which the components of g are constant.
A Spacetime
Authors: Wasserman Robert H 
Published: November 2023

Abstract
In Chapters 18 and 19, we described models of “the motion of systems of particles and rigid bodies” the subject of classical analytical mechanics. In this chapter and the next we describe a certain model of “spacetime,” called Einstein’s theory of relativity.* This is usually more specifically called the special theory of relativity, or the theory of special relativity to distinguish it from Einstein’s theory of gravitation which we will look at in Chapters 22 - 24.
Lie Groups
Authors: Wasserman Robert H 
Published: November 2023

Abstract
We have mentioned Lie groups in passing, in Sections 13.2 and 19.2. To apply tensors and manifolds to current physics a deeper look is indispensable. In particular, we will describe a Lie algebra of vector fields (cf., Section 11.1) on a Lie group, G, whose properties strongly reflect those of G itself.
Introduction to Symplectic Topology
Authors: McDuff Dusa , Salamon Dietmar 
Published: November 2023

Abstract
Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behaviour of a wide rane of physical systems. Over the years much detailed knowledge has accumulated about the behaviour of particular systems, but the modern global theory of sympletic topology has just emerged. Powerful new methods in analysis and topology have led to a series of striking results, such as Gromov's flexiblity theorem on the existance of symplectic structures, and the various proofs of the Arnold conjectures on the number of fixed points of a symplectic map. This book contains an introduction to the subject, which will acquaint the reader with almost all the new methods in the field, providing proofs of the simplier versions of the most important new theorems. The deepest theorems in the book are proved by a new finite dimensional variational analysis of Hofer-Zehnder.
From Classical to Modern
Authors: McDuff Dusa , Salamon Dietmar 
Published: November 2023

Abstract
Symplectic structures first arose in the study of classical mechanical systems such as the planetary system, and almost all the classical work on symplectic geometry was focused on the attempt to understand how these systems behave. Recently, methods have been developed which give insight into the global features of symplectic geometry, and so the field of symplectic topology was born.
Introduction
Authors: Riviere J C 
Published: November 2023

Abstract
Surface analysis in its most general sense continues to be a growth area of remarkable vitality, and this is true particularly of that part of it that is concerned with attempting to establish the composition of a surface. Twenty or so years ago knowledge of the nature and number of elements at or near a surface could be obtained only by indirect means, and the development of surface science can now be seen in hindsight to have been hindered for that reason. The present situation could hardly be in greater contrast. If a surface scientist requires compositional information he now has a very considerable battery of techniques at his disposal, from which he may pick and choose according to the type of information he wants, and to the area and depth from which he wants it. Such is the range of choice that he may even exercise personal preference if he wishes, though few can afford that luxury, since generally the technique(s) must be matched to the problem and if there is one thing that most of them have in common it is high capital cost.
Photon excitation: ultra-violet photoelectron spectroscopy (UPS) and synchrotron radiation photoelectron spectroscopy (SRPS)
Authors: Riviere J C 
Published: November 2023

Abstract
Ultra-violet radiation from a source of the type described under section 3.2.2 and illustrated in Fig. 3.6 illuminates the surface of the sample. The most commonly used line sources are those of Hel at 21.21 eV and of Hell at 40.82 eV, produced by a discharge in helium gas, but Nel (16.8 eV) and Nell (26.9 eV) are also found occasionally. Just as with XPS, the energies of the photoelectrons ejected from the sample are measured in a CHA. Since the photoelectron energies in UPS are so low and span such a narrow range compared to XPS, elemental quantification is impossible.
Ion excitation: secondary neutral mass spectrometry (SNMS) and glow discharge mass spectrometry (GDMS)
Authors: Riviere J C 
Published: November 2023

Abstract
It has already been stated earlier that most of the particles ejected as a result of ion bombardment are neutrals, either atomic or molecular species. Since the neutral flux does not depend on any ionization mechanism but on the sputtering yield, which is only weakly dependent on matrix composition, it is obvious that if the neutral component could be measured independently, an analysis technique would be available that would be both more sensitive and more quantifiable than SSIMS. To measure the neutral signal requires conversion of the neutral flux to ions after ejection from the surface, followed by mass analysis in the usual way, taking care that interference from true secondary ions is avoided. Both SNMS and GDMS depend on postionization of neutrals, and indeed the two techniques are very similar, differing mainly in the precise conditions used for the ionization.
Neutral excitation: fast atom bombardment mass spectrometry (FABMS)
Authors: Riviere J C 
Published: November 2023

Abstract
In its origination this technique was really only an offshoot of SSIMS, arising from efforts to minimize or avoid the charging problems encountered with SSIMS when attempting to analyse non-conducting materials, and the damage problems when analysing large organic molecules. Indeed the very first papers by Barber et al.2 dealt specifically with the mass spectrometric analysis of biochemicals. The same authors found subsequently that a very useful variant of the technique was to disperse the high molecular weight organic in a matrix of low vapour pressure and good dispersing properties, and for this glycerol has been found to have excellent characteristics. Fragments from the glycerol itself are of course found in the mass spectrum, but their interference can be subtracted by computer.
High field excitation: atom probe field ion microscopy (APFIM)
Authors: Riviere J C 
Published: November 2023

Abstract
The technique of atom probe field ion microscopy has grown out of the older technique of Field Ion Microscopy (FIM), originated by Muller,1 which grew in turn out of field emission microscopy, also originated by Muller. Of all the surface-specific analytical techniques, APFIM is the only one with the ultimate in compositional sensitivity, i.e. a single atom. On the other hand, as will be seen below, analysis using APFIM is performed under somewhat extreme conditions of local electrostatic field, which has meant that nearly all its applications have been metallurgical. APFIM was also the brainchild of Muller and co-workers,3 and it is probably true to say that there is no other area of surface analytical technique that has been so dominated in its early and developmental stages by one man, E.W. Muller, as that of ultra-high resolution imaging and analysis.
Quantum crystal
Authors: Dobbs E R 
Published: November 2023

Abstract
The melting curve of He has been measured to 350 MPa by Mills and Grilly (1955) and found to be very similar to that for He, as shown in Fig. 2.1. The lighter mass of the He atom results in a larger zero point energy, and hence a larger molar volume (Chapter 1). It follows that the melting pressure is a little higher for He at all temperatures, the difference being most marked at zero temperature, where it is 3.44 MPa for He compared to 2.62 MPa for He. In similar way, there are three high-pressure phases for each isotope, the two close packed lattices for spherical atoms being present at the highest pressures. The face-centred cubic structure was first detected by Schuch and Mills (1961), while the hexagonal close-packed and body-centred cubic (Fig. 2.3) forms were identified by X-ray diffraction by Schuch et al. (1958). In this section we discuss first the high-pressure, close-packed solid, then the medium-pressure region with the important body-centred phase, and finally the unusual low-pressure melting curve.
Antiferromagnetism in the b.c.c. phase
Authors: Dobbs E R 
Published: November 2023

Abstract
The magnetic phase transition to an ordered state, which had been predicted for a decade to be around 2 mK, was discovered by Halperin et al. (1974) at Cornell University during the formation of the solid in a Pomeranchuk cell (a more modern one is shown in Fig. 2.8). They measured the latent heat dQ and volume change dV at constant temperature produced by the formation of the additional solid in the cell. The volume change was produced by pressurizing the He surrounding the cell and measuring dV capacitatively from the displacement of the He diaphragm. Pressurizing produces cooling and short pulses of a few nanowatts could be applied to produce heating.