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In this paper we develop a general theory of the spin dynamics of anisotropic Fermi superfluids of the generalized BCS type, under conditions which should be realistic for any such phase of liquid 3 He occurring below 3 mK. No restrictions are placed on the nature of the pairing configuration. The system is described in terms of the total spin vector S , and a vector T(n) which describes the amplitude and spin quantization axes of the pairs forming at a given point n on the Fermi surface; the kinematic relations between these quantities are emphasized. An approximation of the Born-Oppenheimer type is used to derive the general equations of motion of S and T ; it is pointed out that relaxation of T due to collisions is inhibited by the coherent nature of the superfluid state. The equations of motion are solved for the particular case of unsaturated c.w. resonance, and it is shown that the nature of the transverse (usual) resonance spectrum is a strong function of the kind of configuration occurring; in particular, either one or two finite-frequency resonances may occur, depending on the configuration. A resonance is also predicted to occur when the r.f. field is polarized along the static external field. Specific predictions of the form of the transverse and “longitudinal” spectra are made for all the unitary l = 1 states, and it is shown that these predictions are unaffected by renormalization effects. The “Balian-Werthamer” state is predicted to show a longitudinal resonance but no transverse shift. The theory is compared with other approaches to the problem and its relevance to the anomalous low-temperature phases of liquid 3 He is discussed.

A previously developed theory of NMR in superfluid $^{3}\mathrm{He}$ is generalized to include relaxation effects. The physical mechanism envisaged is the relaxation of nonequilibrium Cooper-pair concentrations in the different spin bands. The results should describe both linear and nonlinear phenomena for all frequency regimes. The results for continuouswave linewidths disagree with those of Combescot and Ebisawa as to temperature dependence.

This paper reviews the theory of anisotropic superfluid phases and its application to the new A and B phases of liquid $^{3}\mathrm{He}$. It is tutorial in nature and advanced formal techniques are avoided; even the formalism of second quantization is not required. After an initial discussion of the Fermi-liquid theory of Landau and its application to the normal phase of liquid $^{3}\mathrm{He}$, the idea of instability against formation of Cooper pairs is introduced. The effective interaction in liquid $^{3}\mathrm{He}$ is considered, with emphasis on the spin-dependent interaction arising from virtual spin polarization of the medium ("spin fluctuation exchange"). Next, a self-contained discussion of the "weak-coupling" BCS theory as applied to anisotropic superfluids is given, with special attention to the "Ginzburg-Landau" region close to the transition temperature. Formulas are derived for the specific heat, spin susceptibility, normal density tensor, and static spin-dependent correlation properties of superfluids with both singlet and triplet pairing: In the triplet case the ideas of "spin superfluid velocity" and "spin superfluid density" are also introduced. After a preliminary comparison of the weak-coupling theory with experiment, it is shown that feedback effects due to the modification, by formation of Cooper pairs, of the effective interaction connected with spin fluctuation exchange can produce results which are qualitatively different from those of the weak-coupling theory. An attempt is made to reformulate recent graph-theoretical treatments of this phenomenon in a more elementary language, and considerations based on possible invariant forms of the free energy are also introduced. The properties of the so-called Anderson-Brinkman-Morel and Balian-Werthamer states, which are commonly identified with $^{3}\mathrm{He}$-A and B, respectively, are studied in detail. Next, the effects which tend to orient the Cooper pair wave function in a given experimental situation are discussed; in this context the form of the free energy terms arising from spatial variation of the wave function is explored. A semiphenomenological theory of the nuclear magnetic resonance properties is developed and applied in particular to the case of unsaturated cw resonance; the analogy with the Josephson effect is emphasized. The question of relaxation and linewidths is also briefly discussed. A partial account is given of the theory of finite-wavelength collective oscillations, with particular reference to first, second, and fourth sound and spin waves. The splitting of the A-normal transition in a magnetic field is considered, with special attention to the possibility it offers of testing theories of the "spin fluctuation" type. Finally, a brief assessment is made of the extent to which the current experimental data support the conventional identification of $^{3}\mathrm{He}$-A and B and the spin fluctuation theory, and some outstanding problems and possibilities are outlined. Subjects not discussed include "first-principles" theories of the effective interaction in $^{3}\mathrm{He}$ collective excitations in the "collisionless" regime, and the problem of ultrasonic absorption, "orbit waves," and the theory of the kinetic coefficients.

1. 1. Osmiophilic globules, a characteristic morphological feature of intact chloroplast in leaves of higer plants and in algae, have been isolated from leaves of spinach beet (Beta vulgaris L. Cicla) and fractionated into two separate populations distinguished by their behaviour on centrifugation. 2. 2. In aqueous suspension globules 800–2700 A in diameter separate as a cream. A second fraction 550–1400 A in diameter sediments under the same conditions and is associated with a protein component of the chloroplast. 3. 3. The isolation procedure also affords particles of lamellae 38–150 A in diameter and 500–4000 A in length. 4. 4. Some properties of the globules are described and their lipid composition compared to that of the particles of lamellae. 5. 5. Only a trace of chlorophyll is associated with the globules and no β-carotene was detected. Roughly equal amounts of plastoquinone were found in the lamellae and the globules. 6. 6. The presence of another quinone which has an absorption spectrum similar to that of plastoquinone has been confrimed.

This paper discusses various aspects of microscopic Fermi-liquid theory, with particular emphasis on its application to metals. It is shown that under certain conditions we have the inequalities m∗1+13F1⩾m, m∗1+112Z1⩾m The appropriate formulation of the theory is presented for the case that the fermions interact with an arbitrary background (e.g. 3He4He mixtures). A microscopic proof of the stability conditions is given. The effects of the Coulomb and electron-phonon interaction in metals are treated by completely parallel techniques, and explicit expressions are given for the electronic correlation functions in the limits ω 2> ωD and ω ⪡ ωD. Results for the static properties, etc., are in agreement with the recent work of Prange and Sachs. It is shown that the electron-phonon interaction can only enhance the “dynamic effective mass” m∗(1 + 13F1), and that the enhancement tends to zero for forward electron-phonon scattering. It is also shown explicitly that phonon effects on the Landau parameters can affect the static properties in the superconducting state even though they cannot in the normal state. The inequalities obtained are compared as far as possible with experiment, and it is shown that the rough value of Z112(≡B1) recently obtained for Na from CESR experiments is almost certainly not compatible with the optical data. Tentative application is also made to the recently observed Knight shift in superconducting Al.

Equations are derived for the motion of the magnetization and the "spin axes of the Cooper pairs," and solved for the case of unsaturated cw resonance. In general two discrete resonances are predicted, but if a special condition is met, only one occurs. The complete field dependence of the line(s) determines the gap configuration almost uniquely. The predictions are consistent with existing data and in strong conflict with Anderson's theory.

It is shown that in a clean two-band (transition-metal) superconductor there appears a collective excitation corresponding to small fluctuations of th~ relative phase of the two "condensates". In contrast to the transverse collective excitations in ordinary superconduc­ tors, the energy of this mode can be derived directly from existing experimental data ; for Nb it lies about at the middle of the smaller single-particle gap. Direct experimental detec­ tion of this resonance is estimated to be rather beyond the limits of available techniques, but its effect on th~ ultrasound dispersion curve should be easily observable. The pheno­ menon is used to elucidate the physical nature of excitons in superconductors in general.

This article is written for the purpose of describing the character and scope of the work undertaken to promote economy and efficiency in the Department of Water Supply, Gas and Electricity of New York City. The terms "economy" and "efficiency" in their application to the department in question involve two intimately related ideas: efficiency, meaning the attainment of a given result with the minimum ,expenditure of energy; and economy, as signifying the minimum expenditure of money consistent with the attainment of that result. The warranted degree of economy is a relative factor dependent upon the value of the result to be obtained. Good public service cannot be jeopardized by false or mistaken economy due to the disregard of all else but the effort to save money. The aim should be to attain the best public service at the least cost to the city. The practical application of the principles of economy and efficiency necessitates the supervision of the various divisions of the department in order to ascertain: first, if work proposed or in progress is necessary for the effective operation of any function of the department; second, if work deemed necessary is accomplished under present conditions with efficiency; third, if a greater efficiency can be obtained by improved methods and the betterment of physical conditions; fourth, if such improvements will effect a greater economy in operation, consistent with efficient service. To allow of this supervision, and for the purpose of administrative study, summaries of detailed reports prepared in graphic form, when practicable, show the results of work accomplished throughout the department and the cost of operation in order that the principles of economy and (78)

The long-wavelength, low-frequency "collisionless" collective oscillations of a superfluid Fermi liquid are studied throughout the region $0lTl{T}_{c}$ with the help of a field-theoretic formalism developed in a previous paper. It is found that any collective mode (other than the density fluctuation) that is possible in the normal phase persists below ${T}_{c}$ as an oscillation of the normal component, but disappears at some finite temperature which in general depends on the Landau interaction parameters ${F}_{0}$,${F}_{1}$,${Z}_{0}$, etc. The behavior of the density-fluctuation mode depends critically on ${F}_{0}$, if the latter is negative, there is a well-defined collective oscillation only for $T\ensuremath{\ll}{T}_{c}$, while if it is small and positive, the oscillation is well defined for $T\ensuremath{\ll}{T}_{c}$ and $T\ensuremath{-}{T}_{c}\ensuremath{\ll}{T}_{c}$ but not in the intermediate region. If ${F}_{0}$ is large and positive, the density-fluctuation collective mode exists throughout the whole region $0lTl{T}_{c}$ and its velocity is approximately temperature-independent.

It is suggested that the property of nonclassical rotational inertia possessed by superfluid liquid helium may be shared by some solids. In particular, nonclassical rotational inertia very probably occurs if the solid is Bose-condensed as recently proposed by Chester. Anomalous macroscopic effects are then predicted. However, the associated superfluid fraction is shown to be very small (probably $\ensuremath{\lesssim}{10}^{\ensuremath{-}4}$) even at $T=0$, so that these effects could well have been missed. Direct tests are proposed.

It is proposed that the mechanism of the anomalously high thermal transfer rates observed between CAIN and liquid He3 is simply the electromagnetic dipole coupling between electrons and He3 nuclei. A crude theory based on this assumption explains the observed linear dependence of the Kapitza resistanceRK onT, the order of magnitude of the coefficient, and the absence to date of the effect in dilute He3-He4 solutions. We predict that (1)RK(T) should go through a minimum at about 1 mdeg, (2)RK should be decreased by applying a magnetic field, (3) a similar linearT dependence (though with much larger coefficient) should be seen in dilute solutions below 5 mdeg, and (4) a similar, though probably less striking effect, should be observed for ferromagnetic metals in contact with He 3 at sufficiently low temperatures.

We examine the possibility of using NMR and other measurements on very weak solutions of 3 He in liquid 4 He to investigate the superfluid phase transition. It is found that even for these very weak solutions the mass (Dm) and spin (Ds) diffusion coefficients associated with the 3 He behave in radically different ways:Dm is predicted to diverge asT approaches Tλ from above as (T−Tλ) −1/3 , while the behavior ofDs depends on the type of experiment, and for the ordinary spin-echo type has no particular singularity.

The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with $S$-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters ${F}_{0}$, ${F}_{1}$, ${Z}_{0}$, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of ${\mathrm{He}}^{3}$ and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near ${T}_{c}$; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of ${F}_{1}$.

1. 1.|The rate of release of high molecular weight water-soluble components from isolated chloroplasts has been studied. 2. 2.|Chloroplasts have been broken by osmosis and successively washed with hypotonic buffer solutions, or ruptured in a needle-valve disintegrator to free lamellae particles of soluble constituents. The resulting solubilized material has been examined by ultracentrifugation, and by polyacrylamide gel electrophoresis in homogeneous buffer system. 3. 3.|Fraction I protein was more readily liberated from the chloroplasts than the Fraction II components. A component of s20, w = 12 S was observed in some of the extracts, but the bulk of this was only liberated after complete disruption of the lamellae, and it is thought to be situated within the lamellae ‘loculi’ and ‘fret-channels’. 4. 4.|A procedure for the purification of Fraction I protein using DEAE-cellulose chromatography and gel filtration is described. 5. 5.|An investigation of the nature of our preparation of Fraction I protein is reported; the protein has a partial specific volume of 0.744 ml/g, and an s°20, w = 18.30 S. A minimum molecular weight of 24427 has been calculated from the amino acid analysis, and the molecular weight of the macromolecule has been determined by ultracentrifugation (on two preparations) as 585 000 and 561 000. The protein was observed to dissociate into subunits of 2.6–4.8 S, in alkali (pH 11.5), acetic acid (70%), urea (8 M) and sodium dodecyl benzene sulphate (detergent-protein, 1:2, w/w). 6. 6.|The isolated Fraction I protein contains 84% protein; the other material present is thought to be accounted for by carbohydrate and material giving rise to ash. The predominant monosaccharides in the hydrolysates of the protein have been identified as glucose and xylose. 7. 7.|Fraction I protein has been shown to be identical with the enzyme, ribulose-1,5-diphosphate carboxylase (EC 4.1.1.39). Correspondence between the physical properties of Fraction I protein and those of protochlorophyll-protein complex of etiolated tissues indicates another possible identity.

Spin diffusion in a degenerate Fermi liquid is studied, taking into account the effects of the 'molecular field' resulting from the interactions between quasiparticles. It is shown that even in the hydrodynamic limit no equation of the conventional form delta M/ delta t=Dgrad2M exists in general; the true equation is nonlinear and depends on the strength of the interactions. Substantial new effects are therefore predicted when lambda Omega 0 tau D> approximately 1, where Omega 0 is the Larmor frequency, tau D the spin diffusion lifetime and lambda a dimensionless parameter which measures the strength of the molecular field. Specifically, it is predicted that the spin-echo attenuation in a ' phi -180-180' experiment will in general not be exponential and will depend on the external field and the initial pulse angle phi . The new effects should lie in the experimentally accessible region both for pure 3He and for mixtures.

This paper examines the general question: How far can one set lower limits on the entropy density S(T) of a large system at low temperatures by using data of a different type, e.g., scattering data or static susceptibilities ? It is shown for an arbitrary onecomponent system that if we make a single unproved but highly plausible assumption about the fluctuations of large subvolumes, we can obtain an inequality relating S(T) to certain integrals over the temperature-dependent correlation functions of the system; and with one further very weak assumption the zero-temperature correlation functions alone determine a lower limit on S(T). It is then shown that the fluctuations of any locally conserved quantity give rise to a contribution to S of at least a constant times T3; in particular, by considering the density fluctuations we obtain the inequality where So(r) is the “Debye” entropy which would arise from longitudinal phonons propagating at the hydrodynamic sound velocity determined by the macroscopic compressibility. (This result does not assume the existence of such phonons as good elementary excitations of the system.) Some other general results are derived as a byproduct: for instance, it is shown that any system obeying a diffusion equation of a certain type must have an entropy at least proportional to T.

The decay in time of the frequency of the so-called "wall-pinned" mode in the nuclear resonance of $^{3}\mathrm{He}$-$B$ is shown to provide a test of a previously developed theory of spin relaxation and to give a numerical value of a previously unknown parameter of the normal phase.

Cook, Heilbron and Levy1 have recently prepared tetraglycylglycine and several di-peptides by reaction of 2-thio-5-thiazolones with amino-acid derivatives. During the past few years, much interest has also been shown in the polymerization potentialities of the N-carboxy anhydrides of α-amino-acids2–5. Study of the reaction of these anhydrides with simple organic bases has now indicated the mechanism of their polymerization and provided a new method of building up polypeptides by addition of single amino-acid units.

Low temperature physics provides the testing ground for the effects of quantum mechanics on a large scale. Tony Leggett describes the recent work on the new phases on liquid helium and outlines the prospects for future work

Neither of the stable isotopes of helium solidifies under its own vapour pressure down to the lowest temperatures reached. In the case of 4He, below about 2 K the liquid enters a 'superfluid' phase (He-II) with quite extraordinary properties.

The condition for the position of the nuclear magnetic resonance line observed in a many-body system to shift away from the Larmor value gamma H0 is studied. It is shown that shifts of the order of magnitude of that recently observed in liquid 3He below 3 mK are possible only if the system possesses a peculiar ordering property, not hitherto seen in any many-body system, which is called 'spontaneously broken spin-orbit symmetry'. Some general aspects of the behaviour of systems with this property are studied, without making any particular assumptions about the microscopic dynamics.