Showing papers in "Progress of Theoretical Physics in 1961"

A New Approach to the Theory of Classical Fluids. III: General Treatment of Classical Systems

Abstract: A classical system enclosed in a finite volume and affected by external forces is treated in a general way. The main results are partly applicable to solids as well as to fluids. Exact integral equations are found for the one- and two-particle distribution frnctions. Some thermodynamic functions are expressed in terms of these distribution functions. It is shown that there exist variational principles, which require that the grand partition function is at a maximum with respect to the variations in the one- and twoparticle distribntion functions. Variational principles are found also for the Helruholtz free energy. It is suggested that Mayer's theory of condensation may give the end point of the metastable gaseous state. It is pointed out that a hyper-netted chain approximation has a meaning in solids as well as in fluids. (auth)

Self-Trapping of an Electron by the Acoustical Mode of Lattice Vibration. I

Abstract: The importance of the acoustical mode of lattice vibration for self- trapping of an electron is shown. It is shown that when the coupling constant between the electron and the acoustical mode vibration exceeds a certain critical value, the effective mass of the electron changes discontinuously to such an enormous value that the electron is practically allowed to take a localized self- trapping state as an eigenstate. This model is in contrast with the case of the pelaron, in which the effective mass changes continuously with coupling constant. This difference is attributed to the different force range of electron-lattice interaction in the two cases. (auth)

Correlation between Measurements in Quantum Theory

Abstract: Extension of the postulational basis of quantum theory by introducing correlations between the results of measurements, leads to negative joint probabilities for otherwise meaningful sets of measured values. Since the attempt made is probably the only one compatible with the theory of random variables, and is incompatible with the structure of Hilbert space, it is concluded that correlations are absent. This result, though it is tantamount to a denlal of von Neumann's projection postulate and the reduction of wave packets'' on measurement, is shown to be satisfactory from the physical point of view. (auth)

Magnetic Ordering in the Rare-Earth Metals with More than Half-Filled 4f Shells

Abstract: The effect of the anisotropy energy on the screw spin structure is investigated. Spin structures found in dysprosium, holmium, and erbium are shown to be stable if the anisotropy constants of second, fourth, and sixth orders have appropriate magnitudes and signs. Anisotropy energies decrease with rising temperature at different rates according to their orders. This temperature variation of the anisotropy energy causes the magnetic transitions between different spin structures in these rare-earth metals. It is shown that the state with the oscillation of the z component of the spin observed in the high temperature phase of erbium is always stable just below the Neel temperature when the second-order anisotropy makes the easy axis of the spin parallel to the c axis. The change of the pitch of the screw with temperature due to the quadrupole interaction is also calculated on the basis of the molecular field approximation, and it is shown to be too small compared with the experimental result. (auth)

On Energy Matrices for the Independent Particle Model

Abstract: A method which makes use of Fourier transforms of two-body interactions for the calcu­ lations of energy matrices in the independent particle model is proposed. The non-central interactions as well as central ones can be easily expanded into series of tensor products of spherical harmonics by this procedure. ·Furthermore, the radial integrals can be reduced to simple integrals which involve the Fourier transforms of the radial dependence of the inter­ actions. For the harmonic oscillator wave functions, the procedure can be easily carried out and explicit formulas for the integrals are obtained. Useful tables for the calculations of the integrals for the central, tensor and spin-orbit interactions are given,

Interaction between Alpha Particles

Abstract: Effective alpha - alpha potential is investigated from the standpoint of the cluster model using reliable properties of the pion-theoretical nucleon- nucleon potentials. The main features of alpha - alpha potential (outside attraction, inside repulsion, and angular momentum dependence) demanded from the analyses of low energy alpha - alpha scattering phenomena can be qualitatively reproduced. In constructing the alpha - alpha potential, the importance of the Pauli principle, which damps the relative wave function of two alpha -particles at small alpha - alpha distances, should be emphasized. Its connection with nucleon-nucleon potentials is discussed.

On the Plasma Oscillations in Metal Foils

Abstract: The dispersion relations, lifetimes of plasmons in metal foils, and the probability of plasmon excitation by incident electrons are derived quantum mechanically. The results obtained are the generalizations of Ferrell's semi- classical theory. (auth)

Nature of the First Excited States of the Vibrational Even-Even Nuclei

Abstract: The energy of the first excited states of even-even nuclei, and the probability of the electromagnetic transition between this and the ground states are calculated. The calculation covers almost all the known vibrational even- even nuclei, and is performed by assuming that the effective interaction is a sum of the pair and Q-Q interactions, and by employing the Bardeen-Cooper-Schrieffer and Sawada approximations. The agreement of the obtained results with experiments are in general good, although it becomes poor for cases which have a smaller number of nucleon outside closed shells. For such cases rigorous shell model calculation is also performed and comparing the results with the approximate ones, discussions on the validity of those approximations are made. (auth)

Physical chemistry of muscle protein "actin".

Abstract: Taking into consideration a possible role of actin filaments in muscle contraction, the authors give a review on physical chemical properties of actin in vitro, mainly describing the new results obtained in their laboratory. The dynamic aspect of the monomer-polymer equilibrium of actin coupled with the dephosphorylation of adenosine triphosphate is investigated and the cooperative nature of the polymerization is revealed. A new model of fibrous actin polymer is presented and the possibility of. the intermolecular conformational change of actin polymers is analysed. Some experimental results seem to prove such structure change. Discussions are made concerning the mechanism of movement of actin filaments induced by the interaction with myosin.

A New Model for the High Energy Nuclear Interaction

Abstract: The number of secondary particles emitted in shower jets is plotted as a function of log (tan theta ), and it is shown that the particles are emitted in bunches. These bunches, or 'quanta'', are interpreted as follows: in a high- energy collision, several polarized "quanta'' are emitted; each ''quantum'' is identified as a composite baryon-anti-baryon pair, which later decays into pi mesons, K mesons, etc. (T.F.H.)

Nonstatic one-boson-exchange potentials

Abstract: Nonstatic one-boson-exchange potentials between two nucleons are listed. The potentials are obtained exactly in the momentum space. In the coordinate space they are given up to the order M/sup -2/ in the M/sup -1/ expansion. (M is the nucleon mass). (auth)

Geometrical Study of the Pair Distribution Function in the Many-Body Problem

Abstract: The properties of pair distribution functions which are independent of physical natures as statistics, temperature. or potential were studied. We found that the inequalities (23) and (55) are always satisfied by the pair distribution function. Furthermore, the inequalities (9) and (45) are satisfied when the particles have hard-cores. These inequalities will serve as the subsidiary conditions in the variational treatments of many-body problems.

Infrared spectra and secondary structure of deoxyribonucleic acid.

Abstract: Comparisons have been made of the infrared absorption spectra of a few denatured sodium deoxyribonucleates (NaDNA) with that of native NaDNA. An absorption band has been observed at 1710 cm-i of native NaDNA, but it is absent in any denatured NaDNA examined. This fact has been explained to be due to the breakdown of the specific hydrogen bonds between the base residues in the denatured NaDNA. The bands of native NaDNA at 1220, 1084 and 965 cm-1 have been assigned to the PO; antisymmetric stretching, P02 symmetric stretching, and P-0 stretching vibrations, respectively. On the basis of the behaviors of these bands in breaking down the secondary structure of NaDNA, it has been concluded that a kind of "water of crystallization" is necessary for the formation of the double-helix structure of the DNA molecules.

Theory of Polaron Mobility

Abstract: The polaron mobility is calculated by making use of the general theory of electrical conductivity. We take the states determined by Feynman's trial action as the unperturbed states and treat the difference between the true action and the trial action as a perturbation. Numerical values of the polaron mobility at very .low temperatures are given and are dis· cussed in comparison with the results obtained by Shultz and .by Morita. § I. Introduction We have investigated the static properties of polaron at finite temperatures in the previous paper1> (hereafter referred to as I). We shall investigB;te the polaron mobility in the present paper. In the same way as in I, we calculate the polaron mobility by using Feynman's path-integral method. In the polaron problem, the interaction between an electron and lattice vibrations is so large that the usual perturbation theoretic treatment fails. Therefore the calculation of the mobility in the present paper will be based on the general theory of electrical conductivity recently developed by many authors,2 > which is applicable to a system which does not allow us to set up the Boltzmann equation. We take the states determined by Feynman's trial action as unperturbed states and treat the difference between the trial action and the true action as a perturba­ tion which yields a decay of electronic current correlation. The following assumptions will be made in the present paper. i) The electrical conductivity is determined by the asymptotic form of a correlation function of electronic current. ii) This asymptotic form has the property of exponential decay in time. These assumptions are valid in the case of weak interaction. It is not sure whether or not they are applicable to the present problem which includes the case of strong interaction. In the present treat­ ment, however, ~he states determined by Feynman's trial action instead of the states of a free electron are chosen as the unperturbed states. It is expected that the perturbation in the former case may be made weaker than in the latter case and that the above mentioned assumptions may be valid. In fact the self­ energy of polaron at 0°K calculated by using these assumptions agrees with that obtained by Feynman3> as will be shown _in § 3. Therefore, the approxi

Partial Equilibrium Model for Nuclear Reactions

Abstract: A new model for nuclear reactions is proposed in order to investigate the intermediate resonances'' detected experimentally in the intermediate energy region. The basic assumption is that only several nucleons of the target nucleus are excited at the compound system. Calculations are made in terms of the concept of the partial-equilibriumcompound-nucleus and the direct interaction. Numerical results for the level distances of the intermediate resonances'' agree with experiment. The number of excited nucleons in the compound system is about six and depends slightly on the excitation energy or the mass number of target nucleus (in this energy region). Further it is shown that outgoing channels couple with each other to form a gross channel corresponding to the intermediate level'' of the residual nucleus. The average distances between the gross channels are about 300 kev. (auth)

On the Stability of the Hartree-Fock Solution in Many-Body Problem

Abstract: A necessary condition for the stability of the HantreeFock solution in the many-body problem is presented. If this condition is not satisfied, the solution becomes uastable because of one-dimensional spin wave effects. A variational method is proposed for construction of a stable solution having a lower energy than the Hantree-Fock value. The workability of the method is tested in some examples, such as the B.C.S.-Bogolyubov theory of superconductivity. The method is applied to field theory, which seems to be inconsistent in view of the presence of "ghost states." A canonical transformation leads to a new vacuum state with lower energy, but the high momentum part of the coupling is not damped. (auth)

Integral Representations for Scattering Amplitudes in Perturbation Theory

Abstract: Integral representations for scattering amplitudes are proposed that are more general than the Mandelstam representation. Support properties are investigated for practical cases and for the general case in every order of perturbation theory. Nambu-Symanzik's formula is proved in terms of the Feynman parametric integral, and an example (for the two-particle scattering) is given in which stability conditions are satisfied but no dispersion relation holds.

Antisymmetric Treatment of Deuteron-Stripping Reaction Stripping and Heavy-Particle-Stripping Reactions

Abstract: The deuteron stripping reaction is formulated using completely antisymmetric wave functions. The amplitude of the reaction is represented as a sum of "ordinary" stripping and heavy-particle-stripping amplitudes. Analogous to the case of the ordinary stripping, the amplitude of the heavyparticle- stripping can be represented in terms of three reduced width amplitudes of bound nucleons, e.g. those of the captured neutron and proton in the residual nucleus and that of the emitted proton in the target nucleus, or alternatively, in terms of two reduced width amplitudes of the emitted proton and captured deuteron in bound states. This formalism enables calculations of both angular distributions and "magnitudes" of heavy-particle-stripping cross sections. For simplicity, the cutoff Born approximation is employed, though its generalization can be performed easily, as is discussed.

Space-time correlation function in the theory of electrical conductivity

Abstract: A formula is given for the electrical resistivity of metals with the use of the result of excitation-response theory. It is shown that the electrical resistivity is expressed in terms of the four-dimensional Fourier transform of the appropriate pair correlation function in space and time of the scattering systems, by which conduction electrons are scattered to lose their initial velocity. The dependence of the electrical conductivity on the effects of the correlation in the scattering system is discussed systematically by using the correlation functions in some of the typical examples. Especially the electrical resistivity of the fer­ romagnetic metals is discussed in some detail by using the so-called s-d interaction model. In this case it is shown that the inclusion of the effect of the correlation between d spins gives rise to deviations in electrical resistivity from the one given by the simple molecular field approximation.

Internal Structure of Very Massive Stars

Abstract: Models are computed for stars (M = 468M sub solar ) consisting of four regions: a homogeneous radiative envelope, a semiconvective intermediate zone, a radiative intermediate zone, and a homogeneous convective core The semiconvective intermediate zone is formed in the consequence of growing convective instability which is characteristic in very massive stars, and the distribution of composition in this region is determined so as to maintain the convective neutrality taking account of the effect of the gradient of mean molecular weight It is shown that the very massive stars evolve essentially in the same way as less massive stars in their early phase, and the growing convective instability has little influence on the effective temperature and luminosity of stars

Nuclear Forces in the Momentum Space

Abstract: Several fundamental problems concerning a two-nucleon system in the momentum space are discussed. Solutions to these problems should be useful for treating the twonucleon problem completely nonstatically, i.e., without making use of the expansion in terms of the inverse of the mass of the nucleon. General forms for a two-nucleon potential in the momentum space are derived. The integral equations that are the Fourier transform of the Schrodinger equation, along with solutions of these equations are briefly discussed. Formulas for matrix elements of the most general types of potentials are evaluated and are applied to the nonstatic one-pion-exchange potential. (auth)

Parametric Integral Formulas and Analytic Properties in Perturbation Theory

Abstract: The general term in perturbation theory is explicitly given in terms of the Feynman parametric integral. The properties of the parametric functions appearing in this integral are investigated in detail. By using this formula, systematic investigations on the singularities of the general term are extensively developed. Dispersion relations for various forward and non-forward scatterings (and vertex functions) and other integral representations for the vertex function are proved in every order of perturbation theory. (auth)

Nuclear Interactions in the P1/2-g9/2 Configurations

Abstract: Zr 90 offers a very good case for the study of T=1 levels in the p 1/2 -g 9/2 subshells and has recently been explored by several authros. Here earlier calculations of Thankappan and Waghmare are extended and analysed in detail. It is found that a simple central two-body interaction can be constructed which will give correctly the energy levels of the (g 9/2 ) 2 configuration, and hence also the levels of a (g9/2) n configuration. However, the same interaction fails to give correctly the levels of the other configurations (p 1/2 )(g 9/2 ) and (p1/2) 2 . This simple two-body nuclear interaction is thus shown to be configuration dependent. It is pointed out that experimental identification of the as yet unobserved 4 - level would be very helpful for further elucidation of this phenomenon. The results are compared with those of the other authors.

Operator Equations in Two Field Theory Models

Abstract: Two soluble relativistic field theory models are considered. Both models are two-dimensional, and both models have infinite renormalization constants. It is shown that the current operators for these models satisfy local field equations.(T.F.H.)