Showing papers in "Progress of Theoretical Physics in 1964"

Resistance Minimum in Dilute Magnetic Alloys

Abstract: Based on the s-d interaction model for dilute magnetic alloys we have calculated the scattering probability of the conduction electrons to the second Born approximatism. Because of the dynamical character of the localized spin system, the Pauli principle should be taken into account in the intermediate states of the second order terms. Thus the effect of the Fermi sphere is involved in the scattering probability and gives rise to a singular term in the resistivity which involves clog T as a factor, where c is the concentration of impurity atoms. When combin:::d with the lattice resistivity, this gives rise to a resistance min~mum, provided the s-d exchan:~e integral J is negative. The temperature at which the minimum cccurs is proportional to c 15 and the depth of the minimum to c, as is observed. The predicted log T dependence is tested with available experiments and is confirmed. The value of J to have fit with experimmts is about -0.2 ev, which is of reasonable magnitude. Our conclusion is that J should be negative in alloys which show a resistance minimum. It is argued that the resistance minimum is a result of the sharp Fermi surface.

On the “Anharmonic Effects” on the Collective Oscillations in Spherical Even Nuclei. I

Abstract: A new method which enables us to transcribe the dynamics of the system of even num­ ber of fermions 'into that of the boson system is developed, with the purpose of analysing the " anharmonic effects " on the collective oscillations in spherical even nuclei from the standpoint of the microscopic theory of the collective excitations. In the "harmonic ap­ proximation", a pair of bound quasi-pa:I;ticles is replaced by the "phonon" as an ideal boson. This replacement inevitably leads to neglecting two main effects; the dynamical effect due to the residual interactions omitted under the "harmonic approximation" and the effect of the Pauli-principle among the quasi-particles composing the different pairs. Ac­ cording to our theory, the two effects which cause "anharmonic effects" can be evaluated correctly, in principle. It is not our purpose to go into detailed quantitative calculations, but rather to develop the basic idea.

On te Algebra of All Local Observables

Abstract: 4) has a canonical reduction into factors according to the spectrum of its center. We prove that the canonical reduction of the algebra of all local observables also reduces the translation unitary operators. A vacuum sector is defined to be any reduced space in this reduction which contains at least one translationally invariant vector. We prove that the algebra of all local observables is a factor of type I with a unique vacuum state in any vacuum sector. Our main physical conclusion is essentially that the unique vacuum and irreducible algebra of all local observables are the most general situation of interest as far as the existence of a vacuum in the theory is desired.

Collective Excitation of Unlike Pair States in Heavier Nuclei

Abstract: basis of the j-j coupling shell model. It is shown that the even parity states as the coherent mixture of many unperturbed (n-p) states are pushed up by the (n-p) repulsive interactions with T=l. The isobaric state T_l'f£0) can ,be interpreted as a coherent state with Jrr=O+. The coherent states with non-zero spin arise in the high excited energy region but not higher than that of the isobaric state. They may be strongly excited by the (p, n) reaction. The actual numerical calculations assuming zero-range forces are carried out for the J,.. = 1 + states of the nucleus Bi208 which can be produced by the (p, n) reaction using the target nucleus Pb208. The transition strength due to the operator Y_=2}ri-ai concentrates i

The Behavior of Superconducting Thin Films in the Presence of Magnetic Fields and Currents

Abstract: The general Gor'kov equation in the presence of arbitrary vector potential A(x) is solved for a superconducting thin film on the following two assumptions; 1) the ordering parameter Ll is C\)nstant all over the specimen, 2) l/~0~1, where l is the mean free path of an electron and ~0 the coherence length of an electron pair. It is shown that the phase transition due to magnetic field is always of the second order. The critical field is determined from the condition .d=O.

Type of von Neumann Algebra Associated with Free Field

Abstract: A class of von Neumann algebras associated with the normal representation (i.e. the Fock representation) of the canonical commutation relations has been studied in an earlier paper. > The von Neumann algebra in question is always the tensor product of an abelian algebra and a factor of the infinite type. A necessary and sufficient condition for the factor to be of type Icc has been obtained in reference 1). In the present paper it will be shown that the factor in question is of type IIIcc unless it is of type t"'. Recently there have been some interests in the type of von Neumann algebras of local observables in quantum field theory. J,SJ,), ) The von Neumann algebras of 'local observables for a free scalar field) as well as those for a generalized free field belong to the class of von Neumann algebras considered in reference 1) and our result implies that they are either type III"' or t:o. In particular, for those cases where type Icc have been excluded,J,sl, l the algebra must be of type IIICXJ . Our result also implies that the algebra of all creation and annihilation operators in quantum theory of an infinite free Bose gasl is a factor of type IIIcc when no condensation is present.

Quartet Scheme for Elementary Particles

Abstract: A possible unified model for elementary particles is developed by generalizing the viewpoint of Sakata-Nagoya model. Instead of the Sakata triplet (p, nand A), we work with the quartet of new baryons Xo and X CX1, Xz and Xs) of spin 1/2, of which Xo belongs to U(1) whereas the other three to U(3). Strong interactions are subjected to a "broken U(1) X U(3)" symmetry. Baryon octet (N, 1:, A and 3) and meson octets (K, 11:, 71, K; etc.) are interpreted, respectively, as the three (XXXo)­ or two (XX) -body composite systems both belonging to 8-dimensional representations of SU(3). One of the crucial test of the model is the prediction of triplet mesons (XXo), the iso-doublet of which can be identified with /C.-mesons. The baryon quartet, Xo and X, corresponds to four leptons in the sense of "modified" baryon-lepton symmetry. This enables us to explain Cabibbo's pheno­ menological weak interaction as a consequence of the present scheme.

Alpha-Particle Model for Be9

Abstract: The low-energy properties of Be/sup 9/ art investigated on the basis of the alpha -particle model by making use of alpha - alpha and n- alpha interactions. Variational calculations are made in which the effects of the Pauli principle due to the internal structure of alpha particles are taken into account. In particular, the inclusion of the dynamics between alpha particles affects strongly the quadrupole moment, and the predicted value becomes considerably smaller than the value of the usual alpha -particle model. The ground-state moments mu and Q and low-lying negative parity energy levels are consistently explained by the present model. This means that the alpha - clusters in Be/sup 9/ are well localized and the interaction between inner alpha -clusters may be not so much different from the free alpha - alpha interaction. (auth)

Exact Treatment of a Charge Independent Pairing Interaction in a Degenerate Model

Abstract: A charge independent pairing interaction in j-j coupling scheme and a charge-spin independent pairing interaction in L-S coupling scheme are exactly solved in a degenerate model by the aid of group theory. Groups used here are independent of the number of states concerned unlike the usual shell model technique. Our method is deeply connected with the generalized Bogoliubov transformation and it is conjectured that this transformation combined with projection into the definite number and the isospin (symmetry) state is very useful for the treatment of pair-interacting many body system. The classification of states through the group used here are equivalent to the seniority scheme generalized for unlike particles and degenerate levels. Our method simplifies mathematics somewhat and derives easily some new properties of seniority scheme for unlike particles.

Low-Temperature Properties of the Interacting Bose System

Abstract: The low-temperature properties of the interacting Bose system at high density are ·investigated under the random phase approximation and the self-consistent Hartree approxi­ mation based on the" normal-mode analysis". To treat rigorously the temperature-dependent "depletion" effect of the particles in the zero-momentum level, a new approach is proposed. As a result, the critical temperature, Tc, at which the zero-momentum particles disappear is determined. In the region below Tc, the temperature-dependent energy-spectrum of the quasi-particles, which has at the zero-temperature an intimate connection with that of Bogoliubov, is obtained, and the property of superfluidity which disappears at Tc is discussed. It is shown that the quasi-particles are transformed into the normal Bose particles at Tc, and the temperature-dependent energy-spectrum of the normal particles in the region above Tc is. determined. It is noteworthy that the phase transition of the second-order occurs at Tc. In so far as the interaction gives the real and positive value for the energy-spectrum of both the quasi-particles and normal particles, the results above hold true, independent of the magnitude and particular shape of interaction. Some remarks are made on the hard-sphere interaction and on the interaction among the quasi-particles which seems necessary for the investigations of the intermediate-density Bose system.

One Boson Exchange Model in Nucleon-Nucleon Scattering. II

Abstract: In this paper we show that both proton-proton scattering and neutron-proton scattering can be explained except for the S-wave in terms of the observed mesons (p-meson, w-meson and 7}-meson) and 1=0 scalar meson with mass 500'""700 MeV. The coupling constants of p-meson and w-meson are determined. The allowed upper limit of the coupling constant of 7)-meson is obtained.

A Note on the Electronic States in Liquid Metals

Abstract: The energy spectrum of valence electrons in liquid metals is investigated with the nearly­ free-electron approximation (Ziman's picture). The spectrum in monovalent (alkali) liquid metals is essentially the free one with small increase of the density of states on the Fermi surface. In the case of polyvalent metals, the spectrum is distorted by the electron-ion interaction reflecting complicated ionic distribution. The density of states near the Fermi surface increases by a factor of about two compared to that of free electrons. The energy spectrum seems to characterize a liquid metal from others to some extent as it does a solid. Qualitative feature of several electronic properties is discussed in relation to the ionic density correlation, i.e. the structure factor of neutron diffraction of a liquid metal. Several ex­ perimental facts for the electronic structure in liquid metals, e.g. the soft X-ray emission spectrum from liquid aluminium, which are thought to be incompatible with Ziman's picture, are explained reasonq_bly from the viewpoint of nearly-free-electron approximation. The dynamical effect of the electron-ion interaction is investigated in reference to Ziman's plasma term scattering. The effect is shown to cause a mass shift for thermal properties of electrons and in the case of liquid sodium the mass shift is expected to amount to the same order as in the solid.

Cluster Expansion Theory for a System of Random Ising Spins

Abstract: The system under consideration is N Ising spins which interact through two-body exchange interactions and are randomly distributed over NL lattice points. By means of generalized cumulant expansion method, a statistical mechanical treatment of the system is made when the concentration p(=N/NL) is sufficiently low. Thermodynamic quantities are shown to be expressed in a form of cluster expansion similar to that in the theory of classical gases. As an application of the method, ne~rest neighbor ferromagnetic interactions are assumed, and the critical concentration below which there is no Curie temperature is calculated for some crystal structures and is compared with the results of other theories.

Expected Behaviour of the Dirac Monopole in the Cosmic Space

Abstract: Dirac monopoles in the cosmic space are expected to be accelerated by cosmic magnetic fields and decelerated mainly by Hubble's recession of galaxies. The estimated average energy of cosmic monopoles, carrying the Dirac's elementary magnetic charge, is 1020·4±1eV with a rather sharp differential energy spectrum. The hypothesis that most of extensive air showers (EAS) over I018eV are initiated by cosmic monopoles is not in conflict with any of previous experiments conducted in search for monopoles. Preliminary discussions about the structure of monopole initiated EAS's and about more extensive monopole ex­ periments are also given.