Showing papers in "Progress of Theoretical Physics in 1970"

Generator Coordinate Treatment of Composite Particle Reaction and Molecule-like Structures

Abstract: We propose a generator coordinate method as a numerically tractable alternative to the resonating group method for treating the composite particle reaction and for the study of the molecular model of nuclear structure. Adopting the wave function used by Margenau and Brink in their a particle model as a trial function the problem of the relative motion be­ tween composite particles is discussed. We give a method of transformation of the genera­ tor function to the wave function of the relative motion, and show that the solutions of the generator coordinate method include that of the resonating group method in the interaction region. To obtain the scattering amplitude we present the formulation which uses the bound­ ary condition constraint method. As an example our procedure is applied to the phase shift calculation of the a-a scattering case, and good agreement with experiment is obtained show­ ing the utility of our method. We also discuss that the idea of the density localization in the molecular model can be adequately formulated in this method, using the fact that this method has a direct connection with the concept of intrinsic deformation. Some quantitative analyses are given of the a: particle widths of 8Be by our method of generator coordinates, providing the evidence of the molecule-like structure of this nucleus.

Nucleon Electromagnetic Form Factors at High Momentum Transfers in an Extended Particle Model Based on the Quark Model

Abstract: Taking account of the Lorentz contraction effect of the extended nucleon core as a nucleon but not as a quark, it is shown that the Gaussian inner orbital wave function can produce the form factor very close to the dipole formula.

Study of deuteron stripping reaction by coupled channel theory. ii. properties of interaction kernel and method of numerical solution.

Abstract: The purpose of the present series of papers is to study the deuteron stripping reaction in terms of the method of coupled channels in order to investigate the theoretical back ground of distorted wave Born approximation (DWBA) for the nuclear rearrangement collision which has been studied only inadequately compared with the nuclear inelastic scattering, in contrast to the great success of DWBA in the actual analysis of the experiment.

Contribution to the theory of a dilute Heisenberg ferromagnet

Abstract: A theory of a dilute Heisenberg ferromagnet is studied in two ways; the molecular field approximation and the Tyablikov approximation. By considering the Heisenberg model in the molecular field approximation, an expression for the averaged moment at any lattice site is obtained by the use of the diagram method. For a simple cubic crystal, numerical calcu­ lations of the averaged moment with a spin t host are presented. The Curie temperature depending on the concentration of magnetic atoms is presented. In the case of the molecular field approximation, it is shown that the critical concentration at which the ferromagnetic state disappears may not exist. By the use of the Green's function another method based on the Tyablikov approximation is formulated. The theory is a straightforward generalization of the previous paper published in Prog. Theor. Phys. 42 (1969), 477, to finite temperature range. The existence of the critical concentration is also indicated. In a previous paper (referred to as K) /) we have developed a spin-wave theory of a dilute Heisenberg ferromagnet by the use of the Green's function method. For simple lattices with nearest-neighbour interactions, a general forma­ lism of the Green's function was expressed in terms of a function of the con­ centration of magnetic elements. The expression for the energy was applied to determine the critical concentration for which the ferromagnetic ground state is unstable with respect to the formation of long-wavelength spin waves. The critical concentration is defined as the minimum concentration of magnetic atoms, arranged at random in a non-magnetic lattice, for which ferromagnetism will occur. Ferromagnetism is caused by exchange interaction for a greater part between neighboring atoms, and it seems there is no need to have a rigorous periodicity in the distribution of magnetic atoms. For this reason, as was firstly suggested by Gubanov, 2 ) amorphous or vitreous ferromagnets can exist at tem­ peratures low enough so that when they contain the right atoms we have reason to believe they will be ferromagnetic. In this paper, we intend to generalize the previous theory to finite tempera­ ture range in order to obtain the Curie point depending on the concentration of magnetic elements. From this approach, it seems to be possible to clarify the existence of ferromagnetism in the amorphous or vitreous states. Experimentally there are some publications opening the possibility of ferromagnetism in amor­ phous or vitreous states. 3 )

Electromagnetic Inelastic Form Factors of Processes ep →eN* in a Relativistic Extended Particle Model Based on the Quark Model

Abstract: The nucleon elastic form factors are also discussed in the same framework of the model. In particular it is shown that the neutron electric form factor appearing as a relativistic effect is consistent with existing experimental data.

Hc2 and the κ2-Parameter of a Superconductor with Cubic Symmetry

Abstract: The upper critical field Hc2 and the K 2-parameter of a pure superconductor with the cubic crystal symmetry are calculated near the transition temperature. The result obtained for I-Ic 2 is in good agreement with the experimental result of Farrell et al. It is found that the direc­ tion of the induced magnetic field is not parallel to that of the external magnetic field applied in an arbitrary direction. Therefore, the t.:: 2-parameter becomes a tensorial quantity. The ratio MxiMz is found to be about 0.015 at the reduced temperature t=0.7, where iY.lx and Mz are respectively magnetizations perpendicular and parallel to the applied external field. § l. Introduc11:im:Ji Reed et al. have experimentally shown that the upper critical field Hc2 has an anisotropic nature in several cubic type II superconductors and that the re­ lative anisotropy of Hc2 decreases as the reduced temperature t increases, and approaches zero as t-> 1. 1 ) They have attributed this nature to the anisotropy of the Fermi surface and to the non-locality of the Ginzburg-Landau equation. Hohenberg and W erthamer derived expressions for Hc2 in the nearly local limit and also in the limit of small anisotropy. 2 ) They have successfully shown that the anisotropy of Hc2 comes from the non-local correction to the original G-L equation as well as from the cubic symmetry of the Fermi surface. Farrell et al. have recently made precise measurements of the upper critical field of niobium crystal and analyzed their result assuming a four-term Kubic harmonic expression. 3 ) The calculation of Hohenberg and W erthamer in the nearly local limit contains only three-term Kubic harmonics. In this paper, we derive a theoretical expression for 1-Ic 2 involving four-term Kubic harmonics, extending the work of Hohcnberg and Werthamer to a higher order term in the non-locality. Further, we investigate a possible coupled effect from the non-locality and the anisotropic nature of the cubic crystal on the tc 2parameter. We restrict our attention to the study of 1-Ic 2 and tc 2 for a pure superconductor only near the transition temperature region (G-L region). In § 2, we will give the basic G-L equations for our system, and an expres­ sion for 1-Ic2 will be derived in § 3. In § 4 is contained the discussion of the effect of anisotropy on the induced magnetic field and also of the tc 2-parameter.

Ground State Energy of the One-Dimensional Electron System with Short-Range Interaction. I

Abstract: The ground state energy of the one-dimensional electron gas interacting via a delta-func­ tion potential is considered as a function of interaction (c) for the given magnetization. The integral equations of Gaudin and Yang are used. It is shown that the ground state energy can be analytically continued at c=O for non-zero magnetization. This fact holds also for the one-dimensional Hubbard model except for the half-filled case.

On the Singularity of Dynamical Response and Critical Slowing Down

Abstract: Phenomenological arguments on the critical slowing down is presented and "similarity law" is proposed on the indices of the critical slowing down The similarity law is confirm­ ed in linear spin chains near the critical field and in the kinetic Ising model near the critical temperature It is exactly shown in the linear spin chains that the critical index of slowing down is different from that of the static susceptibility and that the dynamical susceptibility has a logarithmic singularity with respect to the frequency at the critical field and at zero temperature Although many investigations have been made on singularities of several kinds of dynamical phenomena near the critical point, there are very few that go essentially beyond a dynamical molecular field theory and afford a unified point of view on anomalies of dynamical responses in the vicinity of the criti­ cal point The purpose of this paper is to discuss the critical slowing down charac­ teristic of dynamical critical phenomena from a unified point of view In § 2, the main results of the Kubo linear response theory 1 ) are summarized for con­ venience to discuss the singularity of dynamical response and critical slowing down in the subsequent sections In § 3, the formulation of relaxation time and its relation with dynamical susceptibility are given for the purpose of phenomeno­ logical arguments on the critical slowing down "Similarity law" on the criti­ cal slowing down is proposed as a working assumption In § 4, as an example, the dynamics of linear spin chains is investigated in detail near the critical field The rigorous analysis yields that the critical index of slowing down is different from that of the corresponding susceptibility and that the "similarity law" holds with respect to the magnetization and partial energy In § 5, we discuss the results obtained by our previous perturbational calculation 2 ) and those obtained by a computer simulation 3 ) from our point of view

Anomalies and Bound State Due to the Anisotropic s-d Exchange Interaction

Abstract: The Kondo problem for the anisotropic s-d exchange interaction is investigated in de­ taiL The scattering amplitude of a conduction electron is calculated in the most divergent approximation (Abrikosov's approximation). The importance of some types of terms over­ looked in the previous work by Miwa and Nagaoka is pointed out. By changing the degree of anisotropy of the exchange integral the behaviors of the obtained scattering amplitude­ especially the divergence difficulties-are examined. To see physical meaning of the diver­ gence difficulties the problem of the existence of the bound state realized as the ground state of this coupled many-body system is discussed by extending the Yosida-Okiji-Yoshimori theory to the anisotropic case. It is shown that the exact solution of the bound state can be obtained also for the anisotropic s-d interaction, and that the divergence difficulties stated above are closely connected with the existence of the bound state.

On the Two-Branch Structure of the Excitation Spectra in Liquid Helium

Abstract: A theory of excitations in liquid helium is developed from the first principle in connection with the new spectrum discovered by Cowley and Woods. In deriving the results a crude estimate has to be done due to computational difficulties. This paper is, therefore, limited to a qualitative theory. Gross structure of two branches of excitation is obtained; one of them is interpreted as a resonance spectrum of particle-particle scattering, while the other corresponds to the phonon-roton spectrum. Physical background of the existence of the res­ onance branch is discussed from the point of view of the Bose condensation of liquid helium.