Showing papers in "Progress of Theoretical Physics in 1973"

CP Violation in the Renormalizable Theory of Weak Interaction

Abstract: In a framework of the renormalizable theory of weak interaction, problems of CP-violation are studied. It is concluded that no realistic models of CP-violation exist in the quartet scheme without introducing any other new fields. Some possible models of CP-violation are also discussed. When we apply the renormalizable theory of weak interaction1l to the hadron system, we have some limitations on the hadron model. It is well known that there exists, in the case of the triplet model, a difficulty of the strangeness chang­ ing neutral current and that the quartet model is free from this difficulty. Fur­ thermore, Maki and one of the present authors (T.M.) have shown2l that, in the latter case, the strong interaction must be chiral SU ( 4) X SU ( 4) invariant as precisely as the conservation of the third component of the iso-spin 13 • In addi­ tion to these arguments, for the theory to be realistic, CP-violating interactions should be incorporated in a gauge invariant way. This requirement will impose further limitations on the hadron model and the CP-violating interaction itself. The purpose of the present paper is to investigate this problem. In the following, it will be shown that in the case of the above-mentioned quartet model, we cannot make a CP-violating interaction without introducing any other new fields when we require the following conditions: a) The mass of the fourth member of the quartet, which we will call (, is sufficiently large, b) the model should be con­ sistent with our well-established knowledge of the semi-leptonic processes. After that some possible ways of bringing CP-violation into the theory will be discussed. We consider the quartet model with a charge assignment of Q, Q -1, Q -1 and Q for p, n, A. and (, respectively, and we take the same underlying gauge group SUweak (2) X SU(1) and the scalar doublet field cp as those of Weinberg's original model.1l Then, hadronic parts of the Lagrangian can be devided in the following way:

New Series of Exact Solutions for Gravitational Fields of Spinning Masses

Abstract: New series of solutions for space-times which are regarded as representing the gravi­ tationaL fields of spinning bound masses is derived from a series of Weyl metrics, following Ernst's formulation on axi-symmetric stationary fields. This series of solutions includes the Kerr metric as a member of the simplest one. Except in the case of the Kerr metric, the space-times have ring singularities outside event horizons, that is, there exist naked singu­ larities. Therefore, these solutions seem to give a very different picture concerning the ulti­ mate fate of 'gravitational collapse compared with a current picture such as the Israel-Carter conjecture. , The naked ring singularity may become an active energy source of gravitational wave, and yield many interesting phenomena in astrophysics.

Nuclear excitation by electron transition and its application to uranium- 235 separation

Abstract: A new mechanism for nuclear excitation is studied theoretically by considering the de­ excitation of electronic states of atom. When an electron of inner shells is kicked off by the bombarded electron or X ray, an electron of the adjacent shells immediately jumps into the vacancy. The energy corresponding to the difference of the binding energies for these two shells, E 1 - E 2, is usually carried away by the emitted characteristic X ray or the Auger electron which is ionized from an outer shell. There is, however, another possibility of this energy release by exciting a nuclear state. That is, the nuclear ground state is excited to the higher energy level by receiving the excess energy of the electronic state by means of electromagnetic interactions between nucleus and electrons. A theory is made for this process, and it is found that the probability of this process is extremely small in most of the cases, but it will be appreciable, if the interaction energy is approximately equal to the energy mismatch EN-CE1-E2), where EN is the nuclear excitation energy. An example of 28;U is discussed in connection with a possible separation of 2a;u from uranium isotopes. § I. Introduction If an atom with several electrons is excited in that an orbital electron of a lower level is raised to a higher level, an· X ray is usually emitted, while an electron of the adjacent shells jumps into the vacancy. Instead, the interactions with electrons in the higher shells lead to the ejection of latter. electrons into a continuous spectrum. This process competes with the· emission of the photon, and it is called the Auger electron emission. In this paper, we wish to point out that there is a third process of the deexcitation mechanism, which we call the nuclear excitation by electron transition. The possibility of this process may be understood as follows: In the process of deexcitation of the atomic system, an electron emits a photon. If this is a real photon, it is the X-ray emission. If the photon is virtual and it is absorbed by an electron of an outer shell, this electron is ejected to the continuous energy state, and it is called the Auger process. Under a certain condition, a virtually emitted photon is absorbed by a nucleus, and the nucleus is excited. This is shown in a more picturesque way in Fig. 1, where a line refers to the nuclear level and the lines with circles refer to electron levels. The line with two solid circles represents symbolically the closed shell with 2j + 1 elec­ trons (j being the total angular momentum of the orbital electron), and the open circle indicates an electron hole. In Fig. 1 (a) there is an electron hole with

On the Integrability of the Toda Lattice

Abstract: This paper presents a variety of computer g.enerated evidence indicating that the Toda lattice behaves remarkably like· an integrable, nonlinear system, where here integrability means that the system Hamiltonian can be brought to an obviously integrable form. In particular, we investigate Toda lattices having three and six particles, using periodic boundary conditions. While computer calculations cannot rigorously prove integrability,. the evidence presented here is sufficiently strong to provide incentive for seeking the general, closed form, analytic so­ lution or, at least, some approximation to it. § I. Introduction The. T oda lattice 1J is of considerable interest to physical scientists because it serves as an example of a nonlinear lattice system which may rigorously be shown to propagafe certain wave forms without change of shape. Moreover the propagation of such unchanging wave forms has been observed experimentally 2> in various physical systems. Additionally in the continuum limit, the T thereby connecting the theory1> o{ the Toda lattice with the KdV soliton theory8> developed by Kruskal, Zabusky, and others. For the KdV equation the unchanging wave form, called a soliton, has been shown8> both theoretically and empirically (on a computer) to be remarkably stable. · Indeed, a recent paper by Zakharov and Faddeev4> definitively establishes the' validity and the source of this stability. In particular these authors' prove that· the KdV equation is a completely integrable Hamiltonian system, where integrability 6> here means that the system Hamiltonian can be reduced to an obvi­ ously integrable (or solvable) form6> by a canonical transformation analytic in the position and momentum variables. Because of the intimate connection7> between the Toda lattice and the KdV equation, the Zakharov-Faddeev result suggests that the Toda lattice may also be integrable and its associated solutions also highly stable; however, extreme caution is needed here. For the class of nonlinear Hamiltonian oscillator systems to which the Toda lattice belongs, Siegel 8) has shown that non-integrability is overwhelmingly the general case. Moreover, Saito9> and coworkers10> have presented computer evi

On Weyl’s Gauge Field

Abstract: A new scalar field, called a measure field, is proposed which plays a role of measure assigned to each world point. By measuring all the quantities with a standard given by the above mentioned measure field, it is shown to be possible to write all the field equations in a manifestly gauge-invariant manner. Weyl's gauge field, when it is written in this fashion, is proved to have a negative energy density and has a tachyon-like property inside material particles. It is shown, however, that such a strange field can not come out of the matter.

On the Inner Repulsive Effect Due to the Pauli Principle between Nuclear Composite Particles

Abstract: The effect of the Pauli exclusion principle in the short range· part of interactions between nuclear composite particles is investigated in the case that there are some relative states which are not exactly forbidden but almost forbidden These "almost forbidden states" (AFS) are coupled only weakly t~ the incoming relative states Thus, the relative wave function is required to be approximately orthogonal to these AFS which are located in the inner region between composite particles This gives rise to a strong repulsive effect characterized by the almost energy-independent inner nodal behavior as observed in the case of a-a scattering However, at the energies characteristic of theAFS, the coupling to the AFS from the incident wave becomes very effective, and resonance-like contributions are brought about within the one-channel approximation With respect to this feature, the Levinson theorem is discussed § I Introduction The effect of the Pauli· principle is remarkably important in interactions between nuclear composite particles The interaction between a-particles pro­ vides us with a typical example The experimental phase shifts in a-a scattering are well reproduced by an energy-independent local potential at low and inter­ mediate energies?J, 2l As striking features of such a phenomenological potential, the inclusion of a strong repulsive core with a radius of about 2 fm is required for the relative s and d states·, and the attractive part outside the core is system­ atically dependent on the angular-momentum (l) By calculations with the re­ sonating group method applied· to a-a scattering,8l it has been shown that the eff·ect of the nonlocality originating from the antisymmetrization is completely responsible for the above features of the a-a phenomenological potential The presence· of the repulsive core can be understood as a result of· the almost energy-independent inner nodal behavior of the a-a relative wave function,'h 6) since the outermost nodal point coincides well with the radius of the repulsive core in a wide region of energies It should be noted ·that the inner nodal bee havior is not due to the -existence of any bound states 6 l A simple picture comprising such important aspects obtained by the res

Productions and Decays of Short-Lived Particles in e+-e- Colliding Beam Experiments

Abstract: ~harmed hadrons and so on)· in e•-e- {\pllidi!lg beam .experiments. ,form!llae which, !ll"e useful for computing the cross section for the production and subsequent decay of a single or a pair of narrow-width particles with spin ! are derived. Approximate but analytical expressions for the combined angular distribution of the decay products from such particles are derived. The production and decay of a single excited muon is alli!'o treated.

X-ray emission from white dwarfs in close binary systems

Abstract: The generation of X-ray sources in close binary systems is studied. It is proposed that one of the stars is a white dwarf and it is accreting material from its companion. The entire treatment applies to the spherically symmetric and the stationary case. The model of this type accounts qualitatively for the observed nature of SCO X-1.

Indefinite-Metric Quantum Theory of Genuine and Higgs-Type Massive Vector Fields

Abstract: On the basis of the indefinite-metric vector field theory proposed previously, Johnson's proposition that the physical mass of a vector field tends to zero as its bare mass goes to zero, is shown to be valid if the vector field couples with a charged scalar field in the minimal interaction. In the case of the theory of spontaneously broken gauge invariance, the reason why the vector field acquires a non-zero mass in spite of the above theorem is clarified. The theory of a vector field which is massive owing to the spontaneous breakdown of gauge invariance is consistently formulated in the framework of the indefinite-metric quantum field theory. In this formalism, both renormalizability and the unitarity of the physical S-rnatrix are self-evident. § I. Introduction Recently, the present author 1 l'*l has proposed an indefinite-metric theroy 2 l of a massive vector field such that as its mass goes to zero the theory smoothly tends to the Landau-gauge quantum electrodynamics.3l' 4 l As one of important consequences of this theory, we can reasonably show the validity of Johnson's proposition 5 l'**l that if the bare mass of the vector field ufo goes to zero, its physical mass must also tend to zero, provided that there are no other massless physical particles, under the assumption that the current j'\" is conserved and does not explicitly depend on ufo. On the other hand, in connection with Weinberg's theory of leptons, BJ much attention has been paid to the spontaneous breakdown of gauge invariance in the massless vector field theories. Several years ago, Higgs and others 7 l noted that if gauge invariance of the theory is spontaneously broken, the massless vector field acquires a non-zero mass, but then Goldstone bosons do not appear in the Coulomb gauge because we do not have manifest covariance, which is necessary for the proof of the Goldstone theorem. 8 l If one reconsiders this situation in a covariant gauge, in which we have to introduce indefinite metric, Goldstone bosons appear but they become unphysical. This interesting phenomenon is now called the Higgs phenomenon. Recently, 't Hoofel has applied it to the Yang-Mills *> Unfortunately, the publication of this paper was much delayed. **> Johnson's reasoning was based on the conventional massive vector field theory whose mass-less limit is non-existent.

Radiative Corrections to Asymmetry and Energy Spectrum of β Rays from Polarized Nuclei

Abstract: We have studied the radiative corrections to the angular distribution and energy spectrum of {3 rays from polarized nuclei. Explicit formulas of the radiative corrections are given for the angle-dependent and angle-independent terms and for the asymmetry factor, under the assumption of the effective current-current interaction of the V -pA type for the {3 decay. The lowest order corrections to the first two are almost the same and depend on the cutoff. The asymmetry factor of the {3-ray angular distribution is scarcely affected by the radiative corrections. In particular, these corrections are independent of the cutoff for the Gamow­ Teller transition. It is also shown that the radiative corrections to the {3-ray spectrum are consistent with those given by Kinoshita and Sirlin, and Berman and Sirlin. Numerical values of the radiative corrections are tabulated for the {3 decays, 12B-')12C+e- + :v and 12N-')12C+e+ +II.

Analysis of Alpha-Decay Widths for Molecular Viewpoints in Light Nuclei

Abstract: Alpha-decay widths of SU/sub 3/, deformed oscillator and cluster model wave functions are calculated quantitatively for the ground band levels of /sup 8/ Be and the first K = 0- band levels of /sup 20/Ne. Tails of the reduced width amplitudes of these model wave functions are amended by two methods, of which one is to connect smoothly the inner original reduced width amplitude with the resonance tail given by the release energy of alpha particle, and the other is to apply the Green's-function method developed by Kawai and Yazaki for the calculation of the radial form factor for the stripping or pick up reactions. From comparisons of the calculated results with experiments It is concluded that the SU/sub 3/ model is insufficient to reproduce large alpha -decay widths. It is further shown that the deformed oscillator model is also considered to be inappropriate for the general explanation of the (rotational) levels with large cluster widths. From these consequences on SU/sub 3/ and deformed oscillator models and by the numerical confirmation that the cluster model wave functions can naturally reproduce the experiments consistently With the variational energy calculations, the importance of the molecular viewpoint in light nuclei is emphasized. (auth)

Renormalization of the Wave-Particle Interaction in Weakly Turbulent Plasmas

Abstract: Partial summation of the perturbation terms is carried out by renormalizing the pro­ pagator of the nonlinear. Vlasov equation. The present analysis of the renormalization procedure clarifies the importance of taking into account not only the most secular terms, but also the dominant parts of the secondary most secular terms. It also accomplishes non­ trivial generalization of the previous results of Dupree and Weinstock on the modification of the wave-particle interaction.