Search

The question whether an accidental degeneracy in quantum mechanical system always implies the internal symmetry group of the system is probed by means of the simple 'model of the three·dimensional harmonic oscillator with a constant spin-orbit potential: H = (1/ 2)(p2+ r2)+ ;\6' L. For the fixed values of ;\ = += 1, this model has an interesting degeneracy of remarkable regularity; in particular, the ground state is infinitely degenerate, consisting of all the nodeless j = 1 ± 1/ 2 states. In order to systematically seek the symmetry group, we first investigate the full dynamical group of the system. To our surprise, we find that the· dynamical group of our system for .an arbitrary value of ;\ is the graded 5p(6R) - a supergroup extension of the dynamical group 5P(6R) of the three-dimensional harmonic oscillator. We find the graded 5U(3) as its subgroup, which is a supergroup extension of the well-known symmetry group 5U(3) of the harmonic oscillator. It is further shown that there exists a natural group chain, gr5P(6R)~5P(2R) XgrO(3), which corresponds to the group chain 5p(6R)~5p(2R)X 0(3), where x denotes the direct­ product. Next, we examine whether any subgroup of the full dynamical group constitutes the symmetry group of the system responsible for the accidental degeneracy. It is shown that there is no such a symmetry group in the system and that, instead of the symmetry group, there exists a special, simple algebraic structure which is essentially responsible for the accidental degeneracy.

Nuclear electroexcitations above the giant resonance energy· region in electron scattering are studied using the quasielastic model. A realistic Woods-Saxon single· particle potential is used in the calculation. The excitation. functions Jor large as welL as small momentum transfers to nuclei are well explained within our model. The position and the width of the quasielastic peak are shown to reflect the binding energies of deep hole states. Our result supports values of the binding energies obtained by the recent (e, e' p) experiment. A scal­ ing hypothesis is considered to connect experimentaJ data on different momentum and energy transfers and use of ,such a hypothesis is discussed in. making an estimate of the non-resonant background term in the giant resonance region.

En employant le formalisme de superespace, on construit un modele de mecanique quantique supersymetrique dans l'espace a 3 dimensions. On peut considerer que ce modele decrit le mouvement d'une particule a spin dans des potentiels central et tensoriel a un corps, dont l'ensemble est determine par un seul superpotentiel. On etudie le modele le plus simple obtenu en prenant le superpotentiel harmonique. On montre que la supersymetrie est une symetrie exacte de ce modele et que le modele possede le supergroupe SU(3/3) comme groupe de symetrie maximale

Possible existence of the universal V=t=A coupling and the global symmetry in the non­ leptonic hyperon decays is discussed. The observed deviations from the expected symmetries in actual decays are explained as effects due to the mesonic structure of hyperons. In a close relation with the idea of the global symmetry a new isotopic spin is defined, which is 1/2' for all the baryons and integer for K. The conservation law of this isotopic spin is satisfied in the non-leptonic decays.

資料番号: SA1004713000

We study those restrictions upon the branching ratios of different decay modes of ${\ensuremath{\Sigma}}^{+}$, ${\ensuremath{\Lambda}}^{0}$, and ${\ensuremath{\theta}}^{0}$ imposed by the invariant property of a system composed of nucleons, pions, hyperons, and heavy mesons under the Wigner time reversal. These restrictions give, in fact, upper and lower limits on the various branching ratios. Later, we use a more or less specific model of hyperons and $\ensuremath{\theta}$ mesons in order to get other possible restrictions on the branching ratios. These results are model-dependent, and subsequently provide a possible test of the model we have chosen.

A simple model for the nucleon-antinucleon interactions is presented, in which the nucleon or the antinucleon is regarded as composed of two parts, the pion cloud and the " core". The latter is characterized by two properties : i) it acts as a n.early black body for an incoming antiparticle wave, and ii) its characteristic time for ato.nihilation is much shorter than the oscillation period of the outer pion cloud. These simple assumptions lead to natural semi-quantitative explanations of the salient features of the experimental information so far available concerning the nucleon-antinucleon reaction and capture processes. Some arguments are added to look for a justification of such an approach.

The SIGMA /sup +/- SIGMA /sup -/ mass difference and the electromagnetic correction on the DELTA I = 1/2 law for non-leptonic hyperon snd K-meson decays are discussed, based on the assumption of charge independence for strong interactions. Simple calculation for the two phenomena reveals the difficulty that larger electromagnetic effects are needed. Various approximate conservation laws in the isotopic spin space and their implications for the understanding of non-leptonic decays are likewise discussed. (auth)

The possibility is considered that there exists a universal V-A interaction and complete symmetry in the nonleptonic decay of hyperons. The departure from the expected symmetry that is observed in actual decays Is explained by effects caused by the mesonic structure of hyperons. In close connection with the idea of complete symmetry, a new isotopic spin is defined, which is equal to 1/2 for all baryons and to 0 or 1 for K mesons. The law of conservation of this isotopic spin holds in nonleptonic decays.

The existence of a sharp pion-pion resonance is assumed for the T=j=l state at about 600 Mev. This resonance state is approximately replaced by a real T= j =1 particle p±' 0 and its interactions with the pion field and the electro-magnetic field are determined. The calculation of pion-nucleon. scatterings through pN intermediate states shows in the Born approximation that very strong attractive forces seem to exist for both T=1/2, dS/2 and T=1/2, f5/2 pionnucleon states at about the p-production threshold energy. The former is identified as the second and the latter as the third resonance 6bserved in the pion-nucleon scatterings. A similar calculation predicts the possible appearance of the second resonance and the suppression of the third one in the photo-pion productions. A tentative model for explaining the fourth maximum observed in the pion-nucleon scattering is proposed along the similar line.

An incorporation of ΔS = − ΔQ decays into the theory of weak interactions is discussed. To this end, a model of weak interactions is proposed on the assumption of intermediate vector boson fields of a particular kind. The fields represent two sets of positive, negative, and neutral charged bosons, the two sets being hermitian conjugates. The weak currents coupled to the fields are derived from the invariance of the weak interactions under two sets of gauge transformations, each set forming a Lie group of rank 1 and order 3. Various predictions of the model are consistent with experiment and further ways to test the model are discussed.

The possibility that some of the intermediate vector bosons of the weak interaction might be produced, several orders of magnitude more strongly than previously estimated, is studied. Intermediate vector bosons interact with the strangeness-non-changing baryon current, the strangeness-changing baryon current, and the lepton current. Circumstance that could give rise to copious production of the intermediate bosons are presented. (C.E.S.)