Table of contents

The equivalence of the functional stochastic quantisation scheme and the canonical perturbation theory is established explicitly to all orders in the context of a scalar theory using a superspace approach.

A very simple semi-quantitative derivation of the Adler-Bell-Jackiw (ABJ) axial anomaly is given, based on an investigation of the absorptive part of the VVA triangle graph and dispersion relations. Essential ingredients of the author's discussion are: normal Ward identities for the absorptive part of the relevant diagram, dimensional analysis, unitarity and energy-momentum conservation. An explanation of the physical origin of the axial anomaly, offered in some earlier treatments within such a dispersive framework, is critically examined. In particular, the interpretation of the ABJ anomaly as an analogue of the Lee-Nauenberg effect occurring in the massless limit of spinor electrodynamics is shown to be fallacious.

The authors synthesize the recent deep-inelastic electron scattering data of Arnold et al. (Phys. Rev. Lett., vol.29, p.249, 1984) in terms of a two-component nuclear wavefunction based on the MIT bag model. The quarks in one component are confined to the nucleons while in the other they are free to move over the nuclear volume. An admixture proportional to A^1/3 which reaches approximately 9% for gold reproduces the experimental data well.

An MIT bag crystal model of nuclear matter is formulated. The energy bands of the quarks are calculated as a function of the overlap between adjacent bags. The authors find a clear indication of substantial overlap. Accordingly, infinite nuclear matter is more similar to a quark gas than to a nucleonic structure.

Dolinszky has observed (ibid., vol.10, p.1639, 1984) that off-shell T matrix elements can be expressed in terms of simple quadratures involving solutions of the radial Schrodinger equation. It is pointed out that this is not true in general for the K matrix. The K matrix equation for separable non-local potentials, however, can be treated by an approach similar to that of Dolinszky.

The authors propose a new cluster model for ²⁴Mg in terms of two ¹²C nuclei. They show how the model can account for the known positive- and negative-parity T=0 spectra and the K^pi =0⁺, 2⁺ interband and intraband transitions.

Absolute ground-state cross sections for ^ASe(t,p) are observed to increase about a factor of 2.5 from ⁸²Se to ⁷⁶Se. They exceed the (1g_9/2)ⁿ expectation by a factor of twenty but are in reasonable agreement with a simple model allowing excitations in 1f_5/2, 2p_3/2, 2p_1/2 and 1g_9/2 orbitals.

The recent experiments of Basile et al. (1981) strongly suggest a similarity in the mechanism of hadron production in e⁺e^- annihilation and pp collision. With this universality assumption the author proposes a simple model that demonstrates the possible inter-relationship between the charged multiplicity distributions in the processes of e⁺e^- annihilation and pp collision. The model gives a fairly good description of the data for the KNO plots, average multiplicities and the relative dispersions in both the processes up to the highest CM energy presently accessible at colliding beam machines.

The spectral structure of ⁹⁰Zr has been studied by carrying out a configuration-mixing shell-model calculation in a deformed basis using Ip_3/2, 0f_5/2, 1p₁2/, 0g_9/2 model space. A modified Kuo-Brown effective interaction has been used. The band structure for the positive- and negative-parity states has been inferred through enhanced intraband E2 transitions as compared with the weak interband transitions. The present calculation describes fairly well the observed positive-parity states including the odd-J states as well as the negative-parity states. Many high-spin states and intraband E2 transition strengths have been predicted.

The author studies a fluid dynamical model, based on the classical limit of the quantal action principle, having as its variational wavefunction the Slater determinant mod Phi )=exp((i/h(cross))( chi +s.p+¹/₂p_alpha p_beta phi _{alpha beta} )) mod Phi _f) where mod Phi _f) includes local equilibrium distortions and chi (x,t), s(x,t) and phi _{alpha beta} (x,t) are variational fields. It is shown that this model satisfies classical sum rules S₁, S₃ and S_-1, for electric modes, which are analogous to the corresponding quantal results. For magnetic modes it is also shown that the sum S₁ agrees with the quantal result and a closed expression is found for the sum S₃.

The determination of Hartree-Fock average core densities is reviewed. It is shown that the agreement between Hartree-Fock and droplet model nuclear core densities, calculated with consistent parameters, is significantly improved when the redistribution and diffuseness corrections to the droplet model are taken into account. The remaining discrepancies are correlated with the compression modulus of nuclear matter, and imply that different values of the parameters rho _infinity and Q should be obtained in Hartree-Fock and droplet model fits to experiment. The agreement between Hartree-Fock and droplet model core densities is, however, partly accidental, because larger discrepancies are found for individual droplet model contributions.

The electron capture decay of ¹⁷⁰Tm is studied using a high-resolution low-energy photon detector. The relative intensities of X- and gamma -ray transitions are reported. The capture probabilities for the ground and first excited states of ¹⁷⁰Er and also the total capture probability are calculated from the experimentally measured X- and gamma -ray transition intensities of ¹⁷⁰Er and ¹⁷⁰Yb. The total electron capture probability is estimated to be 0.177+or-0.017 and the results are discussed.

The average dispersion in arrival time of air-shower particles detected with a scintillator at an impact parameter r is described with accuracy 5-10% by the empirical formula ( sigma _t)= sigma _t0(1+r/r_t)^b, where sigma _t0=1.6 ns, r_t=30 m b=(2.08+or-0.08)-(0.40+or-0.06)sec theta +(0+or-0.06)log(E/10¹⁷ eV), for r<2 km, 10¹⁷ <E<10²⁰ eV and theta <60 degrees . (E is the primary energy and theta is the zenith angle). The amount of fluctuation in sigma _t due to fluctuations in the level of origin and shower development is less than 30%. These results provide a basis for estimating the impact parameters of very large showers with data from very small detector arrays (mini arrays). The energy of such showers with data from very small detector arrays (mini arrays). The energy of such showers can then be estimated from the local particle density. The formula also provides a basis for estimating the angular resolution of air-shower array-telescopes.

The contribution of prompt cosmic-ray muons from charmed particles to the conventional muons from pi and K mesons is investigated. The inclusive cross sections for charmed-particle production are given in both non-diffractive and diffractive processes of primary-air collisions. The minimum contribution is determined by charmed-particle production only in non-diffractive processes. On the other hand, the maximum contribution is estimated by stressing the diffractive characters of the charmed particles produced. By solving the diffraction equations including the above cross sections, the energy spectra of the prompt cosmic-ray muons at sea level are given. The integral intensities of maximum and minimum prompt muons are equal to the vertical conventional one at about 15 and 290 TeV, respectively.

Determination of the cosmic-ray muon energy spectrum above 100 TeV by observing extensive air showers from the horizontal direction (HAS) has been carried out at Akeno for four years. No definite shower of muon origin with size above 10⁵ has been observed at zenith angles above 60 degrees . The upper limit of HAS intensity is 5*10^-12 m^-2 s^-1 sr^-1 (90% confidence level) for sizes greater than 10⁵. This value indicates that the upper limit of the muon flux above 100 TeV is about 1.3*10^-8 m^-2 s^-1 sr^-1, which is in agreement with that expected from the primary spectrum with a 'knee', assuming scaling in the fragmentation region and 40% protons in the primary beam. It also implies that the critical energy at which a muon flux from prompt processes (decay of charmed particles) takes over from that due to conventional process (decay of pions and kaons) is higher than 100 TeV in the horizontal direction.