Table of contents

The Schwinger model is solved in an arbitrary gauge and for any temperature.

The functional stochastic quantisation scheme is employed to show how gauge fixing enters through the initial conditions of the associated Langevin equation of the group variables in the context of an SU(2) gauge theory. The natural emergence of the Faddeev-Popov determinant from the underlying Fokker-Planck dynamics is also demonstrated.

FCC model predictions of nuclear RMS charge radial values are compared with empirical data for 341 isotopes across the periodic table. Using only one adjustable parameter the mean error is 1.55%, as compared with 1.42% in the extended liquid-drop model where three such parameters are required. The FCC model also implies a diffuse nuclear surface, a feature that demands ad hoc adjustments in other models, but is inherent in the FCC build-up procedure.

The contention that one can determine the deuteron asymptotic D-state to S-state wavefunction ratio from sub-Coulomb stripping experiments is investigated. It is shown that the measured quantities are largely insensitive to non-asymptotic properties of the deuteron wavefunction.

Exact formulae for the lowest-order electromagnetic corrections to polarised electron-muon elastic scattering were obtained. The calculations were carried out in Lorentz-invariant form without any approximations.

The inclusive reaction pi ^-Be to phi +X has been studied for 0<or=x_F<or=0.4 and p_T²<or=3.0 (GeV/c)² at 85 GeV/c incident momentum. Differential cross sections d sigma /dx_F and d sigma /dp_T² are presented and it is found that the naive parton model as used by Daum et al. (1983) does not give an adequate description of the data. Furthermore, no significant excess of strange particles is found associated with phi production. The inclusive cross section for the reaction is calculated and found to be 1826+or-29 mu b per Be nucleus. Assuming a linear dependence on the atomic mass number, A, this corresponds to a value of 202+or-3 mu b per nucleon for the above process.

The p(³He, t) Delta ⁺⁺ reaction is considered to proceed in one step where through the exchange of one pion and one rho boson the target proton is converted into the Delta ⁺⁺. Calculations are presented in the DWBA for the angular distribution, energy spectrum at 2 GeV incident energy and the four-momentum transfer (t) distribution for 1.5-2.3 GeV. These results are compared with the experimental data. The model is found to be quite successful.

The nucleon sum rule is calculated for inelastic electron scattering from nuclear matter in the non-relativistic limit. The effect of short-range correlation (SRC) is presented by using LOCV calculations and the Reid soft-core potential. It is found that the non-relativistic version of Bjorken scaling sets in at a momentum transfer of about 1.1 GeV/c and SRC improves the Coulomb sum rule.

The ground-state energy of an atomic nucleus with asymmetry beta is considered to be equivalent to the energy of a perfect sphere made up of infinite nuclear matter of the same asymmetry plus a residual energy eta , called the local energy. eta represents the energy due to shell, deformation, diffuseness and exchange Coulomb effects, etc. Using this picture and the generalised Hugenholtz-Van Hove theorem of many-body theory, the previously proposed mass relation is derived in a transparent way in which eta drops away in a very natural manner. The validity of this mass relation is studied globally using the latest mass table. The model is suitable for the extraction of the saturation properties of nuclear matter. The binding energy per nucleon and the saturation Fermi momentum of nuclear matter obtained through this model are 18.33 MeV and 1.48 fm^-1 respectively, which agree with the recent many-body calculations of Day (1983). A recurrence relation for eta is derived and is found to have an excellent extrapolation property. Using this property and the energy of the sphere of infinite nuclear matter, it is shown in several representative cases in the periodic table that the masses of nuclei in the far unknown region can be reliably predicted.

A nuclear fluid dynamical model, which takes into account the effect of temperature and allows for transverse flow, is derived from a variational principle. The evaporation as well as the fractions of liquid and vapour phases of hot nuclei are investigated. The temperature dependence of the electric and magnetic modes is calculated. The results obtained for magnetic modes are compared with predictions based on sum-rule arguments.

The possibility of shape coexistence within the selenium isotopes and the general features of their structures have been examined within the framework of the DDM, IBM-1 and IBM-2. New data on ⁷⁶Se and ⁷⁸Se were obtained from gamma -ray and IC electron transitions. Levels and transitions in ⁷⁶Se were studied following the beta decay of oriented ⁷⁶As which had been dissolved in iron and cooled to 10.4 mK. The measured anisotropies of gamma transitions provided the multipole mixing ratios of 18 transitions, and previously proposed substantial L=0 mixing in three first-forbidden beta transitions was confirmed. Gamma-ray directional correlations and the IC electron spectrum of transitions in ⁷⁸Se were measured following thermal neutron capture by ⁷⁷Se. The correlation experiments gave the spins of 18 levels and the multipole mixing ratios of the more intense gamma -ray transitions. The good resolution electron spectrum allowed E0 transitions to be identified and also allowed the evaluation of IC coefficients and of X(E0:E2) ratios for Delta I=0 transitions. The 2⁺ levels at 1.778 MeV (⁷⁶Se) and 1.996 MeV (⁷⁸Se) appear to have the features characteristic of the lowest mixed-symmetry state in a vibrational-like nucleus. The level energies, B(E2) ratios, multipole mixing ratios and X values are compared with the results obtained from the DDM and IBM. The comparisons between theoretical and experimental data are extended to even-even selenium isotopes in the range A=72 to 82.

Double beta decays ( beta beta ) from the ⁷⁶Ge ground state (0⁺) to the 0⁺ and 2⁺ states in ⁷⁶Se have been studied by means of a 171 cm³ Ge detector surrounded by a 4 pi -geometry NaI detector for 8621 h at the Kamioka underground laboratory. All beta -ray signals from the Ge detector and gamma -ray ones from the NaI detector were recorded on magnetic tape with a list mode, and were used to select candidates of beta beta events from background events. Lower limits on the neutrinoless double beta decays (0 nu beta beta ) are obtained as T₁2/^{0 nu} 0⁺ to 0⁺)>0.73*10²³ year and T₁2/^{0 nu} (0⁺ to 2⁺)>0.57*10²³ year at the 68% confidence level (CL). The limit on T₁2/^{0 nu} (0⁺ to 0⁺) gives an upper limit on the Majorana neutrino mass of (m_nu )<1.8-4.7 eV, depending on the matrix elements used. The 0⁺ to 2⁺ 0 nu beta beta is due to the right-handed weak current. The present value gives the most stringent limit on the T₁2/^{0 nu} (0⁺ to 2⁺). The lower limit on the half-life for the 0⁺ to 0⁺ 0 nu beta beta process accompanied by the Majoron is T₁2/^{0 nu M}(0⁺ to 0⁺)>2*10²⁰ year. This leads to an upper limit on the coupling strength with the Majoron field as mod (g_B) mod <(0.7-1.8)*10^-3. The lower limit on the half-life for the two-neutrino beta beta is T₁2/^{2 nu} (0⁺ to 0⁺)>1*10²⁰ year.

High-spin states in ¹⁵⁹Er and ¹⁶⁰Er have been populated using the ¹¹⁶Cd+⁴⁸Ca reaction at a ⁴⁸Ca bombarding energy of 210 MeV. Gamma rays were detected in an array (TESSA2) of six escape suppressed germanium spectrometers and a 50 element BGO multiplicity and summed energy detector. Decay scheme and angular correlation data for these nuclei were deduced from the gamma - gamma -BGO coincidence data. In ¹⁵⁹Er the yrast band has been identified up to I^pi =89/2⁺ and three side bands have been observed to 69/2^-(77/2^-), 43/2⁺ and 51/2^-(59/2^-). In ¹⁶⁰Er the lowest energy positive-parity band has been observed up to 38⁺(40⁺) and the two lowest energy negative-parity side bands up to 40^-(44^-) and 39^-(41^-). The ground state level sequence has been observed up to (28⁺). The spin and parity of the low-lying states (I<20h(cross)) in the bands observed in ¹⁶⁰Er were established by measuring gamma -ray angular distributions and internal conversion coefficients following the ¹⁴⁸Nd(¹⁶O, 4n) reaction at a beam energy of 80 MeV. The band structures can be understood in terms of aligning quasiparticles using the cranked shell model. The alignment of the first pair of h_11/2 protons is observed in the three lowest energy bands in each nucleus. The increase in crossing frequency of this alignment with neutron number is further evidence for the increase in deformation for the light Er isotopes. Evidence is presented for the competition of favoured single-particle configurations with the collective structures at the highest spins.

Extensive air shower (EAS) experimental data have been analysed, as registered by the Tien Shan array during an effective running time of 17951 h. It is shown on the basis of EAS, with few muons with energy E_mu >5 GeV and in high energy hadrons, that there exist gamma quanta in the primary cosmic radiation at energies approximately 10¹⁵ eV. The primary gamma-quanta flux is estimated as I_gamma (>4*10¹⁴ eV)=(3.4+or-1.2)*10^-13 cm^-2 s^-1.