Table of contents

Using Schwinger-Dyson equations the author obtains the full photon and electron propagator of massless QED₂ (Schwinger model). The extension of the method to massive QED₂ is discussed.

The authors show that, in the framework of a purely fermionic model, the smallest gauge group which has acceptable fermion representations is SU(16). The simplest embedding of SU(5) into SU(16) implies a maximum number of three chiral families of fermions.

The comparison of secondary stars induced in emulsion by ⁵⁶Fe primary beams at Bevalac energies of approximately 2 GeV/nucleon with primary stars of ³He and ⁴He of the same energy shows a clear difference in the angular distributions of the target fragments as well as in the multiplicity distributions. Moreover, a cut in the secondary alpha data set at a distance D from the point of emission exhibits the peculiar behaviour of those alpha stars which are produced near the emission point. A connection with the anomalon effect seems to be obvious.

The Q value of the reaction ¹¹B(t, p)¹³B has been found to be -233.36+or-1.00 keV, leading to an improved value of the mass defect of 16562.17+or-1.04 keV. The isobaric multiplet mass equation is testing for the A=13 quartet.

Two form factors of ¹²C have been calculated with projected Hartree-Fock functions using the Gartenhaus-Schwartz (1957) and the Tassie-Barker (1958) methods for the separation of the centre-of-mass motion. Comparison of the results gives a justification for using the simple Tassie-Barker method for many light nuclei.

Utilises previous work on the Weyl group (i.e. Poincare group plus dilations), whode unitary irreducible representations describe off-mass-shell relativistic particles, to give a group-theoretically sound basis to the (classical and quantum) theory of the massless relativistic string in d dimensions in both the centre-of-mass gauge and the light-cone gauge. The author defines the centre-of-mass oscillator variables alpha _m^mu (P)=L^-1(P)_nu ^mu alpha _m^nu and shows that in the centre-of-mass gauge, alpha _m⁰(P) approximately=0, the oscillators alpha _mⁱ(P) satisfy a fully constrained off-mass-shell Dirac bracket of the same form as found by Bardeen, Bars, Hanson and Peccei (1976) for d=2. In the quantum theory covariant solution, the author explicitly constructs all the states up to N=2. The author constructs another set of non-covariant oscillators A_m^mu (P) by applying an infinite D+M^0(d-1) transformation to alpha _m^mu (P). There are two different light-cone gauges given by A_m⁺(P) approximately=0 and A_m⁺(P)/(P²)^1/2 approximately=0, which for P² approximately=0 are first class and second class respectively. For P²not approximately=0 they are both second class, and the fully constrained off-mass-shell (Weyl group) Dirac brackets close correctly only for P² approximately=M² and A_m^-(P) approximately=0. The author emphasises that the fundamental difference between the centre-of-mass and light-cone gauges is that, in the light-cone gauges, the constraints L_n approximately=0 are dilatation non-invariant. In the quantum theory elimination-of-variables solution, the author explicitly constructs the eigenstates of the principal spin invariant up to N=3, and shows that they are off-mass-shell continuous spin particles which form spin multiplets only for p²=(N-1)/ alpha ' and p=26. In the quantum theory covariant solution, the author explicitly constructs all the states up to N=2, and shows that for p²=(N-1)/ alpha ' and d=26 the N=2 transverse states are equal to the centre-of-mass gauge physical states plus null states, a result conjectured to be true for all N>or=2.

A shell-model calculation including the complete 1p, 2s, 1d, 2p and 1f shells was performed for the non-normal parity states of the nuclei ¹⁸O and ¹⁸F. The basis is confined to 1h(cross) omega excitations. The nucleus ¹⁶O is assumed to be the core. The spurious states have been eliminated. The two-body effective interactions were chosen from previous works. Spectroscopic factors and EM transition rates were also calculated and compared with the observed values.

Energies, electromagnetic transition probabilities, electric and magnetic moments and spectroscopic factors of positive-parity excited states in the nuclei ^159,161Dy are calculated using the core-quasiparticle coupling model. The energies of all the observed levels in ¹⁵⁹Dy and ¹⁶¹Dy are reproduced by the theory. Calculated spectroscopic factors for the reactions (d,t) and (d,p) are in agreement with experiment. Calculations using the variable moment of inertia give better results that those treating the core as a rigid rotor.

The interaction potential between two heavy ions calculated in the energy-density formalism has been analysed. The elastic scattering angular distributions of a few systems have been calculated and compared with experimental data. The imaginary potential parameters were found by fitting. The evaluation of the general behaviour of the real potential was made by calculating the s-wave fusion barriers and by comparing the value of a proximity parametrisation of the potential at the critical radius with that obtained with a phenomenological Woods-Saxon potential for a wide range of reactions. In all the instances mentioned above the authors have also studied the influence of the Weizsacker correction to the kinetic energy density.

Angular distributions for the elastic and inelastic scattering of ¹²C at 80 MeV by ⁸⁸Sr and of ⁷Li at 36, 42 and 48 MeV by ⁵⁴Fe have been analysed. The optical potentials of ¹²C and ⁷Li ions are calculated in terms of the alpha-particle and triton optical potentials. Coupled-channels calculations using these potentials are performed. Good fits to the experimental data and the phenomenological calculations are obtained for ¹²C projectiles.

Potential energy surfaces for fission studies of a model rare-earth nucleus are calculated in a constrained, static Hartree-Fock approximation using both single-centre and two-centre trial functions. Difficulties in interpreting the results in terms of a fission barrier are discussed. The time evolution of the static configurations boosted by a quadrupole velocity field is studied within the framework of the time-dependent Hartree-Fock theory. Single-centre configurations exhibit a rapidly damped oscillatory behaviour while two-centre configurations can be induced to fission. It is clear that the extreme mean-field picture is inadequate to describe the fission process. The failure lies principally with the single-determinant approximation. Any process, such as pairing, which causes a mixing of determinants will ameliorate the problem. It is not clear which degrees of freedom should be invoked in order to obtain an optimal description of the fission phenomena.

The ratios of partial widths for neutron emission and fission, Gamma _n/ Gamma _f, corresponding to a certain excitation energy E* of heavy nuclei, are extracted from the experimental cross sections for (HI, xn) reactions. The energy dependence of the ratio Gamma _n/ Gamma _f is investigated in the range 7<or=E*<or=70 MeV. It is shown that shell effects disappear in heavy nuclei for E*>or=30 MeV. The liquid-drop fission barriers of transuranium nuclei are obtained from the high-energy data.

The sign of the g factor of the 5.241 MeV 5/2⁺ state in ¹⁵O has been determined in an integral transient field measurement in thick iron using the ³He(¹⁶O, alpha )¹⁵O reaction. After correcting for beam bending the measured rotation was -2.33(85) mrad and a positive moment is assigned to this state. The g factor of the mirror 5.270 MeV 5/2⁺ state in ¹⁵N has been measured by observing the hyperfine modulation of the gamma -ray anisotropy in hydrogen like ions recoiling in vacuum following the ¹H(¹⁸O, alpha )¹⁵N reaction. From the measured spatial frequency the g factor was deduced to be mod g mod =0.94(7). A simultaneous lifetime determination for this state gave a value tau =2.49(24) ps. Combination of these results with previous measurements establishes a value for the isoscalar g factor of g₀=+0.60(4).

Angular distributions have been measured for the ³⁰Si(d, p) ³¹Si reactions and for ³⁰Si(d, d) ³⁰Si elastic scattering at 10 and 17 MeV. Fourteen states not previously observed in ³¹Si are reported. The l assignment for the state at 6.111 MeV (l=(1, 2)) is different from that obtained previously. Investigations of the reaction mechanism indicate that contributions from single- and multistep direct reactions and compound-nucleus processes are necessary to account for the measured cross sections. It is also found that neither the magnitude nor the distribution of the measured spectroscopic strength can be reproduced by shell-model calculations using a full (s, d) basis.

The lateral distribution of Cerenkov light intensity from EAS at sea level has been calculated and its dependence on the distance to maximum development, H_m, investigated. The distribution separates into two regions: outside approximately 125 m radius, the intensity Q decreases as R^{- gamma} with gamma dependent on H_m as found previously; more important, inside 125 m, the steepness decreases markedly for showers with large values of H_m. Several functional forms, for example an exponential Q(R) approximately e^-bR and a power law (R+R₀)^{- gamma} as well as the intensity ratio Q(50)/Q(150), were tried to define the shape in this region. The parameter b and this intensity ratio are equally suitable estimators for H_m les than 5 km. For H_m>or approximately=5 km, where the shape becomes sensitive to the late development of the shower, to the presence of aerosols and to the photocathode spectral response, the ratio is preferred. Typical errors expected are Delta H_m>or approximately=0.4 km below 4 km, increasing to >or approximately=1 km near H_m approximately 7 km. Differences between this theory and that of McComb and Turver (1982) are discussed.

The average multiplicities of charged hadrons produced in p-p collisions have been deduced using newly parametrised inclusive cross sections. A substantial improvement has thus been achieved in the estimation of the average hadron multiplicities. In particular, at very low energies close to the production thresholds for pi ^+or- and kappa ⁺, the result is consistent with the corresponding exclusive reaction data under charge and baryon-number conservation. It is also observed that there is some evidence of a real discrepancy between the bubble chamber method and the counter method for measuring multiplicities. The average multiplicities of the produced neutral hadrons are also discussed in correlation with those of charged hadrons.