Table of contents

The Faddeevian regularization for the chiral Schwinger model is re-examined by means of the Hamiltonian reduction of the model together with the minimal Wess-Zumino term. It is shown to be nothing but the usual regularization with the restriction a=2.

The activation cross section and isomeric ratios for neutron capture are measured at an energy of 14.5 MeV for ¹⁸¹Ta, relative to sigma (¹⁸¹Ta(n,p)¹⁸¹Hf)=2.5 mb. Gamma-ray spectra of the product nuclei were measured with an HPGe detector. Corrections for the influence of lower-energy neutrons were determined by systematically varying the geometric arrangement. The corrected activation capture cross section at 14.5 MeV is found to be: sigma _total=1.0+or-0.2 mb, sigma _m=0.010+or-0.003 mb and the isomeric ratio is found to be 0.010+or-0.004.

The nuclear molecular resonance observed in the inelastic reaction ¹²C(¹²C,¹²C(0₂⁺)) ¹²C(0₂⁺) at energy E_cm=32.5 MeV is described in the dynamical potential model, based on a diatomic-like molecular picture. It is shown that the Morse-like potential, which was successful in describing most of the resonance states in the ¹²C+¹²C system before, can satisfactorily account for this new resonance, whose energy and angular momentum are obtained as 33.09 MeV and 14⁺, respectively. In the light of this, the evidence of six alpha -linear chain configuration of ²⁴Mg in this reaction is examined.

Fusion cross sections, mean angular momenta and partial-wave cross sections for the ⁶⁴Ni+¹⁰⁰Mo system have been determined within a multi-dimensional model and are compared with re-analysed experimental data. The proposed multi-dimensional fusion model takes into account the ion deformations during the tunnelling process through the fusion barrier and the energy dissipation. The sub-barrier fusion cross section, the mean angular momenta and the partial-wave cross sections are strongly enhanced. The agreement between the theoretical predictions and the experimental data is good.

We analyse the unification parameters M_GUT and 1/ alpha _GUT as functions of the numbers of fermion families (F) and Higgs doublets (H and H_SUSY) within the standard model embedded in SU(5) and SUSY SU(5). Analytical (where possible) and numerical solutions to first- and second-order approximations of the evolution equation for the couplings alpha _i are considered. As a result, restrictions on the unification parameters constrain F, H and H_SUSY in such a way that SU(5) is ruled out by constraints on H, and F is severely limited in SUSY SU(5).

We introduce a generalization of the relativistic eikonal amplitude originally developed to describe elastic scattering between structureless particles. The coherent and incoherent proton-nucleus scattering processes are analysed and closed-form expressions for elastic and inelastic amplitudes are derived. In particular, for the incoherent case, an energy conserving version of Glauber's theory is obtained.

It is shown that the meson-nucleus inelastic transition or reaction amplitude can be calculated by means of solving a single integral equation. This integral-equation method represents a useful alternative to solving coupled equations in the usual multichannel formalism. The method can be implemented easily for meson-nucleus reactions leading to two-body final states, eliminating the need to use the distorted-wave Born approximation. With the aid of this integral equation, the quality of the extensively employed distorted-wave Born approximation is assessed quantitatively through an example.

High-spin states were populated in ₅₄¹²²Xe₆₈ using the fusion evaporation reaction ⁹⁶Zr(³⁰Si,4n) at a beam energy of 135 MeV. The level scheme of ¹²²Xe has been extended up to spin approximately 30h(cross). The rotational bands and band crossings in ¹²²Xe are assigned within the framework of the cranked shell model. Three bands are found to lose their rotational character or to branch above spin approximately 20h(cross). This is interpreted as the collective rotation of a prolate nucleus being replaced by a regime of non-collective single-particle states at high spin. Single-particle configurations are suggested for the high-spin non-collective states using modified oscillator and Woods-Saxon potentials. The development of the nuclear shape is analysed employing potential energy and total Routhian surface calculations.

The role of the fermion-pair mixtures are studied for the Pd isotopes in the interacting-boson-plus-fermion-pair model. It was shown that the fermion-pair mixtures are important for the low-lying energy states away from the yrast line. The single-particle degrees of freedom are found to be more important for the nuclei near the closed shell for N=Z=50.

The M1 excitations in three isotope chains, ^{142,146,148,150}Nd, ^{144,148,150,152,154}Sm, and ^156,158Gd, are studied within the quasi-particle random-phase approximation using a mean field given by a deformed Woods-Saxon potential and including quadrupole-quadrupole and spin-spin residual interactions. A residual rotation-vibration coupling ensures the exclusion of the spurious state. The behaviour of the M1 strength distribution is studied systematically in the whole range of experimentally explored excitation energies and compared with the large variety of experimental information, which includes both low-lying orbital and higher-lying spin-flip 1⁺ excitations. We have found a quadratic dependence of the M1 strength summed up to 4 MeV on the nuclear deformation reproducing at the same time the main features of the low-lying M1 spectra. The double-peaked structure of the spin M1 strength distribution found experimentally in several nuclei is qualitatively reproduced and interpreted as isoscalar and isovector peaks.

The production of light photons during beta decay in condensed media is investigated. The internal and external bremsstrahlung processes are considered as mechanisms for the light emission. It has been found that the total number of photons depends on the end-point of the beta spectrum and on the media characteristics. The degree of circular polarization (CP) of the bremsstrahlung light photons emitted during beta decay is analysed. It is suggested that CP of light bremsstrahlung may serve as an additional source of information about the features of the weak interaction in nuclei.

Theoretical upper limits for the neutrino-majoron coupling constant, g, are extracted from a systematic calculation of neutrinoless double-beta decay rates for transitions in ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ¹²⁸Te, ¹³⁰Te and ¹³⁶Xe. The nuclear wavefunctions which we have used to compute the theoretical bounds on g have been tested in calculations involving two-neutrino and neutrinoless double-beta decay rates. The resulting value is of the order of g approximately=10^-4, in good agreement with recently reported data by the Heidelberg-Moscow-LNGS collaboration.

We extend the exotic decay half-life calculations of our previously reported model to include decays from odd-A nuclei and decays where the experimental determination of the mass of the emitted ion is ambiguous. We also present calculations for the decay ¹¹⁴Ba to ¹⁰²Sn+¹²C which is currently being studied, so that we have now made predictions for the half-lives of all exotic decays for which positive experimental evidence of detection is extant. We find that the decays from even-even nuclei are well described by our model as ground-state to ground-state transitions, but that the decays from odd-A nuclei appear to involve predominantly an excited final state.

Besides the Fokker-Planck or master equation approaches, the growth of fluctuation for nucleon transfer processes can be studied by the method of dynamical trajectory simulation within the framework of the "nucleon exchange model". Identifying this simulation process as a continuous-time random walk, it is possible to construct a generalized transport equation which can be used to investigate the validity of the Markovian approximation. By analysing the ⁵⁶Fe+¹⁶⁷Ho we have estimated the time up to which the process exhibits non-Markovian features.

We study the temperature and angular momentum dependence of the shell effects in the fissioning nucleus by means of a theoretical analysis of the total fission probability. We find clear evidence of the disappearance of the shell correction to the fission barrier with both increasing spin and temperature and propose a general method to determine the level density at the saddle-point configuration. The results of the present study might explain the differences between the fission barriers extracted from the heavy-ion reactions and those obtained using light-particle induced fission.

For the example of bremsstrahlung production, we discuss the solutions of general two-particle phase-space integrals, which determine the cross section of the production.