Table of contents

The microscopic-macroscopic method Nilsson and Strutinsky is used to calculate potential energy surfaces with the modified oscillator potential for both neutron deficient, beta-stable and neutron excess nuclei. These calculations reiterate the previous suggestion that in the medium mass nuclei with A ∼ 70-140 moderate deformation results from the cooperative formation of a potential minimum from the anti-shell effect at zero deformation and the rising potential energy of the liquid drop at positive deformation. Regions of deformation suggested by these calculations are for example the neutron excess ₃₈Sr and ₄₀Zr, the neutron deficient ₅₆Ba and rare earth nuclei, and a region of more transitional character, involving the neutron deficient nuclei with proton numbers Z ≃ 36-38. The experimental situations are briefly reviewed for these nuclear regions and the calculations used as a guide to suggest additional experiments. Other regions of nuclear deformation are also discussed briefly.

We study nuclear potential-energy surfaces, ground-state masses and shapes calculated by use of the Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential for 4023 nuclei ranging from ¹⁶O to ²⁷⁹112. We present an overview of the results in the form of four colour contour diagrams vs. proton number Z and neutron number N. The four diagrams show calculated values of |₂| and ₄ at the ground state, ground-state microscopic shell-plus-pairing corrections and the deviations between experimental and calculated masses. The diagrams vividly display the regions of magic and deformed nuclei. In particular, the plot of |₂| vs. Z and N clearly shows the well-known deformed actinide and rare-earth regions and the two new deformed regions around A = 80 and A = 100. The plots indicate differences between the various deformed regions. For instance, there are differences in the magnitude of the deformation and in the character of the transition from spherical to deformed shapes. We discuss extensively the transition from spherical to deformed shapes and study the relation between shape changes and the mass corresponding to the ground-state minimum, and the significance of additional minima in the nuclear potential-energy surface. For a few illustrative cases we discuss the effect of angular momentum on the nuclear shape. The calculated values for the ground-state mass and shape show good agreement with experimental data throughout the periodic system, but some discrepancies remain that deserve further study.

Numerical results to the Higgs scalar equation and the sine-Gordon equation with cylindrical symmetry are reported. Two separated energy regions are found where a Higgs kink develops into pulsons when reaching the origin r = 0, while only for higher energies a reflection is observed. The pulsons to both equations are studied in detail by modifying the initial kink shapes. In comparison with the spherical pulsons the cylindrical ones are extremely long-lived. For amplitudes slightly below half the distance between two (neighboured) vacua of the theories no decrease of the amplitudes and no perceivable radiation have been obtained by the numerical solution, examined during a time of order 1000. On the other hand, "heavy" sine-Gordon pulsons (with amplitudes 3π ∼ 4π) are found to decay fast during a time t ≈ 100 in cylindrical symmetry.

Data on multiplicity distribution of charged shower particles produced in 400 GeV p-Em interactions have been analysed by using a single scaling function. On comparing the findings of the present work with those obtained earlier by other workers using different projectiles in the energy range ∼ (19-405) GeV, it is observed that the scaled multiplicity distribution is independent of the nature and energy of the incident particle. It has further been noted that the multiplicity distribution is independent of N_h and hence v.

The relation between the virial and the potential energy of a closed system leads to the simple specific hydrogenic independent particle model of the atom, which is closely related to the Hartree-Fock model. The single particle potential energies are conveniently split into local and nonlocal parts. A simple algorithm is proposed for the evaluation of the effective charges Z_i, describing individual electrons. As an example, the ionization energies of L- and M-shell electrons thus determined are compared with experimental ones.

The behaviour of atoms in superstrong magnetic fields of the order of 10¹² G is investigated. As a first step, ground-state energies of hydrogen-like and helium-like atoms are calculated and compared with earlier results. Two different approaches are tried for the hydrogen atom; a variational calculation for so-called tightly-bound states and a perturbation-theory approach for so-called hydrogen-like states. In the first case, we make an adiabatic approximation where we neglect effects of the Coulomb interaction in the plane perpendicular to the magnetic field, and in the second case we assume the solution in the direction of the field to correspond to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals" which are mainly "magnetic" in their spatial form.

Ground-state energies and ionization energies are tabulated for field strengths ranging from 10¹⁰ G to 5 × 10¹³ G. At 10¹² G, for instance, the binding energy of a hydrogen atom is changed from - 13.6 eV to approximately - 150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from - 79 eV to approximately - 610 eV, also in reasonable agreement with other calculations. Ionization energies for the "outer" electron are found to be approximately 27 eV for H^--atoms and 220 eV for He-atoms in a magnetic field of 10¹² G.

The absorption spectrum of SrD in the region 7200-8000 Å has been photographed at high resolution. The rotational analysis of seven bands of the A²Π-X²Σ⁺ system has been carried out. Effective rotational constants of the A state are given, as well as equilibrium vibrational and rotational constants of both the A and X states.

The theory of ultrarelativistic gyromagnetic autoresonance is developed with emphasis on destabilizing effect of synchrotron radiation on the particle dynamics. A special regime in which the acceleration, due to the rotating electric field, is nearly or totally compensated by deceleration, due to the radiative braking (Photon Factory Regime) is investigated. The main results are: (1) the Photon Factory Regime is unstable when acceleration and radiative retardation are strictly compensating each other, (2) the phase stability is restored if the magnetic field is maintained at a level slightly lower than that in the case of exact compensation.

A nonlinear rate equation describing nonlinear. explosive type interaction of waves in plasmas is studied, assuming that amplitude saturation occurs due to nonlinear frequency shifts. Emphasis is put on the space dependence of the solution caused by the assumption of a given initial amplitude distribution in space.

An analysis is given of the problem of repetitive peaks governed by the nonlinear rate equation for the time development of the amplitudes of plasma waves and by a Lorentzian shape distribution of the initial amplitudes. We find for the one-dimensional case that the peaks developed by explosive instability move in the direction of lower initial amplitude values, and we determine the speed and the repetition rate of the peaks.

The possible forms of equilibria for the nonlinear rate equation in the explosive case are also studied, including, in addition to the quadratic nonlinearity, diffusion and linear damping effects.

A solution to the nonlinear rate equation including diffusion is also given for the case where the quadratic nonlinearity represents recombination.

The formation and subsequent evolution of a plasma in space and time is considered in a cylindrical case assuming the coefficients of ionization, recombination and diffusion to change in time. The results indicate how the development of the radial distribution of the plasma density depends on the time variation of the coefficients of the plasma reactions and diffusion.

The possibility of accounting for time-dependent coefficients in a non-linear rate equation, including a source term, is studied in circular cylindrical geometry. It is shown that the equation can be transformed to a form which allows for a simple particular solution, provided a certain combination of the time-dependent coefficients is a constant, or nearly a constant. The relevance of the solutions for describing the evolution of a plasma in the ionization phase is considered.

The complex ray tracing method is explained by an analytic continuation of the WKB method in complex space. The complex ray tracing technique is demonstrated in detail by the study of wave tunnelling through a barrier in which the square of the effective refractive index is zero at two boundaries in a stratified parabolic ionosphere. The caustics for the tunnelling wave through a parabolic layer is studied. A complex ray tracing study of the resonant tunnelling in Budden's model is carried out. The technique may be useful in the study of radio wave heating in controlled fusion experimental reactors.

The existence of a low-frequency mode of electromagnetic parametric instabilities occuring in homogeneous collisionless relativistic plasmas is predicted. The development of this mode is found to result in the generation of a quasistationary magnetic field. The hydrodynamical analysis of the mode in question is shown to require the allowance for the transport equation governing the stress tensor.

The fields from test bodies and individual charges in charged particle streams are studied by means of the equations of two-fluid hydrodynamics for charged liquids. In the presence of a current the charges of a plasma are not screened completely. In the case of a small drift velocity compared to the dispersion of the charge velocities the screening is not complete because of the forces of magnetic interaction which is a relativistic effect. In the opposite limit of a high drift velocity the interaction of charges at large distances has the character of the exchange of plasmons. The potential of pair interactions between individual charges in particle streams is calculated. This interaction is anisotropic in space; in the direction perpendicular to the velocity of relative motion it is attractive at large distances. If the electromagnetic self-contraction of the current channel together with the radiation cooling leads to the degeneration of electrons, the electron subsystem may pass to the superconducting state. The estimates using the temperature vertex function show that the transition temperature T_c may be of the order of some hundred degrees. At low electron density T_c is about 10^-3 of the Fermi energy, and falls off exponentially at higher plasma densities.

Stimulated Brillouin scattering has been investigated in the presence of the negative ions in the plasma and it is found that the growth rate of the ion-acoustic wave decreases significantly due to the negative ions.

High-pressure X-ray diffraction studies have been performed on YbH₂ up to 28 GPa. A first order phase transition from an orthorhombic structure to a collapsed hexagonal structure with c/a = 1.34 has been observed at about 15 GPa. The transition is accompanied by a 5.2% decrease in volume. Fitting the V(P) data to Murnaghan's equation of state yields the bulk modulus B₀ = 40.2 GPa and its pressure derivative B'₀ = 4.75 for the orthorhombic phase. For the hexagonal phase we find the bulk modulus to be B = B₀ = 138 GPa independent of pressure, i.e. B'₀ = 0.

The simultaneous doses of thermal and gamma-irradiation have been used as external perturbations for producing a controllable concentration of defects in a-As₄Se₃Te₃. The investigation is made by systematic measurements of the electrical conductivity (over the temperature range from 350 K down to 77 K), X-ray diffraction (λ = 0.1542 nm), and DTA.

Results present evidence for structural defects creation increasing with the dose rate till a saturation value is approached. At thermal annealing temperature T_a = 413 K, a-As₄Se₃Te₃ went to saturation near 1.5 × 10⁶ rad, and for T_a = 493 K at 3 × 10⁴ rad. The change in the X-ray diffraction patterns and the DTA thermograms for samples irradiated at T ≲ T_g = 410 ± 1 K indicate an even relaxed "amorphous" state is produced. Radiation-induced structural transitions, however, have been observed upon annealing near or above the crystallization temperature T_c = 493-535 K, where the activation energy of crystallization is amounted to be 1.2 ± 0.1 eV.