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In view of new high-precision experiments in atomic physics it seems necessary to reexamine nonlinear theories of electrodynamics. The precise calculation of electronic and muonic atomic energies has been used to determine the possible size of the upper limit Emax to the electric field strength, which has been assumed to be a parameter. This is opposed to Born's idea of a purely electromagnetic origin of the electron's mass which determines Emax. We find Emax≥1.7×1020 V/cm.
A general formalism for the scattering of heavy ions, which is especially convenient to study the antisymmetrization effects, is developed. Antisymmetrization effects are investigated by expanding the completely antisymmetrized wave function according to the number of exchanged nucleons. The particle-core model for the scattering of nuclei with loosely bound nucleons is presented. A formula for the additional contribution to the effective potential due to antisymmetrization effects is obtained by calculating the expectation value of the Hamiltonian with intrinsic wave functions. Application of the formalism is illustrated for the 14N + 14N scattering problem and its usefulness is demonstrated.
A fully gauge-invariant, Lorentz-covariant, nonlocal, and nonlinear theory, for coupled spin-½ fields, ψ, and vector fields, A, i.e., "electrons" and "photons," is constructed. The field theory is linear in the ψ fields. The nonlinearity in the A fields arises unambiguously from the requirement of gauge invariance. The coordinates are generalized to admit hypercomplex values, i.e., they are taken to be Clifford numbers. The nonlocality is limited to the hypercomplex component of the coordinates. As the size of the nonlocality is reduced toward zero, the theory goes over into the inhomogeneous Dirac theory. The nonlocality parameter corresponds to an inverse mass and induces self-regulatory properties of the propagators. It is argued that in a gauge-invariant theory a graph-by-graph convergence is impossible in principle, but it is possible that convergence may hold for the complete solution, or for sums over classes of graphs.
The 1s bound state of superheavy atoms and molecules reaches a binding energy of -2mc2 at Z≈169. It is shown that the K shell is still localized in r space even beyond this critical proton number and that it has a width Γ (several keV large) which is a positron escape width for ionized K shells. The suggestion is made that this effect can be observed in the collision of very heavy ions (superheavy molecules) during the collision.
A continuum shell-model calculation based on the collective correlation model has been made for the giant resonance of 12C using the eigenchannel reaction theory. The low-lying negative-parity states of 11C and 11B have been taken into account by corehole coupling. Partial, total, and integrated photoabsorption cross sections are calculated for the region of the giant dipole resonance.
With the use of the cranking formula, the coordinate-dependent mass parameters of the kinetic-energy operator in fission processes and heavy-ion collisions are calculated in the two-center oscillator model. It is shown that the reduced mass and also the classical moment of inertia are obtained for large separations of the fragments. For small separations, however, the mass parameter for the motion of the centers of mass of the fragments is larger than the reduced mass by an order of magnitude.
An upper limit to the electric field strength, such as that of the nonlinear electrodynamics of Born and Infeld, leads to dramatic differences in the energy eigenvalues and wave functions of atomic electrons bound to superheavy nuclei. For example, the 1s1/2 energy level joins the lower continuum at Z=215 instead of Z=174, the value obtained when Maxwell's equations are used to determine the electric field.
The dynamic collective model has been extended to quadrupole giant resonances in spherical nuclei. The splitting of giant dipole and giant quadrupole resonances due to their coupling to surface vibrations has been calculated for Sn isotopes. Agreement with recent γ-absorption measurements of the Livermore group has been found.
A two-center shell model with oscillator potentials, l→·s→ forces, and l→2 terms is developed. The shell structures of the original spherical nucleus and those of the final fragments are reproduced. For small separation of the two centers the level structure resembles the Nilsson scheme. This two-center shell model might be of importance in problems of nuclear fission.
Higher-order effects are calculated in the framework of the eigenchannel theory for elastic and inelastic electron-nucleus scattering in the energy region 100≤E≤250 MeV. A dispersion effect of about 12% is found for the elastic scattering on Ni58 at a momentum transfer q≈500 MeV/c. For inelastic scattering, the reorientation effect is discussed, in addition to the dispersion effect. The total higher-order effect changes the form factor for a hindered first-order transition by 50% at its minima. Furthermore, the dependence of the higher-order effects on the transition potentials of the virtual excitations, the model dependence, and the dependence on the energy E of the electron and the momentum transfer q are discussed. A closed formula for the S matrix is developed by calculating the eigenchannels in stationary perturbation theory.
With a schematic model for the nuclear matter we give a unified treatment of the real and imaginary parts of the elastic O16-O16 scattering potential. The model connects the parameters of the potential with the density and binding properties of the O16-O16 system and reproduces the structure of the excitation function quite well. It is shown that the nuclear compressibility can be obtained from the scattering data, and in the case of the S32 compound system there results an effective compressibility (finite quenching of the nuclei) of about 200 MeV.
The total particle-particle SJ matrix of O16 for spin J=1- and excitation energies between 15 and 27 MeV has been calculated in the eigenchannel reaction theory for several parameters of the Saxon-Woods potential and the two-body force. The many-body problem has been treated in the 1-particle-1-hole approximation. The photon channels have been included by perturbation theory. Surprisingly, the most important structure of the experimental cross sections is reproduced quite well in this simple approximation.
The Coulomb-fission cross sections for 132Xe and 148Nd incident on 238U are calculated in a dynamical classical model. In particular the influence of nuclear forces on the cross sections is studied. Since they are counteracting the Coulomb force, they diminish the cross sections for Coulomb fission significantly and shift the Coulomb barrier towards lower energies.
The theory of collective correlations in nuclei is formulated for giant resonances interacting with surface vibrations. The giant dipole states are treated in the particle-hole framework, while the surface vibrations are described by the collective model. Consequently, this treatment of nuclear structure goes beyond both the common particle-hole model (including its various improvements which take ground-state correlations into account) and the pure collective model. The interaction between giant resonances and surface degrees of freedom as known from the dynamic collective theory is formulated in the particle-hole language. Therefore, the theory contains the particle-hole structures and the most important "collective intermediate" structures of giant resonances. Detailed calculations are performed for 12C, 28Si, and 60Ni. A good detailed agreement between theory and experiment is obtained for all these nuclei, although only 60Ni is in the region where one would expect the theory to work well (50< A <110).
The influence of the Coulomb and nuclear forces on the Coulomb barrier in heavy-ion reactions is studied in a dynamical classical model. It is shown that the fusion barrier is smaller than the conventional Coulomb barrier of two underformed nuclei. The model yields a dynamical picture of the excitation mechanism of surface vibrations and giant resonances. It is suggested that-due to nuclear forces-the excitation of the octupole mode is strongly enhanced over the excitation of the quadrupole mode in experiments at the Coulomb barrier.
Continuum structure of Ca40
(1967)
The total S1- matrix of Ca40 has been calculated for excitation energies between 11 and 28 MeV. As typical results, the (γ, p0) and the total absorption cross sections are shown and compared with experiments. It is shown that the proper treatment of the one-particle, one-hole shell-model continuum accounts for most of the observed structures.
Using the eigenchannel reaction theory we performed coupled-channel calculations for Si28 and computed the differential cross section for Al27(p, γ0)Si28 over the energy range 6 MeV<Ep <16 MeV. The obtained angular distributions are nearly constant over the whole energy range and agree with the experiment in that they are almost isotropic. Thus, it seems that in this framework we can give a natural explanation for the peculiar behavior of the Al27(p, γ0)Si28 cross section.
The theory of Raman scattering is extended to include electric-quadrupole radiation. The results obtained are used to compute the elastic and Raman scattering cross sections of heavy deformed nuclei. The dipole and quadrupole resonances are described by a previously developed theory which includes surface vibrations and rotations. The computed cross sections are compared with experimental data for all those nuclei where both absorption and scattering cross sections are available. Some discrepances still exist in certain details; however, the over-all agreement between theory and experiment is very good.
In a collective treatment the energies of the giant resonances are given by the boundary conditions at the nuclear surface, which is subject to vibration in spherical nuclei. The general form of the coupling between these two collective motions is given by angular-momentum and parity conservation. The coupling constants are completely determined within the hydrodynamical model. In the present treatment the influence of the surface vibrations on the total photon-absorption cross section is calculated. It turns out that in most of the spherical nuclei this interaction leads to a pronounced structure in the cross section. The agreement with the experiments in medium-heavy nuclei is striking; many of the experimental characteristics are reproduced by the present calculations. In some nuclei, however, there seem to be indications of single-particle excitations which are not yet contained in this work.