D.M. Brink

Effective interactions for Hartree-Fock calculations

Abstract An attempt was made to find a phenomenological two-body nucleon-nucleon interaction which would reproduce the binding energies and densities of nuclear matter and of various light nuclei in the Hartree-Fock approximation. We investigated in detail a sum of two Gaussian potentials, a sum of a Gaussian and a delta function, a velocity-dependent interaction which acts in s-states only and a velocity-dependent interaction which acts both in s- and p-states. The parameters of each potential were adjusted so as to give the experimental binding energies of 4He and nuclear matter at about the experimental densities. With the resulting forces we computed the binding energies and densities of the 16O and 40Ca ground states and the same quantities for the deformed 8Be and 12C ground states. Moreover, the single-particle energies and the possibly deformed dipole state, 2p2h and 4p4h states of the 16O nucleus were studied. It appeared that no force could reproduce all experimental data at the same time.

Time-dependent hartree-fock theory with Skyrme's interaction

Abstract The time-dependent Hartree-Fock theory (TDHF) and its adiabatic approximation (ATDHF) are formulated in coordinate space using effective density-dependent interactions of Skyrme type. For this purpose it is necessary to derive the energy density of a Slater determinant without assuming the single-particle states to be invariant under time-reversal. The corresponding Hartree-Fock Hamiltonian is obtained by varying the total energy with respect to the single-particle density matrix. With the Skyrme interaction TDHF theory leads to an equation of continuity for the single-particle density. The ATDHF equation is transformed into a finite set of inhomogeneous differential equations. Hydrodynamic-like expressions for the collective kinetic energy are established in case the single-particle wave functions have certain generalised scaling properties. TDHF and ATDHF are applied to the description of isoscalar monopole vibrations in 16 O and 40 Ca.

Kinematical effects in heavy-ion reactions

Abstract Transfer reactions between heavy ions at energies well above the Coulomb barrier have a large cross-section only, if certain kinematical conditions are satisfied. These relate the Q -value of the reaction to the angular momentum of the transferred nucleons in the initial and final nuclei.

Hartree-Fock calculations with Skyrme's interaction

Abstract Hartree-Fock calculations have been made for closed shell nuclei using a form of density dependent nucleon-nucleon interaction suggested by Skyrme. The results are very good for binding-energies, densities and energies of single particle levels near the Fermi level. Calculations have been made in one superheavy nucleus.

Individual particle and collective aspects of the nuclear photoeffect

Abstract The coordinate corresponding to the dipole photon absorption operator is exactly separable in the oscillator shell model. It is shown that in an electric dipole absorption a mode of the shell model is excited in which the protons vibrate against the neutrons. In shell models other than the oscillator model this collective mode is damped; in heavy nuclei this damping gives a line width of ≈ 4 MeV.

The generator coordinate theory of collective motion

Abstract Collective motion in many-particle systems is studied by using the generator-coordinate method of Griffin, Hill and Wheeler. The equations of the theory are solved in the Gaussian overlap approximation and are shown to be equivalent to the quantal equations of a set of coupled harmonic oscillators. General properties of the solutions are studied, including those resulting from invariance principles and intrinsic symmetries. Similarities with the Tamm-Dancoff approximation and the random phase approximation are pointed out. Normally the generator-coordinate method is formulated in terms of generating functions depending on real parameters. Various difficulties of the “real” approach can be overcome by making an extension to complex parameters. Relations between the real and complex representation are established. To illustrate the general formalism the method is applied to the alpha-particle model of 20Ne.

The angular cross-correlation function of cross-section fluctuations

Abstract The fluctuations of a compound-nucleus cross-section with energy are considered as a function of angle. In general there is a coherence angle, analogous to the coherence energy of the auto-correlation, within which the fluctuations are correlated. The magnitude of the coherence angle is ( kR ) −1 . An analogy is demonstrated between the energy dependent fluctuations of nuclear reactions and the time dependent fluctuations of optics and radio-astronomy. Explicit formulae are given for the magnitude (mean square variation) of nuclear fluctuations, as a function of angle, in terms of the spins of the reacting particles. The special case of electric dipole γ -radiation is discussed in detail.

Investigation of the alpha-particle model for light nuclei

Abstract The alpha-particle model of Margenau, Bloch and Bronk is used to study the ground-state properties, the relative energies of different alpha configurations and configuration mixing of light 4 N nuclei from 12 C to 28 Si.

Interaction potential between two 16O nuclei derived from the Skyrme interaction

Abstract The energy functional for the Skyrme density-dependent force is used to calculate the interaction potential between two 16 O nuclei. A two-centre harmonic oscillator potential is employed to construct the density and kinetic energy density of the ground state of the combined system and of the separated nuclei. The antisymmetrization effects are investigated. The relative motion of the nuclei is taken approximately into account and the energy dependence of the potential derived from the Skyrme force is presented.

Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle

Abstract A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamiltons principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinates and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics.