D. Schütte

An OBE model for the two-nucleon problem based on non-covariant perturbation theory☆

Abstract The NN scattering data and the deuteron properties are calculated within an OBE scheme based upon the treatment of a field theoretical Hamiltonian within old fashioned perturbation theory. The structure of the relevant equations is discussed in detail. The results show that one arrives at a consistent description of NN data — as consistent as with any other OBE model — so that the application of the same scheme to the calculation of meson current corrections to nuclear matter properties should be justified.

A Brueckner theory including mesonic degrees of freedom

Abstract A many-body theory is developed where the Hilbert space is allowed to contain states of nucleons and mesons. The basis of the theory is the treatment of a field theoretical Hamiltonian within non-covariant perturbation theory. Only diagrams corresponding to a one boson exchange (OBE) are taken into account. First the two-body scattering problem is developed, yielding a scattering equation corresponding to that of Kadyshevsky. Then the theory is applied to the binding energy problem of nuclear matter in the two hole line approximation with a choice of the single particle spectrum taken analogously to the Brueckner-Bethe theory. The resulting equations contain meson current corrections which are physically interpreted. The standard Brueckner theory with static OBE forces is obtained in an adiabatic limit.

Pairing and deformation in a solvable model and the validity of different approximation methods

Abstract We consider an exactly solvable nuclear model in order to test the validity of various well-known approximation methods. The model Hamiltonian is built on two shells and contains two essentially different interactions (pairing and monopole coupling); it exhibits typical features of realistic Hamiltonians of heavier nuclei and leads in addition to an understanding of specific nuclear properties in the transitional regions. The energies and the expansion coefficients of the lowest states are determined as functions of the characteristics parameters of the model, i.e. the particle number and the strengths of the interactions. The calculations are based on the generalized quasi-spin method. The Hamiltonian H is expressed by a set of operators which define the Lie algebra of O 5 ; the matrix elements of H for the relevant representations of this algebra are obtained by means of an algebraic computer programs which, in addition, takes care of the remaining diagonalization. The numerical results thus obtained are represented graphically in several diagrams. The characteristics dependences of the relevant quantities on the parameters show the invariance of the “ pairing solution ” (sharp seniority) with respect to the addition of the second interaction within a well-defined interval of relative strength (pairing region) and prove the existence of a transitional region with strong variations of nuclear properties (characteristic admixtures of higher seniorities) to be followed by a “ deformed ” region with extremely low-lying levels. In addition, we find typical “vibrational levels” within the pairing region and their continuous transition to the “rotational states” of the deformed domain. The validity of the Frank-Condon principle is illustrated by the characteristic behaviour of excited states in the transitional region.

A solvable model of boson condensation

Abstract A solvable model of boson condensation is presented. The validity of different approximation techniques (OBE scheme, perturbation theory. Green function methods, extended Hartree-Fock method, generator coordinate method) is tested within the model. The generator coordinate method yields an especially good description of quantum corrections to properties of the system in the normal and deformed cases.

Meson exchange corrections and properties of nuclear matter and neutron matter

Abstract A calculation of meson exchange corrections to the binding energy as function of the density is presented for nuclear matter and neutron matter. The framework is the application of non-covariant perturbation theory to a field theoretical Hamiltonian. Within a Brueckner-type approximation we restrict ourselves to the calculation of those meson exchange corrections which are due to one meson exchange and which produce no mass renormalization corrections. The results are reported in detail and the structure of the results is revealed. As a net effect, we find that our meson exchange corrections give a repulsion in nuclear matter yielding about 5 MeV less binding at the saturation point. For neutron matter, the effects are very small.

Investigations of parity deformation in spherical nuclei

Abstract The possibility of parity deformation for spherical structures is investigated from various viewpoints. We use several criteria of stability for the spherical Hartree-Fock solution (Thouless condition, critical 0 − states in different approximations) as well as different types of two-body forces (a realistic effective interaction and the OPEP) and single-particle spectra (HF, oscillator, Woods-Saxon and experimental) in order to obtain a complete survey. The result is that parity deformation can be excluded in practically all cases. In addition, the positions of the two critical 0 − states of 16 O are in good numerical agreement with experiments if realistic forces and experimental single-particle energies in connection with the random phase or Tamm-Dancoff approximation are used.

APPLICATION OF THE HOLE LINE EXPANSION TO AN EXACTLY SOLVABLE MODEL.

Abstract A purely algebraical definition of the hole line expansion is presented. The predictions of the hole line expansion up to fourth order are then investigated in an exactly solvable model which contains an attractive long-range and a repulsive short-range two-body force. Energies and wave functions are studied in relation to the wound integral and the hole-hole interaction.

Mesonic degrees of freedom and ground-state properties of nuclei

Abstract The influence of a special class of mesonic degrees of freedom on ground-state properties is studied in a meson extended Brueckner-Hartree-Fock (MBHF) method. The mesonic degrees of freedom are eliminated in second order perturbation theory by introducing a suitable (effective) one-boson-exchange potential (OBEP). But opposite to the standard OBEP the energy dependence of this potential is carried over to the nuclear many body problem. Also the nuclear many body problem determines the intermediate nucleon spectrum used to calculate the OBEP. Brueckner-Hartree-Fock (BHF) calculations including these meson exchange corrections show a remarkable improvement for binding energy, charge radius and electron scattering data of 16O relative to BHF calculations with a usual OBEP.

Hartree-Bogoliubov calculations with spherical restriction

The structure of the Hartree-Bogoliubov theory with spherical restrictions (SHB theory) is investigated. The SHB equations exhibit a strong instability if solutions are determined by iterations but this can be overcome by using the splitting of the SHB transformations according to Bloch and Messiah. Results of SHB calculations are presented for such nuclei where comparisons to deformed HB solutions are possible. It is shown that for light nuclei (18 < A < 40) the SHB solutions are energetically rather high (coexistence of spherical and deformed structures), whereas for 18O and the Ca isotopes the SHB solutions have about the same binding compared to the deformed ones, indicating that these nuclei can be treated equivalently as spherical or (weakly) deformed structures.

Investigation of heavy nuclei with sharp seniority wave functions and comparison to the BCS approximation

Abstract Within a realistic model for heavy spherical nuclei, a numerical comparison of the results of the BCS approximation and the seniority 0 and 1 approximation is performed in a detailed way. It is shown that for the characteristic pairing properties there is a good agreement between both computational methods for this range of nuclei if one takes realistic single-particle energies and pairing matrix elements into account.