A self-consistent particle spectrum for Brueckner calculations

The energies of low-lying intermediate states used in Brueckner calculations on ¹⁶O are calculated self-consistently. When the spectrum for higher intermediate states is chosen to join smoothly to the self-consistent results, the binding energy per nucleon for ¹⁶O is found to be about 7 MeV.     

The single-particle interaction in nuclear matter via the relativistic Dirac-Brueckner approach

Within the relativistic Dirac-Brueckner approach and starting from a one-boson-exchange interaction, the nucleon selfenergy is calculated above the nuclear-matter Fermi sea. The effects of Pauli blocking and energy dispersion are studied. At low energy we see a dominance of the Pauli blocking whereas at nucleon energies up to 250 MeV the dispersive effect still has a very large influence on the single-particle interaction. From the selfenergy a Schrödinger optical potential is deduced, for which the DB results nicely agree with empirical values. The density dependence of this optical potential compares well with earlier calculations.     

Nuclear-rainbow scattering and nucleus-nucleus potentials at short distances

The elastic scattering of strongly bound nuclei at energies of 10 to 70 MeV per nucleon shows the phenomenon of “rainbow scattering.” A nuclear rainbow appears because of deflection to negative angles. This process involves a strong overlap of nuclear densities, with values of up to twice the saturation density of nuclear matter. The ¹⁶O+¹⁶O system is studied with a high precision over a wide energy range from 7 to 70 MeV per nucleon in several laboratories. Primary Airy maxima and higher order Airy structures are observed. At all energies, excellent fits are obtained with deep potentials as deduced from the double-folding model involving a nucleon-nucleon interaction weakly dependent on the density. It is shown that Pauli blocking expected at low energies is strongly reduced if the local momenta are calculated self-consistently. Systematics confirms a refractive origin of large-angle scattering, at low energies inclusive. Thus, nuclear-rainbow scattering yields unique information about the properties of cold nuclear matter at higher densities.     

One-boson-exchange potential and the ground state of 16O

Two one-boson-exchange potentials (OBEP), which fit two-nucleon data and give reasonable results in nuclear matter, are tested in ¹⁶O. Ground state properties are calculated in the framework of the Brueckner-Hartree-Fock approach. The density dependence of the reaction matrix elements stemming from the Pauli operator and starting energy are carefully taken into account.     

The orthogonality condition model applied to the inelastic two-step reaction process

An approximate method to take the Pauli principle into account is applied to the analysis of inelastic scattering of α-particles from the 8.88 MeV 2^? state of ¹⁶O, and is found to reproduce the magnitudes and the angular distributions of the cross sections at the incident energies of 40.5 and 65 MeV.     

Variational definition of the single-particle potential in the Brueckner-Hartree-Fock approach

The consequences of the variational definition of the self-consistent potential in Brueckner-Hartree-Fock theory are explored to higher orders even summing up some classes of diagrams to infinity. The consistency of this definition with a diagrammatic expansion are checked. Overcounting terms in the variational approach are pointed out and their numerical influence on the ground state properties of nuclei is checked at the example of¹⁶O. Ambiguities of the potential defined by the variational procedure stemming from the property of the Pauli-operatorQ ² =Q are studied diagrammatically and numerically. The application to¹⁶O shows that the influence of the Pauli rearrangement term is partially cancelled by the higher order starting energy rearrangement terms discussed in this work.     

A nuclear structure approach to the nucleon-nucleus optical potential at low energy

An antisymmetrized microscopic calculation of the optical potential for nucleon-⁴⁰Ca elastic scattering is derived. RPA correlations taken into account in the one-particle mass operator are shown to bring a correction to the first-order real potential at low energies and to lead to an imaginary potential. Both are calculated for incident nucleon energies between 10 and 50 MeV. Their general properties are studied in great detail and, after comparison with empirical imaginary potentials, the reliability of such an approach is discussed according to the value of the incident energy.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

The properties of nuclear matter at zero and finite temperatures

The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T ²-approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.     

The interaction of 605 MeV 63Cu with 197Au

Binary coincident fragments from the ⁶³Cu + ¹⁹⁷Au reaction at a copper energy of 605 MeV have been studied. Fragment energies were measured and fragment masses determined by a kinematic method. Three types of event are defined by suitable adjacent limits in the mass versus total kinetic energy event space. The angular distributions of cross section, average total kinetic energy and average mass have been determined for each event region. Total cross sections determined in the present experiment are compared to those found at lower bombarding energies. Further information on the sequential fission process has been obtained from measurements of yields of radioactive isotopes resulting from bombardment ofthin and thick targets of Au by 605 MeV Cu ions.     

Neutron matter with a relativistic one-boson-exchange potential

The neutron matter properties are studied with our relativistic OBEP derived from covariant perturbation theory and represented in momentum space and helicity state basis. The short-range correlations are treated in the lowest-order Brueckner theory using the angleaveraged Pauli operator, the effective-mass approximation for the self-consistent hole state potential and a free-particle spectrum. The results are compared with those corresponding to other potentials.     

Untersuchung der Reaktion Si28 (γ,p) AI27

A silicon semiconductor detector was irradiated with betatron bremsstrahlung of different end point energies and the energy distributions of the protons originating in the detector itself by the reaction Si²⁸(γ,p) Al²⁷ were measured with good statistical accuracy. The end point energies were varied in 1 MeV steps from 15 to 30 MeV. Using the known spectral distribution of theγ-rays the energy dependence of the total cross section of the studied reaction could be derived from the measured proton spectra. The resulting cross section shows a peak at 20, 5 MeV and a half width of 4 MeV. Approximate values for the branching ratios for transitions to excited states of the residual nucleus could also be obtained.     

Orbital rearrangement in light nuclei

Orbital rearrangement effects due to the removal of a proton are studied. Calculations in the nuclei¹⁶O,²⁰Ne, and⁴⁰Ca are performed using the Yale potential, and the Brink Boeker forceB1. The odd mass nuclei are not restricted to time reversal symmetry which prevents a large overestimation of the rearrangement energies. Although the orbital rearrangement energies are small (<1.5 MeV) utilizing density independent forces one can find larger changes in the wave functions due to the rearrangement as exhibit the discussion of the quadrupole moments and the mass distributions.     

Properties of nuclear S-wave matter

Comparative Brueckner and Jastrow studies of the properties of nuclear matter are somewhat hampered by the complexities of realistic nucleon-nucleon potentials. To avoid some of these difficulties we investigate a nuclear matter model called S-wave matter, which consists of nucleons interacting via various of the Aviles S-wave delta function potentials. These potentials all fit the two-body S-wave scattering data for energies up to 500 meV. By using Jastrow methods we find two-body contributions to the ground state energy ranging from 18 to 29 MeV, depending on the particular potential used; the results for a given potential are in good agreement with the Brueckner results of Haftel. In addition, there are significant Jastrow three-body contributions, indicating that the equivalent three-body Brueckner contributions should be evaluated.     

The 7Li (n,γ)8Li radiative capture at astrophysical energies

The possibility to construct intercluster interaction potentials in continuous and discrete spectra is shown in one‐channel cluster model based on the classification of orbital states according to Young schemes. These potentials usually contain Pauli forbidden states, and correctly describe elastic scattering phase shifts taking into account resonance behavior and main characteristics of the bound states of nuclei in the considering cluster channel. The versions of intercluster interaction potentials describing the resonance nature of some phase shifts of the n⁷Li elastic scattering at low energies and the P₂ ground state of ⁸Li in the n⁷Li cluster channel have been constructed for the demonstration of this approach. The possibility of describing the total cross sections of ⁷Li (n,γ)⁸Li within the energies from 5 meV (5 · 10^‐3 eV) to 1 MeV, including resonance at 0.25 MeV, has been demonstrated for the potentials obtained in the potential cluster model with forbidden states.     

The structure of 4He and phase-shift equivalent potentials

The Hartree-Fock and Brueckner theories are applied to the nucleus ⁴He. A truncated finite space of single-particle oscillator states is used, and different choices of the particle spectrum in Brueckner theory are considered. Results for the total binding energies and wound integrals are presented for the Reid soft-core potential and sets of phase-shift equivalent potentials generated from the Reid potential by a rank-one unitary transformation. The relation of the results to the position of the Emery singularities is investigated.     

The Brueckner-Goldstone method and its application in light nuclei

A new method for solving the reaction matrix equation is described. In this method the Pauli operator is treated exactly and the reaction matrix is found straightforwardly from systems of differential and algebraic equations. The three-body cluster contribution is discussed. The low truncation used in computation of it in other papers is shown to be unsatisfactory. A dependence of computed binding energy on the formally introduced parameter λ, corresponding to the shift of the single-particle spectrum of unoccupied states, is studied. In principle, the exact results should not depend on λ and therefore in an approximate calculation one must achieve a weak dependence on this parameter. It is shown that in this case the consideration of the third order in the Goldstone series is necessary. Various conditions are suggested for choosing the parameter λ. As an example of light nuclei, the ⁴He nucleus is chosen. Its binding energy is found to be about 20 MeV, both for the Reid potential and the RHEL potential.     

Ground-state properties of closed-shell nucleus 56Ni with realistic nucleon–nucleon interactions

We have calculated the ground-state energy of the doubly magic nucleus ⁵⁶Ni within the framework of the Green’s function using the CD-Bonn and N³LO nucleon–nucleon potentials. For the sake of comparison, the same calculations are performed using the Brueckner–Hartree–Fock approximation. Both the continuous and conventional choices of single particle energies are used. Additional binding energy is obtained from the inclusion of the hole–hole scattering term within the framework of the Green function approach. In this study, comparison of the calculated ground-state energies, obtained by using the Brueckner–Hartree–Fock approach using continuous choice and different nucleon–nucleon potentials, with the experimental value is accomplished. The results show good agreement between the calculated values and the experimental one for the ⁵⁶Ni nucleus. The sensitivity of our results to the choice of the model space is examined.