The two-pion-exchange three-nucleon potential and nuclear matter

We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be ? 1.90 ± 0.2 MeV.     

Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces

A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading-order chiral three-nucleon interaction is employed with its parameters fixed in computations of nuclear few-body systems. With this input one finds for the asymmetry energy of nuclear matter the value A(?? ₀) ? 26.5 MeV, compatible with existing semi-empirical determinations. The strength functions of the isovector surface and spin-orbit coupling terms come out much smaller than those of the analogous isoscalar coupling terms and in the relevant density range one finds agreement with phenomenological Skyrme forces. The specific isospin and density dependences arising from the chiral two- and three-nucleon interactions can be explored and tested in neutron-rich systems.     

Relativistic calculations for two- and three-nucleon systems

The relativistic theory for few-nucleon systems developed by Glöckle and Müller is evaluated numerically for a model of scalar particles exchanging scalar mesons to lowest order in the coupling constant. 2-nucleon binding energies and scattering phases and 3-nucleon binding energies are compared with the usual non-relativistic calculation for different choices of the potential. The relativistic treatment gives a weaker binding. The mechanism of this is studied in more detail. We compare our results with the relativistic correction in the 1/c² expansion of Foldy and Krajcik.     

Measurement of two- and three-nucleon short-range correlation probabilities in nuclei

The ratios of inclusive electron scattering cross sections of 4He, 12C, and 56Fe to 3He have been measured at 1 < xB <. At Q2 > 1.4 GeV2, the ratios exhibit two separate plateaus, at 1.5 < xB < 2 and at xB > 2.25. This pattern is predicted by models that include 2- and 3-nucleon short-range correlations (SRC). Relative to A = 3, the per-nucleon probabilities of 3-nucleon SRC are 2.3, 3.1, and 4.4 times larger for A = 4, 12, and 56. This is the first measurement of 3-nucleon SRC probabilities in nuclei.     

Interplay between two- and three-body interaction in light nuclei and nuclear matter

A recent study of different models of three-nucleon interaction (TNI) in ³He, ³H, ⁴He and nuclear matter is extended to study the influence of different choices of the accompanying two-body interaction. A new two-body potential, Argonne υ₁₄, is coupled with both the Tucson and isobar intermediate-state models of two-pion-exchange TNI, with a phenomenological intermediate-range repulsive TNI added to the latter. Variational calculations are carried out for these systems, and compared to the earlier work. We find that a stronger tensor component in the two-body potential, as typified by a larger deuteron D-state percentage, gives more attraction for the TNI, counteracting the saturation effect obtained when only two-body forces are considered.     

Three-body forces in nuclear matter from intermediate Δ-states in three-nucleon clusters

Those three-body force contributions in nuclear matter usually generated through a πN scattering amplitude dominated by the Δ(1236) resonance, are here treated as a three-nucleon cluster, in which one of the nucleons becomes, in an intermediate state, a Δ-resonance. All exchange diagrams are calculated and found to significantly reduce the energy per particle from the direct graph. This is contrary to earlier estimates of the exchanges, using more approximate approaches. The resulting attractive contribution is rather small, −1.1 MeV at κ_F = 1.4 fm⁻¹, but the roughly linear density dependence has a crucial effect on the saturation properties. The sensitivity of the results to the correlations used, and to the two-body force spin structure, is displayed. The energy per particle from clusters with three intermediate Δ-resonances is also estimated.     

Effective interactions and elementary excitations in nuclear matter

We present a polarization potential theory for nuclear matter. Starting from a realistic two-nucleon interaction, position space Pseudopotentials which describe effective nucleon-nucleon interactions are constructed in a manner similar to that used by Aldrich and Pines in the helium liquids. Important modifications which result from tensor forces and three-body interactions are incorporated; exchange and screening effects are included. The resulting momentum-dependent quasiparticle interactions are used to calculate higher-order Fermi liquid parameters, dynamic and static structure functions, and static polarizabilities. Comparisons are made with recent microscopic calculations.     

Saturation of nuclear matter and realistic interactions

In this communication we study symmetric nuclear matter for the Brueckner-Hartree-Fock approach, using two realistic nucleon-nucleon interactions (CD-Bonn and Bonn C). The single-particle energy is calculated self-consistently from the real on-shell self-energy. The relation between different expressions for the pressure is studied in cold nuclear matter. For best calculations the self-energy is calculated with the inclusion of hole-hole (hh) propagation. The effects of hh contributions and a self-consistent treatment within the framework of the Green function approach are investigated. Using two different methods, namely, G-matrix and bare potential, the hh term is calculated. We found that using G-matrix brought about non-negligible contribution to the self-energy, but this difference is very small and can be ignored if compared with the large contribution coming from particle-particle term. The contribution of the hh term leads to a repulsive contribution to the Fermi energy which increases with density. For extended Brueckner-Hartree-Fock approach the Fermi energy at the saturation point fulfills the Hugenholtz-Van Hove relation.     

Investigation of two- and three-nucleon transfer reactions in12C +56Fe

Multi-nucleon transfer reactions⁵⁶Fe(¹²C, X) have been studied at an incident¹²C energy of 60 MeV. Angular distributions of¹⁰Be and⁹Be corresponding to 2p and 2p 1n transfer reactions in transition to low-lying states in the residual nuclei have been measured. The angular distribution data for 2p transfer have been analysed in terms of finite range DWBA calculations assuming a one-step transfer of two protons. The spectroscopic factors for three low-lying transitions observed in⁵⁶Fe(¹²C,¹⁰Be)⁵⁸Ni have been extracted. Transfer probabilities for the ground state transition in two- and three-nucleon stripping channels have been obtained and compared with the corresponding sequential transfer probabilities in order to emphasise the role of direct transfer of nucleons vis-a-vis sequential transfer.     

Realistic and effective interactions in the study of nuclear matter

The equation of state of symmetric nuclear matter is addressed starting both from a realistic interaction derived from nucleon-nucleon scattering processes and from a low-momentum effective potential. The approach is based on finite temperature Green’s functions. The internal energy per particle is estimated from the summation of diagrams and through the Galitskii-Koltun sum rule. The text was submitted by the author in English.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

Molecular structures in two- and three-centre systems

Some recent studies of clustering in carbon and beryllium isotopes using break-up reaction studies are reported. Studies of the ⁷Li(⁹Be,⁹Be+α) and ⁷Li(⁹Be,¹⁰Be+α) reactions provide an insight into clustering in three-centre systems. Similarly, neutron knockout reactions involving the 4n removal channel with a ¹²Be projectile may provide an insight into the nature of molecular states in two-centre systems.     

On the stability of the Hartree-Fock homogeneous density solution for nuclear matter

The nuclear matter energy density used by Overhauser is shown not to be realistic. The consequence of a static density fluctuation thus seems doubtful. The application of the method of Baym, Bethe and Pethik, developed for neutron star matter problems, shows that for a more realistic nuclear energy density containing the Thomas-Fermi part plus gradient terms, both spatially periodic compression and decompression about the saturation density, augment the energy. In addition, positive gradient terms tend to prevent a rippled density.     

Proton-pion and two- pion correlations in eA interactions

We report here the results on studying of proton-pion and two-pion correlations in eA interactions at 5 GeV. Kinematic correlations were studied as a function of the two-particle opening angle, their momenta and proton multiplicity. The universal properties of correlation functions were found with respect to different particle species. Interferometry method was used to determine the size of the interaction region.     

Crystal engineering in two- and three-dimensional systems based on cyanomolybdates: structures, magnetism and intercalation properties

A design of infinite two- and three-dimensional cyano-bridged networks with useful properties has attracted a great deal of attention in contemporary science. A proposal described some investigations in crystal engineering, performed over the past few years on supramolecular coordination polymers based on [Mo(CN)_n]⁴⁻ (n=7,8) building blocks and on their magnetic and intercalation properties.