The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single-particle levels of a potential well (mean field) and interacting through a pairing force in the framework of the Richardson equations. The associated solutions are classified in terms of a number v_l, which reduces to the seniority v in the limit of a large pairing strength G and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the G limit. We express analytically, through the moments of the single-particle levels distribution, the collective mode energy and the two critical values G_cr⁺ and G_cr^- of the coupling which can exist on a single-particle level with no pair degeneracy. Notably G_cr⁺ and G_cr^-, when the number of single particle levels goes to infinity, merge into the critical coupling of a one-pair system G_cr (when it exists), which is not envisioned by the Richardson theory. In correspondence of G_cr, the system undergoes a transition from a mean-field- to a pairing-dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes versus G finding out that the former, for G > G_cr^-, come close to the BCS predictions, whereas the latter display a divergence at G_cr, signaling the onset of a long-range off-diagonal order in the system.     

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.     

The generalised relativistic Lindhard functions

We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular attention is payed to its real part, since it gives rise to substantial difficulties in the definition of the currents entering the dynamics.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

Hyperon-nucleon single-particle potentials with low-momentum interactions

Single-particle potentials in Hartree-Fock approximation for different hyperon-nucleon (YN channels are calculated in the framework of the effective low-momentum YN interaction . In contrast to the nucleon-nucleon interaction, the available experimental data for the YN interaction are scarce. As a consequence, no unique YN low-momentum potential can be predicted from the various bare potentials. The resulting momentum- and density-dependent single-particle potentials for several different bare OBE models and for chiral effective field theory are compared to each other.     

Overview of hadronic parity violation

The subject of hadronic parity violation is nearly fifty years old, but a good deal of uncertainty remains, despite many efforts both theoretical and experimental. A brief summary of the field is presented and a plan is proposed for new experimental work which, when combined with a new theoretical tack based on effective field theory, should lead to resolution of the present difficulties.     

Deuteron radial moments for renormalized chiral potentials

We calculate deuteron positive and negative radial moments involving any bilinear function of the deuteron S and D wave functions for renormalized OPE and TPE chiral potentials. The role played by the strong singularities of the potentials at the origin and the short-distance insensitivity of the results when the potentials are fully iterated is emphasized as compared to realistic potentials.     

The local potential approximation for the Brueckner G-matrix and a simple model of the scalar-isoscalar Landau-Migdal amplitude

The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet ^1S and triplet ³ S + ³ D channels. The complete Hilbert space is split into two domains, the model subspace S₀, in which the two-particle propagator is calculated explicitly, and the complementary one, S', in which the local potential approximation is used. This kind of local approximation was previously found to be quite accurate for the ^1S pairing problem. A set of model spaces S ₀(E ₀) with different values of the energy E₀ is considered, E₀ being the upper limit for the single-particle energies of the states belonging to S₀. The independence of the G-matrix on E₀ is assumed as a criterion for the validity of the local potential approximation. It turns out that such an independence holds within few percents for E ₀ = 10-20 MeV, for both channels under consideration. The G-matrix within the local potential approximation is used for justifying a simple microscopic model for the coordinate-dependent scalar-isoscalar component f (r) of the Landau-Migdal amplitude in terms of the free T-matrix. Received: 2 November 2001 / Accepted: 4 January 2002     

Regularization of singular terms in the N¯ potential model

We suggest a method of singular terms regularization in a potential model of the N¯ interaction. This method is free from uncertainties related to the usual cut-off procedure and is based on the fact that, in the presence of sufficiently strong short-range annihilation, N and ¯ never approach close enough to each other. In such a case the low-energy scattering is shown to be fully determined by the OBEP tail, while any details of the short-range core of the N¯ interaction are excluded from the observables. The obtained results for S- and P-wave scattering lengths are in agreement with the well-established theoretical models.     

Differences between pairing and zero-range effective interactions for nuclear binding energies

In this paper, we show that, although the spectroscopic properties of the monopole pairing force and a zero-range delta-function interaction are very similar, their saturation properties are quite different. In particular, the predictions for binding energies when filling up a major shell are radically different past mid-shell. This has significant consequences for understanding the masses and binding energies of long isotopic chains of nuclei that will be accessible with advanced exotic beam facilities. Received: 29 November 2001 / Accepted: 13 February 2002     

Two-pion-exchange parity-violating potential and np → dγ

We calculate the parity-violating nucleon-nucleon potential in heavy-baryon chiral perturbation theory up to next-to-next-to-leading order. The one-pion exchange enters in leading order and the next-to-next-to-leading order consists of two-pion-exchange and the two-nucleon contact terms. In order to investigate the effect of the higher-order contributions, we calculate the parity-violating asymmetry in n p → dγ at threshold. The one-pion-exchange contribution dominates the physical observable, while the two-pion-exchange contribution is about or less than 10% of the one-pion-exchange one.     

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     

Correlations and the Dirac structure of the nucleon self-energy

The Dirac structure of the nucleon self-energy in symmetric nuclear matter as well as neutron matter is derived from a realistic meson exchange model for the nucleon-nucleon (NN) interaction. It is demonstrated that the effects of correlations on the effective NN interaction in the nuclear medium can be parameterized by means of an effective meson exchange. This analysis leads to a very intuitive interpretation of correlation effects and also provides an efficient parametrization of an effective interaction to be used in relativistic structure calculations for finite nuclei. Received: 29 January 2001 / Accepted: 5 May 2001     

Large-scale mean-field calculations from proton to neutron drip lines using the D1S Gogny force

Large-scale axial mean-field calculations from proton to neutron drip lines have been performed within the Hartree-Fock-Bogoliubov method based on the D1S Gogny force. Nearly 7000 nuclides have been studied under the axial symmetric hypothesis and various properties are displayed on an Internet web site for every individual nucleus. Some global properties are presented such as the positions of the drip lines, the nuclide ground-state deformations and binding energies as well as regions where possible super- or hyper-deformation might be encountered.     

First measurements of the 16O(e, e'pn)14N reaction

This paper reports on the first measurement of the ¹⁶O(e, e'pn)¹⁴N reaction. Data were measured in kinematics centred on a super-parallel geometry at energy and momentum transfers of 215MeV and 316MeV/c. The experimental resolution was sufficient to distinguish groups of states in the residual nucleus but not good enough to separate individual states. The data show a strong dependence on missing momentum and this dependence appears to be different for two groups of states in the residual nucleus. Theoretical calculations of the reaction using the Pavia code do not reproduce the shape or the magnitude of the data. An erratum to this article is available at.     

Probing the convergence of perturbative series in baryon chiral perturbation theory

Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.     

Universal properties and structure of halo nuclei

The universal properties and structure of halo nuclei composed of two neutrons (2n) and a core are investigated within an effective quantum mechanics framework. We construct an effective interaction potential that exploits the separation of scales in halo nuclei and treat the nucleus as an effective three-body system. The uncertainty from higher orders in the expansion is quantified through theoretical error bands. First, we investigate the possibility to observe excited Efimov states in 2n halo nuclei. Based on the experimental data, ²⁰C is the only halo nucleus candidate to possibly have an Efimov excited state, with an energy less than 7 keV below the scattering threshold. Second, we study the structure of ²⁰C and other 2n halo nuclei. In particular, we calculate their matter form factors, radii, and two-neutron opening angles.     

Extension of the spectroscopic Monte Carlo method to realistic effective interactions

We propose an extension of the spectroscopic Monte Carlo method to realistic effective interactions. The scheme is applied to the recently introduced GXPF1 interaction for fp nuclei for the ground state of ⁶⁰Fe, ⁵⁶Ni, ⁶⁴Ni and ⁶⁰Zn. The method hinges on the use of Hartree-Fock-Bogoliubov wave functions (properly projected before variation) and on a reformulation of the effective interaction so that it is a sum of negative squares of Hermitian one-quasi-particle operators, so the application of the Hubbard-Stratonovich transformation to the elementary propagator exp[- ] gives a functional integral over a Hermitian propagator. Limitations and difficulties encountered in the calculation are discussed.