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.     

np → ηd near threshold and the s -wave ηN amplitude

We calculate the process np → ηd near threshold using a separable potential model of the coupled ηN - πN - ππN subystems, and a relativistic three-body calculation for the ηd scattering amplitude. The ππN channels are represented by an effective σN channel, and we compare the case where the σ and π masses are related by m _σ = 2m _π and no width is considered, to another where the mass and width of the σ -meson are taken from ππ scattering data. The np → ηd cross-section can be well described up to about 60MeV by models where the real part of the ηN scattering length lies between 0.4≤Re(a _ηN)≤0.6 fm which allows us to determine the s -wave ηN scattering amplitude for -60≤E≤60 MeV.     

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     

The neutron halo in heavy nuclei calculated with the Gogny force

The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean-field approach.     

Nuclear pairing from chiral pion-nucleon dynamics

We use a recently improved version of the chiral nucleon-nucleon potential at next-to-next-to-leading order to calculate the ¹S₀ pairing gap in isospin-symmetric nuclear matter. The pairing potential consists of the long-range one- and two-pion exchange terms and two short-distance NN-contact couplings. We find that the inclusion of the two-pion exchange at next-to-next-to-leading order reduces substantially the cutoff dependence of the ¹S₀ pairing gap determined by solving a regularised BCS equation. Our results are close to those obtained with the universal low-momentum nucleon-nucleon potential V_low-k or the phenomenological Gogny D1S force.     

Low-energy monopole and dipole response in nuclei at finite temperature

The multipole response of nuclei at temperatures T=0–2 MeV$T=0\text{–}2\text{MeV}$ is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1–2 MeV$T=1\text{–}2\text{MeV}$ additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in ^60,62Ni. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in ⁶⁸Ni and ¹³²Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.     

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     

Charge-independent effective interactions for shell-model studies in the 0g9/2-1p1/2 space

The matrix elements of the effective Hamiltonian in the 0g _9/2-1p _1/2 space are determined by a least-square fit to the energies of 477 levels of nuclei with 38≤Z≤50 and 47≤N≤50. The results of the calculation are found to be in better agreement with experiment than those obtained with previously determined interactions. Received: 31 May 2001 / Accepted: 14 June 2001     

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     

Shell-model structure of exotic nuclei beyond <Superscript>132</Superscript>Sn

We report on a study of exotic nuclei around doubly magic ¹³²Sn in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the bare potential is renormalized by constructing a smooth low-momentum potential, V_low-k, that is used directly as input for the calculation of the effective interaction. In this paper we focus attention on the nuclei ¹³⁴Sn and ¹³⁵Sb which, with an N/Z ratio of 1.68 and 1.65, respectively, are at present the most exotic nuclei beyond ¹³²Sn for which information exists on excited states. Comparison shows that the calculated results for both nuclei are in very good agreement with the experimental data. We present our predictions of the hitherto unknown spectrum of ¹³⁶Sn.     

Structure of even-even beryllium isotopes studied by AMD+GCM method

The ground state properties and the properties of low-lying states of the even-even⁶Be-¹²Be beryllium isotopes are investigated using the extended version of the Antisymmetrized Molecular Dynamics Multi-Slater Determinant model. The theoretical method is found to be very useful to study ground state properties of various nuclei covering light unstable nuclei. Many experimental data can be successfully reproduced by the adopted approach. Binding energies, the energies of the 2 ₁ ⁺ states, electromagnetic transition strengths and quadrupole moments of proton and neutron distribution are calculated. This work is supported in part by Grant-in-Aid for Scientific Research (13740145) from the Ministry of Education, Science and Culture.     

Bounds to the size of halo nuclei

Inspired by the Bertlmann-Martin inequality relating the rms radius of the ground state wave function to the lowest dipole transition energy, we have proposed a dimensional relationship to be used in weakly bound two-body systems. In the present work, it is applied to halo nuclei. Lower and upper bounds to the size of halo nuclei are compared to values obtained from reaction cross sections. The case of the deuteron is also presented. Received: 18 September 1998     

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.     

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.     

Bound-state calculations of the three-dimensional Yakubovsky equations with the inclusion of three-body forces

The four-body Yakubovsky equations in a three-dimensional approach with the inclusion of the three-body forces are proposed. The four-body bound state with two- and three-body interactions is formulated in the three-dimensional approach for identical particles as a function of vector Jacobi momenta, specifically, the magnitudes of the momenta and the angles between them. The modified three-dimensional Yakubovsky integral equations are successfully solved with the scalar two-meson exchange three-body force, where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.     

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.