Nuclear energy density functional from chiral two- and three-nucleon interactions

An improved density-matrix expansion is used to calculate the nuclear energy density functional from chiral two- and three-nucleon interactions. The two-body interaction comprises long-range one- and two-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition we employ the leading order chiral three-nucleon interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in calculations of nuclear few-body systems. With this input the nuclear energy density functional is derived to first order in the two- and three-nucleon interaction. We find that the strength functions $F_\nabla(\rho)$ and $F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant density range reasonably with results of phenomenological Skyrme forces. However, an improved description requires (at least) the treatment of the two-body interaction to second order. This observation is in line with the deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain in the Hartree-Fock approximation with low-momentum two- and three-nucleon interactions.Comment: 16 pages, 12 figures, submitted to Eur. Phys. J.

Computational Nuclear Physics and Post Hartree-Fock Methods

We present a computational approach to infinite nuclear matter employing Hartree-Fock theory, many-body perturbation theory and coupled cluster theory. These lectures are closely linked with those of chapters 9, 10 and 11 and serve as input for the correlation functions employed in Monte Carlo calculations in chapter 9, the in-medium similarity renormalization group theory of dense fermionic systems of chapter 10 and the Green's function approach in chapter 11. We provide extensive code examples and benchmark calculations, allowing thereby an eventual reader to start writing her/his own codes. We start with an object-oriented serial code and end with discussions on strategies for porting the code to present and planned high-performance computing facilities.Comment: 82 pages, to appear in Lecture Notes in Physics (Springer), "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Bonn Potential and Shell-Model Calculations for 206,205,204Pb

The structure of the nuclei 206,205,204Pb is studied interms of shell model employing a realistic effective interaction derived from the Bonn A nucleon-nucleon potential. The energy spectra, binding energies and electromagnetic properties are calculated and compared with experiment. A very good overall agreement is obtained. This evidences the reliability of our realistic effective interaction and encourages use of modern realistic potentials in shell-model calculations for heavy-mass nuclei.Comment: 4 pages, 4 figures, submitted to Physical Review

Many-body perturbation calculation of spherical nuclei with a separable monopole interaction: I. Finite nuclei

We present calculations of ground state properties of spherical, doubly closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of many-body perturbation theory using a separable density dependent monopole interaction. The model gives results in Hartree-Fock order which are of similar quality to other effective density-dependent interactions. In addition, second and third order perturbation corrections to the binding energy are calculated and are found to contribute small, but non-negligible corrections beyond the mean-field result. The perturbation series converges quickly, suggesting that this method may be used to calculate fully correlated wavefunctions with only second or third order perturbation theory. We discuss the quality of the results and suggest possible methods of improvement.Comment: 20 Pages, 11 figure

Variational Calculation on A=3 and 4 Nuclei with Non-Local Potentials

The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The binding energies and other ground state properties of A=3 and 4 nuclei are calculated using the CD Bonn 2000 and N3LO two-body potentials. The results are shown to be in excellent agreement with corresponding ones obtained by other accurate techniques.Comment: 12 pages, 6 tables, RevTex

The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)

We present a charge-dependent nucleon-nucleon (NN) potential that fits the world proton-proton data below 350 MeV available in the year of 2000 with a chi^2 per datum of 1.01 for 2932 data and the corresponding neutron-proton data with chi^2/datum = 1.02 for 3058 data. This reproduction of the NN data is more accurate than by any phase-shift analysis and any other NN potential. The charge-dependence of the present potential (that has been dubbed `CD-Bonn') is based upon the predictions by the Bonn Full Model for charge-symmetry and charge-independence breaking in all partial waves with J <= 4. The potential is represented in terms of the covariant Feynman amplitudes for one-boson exchange which are nonlocal. Therefore, the off-shell behavior of the CD-Bonn potential differs in a characteristic and well-founded way from commonly used local potentials and leads to larger binding energies in nuclear few- and many-body systems, where underbinding is a persistent problem.Comment: 69 pages (RevTex) including 20 tables and 9 figures (ps files

Gamow Shell Model Description of Weakly Bound Nuclei and Unbound Nuclear States

We present the study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing the bound single-particle states, unbound Gamow states, and the non-resonant continuum. In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discuss the basic ingredients of the Gamow Shell Model. The formalism is illustrated by calculations involving {\it several} valence neutrons outside the double-magic core: $^{6-10}$He and $^{18-22}$O.Comment: 19 pages, 20 encapsulated PostScript figure

Signatures of three-nucleon interactions in few-nucleon systems

Recent experimental results in three-body systems have unambiguously shown that calculations based only on nucleon-nucleon forces fail to accurately describe many experimental observables and one needs to include effects which are beyond the realm of the two-body potentials. This conclusion owes its significance to the fact that experiments and calculations can both be performed with a high accuracy. In this review, both theoretical and experimental achievements of the past decade will be underlined. Selected results will be presented. The discussion on the effects of the three-nucleon forces is, however, limited to the hadronic sector. It will be shown that despite the major successes in describing these seemingly simple systems, there are still clear discrepancies between data and the state-of-the-art calculations.Comment: accepted for publication in Rep. Prog. Phy

Fast-timing study of the l -forbidden 12+→32+ M1 transition in Sn 129 FAST-TIMING STUDY of the l -FORBIDDEN ⋯ R. LICǎ et al.

© 2016 authors. Published by the American Physical Society.The levels in Sn129 populated from the β- decay of In129 isomers were investigated at the ISOLDE facility of CERN using the newly commissioned ISOLDE Decay Station (IDS). The lowest 12+ state and the 32+ ground state in Sn129 are expected to have configurations dominated by the neutron s12 (l=0) and d32 (l=2) single-particle states, respectively. Consequently, these states should be connected by a somewhat slow l-forbidden M1 transition. Using fast-timing spectroscopy we have measured the half-life of the 12+ 315.3-keV state, T12= 19(10) ps, which corresponds to a moderately fast M1 transition. Shell-model calculations using the CD-Bonn effective interaction, with standard effective charges and g factors, predict a 4-ns half-life for this level. We can reconcile the shell-model calculations to the measured T12 value by the renormalization of the M1 effective operator for neutron holes