Density functional for pairing with particle number conservation

In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.Comment: Proceeding of the International Symposium: Forefronts of Researches in Exotic Nuclear Structures- Niigata201

Beyond mean-field calculation for pairing correlation

The recently proposed Symmetry-Conserving Energy Density Functional approach [G. Hupin, D. Lacroix and M. Bender, Phys. Rev. C84, 014309 (2011)] is applied to perform Variation After Projection onto good particle number using Skyrme interaction, including density dependent terms. We present a systematic study of the Kr and Sn isotopic chains. This approach leads to non-zero pairing in magic nuclei and a global enhancement of the pairing gap compared to the original theory that breaks the particle number symmetry. The need to consistently readjust the pairing effective interaction strength is discussed.Comment: 7 pages, 9 figure

On the formulation of functional theory for pairing with particle number restoration

The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an alternative that might be advantageous for mass models, nuclear dynamics and thermodynamics, we propose to formulate the functional in terms directly of the one-body and two-body density matrices of the state with good particle number. Our approach does not contain the pathologies recently observed when restoring the particle number in an Energy Density Functional framework based on transition density matrices and can eventually be applied with functionals having arbitrary density dependencies.Comment: 11 pages, 3 figure

Unified description of 6^6Li structure and deuterium-4^4He dynamics with chiral two- and three-nucleon forces

Prototype for the study of weakly bound projectiles colliding on stable targets, the scattering of deuterium ($d$) on $^4$He ($\alpha$) is an important milestone in the search for a fundamental understanding of low-energy reactions. At the same time, it is also important for its role in the Big-bang nucleosynthesis of $^6$Li and applications in the characterization of deuterium impurities in materials. We present the first unified {\em ab initio} study of the $^6$Li ground state and $d$-$^4$He elastic scattering using two- and three-nucleon forces derived within the framework of chiral effective field theory. The six-nucleon bound-state and scattering observables are calculated by means of the no-core shell model with continuum. %and are compared to available experimental data. We analyze the influence of the dynamic polarization of the deuterium and of the chiral three-nucleon force, and examine the role of the continuum degrees of freedom in shaping the low-lying spectrum of $^6$Li. We find that the adopted Hamiltonian correctly predicts the binding energy of $^6$Li, yielding an asymptotic $D$- to $S$-state ratio of the $^6$Li wave function in $d+\alpha$ configuration of $-0.027$ in agreement with the value determined from a phase shift analysis of $^6$Li+$^4$He elastic scattering, but overestimates the excitation energy of the first $3^+$ state by $350$ keV. The bulk of the computed differential cross section is in good agreement with data.Comment: 5 pages, 5 figure

Advances in the ab initio description of nuclear three-cluster systems

We introduce the extension of the ab initio no-core shell model with continuum to describe three-body cluster systems. We present results for the ground state of 6He and show improvements with respect to the description obtained within the no-core shell model and the no-core shell model/resonating group methods.Comment: Proceedings of the 21st International Conference on Few-Body Problems in Physics. May 18-22, 2015. Chicago, Illinois, US

How many-body correlations and α\alpha-clustering shape 6^6He

The Borromean $^6$He nucleus is an exotic system characterized by two `halo' neutrons orbiting around a compact $^4$He (or $\alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {\em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $\alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.Comment: 5 pages, 4 figure