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Background: The $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude.Purpose: In this work we study the properties of $^{9}\mathrm{Li}$ bound states and low-lying resonances and calculate the $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as input.Methods: The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. For the capture cross section calculation, we adjust calculated thresholds to experimental values.Results: Our calculations reproduce the experimentally known bound states as well as the lowest $5/{2}^{\ensuremath{-}}$ resonance of $^{9}\mathrm{Li}$. We predict a $3/{2}^{\ensuremath{-}}$ spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the very narrow $7/{2}^{\ensuremath{-}}$ resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances.Conclusions: Our calculated $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment [Phys. Rev. C 57, 959 (1998)]. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at $\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}0.2$ MeV due to E2/M1 radiation enhanced by the $5/{2}^{\ensuremath{-}}$ resonance.

Recently, the bound and continuum spectrum of $^{11}\mathrm{Be}$ has been calculated within the ab initio no-core shell model with continuum (NCSMC) method, with the parity inversion in the ground state successfully reproduced. The continuum spectrum obtained is in agreement with known experimental levels. The S matrix contained in the NCSMC continuum wave functions of the $\mathrm{n}+^{10}\mathrm{Be}$ system is used in this work for the first time in a transfer-to-the-continuum (TC) reaction calculation. The TC approach is applied to study the excitation energy spectrum of $^{11}\mathrm{Be}$ measured in the $^{9}\mathrm{Be}(^{18}\mathrm{O},^{16}\mathrm{O})^{11}\mathrm{Be}$ reaction at 84 MeV. Previously known levels are confirmed and theoretical and experimental evidence for a 9/${2}^{+}$ state at ${E}_{x}=5.8$ MeV is given, whose configuration is thought to be $^{10}\mathrm{Be}({2}^{+})+\mathrm{n}({d}_{5/2})$.

Background: The production of $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ and $^{3}\mathrm{H}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Li}$ radiative-capture processes are important to determine the $^{7}\mathrm{Li}$ abundance in the early universe and to predict the correct fraction of $pp$-chain branches resulting in $^{7}\mathrm{Be}$ versus $^{8}\mathrm{B}$ neutrinos. The $^{6}\mathrm{Li}(p,\ensuremath{\gamma})^{7}\mathrm{Be}$ has been investigated recently hinting at a possible cross section enhacement near the thershold. The $^{6}\mathrm{Li}(n,^{3}\mathrm{H})^{4}\mathrm{He}$ process can be utilized for tritium breeding in machines dedicated to fusion energy generation through the deuteron-tritium reaction, and is a neutron cross section standard used in the measurement and evaluation of fission cross sections.Purpose: In this work we study the properties of $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems.Methods: The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$.Results: Our calculations reproduce all the experimentally known states of the two systems and provide predictions for several new resonances of both parities. Some of these new possible resonances are built on the ground states of $^{6}\mathrm{Li}$ and $^{6}\mathrm{He}$, and thus represent a robust prediction. We do not find any resonance in the $p+^{6}\mathrm{Li}$ mass partition near the threshold. On the other hand, in the $p+^{6}\mathrm{He}$ mass partition of $^{7}\mathrm{Li}$ we observe an $S$-wave resonance near the threshold producing a very pronounced peak in the calculated $S$ factor of the $^{6}\mathrm{He}(p,\ensuremath{\gamma})^{7}\mathrm{Li}$ radiative-capture reaction.Conclusions: While we do not find a resonance near the thershold in the $p+^{6}\mathrm{Li}$ channel, in the case of $^{6}\mathrm{He}+p$ reaction a resonant $S$-wave state is predicted at a very low energy above the reaction threshold, which could be relevant for astrophysics and its implications should be investigated. We note though that this state lies above the three-body breakup threshold not included in our method and may be influenced by three-body continuum correlations.

The 3He(α,γα,γ)7Be and 3H(α,γα,γ)7Li astrophysical S factors are calculated within the no-core shell model with continuum using a renormalized chiral nucleon–nucleon interaction. The 3He(α,γα,γ)7Be astrophysical S factors agree reasonably well with the experimental data while the 3H(α,γα,γ)7Li ones are overestimated. The seven-nucleon bound and resonance states and the α + 3He/3H elastic scattering are also studied and compared with experiment. The low-lying resonance properties are rather well reproduced by our approach. At low energies, the s-wave phase shift, which is non-resonant, is overestimated.

We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of the Hamiltonian within the harmonic-oscillator expansion of the no-core shell model are coupled with continuous microscopic three-cluster states to correctly describe the nuclear wave function both in the interior and asymptotic regions. We discuss the formalism in detail and give algebraic expressions for the case of core + $n+n$ systems. Using similarity-renormalization-group evolved nucleon-nucleon interactions, we analyze the role of $\phantom{\rule{0.28em}{0ex}}^{4}\mathrm{He}+n+n$ clustering and many-body correlations in the ground and low-lying continuum states of the Borromean $^{6}\mathrm{He}$ nucleus, and study the dependence of the energy spectrum on the resolution scale of the interaction. We show that $^{6}\mathrm{He}$ small binding energy and extended radii compatible with experiment can be obtained simultaneously, without resorting to extrapolations. We also find that a significant portion of the ground-state energy and the narrow width of the first ${2}^{+}$ resonance stem from many-body correlations that can be interpreted as core-excitation effects.

Background: The exotic $^{9}\mathrm{He}$ nucleus, which presents one of the most extreme neutron-to-proton ratios, belongs to the $N=7$ isotonic chain famous for the phenomenon of ground-state parity inversion with decreasing number of protons. Consequently, it would be expected to have an unnatural (positive) parity ground state similar to $^{11}\mathrm{Be}$ and $^{10}\mathrm{Li}$. Despite many experimental and theoretical investigations, its structure remains uncertain. Apart from the fact that it is unbound, other properties including the spin and parity of its ground state, and the very existence of additional low-lying resonances are still a matter of debate.Purpose: In this work, we study the properties of $^{9}\mathrm{He}$ by analyzing the $n+^{8}\mathrm{He}$ continuum in the context of the ab initio no-core shell model with continuum (NCSMC) formalism with chiral nucleon-nucleon interactions as the only input.Methods: The NCSMC is a state-of-the-art approach for the ab initio description of light nuclei. With its capability to predict properties of bound states, resonances, and scattering states in a unified framework, the method is particularly well suited for the study of unbound nuclei such as $^{9}\mathrm{He}$.Results: Our analysis produces an unbound $^{9}\mathrm{He}$ nucleus. Two resonant states are found at the energies of $\ensuremath{\sim}1$ and $\ensuremath{\sim}3.5$ MeV, respectively, above the $n+^{8}\mathrm{He}$ breakup threshold. The first state has a spin-parity assignment of ${J}^{\ensuremath{\pi}}={1/2}^{\ensuremath{-}}$ and can be associated with the ground state of $^{9}\mathrm{He}$, while the second, broader state has a spin parity of ${3/2}^{\ensuremath{-}}$. No resonance is found in the ${1/2}^{+}$ channel, only a very weak attraction.Conclusions: We find that the $^{9}\mathrm{He}$ ground-state resonance has a negative parity and thus breaks the parity-inversion mechanism found in the $^{11}\mathrm{Be}$ and $^{10}\mathrm{Li}$ nuclei of the same $N=7$ isotonic chain.

How does nature hold together protons and neutrons to form the wide variety of complex nuclei in the Universe? Describing many-nucleon systems from the fundamental theory of quantum chromodynamics has been the greatest challenge in answering this question. The chiral effective field theory description of the nuclear force now makes this possible but requires certain parameters that are not uniquely determined. Defining the nuclear force needs identification of observables sensitive to the different parametrizations. From a measurement of proton elastic scattering on ^{10}C at TRIUMF and ab initio nuclear reaction calculations, we show that the shape and magnitude of the measured differential cross section is strongly sensitive to the nuclear force prescription.

The description of structural and dynamical properties of nuclei starting from the fundamental interaction between nucleons has been a long-standing goal in nuclear physics. The ab initio No-Core Shell Model combined with the Resonating-Group Method (NCSM/RGM) is capable of addressing both structural and reaction properties of light-nuclei. While promising results have already been achieved starting from a two-body Hamiltonian, a truly realistic prediction of nuclear observables requires the treatment of the three-nucleon interaction. Using similarity-renormalization-group evolved two- and three-nucleon interactions, we will present recent applications to n-4He scattering process when accounting for the chiral two- plus three-nucleon interaction versus the chiral two-nucleon interaction. We compare our results to phase shifts obtained from R-matrix analysis of data up to 16 MeV neutron energy, below the d-3H threshold., 4 pages, 2 figures, Proceedings of the 22nd European Conference on Few-Body Problems in Physics, Krakow, Poland, 9-13 September 2013

The weakly bound exotic ^{11}Be nucleus, famous for its ground-state parity inversion and distinct n+^{10}Be halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ^{11}Be spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the 3/2_{1}^{-} resonance energy. Finally, we predict low-lying 3/2^{+} and 9/2^{+} resonances that are not or not sufficiently measured in experiments.

The Borromean $^{6}\mathrm{He}$ nucleus is an exotic system characterized by two halo neutrons orbiting around a compact $^{4}\mathrm{He}$ (or $\ensuremath{\alpha}$) 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 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 $^{4}\mathrm{He}+n+n$ cluster degrees of freedom largely solves this issue. We analyze the role played by $\ensuremath{\alpha}$ clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.

The weakly bound exotic ^{11}Be nucleus, famous for its ground-state parity inversion and distinct n+^{10}Be halo structure, is investigated from first principles using chiral two- and three-nucleon forces. An explicit treatment of continuum effects is found to be indispensable. We study the sensitivity of the ^{11}Be spectrum to the details of the three-nucleon force and demonstrate that only certain chiral interactions are capable of reproducing the parity inversion. With such interactions, the extremely large E1 transition between the bound states is reproduced. We compare our photodisintegration calculations to conflicting experimental data and predict a distinct dip around the 3/2_{1}^{-} resonance energy. Finally, we predict low-lying 3/2^{+} and 9/2^{+} resonances that are not or not sufficiently measured in experiments.

Recently, we applied an $ab$ $initio$ method, the no-core shell model combined with the resonating group method, to the transfer reactions with light p-shell nuclei as targets and deuteron as the projectile. In particular, we studied the elastic scattering of deuterium on $^7$Li and the ${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction starting from a realistic two-nucleon interaction. In this contribution, we review of our main results on the ${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction, and we extend the study of the relevant reaction channels, by showing the dominant resonant phase shifts of the scattering matrix. We assess also the impact of the polarization effects of the deuteron below the breakup on the positive-parity resonant states in the reaction. For this purpose, we perform an analysis of the convergence trend of the phase and eigenphase shifts, with respect to the number of deuteron pseudostates included in the model space., Comment: Contribution to TNPI2016

The fundamental description of both structural properties and reactions of light nuclei in terms of constituent protons and neutrons interacting through nucleon-nucleon and three-nucleon forces is a long-sought goal of nuclear theory. I will briefly present a promising technique, built upon the {\em ab initio} no-core shell model, which emerged recently as a candidate to reach such a goal: the no-core shell model/resonating-group method. This approach, capable of describing simultaneously both bound and scattering states in light nuclei, complements a microscopic cluster technique with the use of two-nucleon realistic interactions, and a microscopic and consistent description of the nucleon clusters. I will discuss applications to light nuclei binary scattering processes and fusion reactions that power stars and Earth based fusion facilities, such as the deuterium-$^3$He fusion, and outline the progress toward the inclusion of the three-nucleon force into the formalism and the treatment of three-body clusters., 8 pages, 6 figures, Proceedings of the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japan

The description of nuclei starting from the constituent nucleons and the realistic interactions among them has been a long-standing goal in nuclear physics. In addition to the complex nature of the nuclear forces, with two-, three- and possibly higher many-nucleon components, one faces the quantum-mechanical many-nucleon problem governed by an interplay between bound and continuum states. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from QCD-employing Hamiltonians constructed within chiral effective field theory. After a brief overview of the field, we focus on ab initio many-body approaches - built upon the No-Core Shell Model - that are capable of simultaneously describing both bound and scattering nuclear states, and present results for resonances in light nuclei, reactions important for astrophysics and fusion research. In particular, we review recent calculations of resonances in the $^6$He halo nucleus, of five- and six-nucleon scattering, and an investigation of the role of chiral three-nucleon interactions in the structure of $^9$Be. Further, we discuss applications to the $^7$Be$(p,\gamma)^8$B radiative capture. Finally, we highlight our efforts to describe transfer reactions including the $^3$H$(d,n)^4$He fusion., Comment: Contribution to the Special Physica Scripta Edition - 40 year anniversary - Nobel Prize '75, 71 pages, 29 figures

Background: Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Ab initio approaches have been successfully applied to describe the $^3$H$(d,n)^4$He and $^3$He$(d,p)^4$He fusion processes. Purpose: An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of $(d,p)$ reactions to processes with light $p$-shell nuclei. As a first application, we study the elastic scattering of deuterium on $^7$Li and the ${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction based on a two-body Hamiltonian. Methods: We use the no-core shell model to compute the wave functions of the nuclei involved in the reaction, and describe the dynamics between targets and projectiles with the help of microscopic-cluster states in the spirit of the resonating group method. Results: The shape of the excitation functions for deuteron impinging on ${}^{7}$Li are qualitatively reproduced up to the deuteron breakup energy. The interplay between $d$-$^7$Li and $p$-$^8$Li particle-decay channels determines some features of the ${}^{9}$Be spectrum above the $d$+${}^{7}$Li threshold. Our prediction for the parity of the 17.298 MeV resonance is at odds with the experimental assignment Conclusions: Deuteron stripping reactions with $p$-shell targets can now be computed ab initio, but calculations are very demanding. A quantitative description of the ${}^{7}$Li($d$,$p$)${}^{8}$Li reaction will require further work to include the effect of three-nucleon forces and additional decay channels, and improve the convergence rate of our calculations., 16 pages, 11 figures, submitted to Phys. Rev. C

The ${^3{\rm He}}(\alpha,\gamma){^7{\rm Be}}$ and ${^3{\rm H}}(\alpha,\gamma){^7{\rm Li}}$ astrophysical $S$ factors are evaluated at low collision energies (less than 2.5 MeV in the centre-of-mass frame) within the no-core shell model with continuum approach using a renormalized chiral nucleon-nucleon interaction., Comment: 4 pages, submitted as a proceeding of the 21st International Conference on Few-Body Problems in Physics

Here, we provide a unified ab initio description of the 6Li ground state and elastic scattering of deuterium (d) on 4He (α) using two- and three-nucleon forces from chiral effective field theory. We analyze the influence of the three-nucleon force and reveal the role of continuum degrees of freedom in shaping the low-lying spectrum of 6Li. The calculation reproduces the empirical binding energy of 6Li, yielding an asymptotic D- to S-state ratio of the 6Li wave function in the d+α configuration of –0.027, in agreement with a determination from 6Li–4He elastic scattering, but overestimates the excitation energy of the 3+ state by 350 keV. The bulk of the computed differential cross section is in good agreement with data. These results endorse the application of the present approach to the evaluation of the 2H(α,γ)6Li radiative capture, responsible for the big-bang nucleosynthesis of 6Li.

We extend the recently proposed ab initio no-core shell model with continuum to include three-nucleon (3N) interactions beyond the few-body domain. The extended approach allows for the assessment of effects of continuum degrees of freedom as well as of the 3N force in ab initio calculations of structure and reaction observables of $p$- and lower-$sd$-shell nuclei. As a first application we concentrate on energy levels of the $^{9}\mathrm{Be}$ system for which all excited states lie above the n-$^{8}\mathrm{Be}$ threshold. For all energy levels, the inclusion of the continuum significantly improves the agreement with experiment, which was an issue in standard no-core shell model calculations. Furthermore, we find the proper treatment of the continuum indispensable for reliable statements about the quality of the adopted 3N interaction from chiral effective field theory. In particular, we find the ${\frac{1}{2}}^{+}$ resonance energy, which is of astrophysical interest, in good agreement with experiment.

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, USA

An {\em ab initio} (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable to further our understanding of the fundamental interactions among nucleons, and provide accurate predictions of crucial reaction rates for nuclear astrophysics, fusion-energy research, and other applications. In this contribution we review {\em ab initio} calculations for nucleon and deuterium scattering on light nuclei starting from chiral two- and three-body Hamiltonians, obtained within the framework of the {\em ab initio} no-core shell model with continuum. This is a unified approach to nuclear bound and scattering states, in which square-integrable energy eigenstates of the $A$-nucleon system are coupled to $(A-a)+a$ target-plus-projectile wave functions in the spirit of the resonating group method to obtain an efficient description of the many-body nuclear dynamics both at short and medium distances and at long ranges., Comment: 9 pages, 5 figures, proceedings of the 21st International Conference on Few-Body Problems in Physics

We provide a unified ab initio description of the ^{6}Li ground state and elastic scattering of deuterium (d) on ^{4}He (α) using two- and three-nucleon forces from chiral effective field theory. We analyze the influence of the three-nucleon force and reveal the role of continuum degrees of freedom in shaping the low-lying spectrum of ^{6}Li. The calculation reproduces the empirical binding energy of ^{6}Li, yielding an asymptotic D- to S-state ratio of the ^{6}Li wave function in the d+α configuration of -0.027, in agreement with a determination from ^{6}Li-^{4}He elastic scattering, but overestimates the excitation energy of the 3^{+} state by 350 keV. The bulk of the computed differential cross section is in good agreement with data. These results endorse the application of the present approach to the evaluation of the ^{2}H(α,γ)^{6}Li radiative capture, responsible for the big-bang nucleosynthesis of ^{6}Li.

Low-energy cross sections for elastic scattering and recoil of protons from 4He nuclei (also known as α particles) are calculated directly by solving the Schrodinger equation for five nucleons interacting through accurate two- and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe the concentrations and depth profiles of either hydrogen or helium. Furthermore, we compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among data sets and can be used to predict these cross sections when measurements are not available.

The low-lying continuum spectrum of the $^{6}\mathrm{He}$ nucleus is investigated for the first time within an ab initio framework that encompasses the $^{4}\mathrm{He}+n+n$ three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schr\"odinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known ${J}^{\ensuremath{\pi}}={2}^{+}$ resonance as well as a result consistent with a new low-lying second ${2}^{+}$ resonance recently observed at GANIL at 2.6 MeV above the $^{6}\mathrm{He}$ ground state. We also find resonances in the ${2}^{\ensuremath{-}}$, ${1}^{+}$, and ${0}^{\ensuremath{-}}$ channels, while no low-lying resonances are present in the ${0}^{+}$ and ${1}^{\ensuremath{-}}$ channels.

The low-lying continuum spectrum of the (6)He nucleus is investigated for the first time within an ab initio framework that encompasses the (4)He + n + n three-cluster dynamics characterizing its lowest decay channel. This is achieved through an extension of the no-core shell model combined with the resonating-group method, in which energy-independent nonlocal interactions among three nuclear fragments can be calculated microscopically, starting from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrödinger equation is solved with three-body scattering boundary conditions by means of the hyperspherical-harmonics method on a Lagrange mesh. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we find the known J(π) = 2(+) resonance as well as a result consistent with a new low-lying second 2(+) resonance recently observed at GANIL at 2.6 MeV above the (6)He ground state. We also find resonances in the 2(-), 1(+), and 0(-) channels, while no low-lying resonances are present in the 0(+) and 1(-) channels.

An ab initio (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable as a support tool for accurate evaluations of crucial reaction data for nuclear astrophysics, fusion-energy research, and other applications. We present an efficient many-body approach to nuclear bound and scattering states alike, known as the ab initio no-core shell model with continuum. In this approach, square-integrable energy eigenstates of the A-nucleon system are coupled to (A-A)+A target-plus-projectile wave functions in the spirit of the resonating group method to obtain an efficient description of the many-body nuclear dynamics both at short and medium distances and at long ranges. We show that predictive results for nucleon and deuterium scattering on 4He nuclei can be obtained from the direct solution of the Schröedinger equation with modern nuclear potentials.

The recently proposed symmetry-conserving energy density functional approach [G. Hupin, D. Lacroix, and M. Bender, Phys. Rev. C 84, 014309 (2011)] is applied to perform variation after projection onto the good particle number using the Skyrme interaction, including density-dependent terms. We propose a simplification to reduce the numerical effort to perform the variation. We present a systematic study of the Kr and Sn isotopic chains. This approach leads to nonzero pairing in magic nuclei and a global enhancement of the pairing gap compared to the original theory, which breaks particle number symmetry.

An alternative approach to symmetry restoration within Energy Density Functional, the Symmetry-Conserving EDF is discussed. In this approach, the energy is directly written in terms of the degrees of freedom encoded in the one-, two-... body density matrices of the state having good quantum numbers. The SC-EDF framework is illustrated within Projection After and Before variation applied to particle number restoration., Comment: Proceedings of the YKIS2011 symposium, 11-15 October (2011), Kyoto, Japan

The combination of functional theory where the energy is written as a functional of the density, and the configuration mixing method, provides an efficient description of nuclear ground and excited state properties. The specific pathologies that have been recently observed, show the lack of a clear underlying justification associated to the breaking and the restoration of symmetries within density functional theory. This thesis focuses on alternative treatments of pairing correlations in finite many body systems that consider the breaking and the restoration of the particle number conservation. The energy is written as a functional of a projected quasi-particle vacuum and can be linked to the one obtained within the configuration mixing framework. This approach has been applied to make the projection either before or after the application of the variational principle. It is more flexible than the usual configuration mixing method since it can handle more general effective interactions than the latter. The application to the Krypton isotopes shows the feasibility and the efficiency of the method to describe pairing near closed shell nuclei. Following a parallel path, a theory where the energy is written as a functional of the occupation number and natural orbitals is proposed. The new functional is benchmarked in an exactly solvable model, the pairing Hamiltonian. The efficiency and the applicability of the new theory have been tested for various pairing strengths, single particle energy spectra and numbers of particles.; L'utilisation conjointe d'une théorie où l'énergie est écrite comme une fonctionnelle de la densité et du mélange de configuration, permet de décrire précisément les propriétés des états nucléaires. Les contributions spurieuses observées récemment ont mis en évidence la nécessité de corriger les énergies et soulignent le manque de fondements théoriques associé aux brisures et aux restaurations de symétries dans une approche fonctionnelle. Dans cette thèse, des théories alternatives permettant de briser puis de restaurer la conservation du nombre de particules pour décrire les corrélations d'appariement, ont été proposé. Ainsi, l'énergie peut s'écrire comme une fonctionnelle d'un état de vide de quasi-particule projeté et peut être reliée à celle obtenue à l'aide du mélange de configurations. Cette approche est appliquée soit pour faire des projections après ou avant l'application du principe variationnel et montre une très grande flexibilité par rapport aux méthodes standards. En particulier, il est possible d'utiliser des interactions effectives très générales. Une application à la chaîne isotopique des Kryptons démontre à la fois la faisabilité et l'amélioration du traitement de l'appariement dans les noyaux proches de la magicité. Dans un second temps, une théorie où l'énergie est directement écrite comme une fonction des nombres d'occupation et des orbitales naturelles, est proposée. Cette nouvelle fonctionnelle est validée dans le cas d'un Hamiltonien de pairing exactement soluble. Le pouvoir prédictif de cette approche est démontré dans des conditions diverses de l'intensité de l'appariement, des espacements des énergies à un corps et de nombre de particules.

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., 11 pages, 3 figures

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing Hamiltonian where even and odd systems, using blocking technique are studied, at various particle number and coupling strength, with uniform and random single-particle level spacing. In all cases, a very good agreement is found with a deviation inferior to 1% compared to the exact energy., Comment: 14 pages, 9 figures

In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated in different approaches including the Markovian limit. Large differences with the exact result are seen in the latter case or when only second order in the coupling strength is considered as it is generally assumed in nuclear transport models. On opposite, if fourth order in the coupling or quantum Monte-Carlo method is used, a perfect agreement is obtained., 10 pages, 6 figures, to be published in Phys. Rev. C

A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is benchmarked with the pairing Hamiltonian and reproduces perfectly the energy for any particle number and coupling., Comment: 4 pages, 4 figures, revised version

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- Niigata2010

A quantum Monte-Carlo is proposed to describe fusion/fission processes when fluctuation and dissipation, with memory effects, are important. The new theory is illustrated for systems with inverted harmonic potentials coupled to a heat-bath., Proceedings of the international conference: "Nuclear Structure and related topics, Dubna, June (2009)

The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated in the Caldeira-Leggett model where a harmonic oscillator is coupled to a bath of harmonic oscillators. Similar exact reformulation could be used to extend mean-field transport theories in Many-body systems and incorporate two-body correlations beyond the mean-field one. The connection between open quantum system and closed many-body problem is discussed., Proceedings series of Proceedings of "FUSION08: New Aspects of Heavy Ion Collisions near the Coulomb Barrier", September 22-26, 2008, Chicago, USA

The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional., proceeding of the conference "Many body correlations from dilute to dense Nuclear systems", Paris, February 2011