Quantum Monte-Carlo method applied to Non-Markovian barrier transmission

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.Comment: 10 pages, 6 figures, to be published in Phys. Rev.

Non-Markovian effects in quantum system: an exact stochastic mean-field treatment

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.Comment: Proceedings of the international conference: "Nuclear Structure and related topics, Dubna, June (2009

Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?

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.Comment: proceeding of the conference "Many body correlations from dilute to dense Nuclear systems", Paris, February 201

Ab initio calculations of reactions with light nuclei

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 Physic

Description of Pairing correlation in Many-Body finite systems with density functional theory

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 figure

Quasifission at extreme sub-barrier energies

With the quantum diffusion approach the behavior of the capture cross-section is investigated in the reactions $^{92,94}$Mo + $^{92,94}$Mo, $^{100}$Ru + $^{100}$Ru, $^{104}$Pd + $^{104}$Pd, and $^{78}$Kr + $^{112}$Sn at deep sub-barrier energies which are lower than the ground state energies of the compound nuclei. Because the capture cross section is the sum of the complete fusion and quasifission cross sections, and the complete fusion cross section is zero at these sub-barrier energies, one can study experimentally the unique quasifission process in these reactions after the capture.Comment: 3 pages, 3 figure

Peculiarities of sub-barrier fusion with quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of fusion cross section, angular momentum, and astrophysical S-factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at turning point the decrease rate of the cross section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.Comment: 11 pages, 5 figure

Ab initio alpha-alpha scattering

Processes involving alpha particles and alpha-like nuclei comprise a major part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear supernovae. In an effort towards understanding alpha processes from first principles, we describe in this letter the first ab initio calculation of alpha-alpha scattering. We use lattice effective field theory to describe the low-energy interactions of nucleons and apply a technique called the adiabatic projection method to reduce the eight-body system to an effective two-cluster system. We find good agreement between lattice results and experimental phase shifts for S-wave and D-wave scattering. The computational scaling with particle number suggests that alpha processes involving heavier nuclei are also within reach in the near future.Comment: 6 pages, 6 figure

Sub-barrier capture with quantum diffusion approach: actinide-based reactions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed nuclei at subbarrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleusnucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated and experimental capture cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions leading to superheavy nuclei.Comment: 11 pages, 16 figures, Regular Articl