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

Configuration mixing within the energy density functional formalism: pathologies and cures

Configuration mixing calculations performed in terms of the Skyrme/Gogny Energy Density Functional (EDF) rely on extending the Single-Reference energy functional into non-diagonal EDF kernels. The standard way to do so, based on an analogy with the pure Hamiltonian case and the use of the generalized Wick theorem, is responsible for the recently observed divergences and steps in Multi-Reference calculations. We summarize here the minimal solution to this problem recently proposed [Lacroix et al, arXiv:0809.2041] and applied with success to particle number restoration[Bender et al, arXiv:0809.2045]. Such a regularization method provides suitable corrections of pathologies for EDF depending on integer powers of the density. The specific case of fractional powers of the density[Duguet et al, arXiv:0809.2049] is also discussed.Comment: 5 pages, Proceedings of the French-Japanese Symposium, September 2008. To be published in Int. J. of Mod. Phys.

Quantal Extension of Mean-Field Dynamics

A method is presented for numerical implementation of the extended TDHF theory in which two-body correlations beyond the mean-field approximation are incorporated in the form of a quantal collision term. The method is tested in a model problem in which the exact solution can be obtained numerically. Whereas the usual TDHF fails to reproduce the long time evolution, a very good agreement is found between the extended TDHF and the exact solution.Comment: 22 Latex pages including 7 figure

A Lee-Yang--inspired functional with a density--dependent neutron-neutron scattering length

Inspired by the low--density Lee-Yang expansion for the energy of a dilute Fermi gas of density $\rho$ and momentum $k_F$, we introduce here a Skyrme--type functional that contains only $s$-wave terms and provides, at the mean--field level, (i) a satisfactory equation of state for neutron matter from extremely low densities up to densities close to the equilibrium point, and (ii) a good--quality equation of state for symmetric matter at density scales around the saturation point. This is achieved by using a density--dependent neutron-neutron scattering length $a(\rho$) which satisfies the low--density limit (for Fermi momenta going to zero) and has a density dependence tuned in such a way that the low--density constraint $|a(\rho) k_F| \le 1$ is satisfied at all density scales.Comment: 5 figure

From dilute matter to the equilibrium point in the energy--density--functional theory

Due to the large value of the scattering length in nuclear systems, standard density--functional theories based on effective interactions usually fail to reproduce the nuclear Fermi liquid behavior both at very low densities and close to equilibrium. Guided on one side by the success of the Skyrme density functional and, on the other side, by resummation techniques used in Effective Field Theories for systems with large scattering lengths, a new energy--density functional is proposed. This functional, adjusted on microscopic calculations, reproduces the nuclear equations of state of neutron and symmetric matter at various densities. Furthermore, it provides reasonable saturation properties as well as an appropriate density dependence for the symmetry energy.Comment: 4 figures, 2 table

Nucleon exchange in heavy-ion collisions within stochastic mean-field approach

Nucleon exchange mechanism is investigated in deep-inelastic symmetric heavy-ion collisions in the basis of the Stochastic Mean-Field approach. By extending the previous work to off-central collisions, analytical expression is deduced for diffusion coefficient of nucleon exchange mechanism. Numerical calculations are carried out for ${}^{40}$Ca + ${}^{40}$Ca and ${}^{90}$Zr + ${}^{90}$Zr systems and the results are compared with the phenomenological nucleon exchange model. Also, calculations are compared with the available experimental results of deep-inelastic collisions between calcium nuclei.Comment: 8 pages, 7 figure