We present recent results in theoretical studies on nuclear structure and reaction beyond mean field, using the adiabatic self-consistent collective coordinate method and its extension. We also present new results with the finite-temperature Hartree-Fock-Bogoliubov calculation with the three-dimensional-coordinate-space representation.
We present here a first application of the Fermionic Molecular Dynamics (FMD) approach to low-energy nuclear reactions, namely the $^3$He($alpha$,$gamma$)$^7$Be radiative capture reaction. We divide the Hilbert space into an external region where the
system is described as $^3$He and $^4$He clusters interacting only via the Coulomb interaction and an internal region where the nuclear interaction will polarize the clusters. Polarized configurations are obtained by a variation after parity and angular momentum projection procedure with respect to the parameters of all single particle states. A constraint on the radius of the intrinsic many-body state is employed to obtain polarized clusters at desired distances. The boundary conditions for bound and scattering states are implemented using the Bloch operator. The FMD calculations reproduce the correct energy for the centroid of the $3/2^-$ and $1/2^-$ bound states in $^7$Be. The charge radius of the ground state is in good agreement with recent experimental results. The FMD calculations also describe well the experimental phase shift data in the $1/2^+$, $3/2^+$ and $5/2^+$ channels that are important for the capture reaction at low energies. Using the bound and scattering many-body wave functions we calculate the radiative capture cross section. The calculated $S$ factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments.
The SPIRAL facility at GANIL, operational since 2001, is described briefly. The diverse physics program using the re-accelerated (1.2 to 25 MeV/u) beams ranging from He to Kr and the instrumentation specially developed for their exploitation are pres
ented. Results of these studies, using both direct and compound processes, addressing various questions related to the existence of exotic states of nuclear matter, evolution of new magic numbers, tunnelling of exotic nuclei, neutron correlations, exotic pathways in astrophysical sites and characterization of the continuum are discussed. The future prospects for the facility and the path towards SPIRAL2, a next generation ISOL facility, are also briefly presented.
We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same mod
el space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.
Nuclear reaction rate ($lambda$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the
criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the $R$-layer in the region of $lambda = [1,2.5times10^{1}]$ have a more complicated out-going degree distribution than the one in the region of $lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $lambda = [1, 2.5times10^{1}]$ at $T_{9} = 3$ prefer $(gamma,p)$ and $({gamma,alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $beta$ stable line. This work offers a novel way to the big-data analysis on nuclear reaction network at stellar temperatures.
We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface th
ickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.