Microscopic Nuclear Structure and Reaction Calculations in the FMD Approach

Abstract

Fermionic Molecular Dynamics (FMD) is a microscopic many-body approach which has been used successfully to study the structure of light nuclei in the p-and sd-shell. FMD uses a Gaussian wave packet basis which contains the harmonic oscillator shell model and Brink-type cluster model wave functions as limiting cases. A realistic effective interaction that has been derived from the Argonne V18 interaction by treating explicitly short-range central and tensor correlations is employed. We present here a first application of the FMD approach to low-energy nuclear reactions, namely the 3 He(α,γ) 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. 11th Symposium on Nuclei in the Cosmos

New applications of renormalization group methods in nuclear physics

“…The effective interaction is derived by the Unitary Correlation Operator Method (UCOM) [80], which eliminates short-range and tensor correlations by unitary transformations guided by the SRG. An example of the capabilities of FMD is shown in figure 25, where the calculated astrophysical S-factor for 3 He(α, γ) 7 Be is compared to new high-quality experimental results [81,82,83]. FMD is the only model that has been able to describe both the energy dependence and normalization of the new data.…”

Survey of heavy-ion fusion hindrance for lighter systems

“…These calculations predict the highest S factors at the astrophysical important energies, E 3.67 MeV (T 9 1). Recently, Neff et al [17] have calculated fusion cross sections for the systems 16 Fig. 5.…”

“…Their excitation functions and reaction rates will have to come from theoretical calculations (as done in Refs. [16][17][18]). …”

Scattering of light nuclei

“…Only very recently the Green's function Monte Carlo [10], the no-coreshell model combined with the resonating group method (NCSM/RGM) [11,12] and the fermionic molecular dynamics [13] have made steps in this direction.…”