Fermionic Molecular Dynamics Approach Research Articles

Clusters and halos in light nuclei

The fermionic molecular dynamics approach uses Gaussian wave packets as single-particle basis states. Many-body basis states are Slater determinants projected on parity, angular momentum and total linear momentum. The wave-packet basis is very flexible – FMD contains harmonic oscillator shell model and Brink-type cluster states as special cases. The parameters of the wave packets are obtained by variation. A realistic effective interaction derived from the Argonne V18 interaction by means of the unitary correlation operator method is employed. We discuss the fully microscopic calculation of the 3He(α, γ)7Be capture reaction within the FMD approach. The model space contains frozen cluster configurations at large distances and polarized configurations in the interaction region. The polarized configurations are essential for a successful description of the 7Be bound state properties and for the S- and D-wave scattering states. The calculated cross section agrees well with recent measurements regarding both the absolute normalization and the energy dependence. We also discuss the structure of the cluster states, including the famous Hoyle state, in 12C. From the two-body densities we conclude that the Hoyle state has a spatially extended triangular α-cluster structure, whereas the third 0+ state features a chain-like obtuse triangle structure. We also calculate the NħΩ decomposition of our wave functions to illuminate the challenges of no-core shell model calculations for these cluster states.

New measurement of the3He(α,γ)7Be cross section at medium energies

We report on a new cross-section measurement for the ${}^{3}$He($\ensuremath{\alpha}$, $\ensuremath{\gamma}$)${}^{7}$Be reaction at three medium energies of ${E}_{\mathrm{c}.\mathrm{m}.}$ between 1 and 3 MeV. The interest stems from the significant role played by the reaction in calculating an accurate solar neutrino flux and the primordial ${}^{7}$Li abundance. The energy dependence of the astrophysical ${S}_{34}$ factor observed in the present work, especially above 1 MeV, highlights the need to constrain theories in order to obtain a precise extrapolated value for ${S}_{34}(0)$. In this context, a comparison with the recent theoretical work in a fully microscopic fermionic molecular dynamics approach and a few other representative calculations emphasize the need for further experimental as well as theoretical work to resolve the existing conflicts.

Nuclear Charge Radius ofBe12

The nuclear charge radius of $^{12}$Be was precisely determined using the technique of collinear laser spectroscopy on the $2s_{1/2}\rightarrow 2p_{1/2, 3/2}$ transition in the Be$^{+}$ ion. The mean square charge radius increases from $^{10}$Be to $^{12}$Be by $\delta <r_{\rm c}^2>^{10,12} = 0.69(5) \fm^{2}$ compared to $\delta <r_{\rm c}^2>^{10,11} = 0.49(5) \fm^{2}$ for the one-neutron halo isotope $^{11}$Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of $^{12}$Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.

Microscopic calculation of the 3He(α,γ)7Be reaction rate using realistic interactions

The cross sections for the 3He(α,γ)7Be and the 3H(α,γ)7Li radiative capture reactions are calculated in the fully microscopic Fermionic Molecular Dynamics approach using a realistic effective interaction obtained in the Unitary Correlation Operator Method. The model space is divided in an external region where bound and scattering states are described by antisymmetrized products of 4He and 3He/3H ground states and an internal region where additional many-body wave functions obtained by variation after parity and angular momentum projection enlarge the Hilbert space. These additional configurations, representing polarized cluster configurations, are necessary for a successful description of the bound and scattering states. The calculated S-factor for the 3He(α,γ)7Be reaction is in good agreement with recent experimental data both in absolute normalization and energy dependence. In case of the isospin mirror reaction 3H(α,γ)7Li the calculated S-factor is larger than the experimental data by about 15%. Dipole matrix elements are analyzed in terms of overlap functions calculated from the A-body wave functions.

Microscopic calculation of the 3He(α,γ)7Be reaction rate using realistic interactions

The radiative capture cross sections for the 3He(α,γ)7Be and the 3H(α,γ)7Li reactions are calculated in the fully microscopic fermionic molecular dynamics approach. A realistic effective interaction derived in the unitary correlation operator method is employed. The model space consists of frozen cluster configurations at large distances and polarized configurations, obtained by variation of the many-body wave functions, in the interaction region. These polarized configurations are essential for the description of the 7Be and 7Li bound states and for the S- and D-wave scattering phase shifts. The calculated capture cross section agrees with both the normalization and the energy dependence of the modern 3He(α,γ)7Be data. In case of the 3H(α,γ)7Li reaction the energy dependence of the most recent data is described well but the normalization is larger by about 15% compared to experiment.

Microscopic Calculation of theHe3(α,γ)Be7andH3(α,γ)Li7Capture Cross Sections Using Realistic Interactions

The radiative capture cross sections for the 3He(alpha,gamma)7Be and 3H(alpha,gamma)7Li reactions are calculated in the fully microscopic fermionic molecular dynamics approach using a realistic effective interaction that reproduces the nucleon-nucleon scattering data. At large distances bound and scattering states are described by antisymmetrized products of 4He and 3He/3H ground states. At short distances the many-body Hilbert space is extended with additional many-body wave functions needed to represent polarized clusters and shell-model-like configurations. Properties of the bound states are described well, as are the scattering phase shifts. The calculated S factor for the 3He(alpha,gamma)7Be reaction agrees very well with recent experimental data both in absolute normalization and energy dependence. In case of the 3H(alpha,gamma)7Li reaction the calculated S factor is larger than available experimental data by about 15%.

Towards microscopic ab initio calculations of astrophysical [formula omitted]-factors

Low energy capture cross sections are calculated within a microscopic many-body approach using an effective Hamiltonian derived from the Argonne V18 potential. The dynamics is treated within Fermionic Molecular Dynamics (FMD) which uses a Gaussian wave-packet basis to represent the many-body states. A phase-shift equivalent effective interaction derived within the Unitary Correlation Operator Method (UCOM) that treats explicitly short-range central and tensor correlations is employed. As a first application the 3He(α,γ) 7Be reaction is presented. Within the FMD approach the microscopic many-body wave functions of the 3 / 2 − and 1 / 2 − bound states in 7Be as well as the many-body scattering states in the 1 / 2 + , 3 / 2 + and 5 / 2 + channels are calculated as eigenstates of the same microscopic effective Hamiltonian. Finally the S -factor is calculated from E 1 transition matrix elements between the many-body scattering and bound states. For 3He( α , γ ) 7Be the 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. For the 3H( α , γ ) 7Li reaction the calculated S -factor is about 15% above the data.

Microscopic Description of Few-Body Systems in the Fermionic Molecular Dynamics Approach

Fermionic Molecular Dynamics (FMD) is a microscopic approach for the description of light nuclei in the p- and sd-shell. Many-body basis states are Slater determinants of Gaussian wave-packets localized in phase space. Brink-type cluster states and harmonic oscillator shell model states are contained as special limiting cases in FMD. The FMD approach is used to study the spectrum of 12C with special emphasis on states with pronounced α-clustering including the Hoyle state. The FMD approach is also used to study 17Ne which is a candidate for a two-proton halo nucleus.

CLUSTER AND SHELL STRUCTURES IN THE FERMIONIC MOLECULAR DYNAMICS APPROACH

Nuclei in the p- and sd-shell are studied within the Fermionic Molecular Dynamics (FMD) model that uses Gaussian wave packets as single-particle states. Intrinsic many-body basis states are given by Slater determinants which have to be projected on parity, angular momentum and total linear momentum to restore the symmetries of the Hamiltonian. The flexibility of the Gaussian basis allows to economically describe states with shell structures as well as states featuring clustering or halos. The same effective interaction derived from the realistic Argonne V18 interaction in the Unitary Correlation Operator Method (UCOM) framework is used for all nuclei. We discuss the spectrum of 12 C with a special emphasis on the structure of the first excited 0+ state, the famous Hoyle state. In the FMD approach the Hoyle state is found to be dominated by dilute α-cluster configurations. Recent measurements of the charge radii of Neon isotopes show an intriguing behaviour. This can be explained in FMD calculations by a structure change from 17 Ne and 18 Ne which can be essentially considered as an 15 O or 16 O core plus two protons in s2 or d2 configurations, respectively. For the heavier isotopes we find that the admixture of 3 He and 4 He cluster configurations in the ground states leads to much larger charge radii than obtained in a mean-field calculation.

Nuclear structure and reactions in the fermionic molecular dynamics approach

The Fermionic Molecular Dynamics (FMD) model uses Gaussian wave packets as single-particle states. Intrinsic many-body basis states are constructed as Slater determinants which have to be projected on parity, angular momentum and total linear momentum to restore the symmetries of the Hamiltonian. The flexibility of the Gaussian basis allows to economically describe states with shell structures as well as states featuring clustering or halos. We use an effective interaction that is derived from the realistic Argonne V18 interaction by means of the Unitary Correlation Operator Method (UCOM). A phenomenological momentum-dependent two-body correction simulates contributions from missing three-body forces and three-body correlations. We discuss 12C with a special emphasis on the structure of the excited 0+ and 2+ states. We analyze the degree of α-clustering and confirm, taking inelastic electron scattering data into account, the conjecture that the Hoyle state has to be understood as a loosely bound system of alpha particles. We will also present first results on the application of FMD for the calculation of scattering phase shifts in 3He — 4He.

Clustering and other exotic phenomena in nuclei

Nuclei feature a rich variety of many-body phenomena. Especially the clustering of nucleons, which leads to molecule like structures, and halos formed by weakly bound nucleons are regarded as exotic phenomena that standard many-body methods like the shell model have difficulties to describe. On the other hand cluster models that build in such structures explicitly use very simplistic effective interactions and have often difficulties if shell model like configurations become important. In the Fermionic Molecular Dynamics approach we aim at a consistent description of well bound nuclei with shell structure as well as of nuclei featuring halos or clustering. We achieve this by exploiting the versatility of Gaussian wave packets. These are able to describe harmonic oscillator single-particle states and cluster states on the same footing. If we allow the width parameter to be a free variational parameter also halos can be described well in this basis. The many-body basis is given by Slater determinants of these wave packets. Different levels of sophistication can be achieved. In the simplest approach we perform a mean-field calculation by variation of the energy expectation value with respect to the single-particle parameters. The mean-field state might break the symmetries of the Hamiltonian which can be restored by explicit projection on parity, angular and linear momentum. In a more sophisticated approach we can perform the variation after projection. An approximate variation after projection can be done in the sense of the generator coordinate method where the intrinsic state is varied under constraints on generator coordinates like the radius or quadrupole deformation. Finally we can perform a multiconfiguration mixing calculation by diagonalizing the Hamiltonian in a set of projected many-body basis states. The same effective interaction is used for all nuclei. It is based on the VUCOM interaction derived from the realistic Argonne V18 interaction by explicitly including short-range central and tensor correlations within the Unitary Correlation Operator Method.

Cluster structures within Fermionic Molecular Dynamics

The many-body states in an extended Fermionic Molecular Dynamics approach are flexible enough to allow the description of nuclei with shell model nature as well as nuclei with cluster and halo structures. Different many-body configurations are obtained by minimizing the energy under constraints on collective variables like radius, dipole, quadrupole and octupole deformations. In the sense of the Generator Coordinate Method we perform variation after projection and multiconfiguration calculations. The same effective interaction derived from realistic interactions by means of the Unitary Correlation Operator Method is used for all nuclei. Aspects of the shell model and cluster nature of the ground and excited states of C12 are discussed. To understand energies and radii of neutron-rich He isotopes the soft-dipole mode is found to be important.