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(alpha,gamma)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 alpha-cluster structure, whereas the third 0+ state features a chain-like obtuse triangle structure. We also calculate the N hbar Omega decomposition of our wave functions to illuminate the challenges of no-core shell model calculations for these cluster states.Comment: 7 pages, Proceedings of Horizons of Innovative Theories, Experiments, and Supercomputing in Nuclear Physics (HITES 2012

Microscopic calculation of the 3He(alpha,gamma)7Be and 3H(alpha,gamma)7Li capture 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%.Comment: 4 pages, 5 figures, published versio

Clusters, Halos, And S-Factors In Fermionic Molecular Dynamics

In Fermionic Molecular Dynamics antisymmetrized products of Gaussian wave packets are projected on angular momentum, linear momentum, and parity. An appropriately chosen set of these states span the many-body Hilbert space in which the Hamiltonian is diagonalized. The wave packet parameters - position, momentum, width and spin - are obtained by variation under constraints. The great flexibility of this basis allows to describe not only shell-model like states but also exotic states like halos, e.g. the two-proton halo in 17Ne, or cluster states as they appear for example in 12C close to the \alpha-breakup threshold where the Hoyle state is located. Even a fully microscopic calculation of the 3He(\alpha,\gamma)7Be capture reaction is possible and yields an astrophysical S-factor that compares very well with newer data. As representatives of numerous results these cases will be discussed in this contribution, some of them not published so far. The Hamiltonian is based on the realistic Argonne V18 nucleon-nucleon interaction.Comment: Presented at HIAS 2013, 8.-12. April 2013, Canberr

The Hoyle state and its relatives

The Hoyle state and other resonances in the continuum above the 3 alpha threshold in 12C are studied in a microscopic cluster model. Whereas the Hoyle state is a very sharp resonance and can be treated reasonably well in bound state approximation, the other higher lying states require a proper treatment of the continuum. The model space consists of an internal region with 3 alpha particles on a triangular grid and an external region consisting of the 8Be ground state and excited (pseudo)-states of 8Be with an additional alpha. The microscopic R-matrix method is used to match the many-body wave function to the asymptotic Coulomb behavior of bound states, Gamow states and scattering states. 8Be-alpha phase shifts are analyzed and resonance properties like radii and transition strengths are investigated.Comment: 7 pages, Talk given at SOTANCP3, 3rd International Workshop on State of the Art in Nuclear Cluster Physics, Yokohama, Japan, May 26-30, 201

Towards Microscopic Ab Initio Calculations of Astrophysical S-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(alpha,gamma)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 E1 transition matrix elements between the many-body scattering and bound states. For 3He(alpha,gamma)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(alpha,gamma)7Li reaction the calculated S-factor is about 15% above the data

Nuclear Structure in the Framework of the Unitary Correlation Operator Method

Correlations play a crucial role in the nuclear many-body problem. We give an overview of recent developments in nuclear structure theory aiming at the description of these interaction-induced correlations by unitary transformations. We focus on the Unitary Correlation Operator Method (UCOM), which offers a very intuitive, universal and robust approach for the treatment of short-range correlations. We discuss the UCOM formalism in detail and highlight the connections to other methods for the description of short-range correlations and the construction of effective interactions. In particular, we juxtapose UCOM with the Similarity Renormalization Group (SRG) approach, which implements the unitary transformation of the Hamiltonian through a very flexible flow-equation formulation. The UCOM- and SRG-transformed interactions are compared on the level of matrix elements and in many-body calculations within the no-core shell model and with Hartree-Fock plus perturbation theory for a variety of nuclei and observables. These calculations provide a detailed picture of the similarities and differences as well as the advantages and limitations of unitary transformation methods.Comment: 72 pages, 31 figure

Long Range Tensor Correlations in Charge and Parity Projected Fermionic Molecular Dynamics

Within the framework of Fermionic Molecular Dynamics a method is developed to better account for long range tensor correlations in nuclei when working with a single Slater determinant. Single-particle states with mixed isospin and broken parity build up an intrinsic Slater determinant which is then charge and parity projected. By minimizing the energy of this many-body state with respect to the parameters of the single-particle states and projecting afterwards on angular momentum ground state energies are obtained that are systematically lower than corresponding Hartree-Fock results. The realistic Argonne V18 potential is used and short range correlations are treated with the Unitary Correlation Operator Method. Comparison with exact few-body calculations shows that in $^4$He about one fifth of the correlation energy due to long-range correlations are accounted for. These correlations which extend over the whole nucleus are visualized with the isospin and spin-isospin density of the intrinsic state. The divergence of the spin-isospin density, the source for pion fields, turns out to be of dipole nature.Comment: 12 pages, 4 figure

Short-range correlations in nuclei with similarity renormalization group transformations

$\mathbf{Background:}$ Realistic nucleon-nucleon interactions induce short-range correlations in nuclei. To solve the many-body problem unitary transformations like the similarity renormalization group (SRG) are often used to soften the interactions. $\mathbf{Purpose:}$ Two-body densities can be used to illustrate how the SRG eliminates short-range correlations in the wave function. The short-range information can however be recovered by transforming the density operators. $\mathbf{Method:}$ The many-body problem is solved for $^4$He in the no core shell model (NCSM) with SRG transformed AV8' and chiral N3LO interactions. The NCSM wave functions are used to calculate two-body densities with bare and SRG transformed density operators in two-body approximation. $\mathbf{Results:}$ The two-body momentum distributions for AV8' and N3LO have similar high-momentum components up to relative momenta of about $2.5\,\mathrm{fm}^{-1}$, dominated by tensor correlations, but differ in their behavior at higher relative momenta. The contributions of many-body correlations are small for pairs with vanishing pair momentum but not negligible for the momentum distributions integrated over all pair momenta. Many-body correlations are induced by the strong tensor force and lead to a reshuffling of pairs between different spin-isospin channels. $\mathbf{Conclusions:}$ When using the SRG it is essential to use transformed operators for observables sensitive to short-range physics. Back-to-back pairs with vanishing pair momentum are the best tool to study short-range correlations.Comment: 13 pages, 9 figures, submitted to Phys. Rev.