The first excited 0(+) state in 12C (Hoyle state) has been predicted to be a dilute self-bound gas of bosonic alpha particles, similar to a Bose-Einstein condensate. To clarify this conjecture, precise electron scattering data on form factors of the ground state and the transition to the Hoyle state are compared with results of the fermionic molecular dynamics model, a microscopic alpha-cluster model, and an alpha-cluster model with reduced degrees of freedom (in the spirit of a Bose-Einstein condensed state). The data indicate clearly a dilute density with a large spatial extension of the Hoyle state. A closer inspection of the model calculations, which reproduce the experimental findings, reveals that the term Bose-Einstein condensation of three alpha particles must not be taken too literally.
The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a transformation of the relative distance between particle pairs, general analytic expressions for the correlated wave functions and correlated operators are given. The decomposition of correlated operators into irreducible n-body operators is discussed. The one- and two-body-irreducible parts are worked out explicitly and the contribution of three-body correlations is estimated to check convergence. Ground state energies of nuclei up to mass number A=48 are calculated with a spin-isospin-dependent potential and single Slater determinants as uncorrelated states. They show that the deduced energy- and mass-number-independent correlated two-body Hamiltonian reproduces all "exact" many-body calculations surprisingly well.Comment: 43 pages, several postscript figures, uses 'epsfig.cls'. Submitted to Nucl. Phys. A. More information available at http://www.gsi.de/~fm
We present a unitary correlation operator that explicitly induces into shell model type many-body states short ranged two-body correlations caused by the strong repulsive core and the pronounced tensor part of the nucleon-nucleon interaction. Alternatively an effective Hamiltonian can be defined by applying this unitary correlator to the realistic nucleon-nucleon interaction. The momentum space representation shows that realistic interactions which differ in their short range behaviour are mapped on the same correlated Hamiltonian, indicating a successful provision for the correlations at high momenta. Calculations for 4 He using the one-and twobody part of the correlated Hamiltonian compare favorably with exact many-body methods. For heavier nuclei like 16 O and 40 Ca where exact many-body calculations are not possible we compare our results with other approximations. The correlated single-particle momentum distributions describe the occupation of states above the Fermi momentum. The Unitary Correlation Operator Method (UCOM) can be used in mean-field and shell model configuration spaces that are not able to describe these repulsive and tensor correlations explicitly.
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.Comment: 5 pages, proceedings of the 8th International conference on Clustering Aspects of Nuclear Structure and Dynamics, Nov. 2003, Nara, Japan, to be published in Nucl. Phys.
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