T. Neff

Matrix elements and few-body calculations within the unitary correlation operator method

We employ the unitary correlation operator method (UCOM) to construct correlated, low-momentum matrix elements of realistic nucleon-nucleon interactions. The dominant short-range central and tensor correlations induced by the interaction are included explicitly by an unitary transformation. Using correlated momentum-space matrix elements of the Argonne V18 potential, we show that the unitary transformation eliminates the strong off-diagonal contributions caused by the short-range repulsion and the tensor interaction and leaves a correlated interaction dominated by low-momentum contributions. We use correlated harmonic oscillator matrix elements as input for no-core shell model calculations for few-nucleon systems. Compared to the bare interaction, the convergence properties are dramatically improved. The bulk of the binding energy can already be obtained in very small model spaces or even with a single Slater determinant. Residual long-range correlations, not treated explicitly by the unitary transformation, can easily be described in model spaces of moderate size allowing for fast convergence. By varying the range of the tensor correlator we are able to map out the Tjon line and can in turn constrain the optimal correlator ranges.

Nuclear structure based on correlated realistic nucleon–nucleon potentials

Abstract We present a novel scheme for nuclear structure calculations based on realistic nucleon–nucleon potentials. The essential ingredient is the explicit treatment of the dominant interaction-induced correlations by means of the unitary correlation operator method (UCOM). Short-range central and tensor correlations are imprinted into simple, uncorrelated many-body states through a state-independent unitary transformation. Applying the unitary transformation to the realistic Hamiltonian leads to a correlated, low-momentum interaction, which is well suited for all kinds of many-body models, e.g., Hartree–Fock or shell-model. We employ the correlated interaction, supplemented by a phenomenological correction, in the framework of variational calculations with antisymmetrised Gaussian trial states (fermionic molecular dynamics). Ground state properties of nuclei up to mass numbers A ≲ 60 are discussed. Binding energies, charge radii, and charge distributions are in good agreement with experimental data. We perform angular momentum projections of the intrinsically deformed variational states (projection after variation) to extract rotational spectra. Finally, we discuss perspectives for variation after projection and multi-configuration calculations.

Universality of short-range nucleon-nucleon correlations

RIKEN, Wako 351-0198,JapanIn nuclei, the nuclear interaction induces strong short-range correlations among the nucleons. Realistic nucleon-nucleoninteractions,whichreproducethenucleon-nucleo nscattering phase-shifts and deuteron properties, containshort-range repulsive and tensor components. Due to theshort-range repulsion, nucleon pairs will not be found atdistances below0.5fm. Thisis ree ctedbyahighmomen-tum component in the momentum distribution. The tensorcorrelations induce further momenta above the Fermi mo-mentum. Though these correlations can only be measuredindirectly, some physical observables may ree ct the highmomentum component. These days short-range correla-tionsattractincreasinginterest. Earlymeasurementswhi chtry to extract information on the short-range correlationshave been carried out at JLab [1]. These correlations alsoprovideimportantinformationonthesaturationpropertyi nnuclear matter.We investigate the structure of short-range correlationsin many-body states. The highly correlated many-bodystates are represented with an explicitly correlated basiswhich enables us to get a precise solution of a many-bodySchro¨dinger equation for a realistic interaction [2, 3]. T hevariational parameters in the basis are determined by astochastic variational method [2, 4] and the basis dimen-sion is increased until good convergence is reached. Weinvestigate the wave functions of

STRUCTURE OF LIGHT EXOTIC NUCLEI IN FERMIONIC MOLECULAR DYNAMICS

Helium and Beryllium isotopes are studied in the Fermionic Molecular Dynamics model. No a priori assumptions are made with respect to cluster structure or single-particle properties. An effective interaction based on the Argonne V18 interaction is used for all nuclei. Short-range central and tensor correlations are treated explicitly using a unitary correlation operator. Multiconfiguration calculations using the dipole and quadrupole moments as generator coordinates are able to describe the experimental binding energies and matter radii. The evolution of the cluster structure and the single-particle structure with increasing neutron number is discussed and predictions for yet unmeasured matter and charge radii are given.

From nucleon-nucleon interaction matrix elements in momentum space to an operator representation

Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the partial waves with low angular momentum. As a first application we use this method to obtain an operator representation for the Argonne potential transformed by means of the unitary correlation operator method and discuss the necessity of including momentum dependent operators. The resulting operator representation leads to the same results as the original momentum space matrix elements when applied to the two-nucleon system and various light nuclei. For applications in fermionic and antisymmetrized molecular dynamics, where an operator representation of a soft but realistic effective interaction is indispensable, a simplified version using a reduced set of operators is given.

Studying short-range correlations and momentum distributions with unitarily transformed operators

Short-range correlations in 4He are investigated using many-body wave functions obtained in the no-core shell model. The similarity renormalization group (SRG) is used to evolve the Argonne V8 interaction and the density operators. The effects of short-range correlations are reflected in the two-body densities in coordinate space as a function of the distance between two nucleons, or alternatively in in momentum space as function of the relative momentum between two nucleons. The SRG transformation is performed in two-body approximation. The importance of missing three-body and higher-body contributions is investigated by comparing results obtained for different flow parameters and by comparing to exact results with the bare Argonne V8 interaction obtained in the correlated Gaussian approach.

Nucleon-nucleon potentials in phase-space representation

A phase-space representation of nuclear interactions, which depends on the distance

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

vec{r}

Structure of light nuclei in Fermionic Molecular Dynamics

and relative momentum

Astrophysically important nuclear reactions

vec{p}