T. Papenbrock

Coupled-cluster computations of atomic nuclei

In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.

Evolution of shell structure in neutron-rich calcium isotopes.

We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying J(π) = 2+ states for the isotopes (42,48,50,52)Ca are in good agreement with data, and we predict the excitation energy of the first J(π) = 2+ state in (54)Ca at 1.9 MeV, displaying only a weak subshell closure. In the odd-mass nuclei (53,55,61)Ca we find that the positive parity states deviate strongly from the naive shell model.

Optimized Chiral Nucleon-Nucleon Interaction at Next-to-Next-to-Leading Order

We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next-to-leading order (NNLO). The resulting new chiral force NNLO(opt) yields χ(2)≈1 per degree of freedom for laboratory energies below approximately 125 MeV. In the A=3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLO(opt) to study properties of key nuclei and neutron matter, and we demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.

Accurate nuclear radii and binding energies from a chiral interaction

With the goal of developing predictive ab initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLOsat, yield accurate binding energies and radii of nuclei up to Ca-40, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low-lying collective J(pi) = 3(-) states in O-16 and 40Ca are described accurately, while spectra for selected p- and sd-shell nuclei are in reasonable agreement with experiment.

Coupled Cluster Calculations of Ground and Excited States of Nuclei

The standard and renormalized coupled cluster methods with singles, doubles, and noniterative triples and their generalizations to excited states, based on the equation of motion coupled cluster approach, are applied to the 4He and 16O nuclei. A comparison of coupled cluster results with the results of the exact diagonalization of the Hamiltonian in the same model space shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei. The bulk of the correlation effects is obtained at the coupled cluster singles and doubles level. Triples, treated noniteratively, provide the virtually exact description.

Continuum Effects and Three-Nucleon Forces in Neutron-Rich Oxygen Isotopes

We employ interactions from chiral effective field theory and compute binding energies, excited states, and radii for isotopes of oxygen with the coupled-cluster method. Our calculation includes the effects of three-nucleon forces and of the particle continuum, both of which are important for the description of neutron-rich isotopes in the vicinity of the nucleus 24O. Our main results are the placement of the neutron drip line at 24O, the assignment of spins, parities and resonance widths for several low-lying states of the drip line nucleus, and an efficient approximation that incorporates the effects of three-body interactions.

Medium-mass nuclei from chiral nucleon-nucleon interactions.

We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ a bare chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the coupled-cluster singles-doubles approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.

Colloquium: Random matrices and chaos in nuclear spectra

Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification.

Coupled-cluster theory for three-body Hamiltonians

We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of {sup 4}He. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.

Pairing in low-density Fermi gases

In the theory of fermionic matter, the expansion about the low-density limit has been invaluable for understanding the structure of the theory and the role of the interaction. At low densities, the interaction needs only be characterized by its scattering length to get expansions for the energy density, excitation spectrum, etc. @1#. However, to our knowledge the pairing singularity has never been incorporated into this framework. We have for example only the qualitative statement in Ref. @1# that the pairing singularity is logarithmic and unimportant for integrated quantities. A more quantitative statement is needed to have complete understanding of low-density fermionic matter. Another motivation for our study is the general reexamination of nuclear physics with effective field theory which is now taking place @2‐9#. In the effective field theory approach, the interaction is systematically expanded in a power series in momentum with the object of getting relationships between observables such that the details of the shortdistance interaction need not be parameterized. We shall show here that the BCS theory of pairing is amenable to this approach, and the low-energy theory gives finite and analytic results. Within effective field theory many results can be obtained analytically opposed to the numerical treatment of potential models. In this sense our approach complements the large body of literature of pairing in nuclear and neutron matter that is based on potential models @10‐16#. We consider a Fermi gas with two-fold degeneracy interacting with a short-range attractive interaction. Examples are neutron matter or gaseous 3 He. The Hamiltonian is idealized to be of the form