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 4He. 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.

%B Physical Review C %V 76 %P 11 pages %8 09/2007 %G eng %N 3 %0 Journal Article %J European Physics Journal A %D 2006 %T Ab Initio Coupled-Cluster Calculations for Nuclei Using Methods of Quantum Chemistry %A Piotr Piecuch %A M. Wloch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A T. Papenbrock %A K. Kowalski %XWe report preliminary large scale ab initio calculations of ground and excited states of 16O using quantum chemistry inspired coupled cluster methods and realistic two-body interactions. By using the renormalized Hamiltonians obtained with a no-core G-matrix approach, we obtain the virtually converged results at the level of two-body interactions. Due to the polynomial scaling with the system size that characterizes coupled cluster methods, we can probe large model spaces with up to seven major oscillator shells, for which standard non-truncated shell-model calculations are not possible.

%B European Physics Journal A %V 25 %P 485-488 %8 09/2005 %G eng %N 1 %0 Journal Article %J International Journal of Modern Physics B %D 2006 %T Coupled Cluster Theory for Nuclei %A T. Papenbrock %A D. J. Dean %A J. R Gour %A G. Hagen %A M. {Hjorth-Jensen} %A M. Wloch %K Nuclear structure; light nuclei; coupled-cluster theory %XThis presentation focuses on some of the recent developments in low-energy nuclear structure theory, with emphasis on applications of coupled-cluster theory. We report on results for ground and excited states in 4He and 16O, and about extensions of coupled-cluster theory to treat three-body forces.

%B International Journal of Modern Physics B %V 20 %P 5338-5345 %G eng %N 30-31 %0 Journal Article %J Physical Review C %D 2006 %T Coupled-Cluster Calculations for Valence Systems around 16 O %A Piotr Piecuch %A J. R Gour %A M. {Hjorth-Jensen} %A M. Wloch %A D. J. Dean %XWe study the ground and low-lying excited states of 15O, 17O, 15N, and 17F using modern two-body nucleon-nucleon interactions and the suitably designed variants of the ab initio equation-of-motion coupled-cluster theory aimed at an accurate description of systems with valence particles and holes. A number of properties of 15O, 17O, 15N, and 17F, including ways the energies of ground and excited states of valence systems around 16O change as functions of the number of nucleons, are correctly reproduced by the equation-of-motion coupled-cluster calculations performed in up to eight major-oscillator shells. Certain disagreements with experiment are in part because of the degrees of freedom such as three-body interactions not accounted for in our effective two-body Hamiltonians. In particular, the calculated binding energies of 15O/15N and 17O/17F enable us to rationalize the discrepancy between the experimental and recently published [Phys. Rev. Lett. 94, 212501 (2005)] equation-of-motion coupled-cluster excitation energies for the Jπ=3- state of 16O. Our calculations demonstrate the feasibility of the equation-of-motion coupled-cluster methods to deal with valence systems around closed-shell nuclei and to provide results for systems beyond A=16.

%B Physical Review C %V 74 %P 18 pages %8 8/2006 %G eng %N 2 %0 Journal Article %J Physical Review C %D 2006 %T Coupled-cluster calculations for valence systems around O16 %A J. R Gour %A Piotr Piecuch %A M. {Hjorth-Jensen} %A M. Wloch %A D. J. Dean %XWe study the ground and low-lying excited states of {15O,} {17O,} {15N,} and {17F} using modern two-body nucleon-nucleon interactions and the suitably designed variants of the ab initio equation-of-motion coupled-cluster theory aimed at an accurate description of systems with valence particles and holes. A number of properties of {15O,} {17O,} {15N,} and {17F,} including ways the energies of ground and excited states of valence systems around {16O} change as functions of the number of nucleons, are correctly reproduced by the equation-of-motion coupled-cluster calculations performed in up to eight major-oscillator shells. Certain disagreements with experiment are in part because of the degrees of freedom such as three-body interactions not accounted for in our effective two-body Hamiltonians. In particular, the calculated binding energies of {15O/15N} and {17O/17F} enable us to rationalize the discrepancy between the experimental and recently published {[Phys.} Rev. Lett. 94, 212501 (2005)] equation-of-motion coupled-cluster excitation energies for the Jπ=3- state of {16O.} Our calculations demonstrate the feasibility of the equation-of-motion coupled-cluster methods to deal with valence systems around closed-shell nuclei and to provide results for systems beyond A=16.

%B Physical Review C %V 74 %P 024310 %8 08/2006 %G eng %0 Journal Article %J Physical Review Letters %D 2005 %T Ab Initio Coupled-Cluster Study of 16O %A M. Włoch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %A P. Piecuch %XWe report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0+ state. Incorporation of triples has no effect on the latter finding.

%B Physical Review Letters %V 94 %P 212501 %8 06/2005 %G eng %N 21 %0 Journal Article %J Physical Review Letters %D 2005 %T Ab Initio Coupled-Cluster Study of O %A Piotr Piecuch %A M. Wloch %A D. J. Dean %A J. R Gour %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %XWe report converged results for the ground and excited states and matter density of 16O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and algorithms developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a one-particle, one-hole nature, but it cannot describe the first-excited 0+ state. Incorporation of triples has no effect on the latter finding.

%B Physical Review Letters %V 94 %8 06/2005 %G eng %0 Conference Proceedings %B American Institute of Physics %D 2005 %T Bridging Quantum Chemistry and Nuclear Structure Theory: Coupled-Cluster Calculations for Closed- and Open-Shell Nuclei %A Piotr Piecuch %A M. Wloch %A J. R Gour %A D. J. Dean %A M. {Hjorth-Jensen} %A T. Papenbrock %XWe review basic elements of the single-reference coupled-cluster theory and discuss large scale ab initio calculations of ground and excited states of 15O, 16O, and 17O using coupled-cluster methods and algorithms developed in quantum chemistry. By using realistic two-body interactions and the renormalized form of the Hamiltonian obtained with a no-core G-matrix approach, we obtain the converged results for 16O and promising preliminary results for 15O and 17O at the level of two-body interactions. The calculated properties other than energies include matter density, charge radius, and charge form factor. The relatively low costs of coupled-cluster calculations, which are characterized by the low-order polynomial scaling with the system size, enable us to probe large model spaces with up to 7 or 8 major oscillator shells, for which non-truncated shell-model calculations for nuclei with A = 15 17 active particles are presently not possible. We argue that the use of coupled-cluster methods and computer algorithms developed by quantum chemists to calculate properties of nuclei is an important step toward the development of accurate and affordable many-body theories that cross the boundaries of various physical sciences. ©2005 American Institute of Physics

%B American Institute of Physics %S NUCLEI AND MESOSCOPIC PHYSICS: Workshop on Nuclei and Mesoscopic Physics: WNMP 2004 %I American Institute of Physics %C Melville, NY %V 777 %P 28-45 %8 7/2005 %G eng %0 Conference Proceedings %B Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics %D 2005 %T Coupled Cluster Approaches to Nuclei, Ground States and Excited States %A Piotr Piecuch %A D. J. Dean %A M. Jhorth-Jensen %A K. Kowalski %A T. Papenbrock %A M. Wloch %XWe present recent coupled-cluster studies of nuclei, with an emphasis on ground state and excited states of closed shell nuclei. Perspectives for future studies are delineated.

%B Key Topics in Nuclear Structure, Proceedings of the 8th International Spring Seminar on Nuclear Physics %C Paestum, Italy %8 2005 %G eng %0 Journal Article %J Nuclear Physics A %D 2005 %T Nuclear Structure Calculations with Coupled-Cluster Methods from Quantum Chemistry %A Piotr Piecuch %A D. J. Dean %A J. R Gour %A G. Hagen %A M. {Hjorth-Jensen} %A K. Kowalski %A T. Papenbrock %A M. Wloch %XWe present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.

%B Nuclear Physics A %V 752 %P 299-308 %8 04/2005 %G eng