Computational aspects of nuclear coupled-cluster theory

We discuss computational aspects of the spherical coupled-cluster method specific to the nuclear many-body problem. Using chiral nucleon-nucleon interaction at next-to-next-to-next-to leading order (N3LO) with cutoff Lambda = 500MeV, we present coupled-cluster results for the ground state of 40Ca. Scaling and performance studies are presented together with challenges we meet with when extending the coupled-cluster effort to nuclei mass hundred and beyond.Comment: 9 pages, 5 figures, Proceedings for YKIS2011 Symposiu

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$-scheme, which will eventually permit the treatment of doubly open-shell nuclei. Proof-of-principle calculations in an $N_{\text{max}}=6$ spherical harmonic oscillator basis are performed for $^{16,18,20}$O, $^{18}$Ne, $^{20}$Mg in the BCCD approximation with a chiral two-nucleon interaction, comparing to results obtained in standard coupled cluster theory when applicable. The breaking of $U(1)$ symmetry is monitored by computing the variance associated with the particle-number operator. The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e. potentially to reach several hundred additional mid-mass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei.Comment: 22 pages, 13 figure

Irreversible Investments, Dynamic Inconsistency and Policy Convergence

We study a model where two parties, one from the left and one from the right, compete for position. The election is to be held in the near future and the outcome is uncertain. Prior to the election, the members of both parties nominate their prime ministerial candidates. Investors care about the outcome since they may invest in irreversible domestic production capital. We find that there is political convergence in the nomination process. In some circumstances, it is only the median voter of the left-wing party that elects a more moderate candidate. In other instances, the members of both parties nominate more “conservative” candidates, but there is still convergence. We also show that a higher probability of the left winning the election increases the degree of convergence, while a more globalised economy (greater capital mobility) reduces it.capital mobility, dynamic inconsistency, political competition, policy convergence

Irreversible investments, dynamic inconsistency and policy convergence

We study a model where two parties, one from the left and one from the right, compete for position. The election is to be held in the near future and the outcome is uncertain. Prior to the election, the members of both parties nominate their prime ministerial candidates. Investors care about the outcome since they may invest in irreversible domestic production capital. We find that there is political convergence in the nomination process. In some circumstances, it is only the median voter of the left-wing party that elects a more moderate candidate. In other instances, the members of both parties nominate more "conservative" candidates, but there is still convergence. We also show that a higher probability of the left winning the election increases the degree of convergence, while a more globalised economy (greater capital mobility) reduces it.Policy Objectives; Policy Designs and Consistency; Policy Coordination; International Investment; Long-Term Capital Movements; Personal Income and Other Nonbusiness Taxes and Subsidies; Political Economy.

Electric dipole polarizability: from few- to many-body systems

We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4He and then we move to a heavier nucleus studying 16O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability.Comment: 4 pages, 2 figures, proceedings of the 21st International Conference on Few-Body Problems in Physics (FB21), May 2015, Chicag

Effective Interaction Techniques for the Gamow Shell Model

We apply a contour deformation technique in momentum space to the newly developed Gamow shell model, and study the drip-line nuclei 5He, 6He and 7He. A major problem in Gamow shell-model studies of nuclear many-body systems is the increasing dimensionality of many-body configurations due to the large number of resonant and complex continuum states necessary to reproduce bound and resonant state energies. We address this problem using two different effective operator approaches generalized to the complex momentum plane. These are the Lee-Suzuki similarity transformation method for complex interactions and the multi-reference perturbation theory method. The combination of these two approaches results in a large truncation of the relevant configurations compared with direct diagonalization. This offers interesting perspectives for studies of weakly bound systems.Comment: 18 pages, 17 figs, Revtex