RPA abstracts

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The Selfconsistent Quasiparticle RPA and Its Description of Thermal Pairing Properties in Nuclei

Nguyen Dinh Dang

1 - Heavy-Ion Nuclear Physics Laboratory, Nishina Center for Accelerator-Based Science RIKEN 2-1 Hirosawa, Wako city, 351-0198 Saitama, Japan

2 - Institute for Nuclear Science and Techniques, Vietnam Atomic Energy Commission Hanoi - Vietnam

The Selfconsistent Quasiparticle RPA (SCQRPA) is constructed [1] to study the effects of fluctuations on pairing properties in finite systems. The theory is applied to nuclei at finite temperature [2] and angular momentum [3]. Particle number projection is taken into account within the Lipkin-Nogami method. Several issues such as the smoothing of superfluid-normal phase transition, thermally assisted pairing in hot rotating nuclei, extraction of the nuclear pairing gap using an improved odd-even mass difference are discussed [4]. Finally, a novel approach of embedding the projected SCQRPA eigenvalues in the canonical ensemble (CE) is proposed (the CE-SCQRPA) [5]. Applied to a doubly-folded equidistant multilevel pairing model, the proposed CE-SCQRPA produces results in good agreement with those obtained by using the exact eigenvalues, whenever the latter are possible, and is workable also for large values of particle number (N>14), where the diagonalisation of the pairing Hamiltonian is impracticable.

References

[1] N. Quang Hung and N. Dinh Dang, 
Phys. Rev. C 76 (2007) 054302 and 77 (2008) 029905(E).

[2] N. Dinh Dang and N. Quang Hung, 
Phys. Rev. C 77 (2008) 064315.

[3] N. Quang Hung and N. Dinh Dang, 
Phys. Rev. C 78 (2008) 064315.

[4] N. Quang Hung and N. Dinh Dang, 
Phys. Rev. C 79 (2009) 054328.

[5] N. Quang Hung and N. Dinh Dang, in preparation

The two faces of RPA: density functional theory and many-body perturbation theory

Xavier Gonze

Unité Physico-Chimie et de Physique des Matériaux (PCPM), Université catholique de Louvain, Place Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgique

The RPA expression for total energy might be derived either within density functional theory, (in the adiabatic-connection fluctuation-dissipation framework, by setting the exchange-correlation kernel to zero), or from many-body perturbation theory (from the Nozières functional in the GW approximation for the self-energy, when the green's function corresponds to an energy-independent one-body Hamiltonian). I will review results in which these two faces of RPA appear. First, the RPA exchange-correlation potential is obtained from a linear-response Sham-Schlüter equation [1,2]. Second, the RPA band gap (I-A expression) corresponds to non-renormalized G_0 W_0 [3]. I will also show that density functional theory within the RPA provides a correct description of bond dissociation for the hydrogen dimer in a spin-restricted Kohn-Sham formalism, i.e., without artificial symmetry breaking, with important static (left-right) correlation [4]. Although exact at infinite separation and accurate near the equilibrium bond length [5], the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths [4,6].

References

[1] Y.-M. Niquet, M. Fuchs, X. Gonze, J. Chem. Phys. 118, 9504 (2003)

[2] Y.-M. Niquet, M. Fuchs, X. Gonze, Phys. Rev. A 68, 032507 (2003)

[3] Y.-M. Niquet, X. Gonze, Phys. Rev. B 70, 245115 (2004)

[4] M. Fuchs, Y.-M. Niquet, X. Gonze, K. Burke, J. Chem. Phys. 122, 094116 (2005)

[5] M. Fuchs, X. Gonze, Phys. Rev. B 65, 235109 (2002)

[6] M. Fuchs, K. Burke, Y.-M. Niquet, X. Gonze, Phys. Rev. Lett. 90, 189701 (2003)

How approximate is the random phase approximation? Comparing RPA against full configuration-interaction calculations

Calvin W. Johnson

Department of Physics, San Diego State University, USA

I compare the random phase approximation against numerically exact configuration-interaction calculations in the nuclear shell model and find good, not perfect, results. This is of particular importance when one is using a phenomenological interaction. I also discuss the so-called "collapse" of RPA in "phase changes" and illustrate the difference between first- and second-order phase changes and how collapse occurs in only one.

References

[1]

[2]

RPA and coupled cluster theory & some recent results including range separation

Gustavo E. Scuseria

Department of Chemistry and Department of Physics & Astronomy, Rice University, Houston, Texas, USA

The recent realization that the ground-state correlation energy of the random phase approximation (RPA) is intimately connected to an approximate coupled cluster doubles (CCD) model [1], opens interesting avenues for mixing RPA with DFT [2]. I will describe some of the recent work done in our research group on RPA, including applications to van der waals and noncovalent interactions [3], the importance of the reference state [4], a simple second-order approximation [5], and a second-order exchange (SOSX) correction that restores antisymmetry [6].

References

[1] The ground state correlation energy of the Random Phase Approximation from a ring Coupled Cluster Doubles approach, G. E. Scuseria, T. M. Henderson, and D. C. Sorensen, J. Chem. Phys. 129, 231101 (2008).

[2] Long-range-corrected hybrids including random phase approximation correlation, B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009).

[3] Long-range corrected hybrid functionals including random phase approximation correlation: Application to noncovalent interactions, B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 131, 034110 (2009).

[4] The role of the reference state in long-range random phase approximation correlation, B. G. Janesko and G. E. Scuseria, J. Chem. Phys. 131, 154106 (2009).

[5] Coulomb-only second-order perturbation theory in long-range-corrected hybrid density functionals, B. G. Janesko and G. E. Scuseria, Phys. Chem. Chem. Phys. 11, 9677 (2009).

[6] Hybrid functionals including random phase approximation correlation and second-order screened exchange, J. Paier, B. G. Janesko, T. M. Henderson, G. E. Scuseria, A. Gruneis, and G. Kresse, J. Chem. Phys. submitted.

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