Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
Résumé
Background: Ab initio many-body methods have been developed over the past ten years to address closed-shell nuclei up to mass A ∼ 130 on the basis of realistic two-and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Purpose: 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, as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory. Methods: We formulate and apply 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 the 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 BCCSD code is implemented in m-scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU (2) symmetry associated with angular momentum conservation. Results: Proof-of-principle calculations in an Nmax = 6 spherical harmonic oscillator basis are performed for 16,18,20 O, 18 Ne, and 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. Conclusions: 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. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Mid-term extensions include the approximate treatment of triple corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U (1) and SU (2) symmetries.
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