Beyond integrability for collective pairing systems

May 18, 2016, 2:15 PM





Pairing is an essential ingredient to understand the low-energy structure of atomic nuclei [1]. Whereas the Bardeen-Cooper-Schrieffer (BCS) Ansatz has proven very successful in capturing the collective nature of the nuclear pair excitations, there remain some important deficiencies related to finite-size effects of the nuclear many-body problem [1]. Richardson and Gaudin (RG) have shown that the finite-size reduced (s-wave) BCS Hamiltonian, the simplest yet most insightful model for nuclear pairing, is integrable and solvable using a Bethe Ansatz technique [2,3]. Moreover, the rapidities encoding the Ansatz allow for a clear-cut physical interpretation of the dominant pairing modes in the system [4]. However insightful, the effective applicability of the RG systems is limited due to the integrability constraints of the model. However, turning limitation into opportunity, the on-shell (integrable) Bethe Ansatz can also be used as an ideal starting point that already includes the collective pairing correlations in a qualitative sense, and in which the more realistic pairing correlations can be built in via conventional quantum many-body techniques.

In the present presentation, I will illustrate how the RG Bethe Ansatz offers insight into the pairing dynamics of nuclear systems, and show how one can go beyond integrability (either via variational [5] or coupled-cluster approaches [6]) to describe realistic pairing correlations in atomic nuclei

[1] Ring P and Schuck P 2004 The Nuclear Many-Body Problem 3rd ed (Berlin: Springer)

[2] Richardson R W 1963 Phys. Lett. 3 277

[3] Gaudin M 1976 J. Phys. (Paris) 37 1087

[4] De Baerdemacker S 2012 Phys. Rev. C 86 044332

[5] De Baerdemacker S et. al. (in preparation)

[6] Henderson T M, Scuseria G E, Dukelsky J, Signoracci A and Duguet T 2014 Phys. Rev. C 89 054305

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