Article

# Exactly solvable pairing Hamiltonian for heavy nuclei

Physical Review C (Impact Factor: 3.88). 09/2011; 84. DOI: 10.1103/PhysRevC.84.061301

Source: arXiv

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**ABSTRACT:**The present paper makes a connection between collective bosonic states and the exact solutions of the $p_x + ip_y$ pairing Hamiltonian. This makes it possible to investigate the effects of the Pauli principle on the energy spectrum, by gradually reintroducing the Pauli principle. It also introduces an efficient and stable numerical method to probe all the eigenstates of this class of Hamiltonians.Physical Review B 02/2014; 89(15). · 3.66 Impact Factor -
##### Article: New Kohn-Sham density functional based on microscopic nuclear and neutron matter equations of state

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**ABSTRACT:**A new version of the Barcelona-Catania-Paris energy functional is applied to a study of nuclear masses and other properties. The functional is largely based on calculated ab initio nuclear and neutron matter equations of state. Compared to typical Skyrme functionals having 10–12 parameters apart from spin-orbit and pairing terms, the new functional has only 2 or 3 adjusted parameters, fine tuning the nuclear matter binding energy and fixing the surface energy of finite nuclei. An energy rms value of 1.58 MeV is obtained from a fit of these three parameters to the 579 measured masses reported in the Audi and Wapstra [Nucl. Phys. A 729, 337 (2003)] compilation. This rms value compares favorably with the one obtained using other successful mean field theories, which range from 1.5 to 3.0 MeV for optimized Skyrme functionals and 0.7 to 3.0 for the Gogny functionals. The other properties that have been calculated and compared to experiment are nuclear radii, the giant monopole resonance, and spontaneous fission lifetimes.Physical Review C 06/2013; 87(6). · 3.88 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The exact solution of the SU(2) pairing Hamiltonian with non-degenerate single particle orbits was introduced by Richardson in the early sixties. Since then it has been extended to several families of integrable models, called the Richardson-Gaudin (RG) models. In particular, the rational family of integrable RG models has been widely applied to mesoscopic systems like small grains, quantum dots and nuclear systems where finite size effects play an important role. We introduce these families of integrable models and then we describe a new separable pairing Hamiltonian derived from the hyperbolic family that provides an excellent reproduction of Gogny self-consistent mean-field calculations for heavy nuclei.10/2012;

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