Number-Conserving Approximation for the Theory of the Pairing Interaction in Nuclei

Abstract

735results of this experiment indicate the persistence of rather sharp resonances through the giant-resonance region.Recently, Izumo 34,35 has presented a theory of "partial equilibrium" for nuclear reactions in which a few (3-7) nucleons share excitation energy. The model is an attempt to explain the existence of "intermediate reso nances^ or clumps of oscillator strength ranging in width from 100 to 400 keV. It may be that the reso nances observed in this experiment below 14 MeV are examples of such intermediate resonances.One prediction of the Izumo theory is that the reso-The pairing interaction is studied by means of the equations of motion. An approximation is derived which adheres strictly to particle-number conservation, but is otherwise quite close to the formalism of the Bardeen-Cooper-Schrieffer (BCS) theory. It yields ground-state energies and single-particle properties considerably improved over those of the latter theory, as evidenced by calculations for (i) the model of Pawlikowski and Rybarska, (ii) the model of the Ni isotopes solved exactly by Kerman, Lawson, and Mac Farlane. Though it does not yet surpass in accuracy several alternative improvements of the BCS theory, it is capable of systematic further development, including the treatment of more realistic potentials.

An exact solution of spherical mean-field plus orbit-dependent non-separable pairing model with two non-degenerate j-orbits

“…It has been shown that pairing interactions are key to elucidating ground state and low-energy spectroscopic properties of nuclei [5][6][7]. Though the Bardeen-Cooper-Schrieffer (BCS) [1] and the Hartree-Fock-Bogolyubov (HFB) approximations provide simple and clear pictures [6,8,9], tremendous efforts have been made in finding exact solutions to the problem [10][11][12][13][14][15]. It is known that spherical or deformed mean-field plus the standard (equal strength) pairing interaction can be solved exactly by using the Gaudin-Richardson method [18][19][20], which can now be solved more easily by using the extended Heine-Stieltjes polynomial approach [21][22][23][24].…”

An exact solution of spherical mean-field plus a special separable pairing model

“…In nuclear physics, the pairing interaction is key to elucidate ground state and low-energy spectroscopic properties of nuclei, such as binding energies, oddeven effects, single-particle occupancies, excitation spectra, and moments of inertia, etc [5][6][7]. Though the Bardeen-Cooper-Schrieffer (BCS) [1] and the more refined Hartree-Fock-Bogolyubov (HFB) approximations provide simple and clear pictures in nuclei [6,8,9], tremendous efforts have been made in finding accurate solutions to the problem [10][11][12][13][14][15] to overcome serious drawbacks in the BCS and the HFB resulting from particle number-nonconservation effects [13,[15][16][17]. It is known that either spherical or deformed mean-field plus the standard orbit independent pairing interaction can be solved exactly by using the Gaudin-Richardson method [18][19][20].…”

An exactly solvable spherical mean-field plus extended monopole pairing model

“…[1][2][3]. While the Bardeen-Cooper-Schrieffer (BCS) and the more refined Hartree-Fock-Bogolyubov (HFB) approximations provide a simple and clear demonstration of the role of pairing correlations in nuclei [2,4,5], tremendous efforts have been made in finding accurate solutions to the problem [6][7][8][9][10][11] to overcome serious drawbacks in the BCS and the HFB, such as spurious states, nonorthogonal solutions, etc., resulting from particle number-nonconservation effects in these approximations [9,[11][12][13]. It is known that either spherical or deformed mean-field plus the standard pairing interaction can be solved exactly by using the Gaudin-Richardson method [14][15][16].…”