<i>Technical Aspects of Sound</i>

Richardson, E. G.; Meyer, Erwin; Mayer, Walter G.

doi:10.1063/1.3050940

Cited by 54 publications

(90 citation statements)

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“…This challenge elicited a series of increasingly sophisticated canonical treatments of pairing correlations [33][34][35][36][37][38][39][40][41], based on a simple reduced BCS-Hamiltonian for discrete energy levels, which showed that the crossover is completely smooth, but, interestingly, depends on the parity of the number of electrons on the grain, as pointed out by von Delft et al [21]. Very recently, the main conclusions of these works were confirmed [39] using an exact solution of the reduced BCS model, discovered by Richardson in the context of nuclear physics in the 1960s [46][47][48][49][50][51][52][53][54]. (The existence of this solution came as a surprise -in the form of a polite letter from its inventor -to those involved with ultrasmall grains, since hitherto it had apparently completely escaped the attention of the condensed-matter community.…”

Section: Introductionsupporting

confidence: 57%

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Spectroscopy of discrete energy levels in ultrasmall metallic grains

2001

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We review recent experimental and theoretical work on ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an individual grain can be measured by the technique of single-electron tunneling spectroscopy: the spectrum is extracted from the current-voltage characteristics of a single-electron transistor containing the grain as central island. We review experiments studying the influence on the discrete spectrum of superconductivity, nonequilibrium excitations, spin-orbit scattering and ferromagnetism. We also review the theoretical descriptions of these phenomena in ultrasmall grains, which require modifications or extensions of the standard bulk theories to include the effects of level discreteness.

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Section: Introductionsupporting

confidence: 57%

“…Models of this kind had previously been studied by Richardson [46][47][48][49][50][51][52][53][54], Strongin et al [93], Mühlschlegel et al [94,95] and Kawataba [96,97]. The first application to RBT's grains for h = 0 was by von Delft et al [21] and for h = 0 by Braun et al [21][22][23].…”

Section: A Simple Reduced Bcs Interaction Plus a Zeeman Termmentioning

confidence: 99%

Spectroscopy of discrete energy levels in ultrasmall metallic grains

2001

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“…When k = 2, (22) becomes (12). However, every term for fixed ν in the sum of (22) dependents on {x (ζ) ν,i } with ν µ, which is different from that in the Gaudin-Richardosn solution of the standard pairing model [3,4], and must be considered together to be solved as shown in (22). In addition, it is obvious that W(…”

Section: The Model and Its General Solutionmentioning

confidence: 99%

“…In nuclear physics, pairing interaction is considered as one of important types of residual interactions in a nuclear mean-field to describe ground state and low-energy spectroscopic properties of nuclei, such as binding energies, odd-even effects, single-particle occupancies, excitation spectra, and moments of inertia, etc [1,2]. It has been shown that either spherical or deformed mean-field plus the standard (orbit-independent) pairing interaction can be solved exactly by using the Gaudin-Richardson method [3][4][5]. The Gaudin-Richardson equations in this case can be solved more easily by using the extended Heine-Stieltjes polynomial approach [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Exact solution of the mean-field plus separable pairing model reexamined

et al. 2017

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Exact solution of the nuclear mean-field plus separable pairing model is reexamined. New auxiliary constraints for solving the Bethe ansatz equations of the model are proposed. By using these auxiliary constraints, the Bethe ansatz form of eigenvectors of the mean-field plus separable pairing Hamiltonian with non-degenerate single-particle energies and non-degenerate separable pairing strengths purposed previously is verified. Since the solutions of the model with one-and two-orbit cases are known, verification of the solutions for these two special cases is made. In order to demonstrate structure and features of the solution, the model with three orbits in the ds-shell is taken as a nontrivial example, of which two-pair results and the ground state of the three-pair case are provided explicitly. Since the number of equations involved increases with the number of orbits and pairs, to solve these equations for large number of orbits and pairs seems still difficult.

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“…According to the Richardson-Gaudin method [30], the exact k-pair eigenstates of (1) with ν i = 0 for even systems or ν i = 1 for odd systems, in which i is the label of the Nilsson level that is occupied by an unpaired single particle, can be written as…”

Section: The Nilsson Mean-field Plus Standard Pairing Model and Imentioning

confidence: 99%

Ground state phase transition in the Nilsson mean-field plus standard pairing model

Guan¹,

Xu²,

Zhang³

et al. 2016

Phys. Rev. C

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The ground state phase transition in Nd, Sm and Gd isotopes is investigated by using the Nilsson mean-field plus standard pairing model based on the exact solutions obtained from the extended Heine-Stieltjes correspondence. The results of the model calculations successfully reproduce the critical phenomena observed experimentally in the odd-even mass differences, odd-even differences of two-neutron separation energy, α-decay and double β − -decay energy of these isotopes. Since the odd-even effects are the most important signatures of pairing interactions in nuclei, the model calculations gain microscopic insight into the nature of the ground state phase transition manifested by the standard pairing interaction.

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Technical Aspects of Sound

Cited by 54 publications

References 0 publications

Spectroscopy of discrete energy levels in ultrasmall metallic grains

Spectroscopy of discrete energy levels in ultrasmall metallic grains

Exact solution of the mean-field plus separable pairing model reexamined

Ground state phase transition in the Nilsson mean-field plus standard pairing model

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