Spectra and symmetry in nuclear pairing

Balantekin, A. B.; Jesus, J. H. de; Pehlivan, Y.

doi:10.1103/physrevc.75.064304

Cited by 25 publications

(45 citation statements)

References 13 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…IV A. Furthermore the η = 0 state is already extensively discussed by [26,27]. The paths of the real and imaginary parts of the RG variables of a toy model, with 12 doubly degenerate levels, and equidistant D i = i, occupied by six pairs, as functions of the interaction constant are depicted in Fig.…”

Section: The Hyperbolic Richardson-gaudin Modelmentioning

confidence: 99%

“…So by having a method to solve the η = 0 case we are able to generate the solutions of the η = 0 case. The Bethe ansatz solution of the η = 0 state was first explored by Pan et al [26] and later by Balantekin et al [27] who explored some symmetry properties of the Bethe ansatz equations. Two separate sets of Bethe ansatz equations were found: solutions of the first set were zero and the solutions of the other set were not restricted to zero.…”

Section: A the η = 0 Hamiltonianmentioning

confidence: 99%

See 1 more Smart Citation

Exact solution of thepx+ipypairing Hamiltonian by deforming the pairing algebra

2014

View full text Add to dashboard Cite

Recently, interest has increased in the hyperbolic family of integrable Richardson-Gaudin (RG) models. It was pointed out that a particular linear combination of the integrals of motion of the hyperbolic RG model leads to a Hamiltonian that describes p-wave pairing in a two-dimensional system. Such an interaction is found to be present in fermionic superfluids ( 3 He), ultracold atomic gases, and p-wave superconductivity. Furthermore the phase diagram is intriguing, with the presence of the Moore-Read and Read-Green lines. At the Read-Green line a rare third-order quantum phase transition occurs. 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. We extend the phase diagram to repulsive interactions, an area that was not previously explored due to the lack of a proper mean-field solution in this region. We found a connection between the point in the phase diagram where the ground state connects to the bosonic state with the highest collectivity, and the Moore-Read line where all the Richardson-Gaudin (RG) variables collapse to zero. In contrast with the reduced BCS case, the overlap between the ground state and the highest collective state at the Moore-Read line is not the largest. In fact it shows a minimum when most other bosonic states show a maximum of the overlap. We found remnants of the Read-Green line for finite systems, by investigating the total spectrum. A symmetry was found between the Hamiltonian with and without single-particle part. When the interaction was repulsive we found four different classes of trajectories of the RG variables.

show abstract

Section: The Hyperbolic Richardson-gaudin Modelmentioning

confidence: 99%

Section: A the η = 0 Hamiltonianmentioning

confidence: 99%

Exact solution of thepx+ipypairing Hamiltonian by deforming the pairing algebra

2014

View full text Add to dashboard Cite

show abstract

“…[8][9][10]. If the shell is more than half full, it is easier to work with hole pairs instead of particle pairs.…”

mentioning

confidence: 98%

Solutions of nuclear pairing

Balantekin

Pehlivan

2007

Phys. Rev. C

Self Cite

View full text Add to dashboard Cite

We give the exact solution of orbit dependent nuclear pairing problem between two nondegenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including Richardson's treatment of reduced pairing in terms of rational Gaudin algebra operators.Pair correlations are manifest in a remarkable range of quantum many-body systems. Originally the idea of pairing and the methods were developed in the context of superconductivity in macroscopic systems by Bardeen, Cooper, and Schrieffer [1] and by Bogoliubov [2]. In nuclear physics, it has been long known that the independent particle picture must be improved with the addition of a nondiagonal two-particle force as evidenced by the absence of single particle excitations at low energies [3] and soon the idea of the pairing was carried over [4,5]. But methods borrowed from superconductivity in infinite systems were inconvenient for the finite nucleus because the former is based on wave functions with indefinite number of particles. Although it is known that the pairing effects play a major role in determining nearly all nuclear properties including the excitation spectra, the transition probabilities and the equilibrium shape, an exact number-conserving solution to nuclear pairing problem is still lacking except in three limits. The limit in which single particle energy levels are degenerate and all pairing strengths are the same was solved by Kerman using the quasispin algebra [6]. Later Richardson solved the limit in which the single particle energy levels are nondegenerate but the pairing strengths are the same [7]. Finally, the limit in which the single particle levels have different pairing strengths but are all degenerate is solved by Pan et al. [8] and by Balantekin et al. [9,10]. On the other hand, in many cases it is the interplay between the one-body and the two-body effects which determine the equilibrium properties of the nucleus and a full solution of the nuclear pairing problem is highly desirable as a realistic model. The purpose of this Rapid Communication is to present an exact solution of the pairing problem away from the above mentioned limits, i.e., with orbit dependent pairing strengths and nondegenerate single particle energies, in the presence of two nuclear levels.The problem is described by the Hamiltonian H P

show abstract

“…• The limit with separable pairing in which the energy levels are degenerate (the one-body term becomes a constant for a given number of pairs) [27][28][29]…”

Section: Physics Applications a Pairing Problem In Nuclear Physicsmentioning

confidence: 99%

Symmetries, Supersymmetries, and Pairing in Nuclei

Balantekin¹,

Bijker²,

Castaños³

et al. 2011

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

These summer school lectures cover the use of algebraic techniques in various subfields of nuclear physics. After a brief description of groups and algebras, concepts of dynamical symmetry, dynamical supersymmetry, and supersymmetric quantum mechanics are introduced. Appropriate tools such as quasiparticles, quasispin, and Bogoliubov transformations are discussed with an emphasis on group theoretical foundations of these tools. To illustrate these concepts three physics applications are worked out in some detail: i) Pairing in nuclear physics; ii) Subbarrier fusion and associated group transformations; and iii) Symmetries of neutrino mass and of a related neutrino many-body problem.

show abstract

Spectra and symmetry in nuclear pairing

Cited by 25 publications

References 13 publications

Exact solution of thepx+ipypairing Hamiltonian by deforming the pairing algebra

Exact solution of thepx+ipypairing Hamiltonian by deforming the pairing algebra

Solutions of nuclear pairing

Symmetries, Supersymmetries, and Pairing in Nuclei

Contact Info

Product

Resources

About