The T = 1 pairing Hamiltonian in a two-level model

Dussel, G.G.; Maqueda, E.E.; Perazzo, R.P.J.

doi:10.1016/0375-9474(70)90786-4

Cited by 29 publications

(16 citation statements)

References 6 publications

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“…[64], the principal axes tilted against the neutron and proton gauge-angle space have been reported in the reduced energy kernel when neutrons and protons are superconducting. The opposite sign of J np is consistent with the isorotation picture, whose rotational energy is proportional to T (T + 1) [7,65,66], and produces a negative sign for the neutron-proton term. Figure 6 shows the pairing rotational energies measured from 130 Xe along the Xe isotope direction, the N = 76 isotone direction, the A = 130 isobar direction, and the T z = 11 direction.…”

Section: B Mixing Of Neutron and Proton Pairing Rotational Modessupporting

confidence: 60%

Collective inertia of the Nambu-Goldstone mode from linear response theory

Hinohara

2015

Phys. Rev. C

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Background: Spurious zero-energy Nambu-Goldstone (NG) modes appear when the symmetry of a system is spontaneously broken. The Thouless-Valatin inertia, the collective inertia of the NG mode, contains important information concerning collective motion.Purpose: To establish an efficient and precise method for deriving the collective inertia and the conjugate operator of a NG mode, we derive an expression for the response function in terms of the coordinate-momentum representation of the quasiparticle random-phase approximation which is valid even if a symmetry-restoring zeroenergy mode is present.Methods: We use the finite amplitude method for computing the response function of superfluid nuclei with the nuclear density functional theory.Results: We derived analytically the collective inertia and the conjugate coordinate operator of the NG mode from the zero-energy linear response with the momentum operator of the NG mode. The formulation is tested in the cases of translational and pairing rotational modes. Illustrative calculations are performed for the neutron pairing rotation in Sn isotopes, the proton pairing rotation in N = 82 isotones, and the neutron and proton pairing rotations around the 130 Xe nucleus. Conclusions:The proposed formulation allows us to compute the collective inertia of the NG mode precisely and efficiently. The conjugate coordinate operator can be utilized to remove spurious contributions to the strength distribution in the finite amplitude method.

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Section: B Mixing Of Neutron and Proton Pairing Rotational Modessupporting

confidence: 60%

Collective inertia of the Nambu-Goldstone mode from linear response theory

Hinohara

2015

Phys. Rev. C

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“…Naturally, the spectrum strongly deviates from the RPA and cranking estimates in the cross-over region 1 < y < 2. [7].…”

Section: Two-shell Modelmentioning

confidence: 99%

“…They introduced a collective Hamiltonian in analogy to the Bohr Hamiltonian for the quadrupole shape degree of freedom, which allowed them to describe both the rotational and the vibrational regimes and the cross-over between them. The behavior of the energies and transition matrix elements of the discussed two-shell model [7,65] were explained in detail by deriving the potential for the pair degrees of freedom from the mean field solution, where Ref. [7] studied the approximate solutions of the pair vibrational type and the isorotational type and Ref.…”

Section: Collective Motion Of the Isovector Pair Fieldmentioning

confidence: 99%

“…The behavior of the energies and transition matrix elements of the discussed two-shell model [7,65] were explained in detail by deriving the potential for the pair degrees of freedom from the mean field solution, where Ref. [7] studied the approximate solutions of the pair vibrational type and the isorotational type and Ref. [65] found numerical solutions for full collective Hamiltonian.…”

Section: Collective Motion Of the Isovector Pair Fieldmentioning

confidence: 99%

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Overview of neutron–proton pairing

Frauendorf

Macchiavelli

2014

Progress in Particle and Nuclear Physics

188

179

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The role of neutron-proton pairing correlations on the structure of nuclei along the N = Z line is reviewed. Particular emphasis is placed on the competition between isovector (T = 1) and isoscalar (T = 0) pair fields. The expected properties of these systems, in terms of pairing collective motion, are assessed by different theoretical frameworks including schematic models, realistic Shell Model and mean field approaches. The results are contrasted with experimental data with the goal of establishing clear signals for the existence of neutron-proton (np) condensates. We will show that there is clear evidence for an isovector np condensate as expected from isospin invariance. However, and contrary to early expectations, a condensate of deuteron-like pairs appears quite elusive and pairing collectivity in the T = 0 channel may only show in the form of a phonon. Arguments are presented for the use of direct reactions, adding or removing an np pair, as the most promising tool to provide a definite answer to this intriguing question.

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“…Many insights were gained by simple solvable models employing symmetrydictated interactions [104][105][106][107][108][109][110][111]. Two families of models were used, one based on the j-j coupling with the symmetry SO(5) (appropriate for the T =1 pairing) and the other based on the L-S coupling with the symmetry SO(8) (appropriate for the T =0 and T =1 pairing).…”

Section: Proton-neutron Pairing a Concise Overviewmentioning

confidence: 99%

Local density approximation for proton-neutron pairing correlations: Formalism

et al. 2004

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In the present study we generalize the self-consistent Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the case which incorporates an arbitrary mixing between protons and neutrons in the particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define the HFB density matrices, discuss their spin-isospin structure, and construct the most general energy density functional that is quadratic in local densities. The consequences of the local gauge invariance are discussed and the particular case of the Skyrme energy density functional is studied. By varying the total energy with respect to the density matrices the self-consistent one-body HFB Hamiltonian is obtained and the structure of the resulting mean fields is shown. The consequences of the time-reversal symmetry, charge invariance, and proton-neutron symmetry are summarized. The complete list of expressions required to calculate total energy is presented.

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The T = 1 pairing Hamiltonian in a two-level model

Cited by 29 publications

References 6 publications

Collective inertia of the Nambu-Goldstone mode from linear response theory

Collective inertia of the Nambu-Goldstone mode from linear response theory

Overview of neutron–proton pairing

Local density approximation for proton-neutron pairing correlations: Formalism

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