Erratum to: “On the impact of large amplitude pairing fluctuations on nuclear spectra” [Phys. Lett. B 704 (2011) 520]

Vaquero, Nuria López; Rodrı́guez, T.; Egido, J.L.

doi:10.1016/j.physletb.2011.10.019

Cited by 24 publications

(38 citation statements)

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“…We find that this is not the case in the PNP approaches where the minima correspond to δ ≈ 2.5. The energy difference corresponding to the different δ values amounts to a difference in pairing energies of a few MeV [65]. The equipotential surfaces of panels (e) and (f) look very similar though in detail they are different, c.f.…”

Section: The β and Pairing Degrees Of Freedommentioning

confidence: 93%

State-of-the-art of beyond mean field theories with nuclear density functionals

Egido

2016

Phys. Scr.

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We present an overview of different beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in many body nuclear physics with effective forces. In a first step a short reminder of the Hartree-Fock-Bogoliubov (HFB) theory is given. A general discussion of the shortcomings of any mean field approximation (MFA), stemming either from the lack of the elementary symmetries (like particle number and angular momentum) or the absence of fluctuations around the mean values, is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is also needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. A whole chapter is devoted to illustrate with examples the convenience of recovering symmetries and the differences between the projection before and after the variation. The lack of fluctuations around the average values of the MFA is a big shortcoming inherent to this approach. To build in correlations in BMFT one selects the relevant degrees of freedom of the atomic nucleus. In the low energy part of the spectrum these are the quadrupole, octupole and the pairing vibrations as well as the single particle degrees of freedom. In the GCM the operators representing these degrees of freedom are used as coordinates to generate, by the constrained (Projected) HFB theory, a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. The flexibility of the GCM Ansatz allows to describe a whole palette of physical situations by conveniently choosing the generator coordinates. We discuss the classical β and γ vibrations by considering the quadrupole operators as coordinates. We present pairing fluctuations by considering the pairing gaps as generator coordinates. The combination of quadrupole and pairing fluctuations mirrors the elementary modes of excitation of the atomic nucleus and provides a realistic description of it. Lastly the explicit consideration of the time reversal symmetry breaking (TRSB) in the HFB wave function by the cranking procedure allows the alignment of nucleon pairs opening a new dimension in the BMFT calculations. Abundant calculations with the finite range density dependent Gogny force applied to exotic nuclei illustrate the state-of-the-art of beyond mean field theories with nuclear density functionals. We conclude with a thorough discussion on the potential poles of the theory.

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Section: The β and Pairing Degrees Of Freedommentioning

confidence: 93%

State-of-the-art of beyond mean field theories with nuclear density functionals

Egido

2016

Phys. Scr.

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“…LSSM calculations have shown that this state is very sensitive to a subtle mixing of spherical 0p-0h and superdeformed 4p-4h configurations [25]. In the present framework, the inclusion of pairing fluctuations [9] and/or explicit quasiparticle excitations could help to solve this problem since the excited 0 + states are mainly affected by such a degree of freedom, lowering the excitation energies of those states.…”

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confidence: 89%

Symmetry conserving configuration mixing method with cranked states

2015

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We present the first calculations of a symmetry conserving configuration mixing method (SCCM) using time-reversal symmetry breaking Hartree-Fock-Bogoliubov (HFB) states with the Gogny D1S interaction. The method includes particle number and tridimensional angular momentum symmetry restorations as well as configuration mixing within the generator coordinate method (GCM) framework. The nucleus 32Mg is chosen to show the performance and reliability of the calculations. Additionally, 01+, 21+ and 41+ states are computed for the magnesium isotopic chain, where a noticeable compression of the spectrum is obtained by including cranked states, leading to a very good agreement with the known experimental dataThis work was supported by the Ministerio de Economía y Competitividad under contracts FPA2011-29854-C04-04, BES-2012-059405 and Programa Ramón y Cajal 2012 number 1142

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“…The finite range of the interaction used in the calculations (Gogny [32]), with a common source for the long and short range parts of the force, guarantees a self-consistent interplay of the shape and pairing fluctuations. In this framework, following the generator coordinate method (GCM) [33,34], the many body nuclear states are described as a linear combination (mixing) of particle number and angular momentum projected Hartree-Fock-Bogoliubov (HFB) wave functions with different shapes and pairing content [35]:where I is the angular momentum, σ labels the different states for a given angular momentum, β 2 and δ are the intrinsic axial quadrupole and pairing degrees of freedom respectively, g Iσ i/f (β 2 , δ) are the coefficients found by solving the Hill-Wheeler-Griffin (HWG) equations [33,35] and the projected wave functions are defined as:|Ψ I i/f (β 2 , δ) = P N i/f P Z i/f P I |φ(β 2 , δ)with P N (Z) and P I being the neutron (proton) number and angular momentum projection operators respec-arXiv:1401.0650v1 [nucl-th]…”

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confidence: 99%

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confidence: 99%

“…where I is the angular momentum, σ labels the different states for a given angular momentum, β 2 and δ are the intrinsic axial quadrupole and pairing degrees of freedom respectively, g Iσ i/f (β 2 , δ) are the coefficients found by solving the Hill-Wheeler-Griffin (HWG) equations [33,35] and the projected wave functions are defined as: projected potential energy surfaces:…”

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confidence: 99%

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Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements

2013

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Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of 10%-40% in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predicted half-lives of these isotopes. The possible detection of lepton number violating processes such as neutrinoless double beta decay (0νββ) is one of the current main goals for particle and nuclear physics research. In this process, an atomic nucleus decays into its neighbor with two neutron less and two proton more emitting only two electrons. Fundamental questions about the nature of the neutrino such as its Dirac or Majorana character, its absolute mass scale as well as its mass hierarchy can be determined if this process is eventually measured [1]. On the one hand, searching for 0νββ decays represents an extremely difficult experimental task because an ultra low background is required to distinguish the predicted scarce events from the noise. Recently, the controversial claim of detection in 76 Ge by the Heidelberg-Moscow (HdM) collaboration [2] has been overruled by the latest data released by . Nevertheless, these results are challenging the experiments that are already running or in an advanced stage of development to detect directly this process [3,[6][7][8][9][10][11][12][13][14]. On the other hand, in the most probable electroweak mechanism to produce 0νββ, namely, the exchange of light Majorana neutrinos [1,15], the half-life of this process is inversely proportional to the effective Majorana neutrino mass m ν , a kinematic phase space factor G 01 and the nuclear matrix elements M 0ν (NME):where m e is the electron mass and m ν = | k U 2 ek m k | is the combination of the neutrino masses m k provided by the neutrino mixing matrix U . The kinematic phase space factor can be determined precisely from the charge, mass and the energy available in the decay [16] while the nuclear matrix elements must be calculated using nuclear structure methods. The most commonly used ones are the quasiparticle random phase approximation [17][18][19][20][21] (QRPA), large scale shell model [22][23][24] (LSSM), interacting boson model [25,26] (IBM), projected HartreeFock-Bogoliubov [27] (PHFB) and energy density functional [28][29][30] (EDF). In recent years, most of the basic nuclear structure aspects of the NMEs have been understood within these different frameworks. In particular, the decay is favored when the initial and final nuclear states have similar intrinsic deformation [28,30,31]. Indications [18,21,23,28,30] about the strong sensitivity of the transition operator to pairing correlations suggest that fluctuations in this degree ...

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Erratum to: “On the impact of large amplitude pairing fluctuations on nuclear spectra” [Phys. Lett. B 704 (2011) 520]

Cited by 24 publications

References 0 publications

State-of-the-art of beyond mean field theories with nuclear density functionals

State-of-the-art of beyond mean field theories with nuclear density functionals

Symmetry conserving configuration mixing method with cranked states

Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements

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