Linear response strength functions with iterative Arnoldi diagonalization

Toivanen, Jari; Carlsson, B. G.; Dobaczewski, J.; Mizuyama, Kazuhito; Rodrı́guez-Guzmán, R.; Toivanen, Pekka; Veselý, Petr

doi:10.1103/physrevc.81.034312

Cited by 42 publications

(60 citation statements)

References 28 publications

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“…For states with large transition probabilities, the number of iterations needed can however be reduced by instead starting from an initial pivot vector whose matrix elements are set to the matrix elements of the corresponding electromagnetic multipole operator [4]. In the case where pairing disappears (and the numerical accuracy is high) the electromagnetic pivot also filters out the states that have an overlap with the pivot and thus removes states which correspond to pair addition or removal.…”

Section: A Iterative Solutionsmentioning

confidence: 99%

“…As with the iterative Arnoldi method of Ref. [4], the IRA method generates a set of basis vectors, usually called Ritz vectors, which span a vector space called the Krylov subspace, and uses these vectors to represent the QRPA eigenvectors. However, the IRA method's use of restarting allows it to gradually improve the accuracy of a set of eigenstates during iteration, using a reasonably small number of Ritz vectors (typically a few hundred at most).…”

Section: A Iterative Solutionsmentioning

confidence: 99%

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Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

2012

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Collective vibrational states within the fast iterative quasiparticle random-phase approximation methodCarlsson, Gillis; Toivanen, J.; Pastore, A. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. An iterative method we previously proposed to compute nuclear strength functions [Toivanen et al., Phys. Rev. C 81, 034312 (2010)] is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasiparticle random-phase approximation (QRPA) and uses an iterative non-Hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest-lying 2 + and 3 − states in Pb, Sn, Ni, and Ca isotopes using three different Skyrme interactions and a separable Gaussian pairing force.

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Section: A Iterative Solutionsmentioning

confidence: 99%

Section: A Iterative Solutionsmentioning

confidence: 99%

Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

2012

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“…Recently, the FAM has been applied to the electric dipole excitations in nuclei using the Skyrme energy functionals [18]. There has been also a calculation making use the iterative Arnoldi algorithm for a solution of the RPA equation [19]. These newly developed technologies in conjunction with fast solving algorithms for linear systems open the possibility to explore systematically the nuclear excitations over the entire nuclear chart.…”

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confidence: 99%

“…So far, these new techniques [17][18][19] have been developed for solutions of the RPA without the pairing correlations. It is well known, however, that almost all but magic nuclei display superfluid features.…”

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confidence: 99%

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Finite amplitude method for the quasiparticle random-phase approximation

2011

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We present the finite amplitude method (FAM), originally proposed in Ref. [17], for superfluid systems. A Hartree-Fock-Bogoliubov code may be transformed into a code of the quasi-particlerandom-phase approximation (QRPA) with simple modifications. This technique has advantages over the conventional QRPA calculations, such as coding feasibility and computational cost. We perform the fully self-consistent linear-response calculation for a spherical neutron-rich nucleus 174 Sn, modifying the HFBRAD code, to demonstrate the accuracy, feasibility, and usefulness of the FAM.

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The Nuclear Energy Density Functional Formalism

Duguet

2014

Lecture Notes in Physics

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The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a Hamiltonian-based picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel E[g ′ , g] at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a mathematically meaningful fashion even if E[g ′ , g] does not derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making any reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a physical standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.

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Linear response strength functions with iterative Arnoldi diagonalization

Cited by 42 publications

References 28 publications

Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

Finite amplitude method for the quasiparticle random-phase approximation

The Nuclear Energy Density Functional Formalism

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