Scaling analysis of the fluctuating strength function

Aiba, Hirokazu

doi:10.1103/physrevc.60.034307

Cited by 20 publications

(37 citation statements)

References 34 publications

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“…Aiba and Matsuo [12] have proposed a technique for the analysis of fine structure by the determination of a local scaling dimension calculated from a subpartitioning of the data. This scheme is based on the scaling analysis of a series having a self-similar multifractal character.…”

Section: A Methodsmentioning

confidence: 99%

“…The method has been used to extract characteristic scales from shell-model calculations of the ISGQR and the isovector giant quadrupole resonance (IVGQR) in 40 Ca [17]. Careful treatment of the boundaries of the data are needed [12] to avoid artifacts in the results. In our case, the method was applied to multiple repeats of the region of interest, thus giving, essentially, periodic boundary conditions.…”

Section: A Methodsmentioning

confidence: 99%

“…For a fractal distribution of fluctuations, the partition function will have a nontrivial scaling depending on some fractal dimension. When dealing with more general data having specific energy scales, the fractal dimension is extended by the definition of a local scaling dimension D m (δE) to characterize the type of fluctuations that might arise in the damping of giant resonances [12],…”

Section: A Methodsmentioning

confidence: 99%

“…In this work, we concentrate on the evaluation of several new methods proposed for the extraction of such scales, viz. the local scaling dimension approach [12], the entropy index method [13], and the use of wavelet techniques [6], and compare the latter to older techniques such as Fourier analysis. As a test case, we investigate data on the ISGQR in 208 Pb from high-energy-resolution (p, p ) experiments and a calculation of the corresponding isoscalar E2 strength function within the quasiparticle-phonon model (QPM).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of fine structure in the nuclear continuum

et al. 2008

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Fine structure has been shown to be a general phenomenon of nuclear giant resonances of different multipolarities over a wide mass range. In this article we assess various techniques that have been proposed to extract quantitative information from the fine structure in terms of characteristic scales. These include the so-called local scaling dimension, the entropy index method, Fourier analysis, and continuous and discrete wavelet transforms. As an example, results on the isoscalar giant quadrupole resonance in 208 Pb from high-energy-resolution inelastic proton scattering and calculations with the quasiparticle-phonon model are analyzed. Wavelet analysis, both continuous and discrete, of the spectra is shown to be a powerful tool to extract the magnitude and localization of characteristic scales.

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Section: A Methodsmentioning

confidence: 99%

Section: A Methodsmentioning

confidence: 99%

Section: A Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of fine structure in the nuclear continuum

et al. 2008

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“…The former mechanism gives rise to an escape width, while the latter yields spreading widths (Γ ↓ ). An understanding of lifetime characteristics associated with the cascade of couplings and scales of fragmentations arising from this coupling (cf [4,5,6,7]) remains a challenge. A recent highresolution experiment of the Isoscalar Giant Quadrupole Resonance (QR) [8,9,10] provides new insight for this problem.…”

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confidence: 99%

Time scales in nuclear giant resonances

2010

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We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative selfenergy which contains all information about fragmentations. Using a wavelet analysis, we demonstrate the extraction of time scales of cascading decays into configurations of different complexity of the resonance. We argue that the spreading widths of collective excitations in nuclei are determined by the number of fragmentations as seen in the power spectrum. An analytic treatment of the wavelet analysis using a Fourier expansion of the cross section confirms this principle. A simple rule for the relative life times of states associated with hierarchies of different complexity is given.PACS numbers: 24.30. Cz, 24.60.Ky, 24.10.Cn Nuclear Giant Resonances (GR) have been the subject of numerous investigations over several decades [1]. Some of the basic features such as centroids and collectivity (in terms of the sum rules) are reasonably well understood within microscopic models [2,3]. However, the question how a collective mode like the GR disseminates its energy is one of the central issues in nuclear structure physics.According to accepted wisdom, GRs are essentially excited by an external field being a one-body interaction. It is natural to describe these states as collective 1p-1h states. Once excited, the GR disseminates its energy via direct particle emission and by coupling to more complicated configurations (2p-2h, 3p-3h, etc). The former mechanism gives rise to an escape width, while the latter yields spreading widths (Γ ↓ ). An understanding of lifetime characteristics associated with the cascade of couplings and scales of fragmentations arising from this coupling (cf [4,5,6,7]) remains a challenge. A recent highresolution experiment of the Isoscalar Giant Quadrupole Resonance (QR) [8,9,10] provides new insight for this problem.It has been shown by Shevchenko et al. [8] that the fine structure of the QR observed in (p, p ′ ) experiments is largely probe independent. Furthermore, a study of the fine structure using wavelet analysis [11,12,13] reveals energy scales [9,10] in the widths of the fine structure displaying a seemingly schematic pattern, as can be seen in Fig.2. This pattern varies with the structure of the nucleus being studied. While the physical meaning of the results of such an analysis is still being debated, we try here to offer a general explanation. However, we do not embark on a specific microscopic analysis, but rather make use of general and well-established techniques of many-body theory. Gross effects due to nuclear deformation and coupling to the continuum [5] are not discussed; we rather focus on the decay of the QR into configurations of various complexity.To proceed we use the Green's function approach. A central role is played by the self-energy whose finer structure is imparted upon the Green's function via the solution of Dyson's equation which reads [14]where we assume G 0 (ω) = ...

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High Energy-Resolution Experiments with the K600 Magnetic Spectrometer at Intermediate Energies

Usman

2013

Exciting Interdisciplinary Physics

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Scaling analysis of the fluctuating strength function

Cited by 20 publications

References 34 publications

Analysis of fine structure in the nuclear continuum

Analysis of fine structure in the nuclear continuum

Time scales in nuclear giant resonances

High Energy-Resolution Experiments with the K600 Magnetic Spectrometer at Intermediate Energies

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