Chaoticity and shell effects in the nearest-neighbor distributions for an axially-symmetric potential

Błocki, J.; Magner, A. G.

doi:10.1103/physrevc.85.064311

Cited by 12 publications

(24 citation statements)

References 34 publications

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“…hanced for the K = 2 (c) [or 4 (d)] case than for K = 0 (b). Thus, we found a similar effect of the symmetry breaking like in the single-particle spectra [28], that was explained by decreasing the number of single-valued integrals of motion. This analysis confirms also a proposed explanation of NNSD shifts to the Poisson limit with increasing the angular momentum 0 + , 2 + and 4 + (Fig.…”

Section: Discussion Of Resultssupporting

confidence: 71%

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Simple approach to the chaos-order contributions and symmetry breaking in nuclear spectra

2018

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The simple one-parameter nearest neighbor-spacing distribution (NNSD) is suggested for statistical analysis of nuclear spectra. This distribution is derived within the Wigner-Dyson approach in the linear approximation for the level repulsion density of quantum states. The obtained NNSD gives the individual information on the Wigner and Poisson contributions in agreement with that of the statistical experimental distributions of collective states in deformed nuclei. Using this NNSD, one finds that the symmetry breaking due to the fixing of projections of the angular momentum of collective states enhances a chaos as a shift of the NNSD from the Poisson to Wigner distribution behavior.

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Section: Discussion Of Resultssupporting

confidence: 71%

“…For analysis of the statistical properties in terms of the mixed Poisson and Wigner distributions, the linear WD (LWD) approximation to the level repulsion density g(s) was suggested in Refs. [28,29]. It is the two-parameter LWD (LWD2, see Appendix); in contrast, e.g., to the one-parameter Brody approach [10].…”

Section: Introductionmentioning

confidence: 99%

Simple approach to the chaos-order contributions and symmetry breaking in nuclear spectra

2018

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“…As the angular momentum projection K is fixed in (b-d), one observes mainly a shift of the NNSDs to the chaotic Wigner contribution, in agreement with the results for the s.p. spectra [21]. It is transparently shown in Sec.…”

Section: B Analytical Nnsd Approximationsmentioning

confidence: 83%

“…The new LWD approach is based on the expression for NNSD p(s) within the Wigner-Dyson theory [21,22],…”

Section: B Analytical Nnsd Approximationsmentioning

confidence: 99%

Two-neutron transfer reactions and the quantum chaos measure of nuclear spectra

Levon¹,

Magner²

2019

Nucl. Phys. At. Energy

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A new statistical interpretation of the nuclear collective states is suggested and applied recently in rare earths and actinide nuclei by the two-neutron transfer reactions in terms of the nearest neighborspacing distributions (NNSDs). Experimental NNSDs were obtained by using the complete and pure sequences of the collective states through an unfolding procedure. The two-neutron transfer reactions allow to obtain such a sequence of the collective states that meets the requirements for a statistical analysis. Their theoretical analysis is based on the linear approximation of a repulsion level density within the Wigner-Dyson theory. This approximation is successful to evaluate separately the Wigner chaos and Poisson order contributions. We found an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs turn out to be shifted from a chaos to order with increasing the length of spectra and the angular momentum of collective states. Perspectives for the statistical analysis of the symmetry breaking of states with the fixed projection of angular momenta K are discussed.

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“…However, the LWD approximation, as based on a smooth analytical (linear) function g(s) of s, can be founded within the WD theory (see Refs. [7,24] and Appendix). Moreover, it gives a proper information on the separate Poisson order-like and Wigner chaos-like contributions.…”

Section: Introductionmentioning

confidence: 99%

Statistical analysis of excitation energies in actinide and rare-earth nuclei

2018

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Statistical analysis of distributions of the collective states in the actinide and rare-earth nuclei is performed in terms of the nearest neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of the rare-earth and actinide nuclei. They are more close to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings. *

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Chaoticity and shell effects in the nearest-neighbor distributions for an axially-symmetric potential

Cited by 12 publications

References 34 publications

Simple approach to the chaos-order contributions and symmetry breaking in nuclear spectra

Simple approach to the chaos-order contributions and symmetry breaking in nuclear spectra

Two-neutron transfer reactions and the quantum chaos measure of nuclear spectra

Statistical analysis of excitation energies in actinide and rare-earth nuclei

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