Abstract
We have used kernel density estimation (KDE) technique to analyze the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distribution. The deviations to regular and chaotic dynamics are described by closer distances to Poisson and Wigner limits, respectively which have calculated via Kullback–Leibler divergence measure. The level statistics of nuclei provide empirical evidences for three dynamical symmetry limits of interacting boson model, considering oblate and prolate nuclei. The predictions of KDE technique suggest a considerable reduction in the uncertainties of chaocity degrees and also more regular dynamics in comparison with other estimation methods for considered systems.
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References
M L Mehta Random Matrices (United States: Academic Press) (2004)
T A Brody, J Flores, J B French, P A Mello, A Pandey and S S M Wong Rev. Mod. Phys 53 385 (1981)
J F Shriner Jr, G E Mitchell, T von Egidy Z. Phys. A 338 309 (1991)
F J Dyson and M L Mehta J. Math. Phys 4 701 (1963)
S Raman et al. Phys. Rev. C 43 521 (1991)
D Biswas, S Pal and A Chaudhuri Phys. Rev. A 46 6817(1992)
T Timberlake Am. J. Phys 74 547 (2006)
T A Brody Lett. Nuovo Cimento 7 482 (1973)
M V Berry and M Robnik J. Phys. A 17 2413 (1984)
M A Jafarizadeh, N Fouladi, H Sabri and B R Maleki (nucl th/1106.2497) (2011)
A Y Abul-Magd, H L Harney, M H Simbel and H A Weidenmüller Phys. Lett. B 579 278 (2004)
M A Jafarizadeh, N Fouladi, H Sabri and B R Maleki Nucl. Phys. A 890–891 29 (2012)
A Y Abul-Magd, H L Harney, M H Simbel and H A Weidenmüller Ann. Phys. 321 560 (2006)
O C De Jager, B C Raubenheimer and J W H Swanepoel, Astron. Astrophys. 221 180 (1989)
A W Bowman and Adelchi Azzalini Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations (Oxford UK: Clarendon Press) (1997)
M J Baxter, C C Beardah and R V S Wright J. Arch. Sci. 24 347 (1997)
P Frederic Miller, F Agnes Vandome and J McBrewster Kernel Density Estimation (German: Alphascript Publishing) (2010)
D W Scott Multivariate Density Estimation: Theory, Practice, and Visualization (United States: John Wiley & Sons) (2009)
M Rodchuen and P Suwattee Chiang Mai J. Sci. 38 1 (2011)
M Rudemo Scand. J. Statist. 9 65 (1982)
G R Terrell and David W Scott The Annals of Statistics 20 1236 (1992)
A Elgammal, R Duraiswami, D Harwood and L S Davis Proc. IEEE 90 1151 (2002)
S J Sheather and M C Jones Royal Statistical Society. Series B (Methodological) 53 683 (1991)
J Shi, M Luo and C Huang Indian J. Phys. 84 1229 (2010)
S Marinai and H Fujisawa Machine Learning in Document Analysis and Recognition (UK: Springer) (2008)
A Kaplan, H Büyükuslu, E Tel, A Aydin and M H Bölükdemir Indian J. Phys. 85 1615 (2011)
D Kalita and K Boruah Indian J. Phys. 87 289 (2013)
H Aytekin and D Demirbağ Indian J. Phys. 87 487 (2013)
National Nuclear Data Center (Brookhaven National laboratory) chart of nuclides (http://www.nndc.bnl.gov/chart/reColor.jsp?newColor=dm)
Nuclear data sheets (http://www.journals.elsevier.com/nuclear-data-sheets/)
P Möller, J R Nix, W D Myers and W J Swiatecki At Data Nucl Data Tables 59 185(1995)
F Iachello and A Arima The Interacting Boson Model (UK: Cambridge Univ Press) (1987)
P Cejnar, J Jolie and R F Casten Rev. Mod. Phys. 82 2155 (2010)
A Bohr and B R Mottelson Nuclear structure: Nuclear Deformation (Singapore: World Scientific) Vol II (1998)
W Greiner, J A Maruhn and D A Bromley Nuclear Models (Berlin Heidelberg: Springer) (2008)
A Y Abul-Magd and A Al-Sayed Phys. Rev. C 74 037301 (2006)
H Y Abdullah et al. Indian J. Phys. (DOI: 10.1007/s12648-013-0257-9)
V Paar and D Vorkapic Phys. Lett. B 205 7 (1988); ibid. Phys. Rev. C 41 2397 (1990)
Y Alhassid and N Whelan Phys. Rev. Lett 67 816 (1993); ibid. Nucl. Phys. A 556 42 (1993)
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Jafarizadeh, M.A., Fouladi, N., Sabri, H. et al. A non-parametric estimation approach in the investigation of spectral statistics. Indian J Phys 87, 919–927 (2013). https://doi.org/10.1007/s12648-013-0311-7
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DOI: https://doi.org/10.1007/s12648-013-0311-7
Keywords
- Kernel density estimation (KDE)
- Nearest neighbor spacing distribution (NNSD)
- Kullback–Leibler divergence (KLD) measure
- Interacting boson model (IBM)