Level Density Analysis of Nuclear Resonances

nuclear level densities;random matrix theory;neutron resonances;proton resonances;level statistics;spacing and width distributions;missing level correction

Agvaanluvsan, Undraa ; Prof. Gary E. Mitchell, Committee Chair,Agvaanluvsan, Undraa ; Prof. Gary E. Mitchell ; Committee Chair

University:North Carolina State University

关键词: nuclear level densities;    random matrix theory;    neutron resonances;    proton resonances;    level statistics;    spacing and width distributions;    missing level correction;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/4284/etd.pdf?sequence=1&isAllowed=y

美国|英语

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【 摘 要 】

Direct counting of nuclear resonances is the most straightforward way to obtain detailed information about nuclear level densities.In order to test recently developed theories more accurate experimental results for level densities are needed.Because of experimental limitations some fraction of the resonances is not observed. Therefore the observed level density must be corrected for the missing fraction of levels. Two analysis methods are developed and methods applied to nuclear resonance data. The standard correction method based on the resonance widths and the Porter-Thomas distribution is reconsidered. The Wigner distribution describes the nearest neighbor spacings of perfect sequences (all levels observed). A general expression for the probability density function of the spacing distribution for imperfect sequences is derived using the maximum entropy principle. This expression contains the Wigner distribution and the higher order spacing distributions. The general expression is tested extensively with numerically generated data. A simple approximation for the higher order spacing distribution functions is obtained. A spacing analysis method to determine the fraction of missing levels is developed using the probability density function and the maximum likelihood technique. Using the two methods (based on resonance widths and spacings) enables the determination of improved level densities from experimental data. The width and spacing analysis methods are applied to 15 proton and 2 neutron resonance data sequences and the observed fraction of levels for each sequence is corrected in two ways. Agreement between the two methods is good. Results from the two methods are combined to make a correction to the level density. Values for the level density and strength function for each sequence are obtained and the spin and parity dependence of the level densities is considered. General agreement is found with previous theory.