Fluctuations in Nuclear Reactions

Statistical properties of cross sections are studied for an open system of interacting fermions. The description is based on the effective non-Hermitian Hamiltonian that accounts for the existence of open decay channels preserving the unitarity of the scattering matrix. The intrinsic interaction is modelled by the two-body random ensemble of variable strength. In particular, the crossover region from isolated to overlapping resonances accompanied by the effect of the width redistribution creating super-radiant and trapped states is studied in detail. The important observables, such as average cross section, its fluctuations, autocorrelation functions of the cross section and scattering matrix, are very sensitive to the coupling of the intrinsic states to the continuum around the crossover. A detailed comparison is made of our results with standard predictions of statistical theory of cross sections, such as the Hauser-Feshbach formula for the average cross section and Ericson theory of fluctuations and correlations of cross sections. Strong deviations are found in the crossover region, along with the dependence on intrinsic interactions and degree of chaos inside the system.

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“…The starting point of the conventional theory [2,3,4] can be summarized as follows. The scattering amplitude…”

Section: Ericson Fluctuationsmentioning

confidence: 99%

“…Since the individual properties of resonances cannot be predicted, only statistical description is practical and sensible. The average cross sections are usually described according to Hauser-Feshbach [1], while the fluctuations and correlations of cross sections are treated in terms of Ericson theory [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

et al. 2007

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“…[19,20] in the regions of isolated and overlapping resonances, illustrates parallels with studies conducted in Refs. [21,22] in the context of nuclear physics [3,23,24]. In addition, the effect of time-reversal invariance (T ) violation, which has been tested in nuclear spectra [25] and for the Ericson region in compound-nucleus reactions [26][27][28][29][30][31], is inspected in this regard.…”

Section: Introductionmentioning

confidence: 99%

Cross-section fluctuations in open microwave billiards and quantum graphs: The counting-of-maxima method revisited

Dietz¹,

Richter²,

Samajdar³

2015

Phys. Rev. E

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The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Γcorr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Γcorr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.

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“…At 8 MeV the resulting energy spread in the entrance channel was 120keV. If this is compared with an expected mean level width in the compound nucleus of ~20keV [13] and the relation between the number of maxima and the mean level width [14] is used, we expect to obtain averaging over 3 to 4 statistical fluctuations at this energy. This expectation is sup- Ecm=7.4MeV ported by the structure in the observed peak shapes ( Fig.…”

Section: Methodsmentioning

confidence: 97%

Resonances in low energy elastic scattering of ?-particles from28Si

Lawrie

Cowley

Whittal

et al. 1986

Z. Physik A - Atomic Nuclei

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The elastic scattering of e-particles from 2sSi at incident energies between 5 and 12MeV (4.4 and 10.5MeV in the centre-of-mass system) was studied to ascertain whether quasimolecular states exist for the e+ 28Si system, as predicted in the literature in terms of a microscopic theory based on the generator coordinate method. Angular distributions were obtained for angles larger than 70 ~ in energy steps of 100keV. Analysis of the experimental data was performed by coherently adding specific resonances to an underlying optical model which describes the background portion of the direct elastic scattering amplitude. As is usual, it was furthermore assumed that the average compound elastic contribution adds incoherently to the total cross section. In spite of the presence of a resonance characterized by an angular momentum value of J =3 in the energy region, as required by theory, no evidence could be found for the existence of other resonances with the expected J-sequence. We conclude that our experiment and analysis do not support the predictions of the microscopic theory.

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Fluctuations in Nuclear Reactions

Cited by 366 publications

References 1 publication

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

Open system of interacting fermions: Statistical properties of cross sections and fluctuations

Cross-section fluctuations in open microwave billiards and quantum graphs: The counting-of-maxima method revisited

Resonances in low energy elastic scattering of ?-particles from28Si

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