arXiv subjects
Publications and source records attributed to M. S. Hussein.
The Jensen theorem is used to derive inequalities for semi-classical tunneling probabilities for systems involving several degrees of freedom. These Jensen inequalities are used to discuss several aspects of sub-barrier heavy-ion fusion reactions. The inequality hinges on general convexity properties of the tunneling coefficient calculated with the classical action in the classically forbidden region.
The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, Random Matrix Theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of Small World (SW) networks using an extension of the Gaussian Orthogonal Ensemble. This RMT ensemble, coined the Deformed Gaussian Orthogonal Ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics till certain range of eigenvalues correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.
To comprehend the recent Brookhaven National Laboratory experiment E788 on $^4_Λ$He, we have outlined a simple theoretical framework, based on the independent-particle shell model, for the one-nucleon-induced nonmesonic weak decay spectra. Basically, the shapes of all the spectra are tailored by the kinematics of the corresponding phase space, depending very weakly on the dynamics, which is gauged here by the one-meson-exchange-potential. In spite of the straightforwardness of the approach a good agreement with data is acheived. This might be an indication that the final-state-interactions and the two-nucleon induced processes are not very important in the decay of this hypernucleus. We have also found that the $π+K$ exchange potential with soft vertex-form-factor cutoffs $(Λ_π\approx 0.7$ GeV, $Λ_K \approx 0.9$ GeV), is able to account simultaneously for the available experimental data related to $Γ_p$ and $Γ_n$ for $^4_Λ$H, $^4_Λ$He, and $^5_Λ$He.
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear first-order differential equations for the low energy scattering parameters like scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.
This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.
We study the effects of final state interactions in two-proton emission by nuclei. Our approach is based on the solution the time-dependent Schrödinger equation. We show that the final relative energy between the protons is substantially influenced by the final state interactions. We also show that alternative correlation functions can be constructed showing large sensitivity to the spin of the diproton system.
The semi-classical limit of quantum-mechanical scattering in two dimensions (2D) is developed. We derive the Wentzel-Kramers-Brillouin and Eikonal results for 2D scattering. No backward or forward glory scattering is present in 2D. Other phenomena, such as rainbow or orbiting do show up.
We discuss the applicability, within the Random Matrix Theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both twofold and threefold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequecies is considered to be missing in the sample. Our findings are relevant to isospin violation study in nuclei.
We discuss the connection between absorption, averages and fluctuations in nuclear reactions. The fluctuations in the entrance channel result in the compound nucleus, Hauser-Feshbach, cross section, the fluctuations in the intermediate channels, result in modifications of multistep reaction cross sections, while the fluctuations in the final channel result in hybrid cross sections that can be used to describe incomplete fusion reactions. We discuss the latter in details and comment on the validity of the assumptions used in the develpoment of the Surrogate method. We also discuss the theory of multistep reactions with regards to intermediate state fluctuations and the energy dependence and non-locality of the intermediate channels optical potentials.
We discuss the derivation of an equivalent \textit{l}-independent polarization potential for use in the optical Schrödinger equation that describes the elastic scattering of heavy ions. Three diffferent methods are used for this purpose. Application of our theory to the low energy scattering of the halo nucleus $^{11}$Li from a $^{12}$C target is made. It is found that the notion of \textit{l}-independent polarization potential has some validity but can not be a good substitute for the \textit{l}-dependent local equivalent Feshbach polarization potential.
A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such experimental/theoretical study may supply a powerful means to discern intrinsic symmetry of physical systems.
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such experimental/theoretical study may supply powerful means to discern intrinsic symmetries in physical systems.
We derive closed expressions for the nuclear breakup cross sections in the adiabatic limit using the Austern-Blair theory. These expressions are appropriate for the breakup of weakly bound nuclei. The concept of an exit doorway that mediates the coupling between the entrance channel and the breakup continuum is used. We prove the validity of the scaling law that dictates that the nuclear breakup cross section scales linearly with the radius of the target. We also compare our results for the nuclear breakup cross section of $^{11}$Be, $^8$B on several targets with recent CDCC calculation.
We discuss the geometry of the highly quantal nuclear three-body systems composed of a core plus two loosely bound particles. These Borromean nuclei have no single bound two-body subsystem. Correlation plays a prominent role. From consideration of the $B(E1)$ value extracted from electromagnetic dissociation, in conjunction with HBT-type analysis of the two valence-halo particles correlation, we show that an estimate of the over-all geometry can be deduced. In particular we find that the opening angle between the two neutrons in $^{6}$He and $^{11}$Li are, respectively, $θ_{nn} = {83^{\circ}}^{+20}_{-10}$ and ${66^{\circ}}^{+22}_{-18}$. These angles are reduced by about 12% to $θ_{nn} = {78^{\circ}}^{+13}_{-18}$ and ${58^{\circ}}^{+10}_{-14}$ if the laser spectroscopy values of the rms charge radii are used to obtain the rms distance between the cores and the center of mass of the two neutrons. The opening angle in the case of $^{11}$Li is more than 20% larger than recently reported by Nakamura \cite{Nak06}. The analysis is extended to $^{14}$Be and the two-proton Borromean nucleus $^{17}% $Ne where complete data is still not available. Using available experimental data and recent theoretical calculations we find, $θ_{nn} = {64^{0}}^{+9}_{-10}$ and $θ_{pp} = 110^{0}$, respectively.
We investigate the effect of Pauli non-locality in the heavy-ion optical potential on sub-barrier fusion reactions. The São Paulo potential, which takes into account the Pauli non-locality and has been widely used in analyzing elastic scattering, has also recently been applied to heavy-ion fusion. However, the approximation employed in deriving the São Paulo potential, based on the Perey-Buck semi-classical treatment of neutron induced reactions, must be assessed for charged particles tunneling through a barrier. It is the purpose of this note to look into this question. We consider the widely studied system $^{16}$O + $^{208}$Pb at energies that span the barrier region from 10 MeV below to 10 MeV above. It seems that the non-locality plays a minor role. We find the São Paulo potential to be quite adequate throughout the region.
It is pointed out that the usual threshold anomaly, found operative in the energy behavior of the imaginary and real parts of the optical potential representing the elastic scattering of tightly bound nuclei at near- and below-barrier energies, suffers a drastic qualitative change in the case of the elastic scattering of weakly bound nuclei. Owing to the strong coupling to the breakup channel even at sub-barrier energies, the imaginary potential strength seems to increase as the energy is lowered down to below the natural, barrier, threshold, accompanied by a decrease in the real potential strength. This feature is consistent with the dispersion relation. The system $^{6}$Li + $^{208}$Pb is analyzed to illustrate this new phenomenon.
We present an exploratory study of structure of 13C, 15C, 17C and 19C, showing that the simple one-quasiparticle projected BCS (PBCS) model is capable to account for several important properties of these nuclei. Next we discuss the importance of the Pauli Principle in the particle-core models of normal-parity states in 13C and 11Be. This is done by considering the pairing interaction between nucleons moving in an over-all deformed potential. To assess the importance of pairing correlations in these light nuclei we use both the simple BCS and the PBCS approximations. We show that the Pauli Principle plays a crucial role in the parity inversion in 11Be. It is also found that the effect of the particle number conservation in relatively light and/or exotic nuclei is quite significant. Comparison of our results with several recent papers on the same subject, as well as with some experimental data, is presented.
We review the theoretical methods to evaluate fusion cross sections in collisions of weakly bound nuclei. We piont out that in such collisions the coupling to the breakup channel leads to the appearance of different fusion processes. The extentsion of the coupled-channel method to coupling with the continuum is the most successful treatment for these collisions. However, evaluating separate cross section for each fusion process remains a very hard task.