1,720,991 research outputs found
Finite-rank potentials with Coulomb interactions
No full textScattering due to finite-rank potentials with exact treatment of Coulomb
interactions is discussed
Coupled-channel effects in a quasi-separable potential model
No full textCoupled-channel effects are studied in the framework of an exactly solvable multichannel scattering formalism based on separable nuclear interactions. In the limit of weak coupling between channels, explicit expressions for the single-level Breit-Wigner resonance parameters are obtained. Some typical effects of many overlapping resonances are analyzed by means of multilevel and strong-coupling calculation
Separable expansions for realistic multichannel scattering problems
No full textA new approach to the multichannel scattering problem with realistic local or nonlocal interactions is developed. By employing the negative-energy solutions of uncoupled Sturmian eigenvalue problems referring to simple auxiliary potentials, the coupling interactions appearing in the original multichannel problem are approximated by finite-rank potentials. By resorting to integral-equation techniques the coupled-channel equations are then reduced to linear algebraic equations which can be straightforwardly solved. Compact algebraic expressions for the relevant scattering matrix elements are thus obtained. The convergence of the method is tested in the single-channel case with realistic optical potentials. Excellent agreement is obtained with a few terms in the separable expansion for both real and absorptive interactions
Analysis of the optical potential with coupled-channel scattering equations: Energy dependence and coordinate-space behavior
No full textWe apply a Sturmian-expansion method we have recently developed to perform an exact multichannel analysis of the optical potential. By combining this method with momentum-space integral-equation techniques we can obtain a finite-rank representation of the nonlocal optical potential in which coupling effects are exactly taken into account. In the framework of this approach we provide also detailed expressions of the various contributions arising when couplings are treated perturbatively. These iterative-perturbative approximation schemes are generally employed in phenomenological optical-potential calculations. Our results do not apply to low-order terms only, but can be extended to any desired order. We find that a proper treatment of inelastic-inelastic couplings may be necessary in order to reproduce the detailed nonlocal structure of the optical potential. We then perform an energy-dependent analysis of the resulting optical potential. To this end, the rapid fluctuations in energy due to compound or quasicompound resonances are subtracted off by means of a direct algebraic procedure. The connection of this subtraction method with Feshbachs general reaction theory is clarified. We analyze the energy dependence of the smooth optical interaction in the light of a dispersion-theoretic approach, by resorting to simple analytic parametrizations of the real and imaginary parts. Both a model multichannel problem and the realistic neutron-208Pb case have been considered
A fast converging separable expansion for realistic nuclear potentials
No full textA new separable-expansion method for realistic multichannel scattering problems is proposed. The approximate finite-rank potentials are obtained by resorting to a complete set of sturmians referring to a fixed negative energy. These basis functions are solutions of a coupled-channel auxiliary eigenvalue problem embodying the main physical features of the original interactions. The coupled sturmian equations are solved through a simple diagonalization procedure by employing another set of auxiliary sturmians given in closed analytic form. The method is applied to uncoupled as well as to coupled states for the Reid potential. Good convergence properties are found both on and off the energy shell. The method can be applied to general coupled-channel problems, and can be extended so as to treat absorptive and/or energy-dependent interaction
On the coupled-channel calculation of the optical potential with full inclusion of coupling effects
No full textWe develop a method for a coupled-channel calculation of the optical potential in which the multichannel Green's function is evaluated exactly. The quantum-mechanical coupled-channel problem is solved by expanding the multichannel interactions in terms of coupled sturmians. Closed- and open-channel effects are straightforwardly included by the use of energy-dependent basis functions. An application in the framework of a schematic multichannel model is developed
Exactly soluble multichannel scattering problems with Coulomb interactions
No full textA general separable potential approach to elastic and inelastic scattering processes is developed which takes account of Coulomb interactions in an exact way. Effective nuclear interactions are used that are separable in the channel relative motion variables and take explicit account of the coupled-channel nature of the problem. After solving the coupled-channel integral equations by means of both matrix inversion techniques and a suitable channel-decoupling procedure, we arrive at exact manageable expressions of the Coulomb-corrected nuclear transition amplitudes
A separable potential approach to nucleon-nucleus scattering with exact treatment of Coulomb interactions
No full textA suitable, physically reasonable choice of separable nucleon-nucleus potential is made, which leads to very simple analytic expressions for the form factors in the Coulomb-state representation. This allows one to take account of Coulomb effects in an exact and simple way. The model is applied to the analysis of the elastic scattering of nucleons by 4He, 12C and 16O targets. A good fit of the experimental phase shifts is obtained with almost the same values of the potential parameters for neutron-nucleus and proton-nucleus elastic scattering
A multichannel quasi-separable potential approach to nucleon-nucleus scattering
No full textA quasi-separable potential model for two-body multichannel scattering is developed. Spin and Coulomb effects are taken into account. By a suitable choice of the separable nuclear interactions we arrive at simple analytic expressions for the transition amplitudes. Our model is applied to the study of the n-12C and p-12C scattering processes. Effects arising from the excitation of the target nucleus are well reproduced
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