Union of Discretized Spectra for Scattering Calculations

Here we propose a new technique which allows to find scattering phase shifts and parameters of resonances directly from the discretized continuous spectra of the asymptotic and total Hamiltonians, when these operators are represented by a matrices in some finite square-integrable basis. The proposed...

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Bibliographic Details
Published in:Physics of atomic nuclei 2022-12, Vol.85 (6), p.1087-1101
Main Authors: Pomerantsev, V. N., Rubtsova, O. A.
Format: Article
Language:English
Subjects:
Asymptotic properties
Continuous spectra
Discretization
Electric power grids
ELEMENTARY PARTICLES AND FIELDS/Theory
Hamiltonian functions
Invariance
Operators (mathematics)
Parameters
Particle and Nuclear Physics
Physics
Physics and Astronomy
Resonance scattering
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Summary:Here we propose a new technique which allows to find scattering phase shifts and parameters of resonances directly from the discretized continuous spectra of the asymptotic and total Hamiltonians, when these operators are represented by a matrices in some finite square-integrable basis. The proposed approach is based on the possibility of approximating the discretized spectrum by a continuous spectral function. Using the example of the Gaussian basis, the invariance of the discretized spectrum with respect to the transformation of the basis caused by the shift of the indices in the set of basis parameters is demonstrated. This invariance property allows us to combine spectra obtained using different bases of the same dimension into one common spectral set. Such a union of spectra makes it possible to find the phase shifts of scattering on a dense energy grid, as well as to determine the parameters of resonances with good accuracy by using basis sets with a moderate dimension. The invariance property is also employed in a multichannel problem where it allows to construct a degenerate discretized multichannel spectrum of asymptotic Hamiltonian and to find eigenphase shifts as well. It is also shown how to employ the union of discretized spectra to find narrow resonance parameters in a multichannel problem.
ISSN:1063-7788
1562-692X
DOI:10.1134/S1063778823010441