A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials
A method is presented to reduce the singular Lippmann-Schwinger integral equation to a simple matrix equation. This method is applied to calculate the matrix elements of the reaction and transition operators, respectively, on the real axis and on the complex plane. The phase shifts and the different...
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| Format: | Article |
| Language: | English |
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Isfahan University of Technology
2007-09-01
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| Series: | Iranian Journal of Physics Research |
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| Online Access: | http://ijpr.iut.ac.ir/browse.php?a_code=A-10-1-111&slc_lang=en&sid=1 |
| _version_ | 1828911011414933504 |
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| author | E. Ghanbari Adivi |
| author_facet | E. Ghanbari Adivi |
| author_sort | E. Ghanbari Adivi |
| collection | DOAJ |
| description | A method is presented to reduce the singular Lippmann-Schwinger integral equation to a simple matrix equation. This method is applied to calculate the matrix elements of the reaction and transition operators, respectively, on the real axis and on the complex plane. The phase shifts and the differential scattering amplitudes are computable as well as the differential cross sections if the R- and/or T-matrix elements on the energy-shell are known. The method is applicable by using the Gaussian quadratures based on the Legenre, Laguer Chebyshev and shifted Chebyshev polynomials. Choosing the nodal points and weight functions depends on the aspects of the problem. |
| first_indexed | 2024-12-13T18:54:09Z |
| format | Article |
| id | doaj.art-8fc0a91b2937462cb7b3b395907ac288 |
| institution | Directory Open Access Journal |
| issn | 1682-6957 |
| language | English |
| last_indexed | 2024-12-13T18:54:09Z |
| publishDate | 2007-09-01 |
| publisher | Isfahan University of Technology |
| record_format | Article |
| series | Iranian Journal of Physics Research |
| spelling | doaj.art-8fc0a91b2937462cb7b3b395907ac2882022-12-21T23:34:51ZengIsfahan University of TechnologyIranian Journal of Physics Research1682-69572007-09-0173161170A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentialsE. Ghanbari AdiviA method is presented to reduce the singular Lippmann-Schwinger integral equation to a simple matrix equation. This method is applied to calculate the matrix elements of the reaction and transition operators, respectively, on the real axis and on the complex plane. The phase shifts and the differential scattering amplitudes are computable as well as the differential cross sections if the R- and/or T-matrix elements on the energy-shell are known. The method is applicable by using the Gaussian quadratures based on the Legenre, Laguer Chebyshev and shifted Chebyshev polynomials. Choosing the nodal points and weight functions depends on the aspects of the problem.http://ijpr.iut.ac.ir/browse.php?a_code=A-10-1-111&slc_lang=en&sid=1Lippmann-Schwinger equationtransition matrixreaction matrixphase shiftsGaussian quadratures |
| spellingShingle | E. Ghanbari Adivi A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials Iranian Journal of Physics Research Lippmann-Schwinger equation transition matrix reaction matrix phase shifts Gaussian quadratures |
| title | A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials |
| title_full | A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials |
| title_fullStr | A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials |
| title_full_unstemmed | A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials |
| title_short | A numerical method to solve the Lippmann-Schwinger integral equation with radial interaction potentials |
| title_sort | numerical method to solve the lippmann schwinger integral equation with radial interaction potentials |
| topic | Lippmann-Schwinger equation transition matrix reaction matrix phase shifts Gaussian quadratures |
| url | http://ijpr.iut.ac.ir/browse.php?a_code=A-10-1-111&slc_lang=en&sid=1 |
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