| Автор | K T R Davies |
| Автор | M R Strayer |
| Автор | G D White |
| Дата выпуска | 1988-07-01 |
| dc.description | A general program is being developed for the systematic and careful evaluation of Green functions in pion-nucleon problems. This paper is the first in a series of projects involving integral method for the calculation of the pion and nucleon propagators. A method is presented for evaluating efficiently and accurately integrals of the form integral r<sup>m</sup> chi <sub>l1</sub>(k<sub>1</sub>r) chi <sub>l2</sub>(k<sub>2</sub>r). . . chi <sub>ln</sub>(k<sub>n</sub>r) dr, where m and n are arbitrary integers and chi <sub>l</sub>(x) can be either a spherical Bessel function, j<sub>l</sub>(x), or a spherical Neumann function, n<sub>l</sub>(x). The range of integration depends upon the particular problem encountered. The prototype integral studied is I<sub>ll'L</sub>(kk'P) identical to integral <sub>0</sub><sup>infinity </sup>r<sup>2</sup>j<sub>l</sub>(kr) j<sub>l'</sub>(k'r)j<sub>L</sub>(pr)dr whose integrand for large r has a slowly decreasing oscillatory behaviour. Rapid convergence is ensured by rotating, in the complex plane, the upper part of this integral, giving an integrand which decreases exponentially. A scaling formula is used to evaluate I<sub>ll'L</sub>(kk'p) for very small or very large values of the momenta. Also, it is shown that, if l, l' and L satisfy triangular inequalities and if l+l'+L is even, then k, k' and p must also satisfy triangular inequalities, which is the condition required by the vector delta function delta (k+k'-p). Finally the authors present sum rules and integral relations for I<sub>ll'L</sub>(kk'p). |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Complex-plane methods for evaluating highly oscillatory integrals in nuclear physics. I |
| Тип | paper |
| DOI | 10.1088/0305-4616/14/7/014 |
| Print ISSN | 0305-4616 |
| Журнал | Journal of Physics G: Nuclear Physics |
| Том | 14 |
| Первая страница | 961 |
| Последняя страница | 972 |
| Аффилиация | K T R Davies; Oak Ridge Nat. Labs., TN, USA |
| Аффилиация | M R Strayer; Oak Ridge Nat. Labs., TN, USA |
| Аффилиация | G D White; Oak Ridge Nat. Labs., TN, USA |
| Выпуск | 7 |
