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On the connection between fredholm determinant and Jost function for nonlocal potentials

О соотнощении между детерминантом Фредгольма и функцией оста для нелокальных потенциалов

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Il Nuovo Cimento A (1965-1970)

Summary

The assertion that the Jost function of ans-wave nonlocal potential is equivalent to the ratio of the Fredholm determinants of the integral equations corresponding to the physical and regular solutions has been analysed in detail. The results have been verified from first principles by taking into account a model (square-well) separable potential. A numerical analysis reflects the influence of the results so obtained on the enhancement factor.

Riassunto

Si esamina dettagliatamente l’asserzione secondo cui la funzione di Jost di un potenziale non locale di un’ondas è equivalente al rapporto dei determinanti di Fredholm delle equazioni integrali corrispondenti alle soluzioni fisica e regolare. Si è compiuta la verifica dei risultati a partire dai principi primi tenendo conto di un potenziale separabile (a buca quadra) modello. Un’analisi numerica rivela l’influenza dei risultati così ottenuti sul fattore d’incremento.

Реэюме

Подробно аналиэируется утверждение, что функций оста дляs-волнового нелокального потенциала зквивалентна отнощению детерминантов Фредгольма для интегральных уравнений, соответствуюших фиэическим регулярным рещениям. Полученные реэультаты были проверены иэ первых принципов, испольэуя модельный (прямоугольная яма) раэделяемый потенциал. Численный аналиэ отра?жает влияние полученных реэультатов для фактора увеличения.

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References

  1. A. N. Mitra andJ. H. Naqvi:Nucl. Phys.,25, 307 (1961);F. Tabakin:Ann. of Phys.,30, 51 (1964);T. R. Mongan:Phys. Rev.,175, 1260 (1968);178, 1597 (1969).

    Article  MathSciNet  Google Scholar 

  2. J. A. Wheeler:Phys. Rev.,52, 1107 (1937);K. A. Brueckner:Phys. Rev.,100, 36 (1955);H. A. Bethe andJ. Goldstone:Proc. Roy. Soc., A238, 267 (1957).

    Article  ADS  MATH  Google Scholar 

  3. Y. Yamaguchi andY. Yamaguchi:Phys. Rev.,95, 1635 (1954);F. Tabakin:Phys. Rev.,177, 1443 (1969);J. Pigeon, J. Barguil, C. Fayard, G. H. Lamot andE. Elbaz:Phys. Rev. C,4, 704 (1971);G. Pisent andS. S. Ahmad:Nuovo Cimento,12 A, 665 (1972);C. Lovelace:Phys. Rev.,135, B 1225 (1964);A. N. Mitra:Advances in Nuclear Physics, Vol.3, edited byM. Baranger andE. Vogt (New York, N. Y., 1969).

    Article  ADS  Google Scholar 

  4. M. Baranger, B. Giraud, S. K. Mukhopadhyay andP. U. Sauer:Nucl. Phys.,138 A, 1 (1969);O. P. Bahethi andM. G. Fuda:Phys. Rev. C,6, 1956 (1972);G. Cattapan andV. Vanzani:Nuovo Cimento,12 A, 297 (1972);O. Zohni:Journ. Math. Phys.,14, 205 (1973);M. G. Fuda andJ. S. Whiting:Phys. Rev. C,8, 1255 (1973).

    Article  ADS  Google Scholar 

  5. H. Feshbach:Ann. of Phys.,5, 357 (1958);19, 287 (1962);F. G. Perey:The Proceedings of the Conference on Direct Interaction and Nuclear Reaction Mechanisms, edited byE. Clement andC. Villi (New York, N. Y., 1963);M. Coz:Progr. Theor. Phys.,50, 111 (1973).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. J. Gillespie:Phys. Rev.,160, 1432 (1967).

    Article  ADS  Google Scholar 

  7. M. Bertero, G. Talenti andG. A. Viano:Nuovo Cimento,46, 337 (1966);Comm. Math. Phys.,6, 128 (1967);Nucl. Phys.,113, A, 635 (1968);115 A, 395 (1968).

    Article  ADS  Google Scholar 

  8. S. S. Ahmad: D.P. Thesis (unpublished), University of Padua (1973);S. S. Ahmad andG. Pisent:Nuovo Cimento,22 A, 79 (1974).

  9. R. Jost:Physica,12, 509 (1946);Helv. Phys. Acta,20, 256 (1947);R. Jost andA. Pais:Phys. Rev.,82, 840 (1951);R. G. Newton:Journ. Math. Phys.,1, 319 (1960);V. De Alfaro andT. Regge:Potential Scattering (Amsterdam, 1965).

    Article  MathSciNet  ADS  Google Scholar 

  10. M. Coz, A. D. MacKellar andL. G. Arnold:Ann. of Phys.,58, 504 (1970);59, 219 (1970);F. Capuzzi:Nuovo Cimento,11 A, 801 (1972).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. C. S. Warke andR. K. Bhaduri:Nucl. Phys.,162 A, 289 (1971).

    Article  MathSciNet  ADS  Google Scholar 

  12. J. J. Giambiagi andT. W. B. Kibble:Ann. of Phys.,7, 39 (1959);J. Gillespie:Final State Interactions, Chap. 3 (San Francisco, Calif., 1964).

    Article  MathSciNet  ADS  Google Scholar 

  13. S. G. Mikhlin:Integral Equations, Chap. II (London, 1957).

  14. K. W. McVoy:Nucl. Phys.,115 A, 481 (1968);S. Okai, S. Saito andR. Tamagaki:Progr. Theor. Phys.,47, 484 (1972).

    Article  ADS  Google Scholar 

  15. D. Gutkowski andA. Scalia:Journ. Math. Phys.,9, 588 (1968);M. G. Fuda:Phys. Rev. C,1, 1910 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  16. D. Blasczak andM. G. Fuda:Phys. Rev. C,8, 1665 (1973).

    Article  ADS  Google Scholar 

  17. S. S. Ahmad:Proceedings of the Fifth AINSE Nuclear Physics Conference, ANU Canberra, February 11–13, 1974 (unpublished).

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Author notes

  1. S. S. Ahmad

    Present address: Department of Theoretical Physics, Research School of Physical Sciences, The Australian National University, 2600, Canberra, A.C.T.

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  1. Scuola di Perfezionamento in Fisica dell’Università, Padova

    S. S. Ahmad

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Supported in part by Ministry of Foreign Affairs, Roma.

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Ahmad, S.S. On the connection between fredholm determinant and Jost function for nonlocal potentials. Nuov Cim A 23, 362–374 (1974). https://doi.org/10.1007/BF02739491

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  • DOI: https://doi.org/10.1007/BF02739491

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