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Off-shell effects in nucleon-exchange reactions

Влияние поведения вне знергетическои поверхности на реакции с обменом нуклоном

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Il Nuovo Cimento A (1971-1996)

Summary

Nucleon-nucleus rearrangement reactions proceeding via a nucleon-exchange mechanism are investigated in the framework of a three-body model. Starting from the Alt, Grassberger and Sandhas representation for the transition operators, we derive, by means of a suitable operator multiplier technique, an uncoupled integral equation showing in the inhomogeneous term the role of the nucleon-nucleon off-energy-shellt-matrix. The knock-out triangular diagram amplitude involving the off-energy-shellt-matrix is compared with the corresponding amplitude in the Born approximation for thet-matrix. Our results show that the kneck-out amplitude is rather sensitive to the off-shell behaviour of the two-nucleon interactions.

Riassunto

N ell’ambito di un modello a tre corpi si studiano le reazioni nucleari, indotte da nucleoni, che procedono attraverso un meccanismo di scambio di un nucleone. Partendo dalla rappresentazione di Alt, Grassberger e Sandhas per gli operatori di transizione, si deriva, con una tecnica che fa uso di opportuni moltiplicatori operatoriali, un’equazione integrale non accoppiata che contiene nel termine inomogeneo la matrice di diffusione nucleone-nucleonet per valori non fisici dell’energia (« off energy shell »). Si stabilisce un confronto fra l’ampiezza del grafico triangolare, che descrive il meccanismo di scambio e che contiene la matricet completa, e la corrispondente ampiezza valutata nell’approssimazione di Born per la matricet. Da un tale confronto risulta che i contributi « off energy shell » giocano un ruolo importante.

Реэуме

В рамках трех-частичнои модели исследуутся реакции нуклон-ядернои перегруппировки череэ механиэм нуклонного обмена. Исходя иэ представления Алята, Грассбергера и Сандаса для операторов перехода, мы выводим с помошяу техники соответствуушего умнозения операторов несвяэанное интеграляное уравнение, неоднородныи член которого покаэывает роля нуклон-нуклонноиt-матрицы вне знергетическои поверхности. Амплитуда выбивания, описываемая треуголянои диаграммои, которая вклучаетt-матрицу вне знергетическои поверхности, сравнивается с соответствуушеи амплитудои в борновском проблизении дляt-матрицы. Нащи реэулятаты покаэываут, что амплитуда выбивания доволяно чувствителяна к поведениу двух-нуклонных вэаимодеиствии вне знергетическои поверхности.

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References

  1. L. D. Faddeev:Sov. Phys. JETP,12, 1014 (1961);Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory (Jerusalem, 1965).

    MathSciNet  Google Scholar 

  2. L. Rosenberg:Phys. Rev.,133, B 232 (1964);J. Weyers:Phys. Rev.,145, 1236 (1966);151, 1159 (1966);P. Grassberger andW. Sandhas:Nucl. Phys.,2 B, 181 (1967);R. G. Newton:Journ. Math. Phys.,8, 851 (1967);O. A. Yakubovskiĭ:Sov. Journ. Nucl. Phys.,5, 937 (1967);R. Omnès:Phys. Rev.,165, 1265 (1968);V. V. Komarov andA. M. Popova:Sov. Journ. Nucl. Phys.,10, 621 (1970).

    Article  MathSciNet  Google Scholar 

  3. V. Vanzani:Nuovo Cimento,2 A, 525 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  4. V. Vanzani:Lett. Nuovo Cimento,2, 706 (1969).

    Article  Google Scholar 

  5. G. R. Satchler:Nucl. Phys.,95 A, 1 (1967) (see in particular p. 34);W. G. Love:Nucl. Phys.,127 A, 129 (1969).

    Article  ADS  Google Scholar 

  6. W. G. Love andG. R. Satchler:Nucl. Phys.,159 A, 1 (1970).

    Article  ADS  Google Scholar 

  7. G. R. Satchler:Nucl. Phys.,55, 1 (1964);Lectures in Theoretical Physics, Vol.8 C (Boulder, Colo., 1966), p. 73.

    Article  Google Scholar 

  8. R. M. Haybron andH. McManus:Phys. Rev.,136, B 1370 (1964);160, 756 (1967).

    Article  Google Scholar 

  9. K. L. Lim andI. E. McCarthy:Nucl. Phys.,88, 433 (1966).

    Article  Google Scholar 

  10. K. A. Amos, V. A. Madsen andI. E. McCarthy:Nucl. Phys.,94 A, 103 (1967).

    Article  ADS  Google Scholar 

  11. E. F. Redish, G. J. Stephenson jr. andG. M. Lerner:Phys. Rev. C,2, 1665 (1970).

    Article  ADS  Google Scholar 

  12. L. R. Dodd andK. R. Greider:Phys. Rev.,146, 675 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  13. C. Lovelace:Strong Interactions and High-Energy Physics (London, 1964), p. 437;Phys. Rev.,135 B, 1225 (1964).

  14. E. O. Alt, P. Grassberger andW. Sandhas:Nucl. Phys.,2 B, 167 (1967);W. Sandhas:Acta Phys. Austr., Suppl.,6, 454 (1969).

    Article  ADS  Google Scholar 

  15. V. Vanzani andG. Cattapan:Lett. Nuovo Cimento,1, 1057 (1971).

    Article  MathSciNet  Google Scholar 

  16. R. Blankenbecler andR. Sugar:Phys. Rev.,136 B, 472 (1964).

    MathSciNet  Google Scholar 

  17. P. A. Kazaks andK. R. Greider:Phys. Rev. C,1, 856 (1970).

    Article  ADS  MathSciNet  Google Scholar 

  18. I. S. Shapiro:Selected Topics in Nuclear Theory (Vienna, 1963), p. 85;Rendiconti S.I.F., Course ĭVIII (New York, 1967), p. 210;L. D. Blokhintsev, E. I. Dolinskiĭ andV. S. Popov:Nucl. Phys.,40, 117 (1963);H. J. Schnitzer:Rev. Mod. Phys.,37, 666 (1965).

  19. E. O. Alt, P. Grassberger andW. Sandhas:Nucl. Phys.,139 A, 209 (1969).

    Article  ADS  Google Scholar 

  20. E. I. Dolinskiĭ, L. D. Blokhintsev andA. M. Mukhamedzhanov:Nucl. Phys.,76, 289 (1966).

    Article  Google Scholar 

  21. R. Anni, L. Taffara andV. Vanzani:Nucl. Phys.,178 A, 214 (1971).

    Article  ADS  Google Scholar 

  22. G. Cattapan andV. Vanzani:On a generalized distorted-wave approximation for nuclear rearrangement reactions. Report INFN/BE-72/5 (1972).

  23. J. C. Y. Chen andC. J. Joachain:Physica,53, 333 (1971).

    Article  ADS  Google Scholar 

  24. I. H. Sloan:Phys. Rev.,185, 1361 (1969).

    Article  ADS  Google Scholar 

  25. K. R. Greider andL. R. Dodd:Phys. Rev.,146, 671 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  26. N. Austern:Direct Nuclear Reaction Theories (New York, 1970), p. 78 and 81.

  27. The inhomogeneous term (2.11) of eq. (2.12) can also be directly obtained in the framework of the Yakubovskiĭ formalism applied to the three-body case (3)|V. Vanzani:Nuovo Cimento,2 A, 525 (1971).

    Article  ADS  MathSciNet  Google Scholar 

  28. With the symbolsk α,p α we denote physical momenta and not the normalized ones, as in ref. (13). See the kinematic considerations developed in ref. (22).

  29. L. Taffara andV. Vanzani:Nuovo Cimento,61 B, 365 (1969).

    Article  ADS  Google Scholar 

  30. R. Aaron, R. D. Amado andY. Y. Yam:Phys. Rev.,140, B 1291 (1965).

    Article  ADS  Google Scholar 

  31. A. C. Phillips:Phys. Rev.,142, 984 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  32. E. O. Alt, P. Grassberger andW. Sandhas:Phys. Rev. C,1, 85 (1970).

    Article  ADS  Google Scholar 

  33. Y. Yamaguchi:Phys. Rev.,95, 1628 (1954).

    Article  ADS  Google Scholar 

  34. H. P. Noyes:Phys. Rev.,130, 2025 (1963).

    Article  ADS  Google Scholar 

  35. Since our three-body model involves a definite pair of nucleons (the incident proton and the emitted neutron, orvice versa) and the inert core c, we do not take an average over the np and nn singlet data to determine the singlet parameters. The average values would be slightly different from the values (3.18b). Furthermore, notice that exchange terms arising from antisymmetric properties with respect to all the nucleons (included the core ones), cannot be taken into account in our three-body context. However, their effect on the shape of the angular distribution is expected to be small (see ref. (10,33)).

  36. J. Atkinson andV. A. Madsen:Phys. Rev. Lett.,21, 295 (1968);Phys. Rev. C,1, 1377 (1970);R. F. Bentley, J. D. Carlson, D. A. Lind, R. B. Perkins andC. D. Zafiratos:Phys. Rev. Lett.,27, 1081 (1971).

    Article  ADS  Google Scholar 

  37. E. I. Dolinskiĭ andA. M. Mukhamedzanov:Sov. Journ. Nucl. Phys.,3, 180 (1966).

    Google Scholar 

  38. I. M. Guelfand andG. E. Chilov:Les distributions (Paris, 1962), p. 43.

  39. I. H. Sloan:Phys. Rev.,165, 1587 (1968).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Istituto di Fisica dell’Università, Padova, Italy

    G. Cattapan & V. Vanzani

  2. Istituto Nazionale di Fisica Nucleare, Laboratori di Legnaro, Padova, Italy

    G. Cattapan & V. Vanzani

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  1. G. Cattapan
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Cattapan, G., Vanzani, V. Off-shell effects in nucleon-exchange reactions. Nuov Cim A 12, 297–320 (1972). https://doi.org/10.1007/BF02729546

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