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A mathematical approach to the nuclear-matter problem

Математический подход к проблеме ядерного вещества

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

The aim of this paper is to outline a mathematical scheme for the description of the overall behaviour of infinite nuclear matter: it has been conceived with the pragmatic purpose of providing simple tools for carrying out realistic numerical calculations. To this end we shall revive some insufficiently explored aspects of vintage theories, which seem to have been by-passed by recent theoretical developments.

Riassunto

Scopo di questa nota è di delineare uno schema matematico per la descrizione del comportamento globale della materia nucleare infinita. Esso è stato concepito con lo scopo pragmatico di fornire un semplice strumento analitico per eseguire calcoli numerici attendibili. A questo scopo sono stati anche riesaminati alcuni aspetti finora insufficientemente esplorati di ben note teorie che sembrano essere del tutto ignorate dai piú recenti sviluppi teorici.

Резюме

Цель этой статьи—развитие математической схемы для описания поведения бесконечного ядерного вещества. Предложенный подход развит с прагматической целью получения простого метода для проведения реалистичных численных вычислений.

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References

  1. N. H. Hugenholtz andL. Van Hove:Physica (The Hague),24, 363 (1958).

    Article  ADS  MATH  Google Scholar 

  2. P. E. Hodgson:The Optical Model of Elastic Scattering (Oxford, 1963);Nuclear Reactions and Nuclear Structure (Oxford, 1971).

  3. K. A. Brueckner andK. S. Masterson:Phys. Rev.,128, 2267 (1963); see alsoR. Rajaraman andH. A. Bethe:Rev. Mod. Phys.,39, 249, 745 (1967).

    Article  ADS  Google Scholar 

  4. M. Razavy:Phys. Rev.,130, 1091 (1963).

    Article  ADS  Google Scholar 

  5. K. A. Brueckner andT. D. Goldman:Phys. Rev.,117, 207 (1960); see alsoK. A. Brueckner, J. L. Gammel andJ. T. Kubis:Phys. Rev. 118, 1438 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  6. K. A. Brueckner, C. A. Levinson andH. M. Mahmoud:Phys. Rev.,95, 219 (1954);K. A. Brueckner:Phys. Rev.,96, 1558 (1956);N. Fukuda andR. G. Newton:Phys. Rev.,103, 1558 (1956).

    Article  ADS  Google Scholar 

  7. H. A. Bethe:Phys. Rev. B,4, 804 (1965).

    Article  Google Scholar 

  8. D. W. L. Sprung, P. C. Bhargava andT. K. Dahlblom:Phys. Lett.,21, 538 (1966); the quoted results are wrong also because based on an incorrect application of Bethe’s three-body theory (seeD. B. Day:Rev. Mod. Phys.,39, 719, 743 (1967)).

    Article  ADS  Google Scholar 

  9. F. Seitz:The Modern Theory of Solids (New York, N. Y., 1940).

  10. K. A. Brueckner:The Many Body Problem, Vol. I (Paris, 1959), p. 169;M. A. Preston:Physics of the Nucleus (Reading, Mass., 1962), p. 202. A rather queer criterion for calculatingM ** has been suggested byL. C. Gomes, J. D. Walecka andV. F. Weisskopf:Ann. Phys. (N. Y.),3, 241, 252 (1958). Recently, definition (3.6) has been adopted also byJ. P. Blaizot in his review paper on nuclear compressibilities (Phys. Rep.,64, 171 (1980), formula (7.1), p. 234). See alsoK. A. Brueckner andJ. L. Gammel:Phys. Rev.,109, 1840 (1958), formula (21).

    Google Scholar 

  11. L. G. Dubuat:Principles d’hydraulic, Vol. II (Paris, 1816), p. 222).

    Google Scholar 

  12. G. Green:Mathematical Papers, Vol. I (London, 1833), p. 315;G. Stokes:Mathematical and Philosophical Papers, Vol. I (London, 1834), p. 17.

    Google Scholar 

  13. G. Birkhoff:Hydrodynamics (Princeton, N. J., 1950); see alsoH. Lamb:Hydrodynamics (New York, N. Y., 1945), p. 123.

  14. H. A. Bethe:Phys. Rev.,103, 1353 (1956); see formulae from (9.17) to (9.25).

    Article  ADS  MATH  Google Scholar 

  15. H. A. Bethe:Phys. Rev.,103, 1353, 1372 (1956)

    Article  ADS  MATH  Google Scholar 

  16. K. A. Brueckner:The Many Body Problem, Vol. I (Paris, 1959), p. 160.

    Google Scholar 

  17. K. A. Brueckner andJ. L. Gammel:Phys. Rev.,105, 1679 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  18. R. J. Eden, V. J. Emery andS. Sampanthar:Proc. R. Soc. London Ser. A,253, 177, 186 (1959); see alsoD. J. Thouless:The Quantum Mechanics of Many-Body Systems (New York, N. Y., 1961).

    Article  ADS  Google Scholar 

  19. J. M. Blatt andV. F. Weisskopf:Theoretical Nuclear Physics (New York, N. Y., 1952), p. 129.

  20. This idea has been suggested to the author byL. Rosenfeld; see alsoL. Rosenfeld:Interactions nucléaires aux basses energies et structure des noyaux (Paris, 1959), p. 330;C. Villi:Nucl. Phys.,9, 306 (1959).

  21. C. Villi:Atti dell’Istituto Veneto di Scienze, Lettere ed Arti, Tomo CXXXVIII,1 (1979–1980).

  22. T. Koopmans:Physica (The Hague),1, 104 (1933); see alsoW. Jones andN. H. March:Theoretical Solid State Physics (London, 1973).

    Article  ADS  MATH  Google Scholar 

  23. W. A. Harrison:Solid State Theory (New York, N. Y., 1970).

  24. C. Villi:Nuovo Cimento A,67, 178 (1982).

    Article  ADS  Google Scholar 

  25. L. Rosenfeld:Nuclear Forces, Part III (Amsterdam, 1948); see alsoR. Huby:Proc. Phys. Soc. London Sect. A,62, 62 (1949).

  26. A. L. Fetter andJ. D. Walecka:Quantum Theory of Many-Particle Systems (New York, N. Y., 1971).

  27. L. C. Gomes, J. D. Walecka andV. F. Weisskopf:Ann. Phys. (N. Y.),3, 241 (1958).

    Article  ADS  MATH  Google Scholar 

  28. K. A. Brueckner:Phys. Rev.,97, 1353 (1955).

    Article  ADS  MATH  Google Scholar 

  29. K. L. Mill, A. M. Sessler, S. A. Moskowski andD. G. Shaukland:Phys. Rev. Lett.,3, 383 (1959).

    ADS  Google Scholar 

  30. K. A. Brueckner andW. Wada:Phys. Rev.,103, 1008 (1956).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. General solutions of the differential equation of nuclear matter have been searched for byT. A. Minelli:Atti e Memorie dell’Accademia Patavina di Scienze, Lettere ed Arti, Vol. LXXXV, Part. II (1972–1973).

  32. H. A. Bethe:Annu. Rev. Nucl. Sci.,21, 93 (1971); see alsoW. Kundt andE. T. Newman:J. Math. Phys. (N. Y.),9, 2193 (1967).

    Article  ADS  Google Scholar 

  33. K. A. Brueckner andW. Wada:Phys. Rev.,103, 1008 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  34. K. A. Brueckner:Phys. Rev.,97, 1353 (1955).

    Article  ADS  MATH  Google Scholar 

  35. W. Cheid, R. Ligensa andW. Greiner:Phys. Rev. Lett.,21, 1479 (1968).

    Article  ADS  Google Scholar 

  36. A. Bohr andB. R. Mottelson:Nuclear Structure, Vol.I (New York, N. Y., 1969), p. 257.

    Google Scholar 

  37. H. A. Bethe:Proceedings of the International Nuclear Physics Conference, Gatlinburg (New York, N. Y., 1967), p. 625.

  38. K. A. Brueckner andJ. L. Gammel:Phys. Rev.,109, 1023 (1958).

    Article  MathSciNet  ADS  Google Scholar 

  39. J. P. Blaizot:Phys. Rep.,64, 171 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  40. H. G. Baumgardt, J. U. Scott, Y. Sakamoto, E. Schopper, H. Stoecker, J. Hofmann, W. Cheid andW. Greiner:Z. Phys. A,273, 359 (1975).

    Article  ADS  Google Scholar 

  41. L. Zamick:Phys. Lett. B,45, 313 (1973); see also the paper byBlaizot.Phys. Rep.,64, 171 (1980).

    Article  ADS  Google Scholar 

  42. T. H. R. Skyrme:Nucl. Phys.,9, 615 (1959); see alsoD. Vantherin andD. M. Brink:Phys. Lett. B,32, 149 (1970).

    Article  MATH  Google Scholar 

  43. See ref. (25).

    Article  ADS  Google Scholar 

  44. Private communication fromH. A. Bethe toB. D. Day (seeB. D. Day:Rev. Mod. Phys.,4, 719 (1967), p. 743).

    Article  ADS  Google Scholar 

  45. K. A. Brueckner, R. J. Eden andN. C. Francis:Phys. Rev.,100, 891 (1955).

    Article  ADS  Google Scholar 

  46. D. Wilmore andP. E. Hodgson:Nucl. Phys.,55, 673 (1964).

    Article  Google Scholar 

  47. M. M. Giannini, G. Ricco andA. Zucchiatti:Microscopic Optical Potentials, Proceedings of the Hamburg Conference, edited byH. V. von Geramb (Berlin, 1978), p. 126.

  48. W. E. Frahn:Nuovo Cimento,5, 393 (1957); see alsoW. E. Frahn:Nuovo Cimento,4, 314 (1956).

    Article  MathSciNet  MATH  Google Scholar 

  49. B. Sinha:Phys. Rep. C,20, 1 (1975).

    Article  ADS  Google Scholar 

  50. E. Clementel andC. Villi:Nuovo Cimento,1, 176 (1955);A. M. Lane andC. F. Wandel:Phys. Rev.,98, 1524 (1955).

    Article  Google Scholar 

  51. J. P. Jenkenue, A. Lejeune andC. Mahaux:Nuclear Optical Model Potential, edited byS. Boffi andG. Passatore (Berlin, 1976), p. 72;B. Sinha andF. Duggan:Phys. Lett. B,47, 389 (1973);B. Sinha andF. Duggan:Nucl. Phys. A,226, 31 (1974).

  52. H. Feshbach, C. E. Porter andV. F. Weisskopf:Phys. Rev.,96, 448 (1954).

    Article  ADS  MATH  Google Scholar 

  53. M. L. Goldberger:Phys. Rev.,74, 1269 (1948).

    Article  ADS  Google Scholar 

  54. Y. Yamaguchi:Progr. Theor. Phys.,5, 332 (1950).

    Article  ADS  Google Scholar 

  55. More complete information is given in the review paper byL. Beretta, C. Villi andF. Ferrari:Nuovo Cimento, Suppl.,12, 499 (1954).

    Article  Google Scholar 

  56. S. Hayakawa, M. Kawai andK. Kikuchi:Progr. Theor. Phys.,13, 415 (1955); the approximationc 2=0 has been adopted also byB. Sinha:Phys. Rev. C,11, 1546 (1975).

    Article  ADS  MATH  Google Scholar 

  57. H. Margenau andG. M. Murphy:The Mathematics of Physics and Chemistry (New York, N. Y., 1943).

  58. M. M. Giannini, G. Ricco andA. Zucchiatti:Ann. Phys. (N.Y.),124, 208 (1980), fig. 11.

    Article  ADS  Google Scholar 

  59. W. B. Riesenfeld andK. M. Watson:Phys. Rev.,102, 1157 (1956).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  60. R. M. Frank, J. L. Gammel andK. M. Watson:Phys. Rev.,101, 891 (1956);R. M. Sternheimer:Phys. Rev.,106, 1027 (1957).

    Article  ADS  MATH  Google Scholar 

  61. B. D. Day:Rev. Mod. Phys.,39, 719 (1967), p. 738.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Istituto di Fisica dell’Università, Padova

    C. Villi

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova, Italia

    C. Villi

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Villi, C. A mathematical approach to the nuclear-matter problem. Nuov Cim A 74, 37–116 (1983). https://doi.org/10.1007/BF02829860

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