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A quantal toy model for heavy-ion collisions

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Zeitschrift für Physik A Atomic Nuclei

Abstract

A one-dimensional toy model of two moving finite boxes is analysed with respect to quantal phenomena associated with heavy-ion dynamics at low and intermediate energies. Special attention is payed to the relation between energy and momentum of the nucleons inside and outside the time-dependent mean field. A Wigner transformation of the one-body density matrix in space and time allows for a unique comparison with classical phase-space dynamics. It is found that high momentum components of the nuclear groundstate wave function approximately become on-shell during the heavy-ion reaction. This leads to the emission of energetic nucleons which do not appear classically. It is furthermore shown, that the low lying eigenstates of the dinuclear system for fixed time are only partly occupied throughout the reaction at intermediate energies. This opens up final phase space for nucleons after producing e.g. a pion or energetic photon. Though the present model does not allow for a reliable calculation of double differential nucleon spectra, pion or photon cross sections, it transparently shows the peculiar features of quantum dynamics in heavy-ion collisions.

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References

  1. Gobbi, A., Nörenberg, W.: In: Heavyion collisions. Bock, R. (ed.), Vol. 2. Amsterdam: North-Holland 1980

    Google Scholar 

  2. Schröder, W.U., Huizenga, J.R.: Treatise in heavy ion science. Bromley, D.A. (ed.), Vol. 2. New York: Plenum Press 1984

    Google Scholar 

  3. Glas, D., Mosel, U.: Nucl. Phys. A264, 268 (1976)

    Google Scholar 

  4. Negele, J.W.: Rev. Mod. Phys.54, 913 (1982)

    Google Scholar 

  5. Langanke, K., Friedrich, H.: Adv. Nucl. Phys.16 (to appear)

  6. Reinhard, P.G., Goeke, K.: Rep. Prog. Theor. Phys. (to appear)

  7. Hofmann, H., Siemens, P.J.: Nucl. Phys. A257, 165 (1976); A275, 464 (1977)

    Google Scholar 

  8. Nörenberg, W.: Phys. Lett.52B, 289 (1974); Z. Phys. A —Atoms and Nuclei274, 241 (1975); Z. Phys. A — Atoms and Nuclei276, 84 (1976)

    Google Scholar 

  9. Agassi, A., Ko, C.M., Weidenmüller, H.A.: Ann. Phys. (NY)107, 140 (1977);117, 404 (1979)

    Google Scholar 

  10. Weidenmüller, H.A.: Prog. Part. Nucl. Phys.3, 49 (1980)

    Google Scholar 

  11. Gross, D.H.E.: Nucl. Phys. A240, 472 (1975)

    Google Scholar 

  12. Blocki, J., Boneh, Y., Nix, J.R., Randrup, J., Robel, M., Sierk, A.J., Swiatecki, W.J.: Ann. Phys. (NY)113, 330 (1978)

    Google Scholar 

  13. Beck, F.: Phys. Lett.62B, 385 (1976)

    Google Scholar 

  14. Beck, F., Blocki, J., Dworzecka, M., Wolschin, G.: Phys. Lett.76B, 35 (1978)

    Google Scholar 

  15. Beck, F., Blocki, J., Dworzecka, M., Feldmeier, H.: Phys. Lett.99B, 13 (1981)

    Google Scholar 

  16. Randrup, J.: Nucl. Phys. A327, 490 (1979); A383, 468 (1982)

    Google Scholar 

  17. Feldmeier, H., Spangenberger, H.: Nucl. Phys. A435, 229 (1985)

    Google Scholar 

  18. Takigawa, N., Niita, K., Okuhara, Y., Yoshida, S.: Nucl. Phys. A371, 130 (1981)

    Google Scholar 

  19. Niita, K., Takigawa, N.: Nucl. Phys. A397, 141 (1983)

    Google Scholar 

  20. Nörenberg, W.: Phys. Lett.104B, 107 (1981)

    Google Scholar 

  21. Cassing, W., Nörenberg, W.: Nucl. Phys. A401, 467 (1983); A433, 467 (1985)

    Google Scholar 

  22. Lukasiak, A., Cassing, W., Nörenberg, W.: Nucl. Phys. A426, 181 (1984)

    Google Scholar 

  23. Cassing, W.: Nucl. Phys. A433, 479 (1985); A438, 253 (1985)

    Google Scholar 

  24. Wong, C.Y., Tang, H.F.: Phys. Rev. Lett.40, 1070 (1978)

    Google Scholar 

  25. Orland, H., Schaeffer, R.: Z. Phys. A — Atoms and Nuclei290, 191 (1979)

    Google Scholar 

  26. Köhler, H.S.: Nucl. Phys. A343, 315 (1980); A378, 159 (1982); A378, 181 (1982)

    Google Scholar 

  27. Ayik, S.: Z. Phys. A — Atoms and Nuclei298, 83 (1980); Nucl. Phys. A370, 317 (1981); A422, 331 (1984)

    Google Scholar 

  28. Balian, R., Vénéroni, M.: Ann. Phys.135, 270 (1981)

    Google Scholar 

  29. Grangé, P., Weidenmüller, H.A., Wolschin, G.: Ann. Phys.136, 190 (1981)

    Google Scholar 

  30. Münchow, L., Pfitzner, A.: Z. Phys. A — Atoms and Nuclei314, 97 (1983)

    Google Scholar 

  31. Buck, P., Feldmeier, H.: Phys. Lett.129B, 172 (1983)

    Google Scholar 

  32. Reinhardt, H., Balian, R., Alhassid, Y.: Nucl. Phys. A422, 349 (1984)

    Google Scholar 

  33. Wang, S.J., Cassing, W.: Ann. Phys.159, 328 (1985)

    Google Scholar 

  34. Brack, M., Guet, C., Håkansson, H.-B.: Phys. Rev.123, 275 (1985)

    Google Scholar 

  35. Bartel, J., Brack, M., Durand, M.: Nucl. Phys. A445, 263 (1985)

    Google Scholar 

  36. Brack, M.: Phys. Rev. Lett.53, 119 (1984);54, 851 (1985)

    Google Scholar 

  37. Durand, M., Ramamurthy, V.S., Schuck, P.: Phys. Lett.113B, 116 (1982)

    Google Scholar 

  38. Durand, M., Schuck, P.: Phys. Lett.172B, 235 (1986)

    Google Scholar 

  39. Schuck, P., Ghosh, G., Hasse, R.W.: Phys. Lett.118B, 237 (1982)

    Google Scholar 

  40. Hasse, R.W., Schuck, P.: Nucl. Phys. A438, 157 (1985); A445, 205 (1985)

    Google Scholar 

  41. Carruthers, P., Zachariasen, F.: Rev. Mod. Phys.55, 245 (1983)

    Google Scholar 

  42. Cassing, W.: Habilitationsschrift, TH Darmstadt 1985; GSI-Report 86-6

  43. Cassing, W.: Phase-space approach to nuclear dynamics. Di Toro, M. (ed.), pp. 64–93. Singapore: World Scientific Pub. Comp. 1986

    Google Scholar 

  44. Bertsch, G., Kruse, H., Das Gupta, S.: Phys. Rev. C29, 673 (1984)

    Google Scholar 

  45. Kruse, H., Jacak, B., Stöcker, H.: Phys. Rev. Lett.54, 289 (1985)

    Google Scholar 

  46. Kruse, H., Jacak, B., Molitoris, J.J., Westfall, G.D., Stöcker, H.: Phys. Rev. C31, 1770 (1985)

    Google Scholar 

  47. Gregoire, C., Remaud, B., Scheuter, F., Sébille, F.: Nucl. Phys. A436, 365 (1985)

    Google Scholar 

  48. Uehling, E.A., Uhlenbeck, G.E.: Phys. Rev.43, 552 (1933)

    Google Scholar 

  49. Aichelin, J.: Phys. Lett.164B, 261 (1985)

    Google Scholar 

  50. Bauer, W., Bertsch, G., Cassing, W., Mosel, U.: Preprint MSU, Aug. 1986. Phys. Rev. C (in press)

  51. Aichelin, J., Bertsch, G.: Phys. Rev. C31, 1730 (1985)

    Google Scholar 

  52. Tohyama, M., Kaps, R., Masak, D., Mosel, U.: Phys. Lett.136B, 226 (1984); Nucl. Phys. A437, 739 (1985)

    Google Scholar 

  53. Cassing, W., Biro, T., Mosel, U., Tohyama, M., Bauer, W.: Preprint UGI 86-6. Phys. Lett. B (in press)

  54. Holub, E., Hilscher, D., Ingold, G., Jahnke, U., Orf, H., Rossner, H., Zank, W.P., Schröder, W.U., Gemmeke, H., Keller, K., Lassen, L., Lücking, W.: Phys. Rev. C33, 143 (1986)

    Google Scholar 

  55. Chitwood, C.B., Fields, D.J., Gelbke, C.K., Klesch, D.R., Lynch, W.G., Tsang, M.B., Awes, T.G., Ferguson, R.L., Obenshain, F.E., Plasil, F., Robinson, R.L., Young, G.R.: Preprint MSUCL-566, June 1986

  56. Rösch, W., Brendel, C., Richter, A., Schrieder, G., Gentner, R., Keller, K., Lassen, L., Lücking, W., Schreck, R., Cassing, W., Schüll, D., Gemmeke, H.: GSI Annual Report, p. 81, 1985

  57. Stachel, J.: Proceedings of the International Workshop on Gross Properties of Nuclei and Nuclear excitations XIII, p. 1. Hirschegg, Jan. 1985

  58. Grosse, E.: Proceedings of the International Workshop on Gross Properties of Nuclei and Nuclear Excitations XIII, p. 65. Hirschegg, Jan. 1985

  59. Cusson, R.Y., Smith, R.K., Maruhn, J.A.: Phys. Rev. Lett.36, 1166 (1976)

    Google Scholar 

  60. Cusson, R.Y., Maruhn, J.A., Meldner, A.W.: Phys. Rev. C18, 2589 (1978)

    Google Scholar 

  61. Cusson, R.Y., Meldner, A.W.: Phys. Rev. Lett.42, 694 (1979)

    Google Scholar 

  62. Cassing, W., Dhar, A.K., Lukasiak, A., Nörenberg, W.: Z. Phys. A — Atoms and Nuclei314, 309 (1983)

    Google Scholar 

  63. Feldmeier, H.: Lecture Notes in Physics. Vol. 171, p. 111. Berlin, Heidelberg, New York: Springer-Verlag 1982

    Google Scholar 

  64. Buck, P., Feldmeier, H.: Nucl. Phys. A394, 334 (1983)

    Google Scholar 

  65. Buck, P.: Ph.D. Thesis, TH Darmstadt 1985

  66. Prakash, M., Shlomo, S., Nilsson, B.S., Bondorf, J.P., Serr, F.E.: Nucl. Phys. A385, 483 (1982)

    Google Scholar 

  67. Beth, E., Uhlenbeck, G.: Physica4, 915 (1937)

    Google Scholar 

  68. Mosel, U.: Phys. Lett.46B, 8 (1973)

    Google Scholar 

  69. Franz, W.: Quantentheorie. Berlin: Springer 1970

    Google Scholar 

  70. Cassing, W.: Coincident particle emission from continuum states in nuclei. Machner, H., Jahn, P. (eds.), pp. 340–376. Singapore: World Scientific Publ. Comp. 1984

    Google Scholar 

  71. Alamanos, N., Braun-Munzinger, P., Freifelder, R.F., Paul, P., Stachel, J., Awes, T.C., Ferguson, R.L., Obenshain, F.E., Plasil, F., Young, G.R.: Phys. Lett.173B, 392 (1986)

    Google Scholar 

  72. Herrmann, N., Albinski, J., Bock, R., Feng, E.P., Freifelder, R., Gobbi, A., Grimm, P., Grosse, E., Hildenbrand, K.D., Liu, H.T., Müller, W.F.J., Stelzer, H., Braun-Munzinger, P., Stachel, J., Maurenzig, P.R., Olmi, A., Stefani, A.A.: GSI Annual Report, p. 86, 1985

  73. Cassing, W.: Z. Phys. A — Atoms and Nuclei326, 21 (1987)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Giessen, Giessen, Federal Republic of Germany

    W. Cassing

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  1. W. Cassing
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Dedicated to Professor Friedrich Beck on the occasion of his 60th birthday

Supported by BMFT and GSI Darmstadt, FRG

The author likes to thank U. Mosel for a series of interesting discussions as well as R. Kaps for a critical reading of the manuscript.

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Cassing, W. A quantal toy model for heavy-ion collisions. Z. Physik A - Atomic Nuclei 326, 21–31 (1987). https://doi.org/10.1007/BF01294567

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