Abstract
The two-dimensional Fokker-Planck equation describing the phase-space evolution of the reduced density matrixf(r, v; t) with respect to radial distancer and radial velocityv is numerically solved for various cases of inelastic heavy-ion collisions. A comparison of the exact solution with the global moment approach (GMA) used so far by several authors clearly shows that the GMA is not applicable for deeply inelastic collisions. A local moment approach (LMA) is proposed as an approximate solution to the Fokker-Planck equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gobbi, A., Nörenberg, W.: In: Heavy-ion collisions. Bock, R. (ed.), Vol. 2. Amsterdam: North Holland 1980;
Nörenberg, W., Weidenmüller, H.A.: Introduction to the theory of heavy-ion collisions. Lecture Notes in Physics. 2nd edn., Vol. 51. Berlin, Heidelberg, New York: Springer 1980;
Weidenmüller, H.A.: In: Progress in particle and nuclear physics. Wilkinson, D.H. (ed.), Vol. 3. Oxford: Pergamon Press 1980;
Grangé, P., Weidenmüller, H.A.: Fission probability and the nuclear friction constant. Preprint CRN/PN 80-24
Nix, J.R., Sierk, A.J.: Proceedings of the International Workshop on Gross Properties of Nuclei and Nuclear Excitations IX, Hirschegg, Austria, Jan. 19–24, 1981, p. 74
Ngô, C., Hofmann, H.: Z. Phys. A — Atoms and Nuclei282, 83 (1977);
Berlanger, M., Ngô, C., Grangé, P., Richert, J., Hofmann, H.: Z. Phys. A — Atoms and Nuclei284, 61 (1978);
Berlanger, M., Grangé, P., Hofmann, H., Ngô, C., Richert, J.: Z. Phys. A — Atoms and Nuclei286, 207 (1978)
Riedel, C., Wolschin, G.: Z. Phys. A — Atoms and Nuclei294, 17 (1980)
Cassing, W., Knoll, J.: Phys. Lett.106 B, 443 (1981)
Yadav, H.L., Nörenberg, W.: Private communications
Schmidt, R., Wolschin, G.: Z. Phys. A — Atoms and Nuclei296, 215 (1980);
Grossmann, S.: Z. Phys. A — Atoms and Nuclei296, 251 (1980)
Brosa, U.: Z. Phys. A — Atoms and Nuclei298, 77 (1980)
Cassing, W., Friedrich, H.: Z. Phys. A — Atoms and Nuclei291, 339 (1979)
Huang, K.: Statistical mechanics. New York, London: John Wiley & Sons 1963
Gobbi, A.: Private communication
Birkelund, J.R., Tubbs, L.E., Huizenga, J.R., De, J.N., Sperber, D.: Phys. Rep.56, 107 (1979)
Brosa, U.: Proceedings of the International Workshop on Gross Properties of Nuclei and Nuclear Excitation IX, Hirschegg, Austria, Jan. 19–24, 1981, p. 167
Peaceman, D.W., Rachford, H.H., Jr.: SIAM J.3, 28 (1955)
Isaacson, E., Keller, H.B.: Analysis of numerical methods, pp. 55–58. New York: Wiley 1966
Courant, R., Friedrichs, K.O., Lewy, H.: Math. Ann.100, 32 (1928)
Roscoe, D.F.: J. Inst. Math. Appl.16, 291 (1975)
Author information
Authors and Affiliations
Additional information
The authors acknowledge valuable discussions with Prof. W. Nörenberg and Dr. H.L. Yadav. One of us (U.B.) is grateful to the MINERVA foundation for a stay in the Weizmann Institute where part of this work was done.
Rights and permissions
About this article
Cite this article
Brosa, U., Cassing, W. Numerical studies on the phase-space evolution of relative motion of two heavy ions. Z Physik A 307, 167–174 (1982). https://doi.org/10.1007/BF01414832
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01414832