Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics

ity a nonlocal potential which could fit neutron elastic scattering data in the energy range from 0.4 to 24 MeV and where the optical-model parameters were energy independent. This is, of course, a remarkable result since we know that the absorption, for instance, is changing quite dramatically by going from 0.4 to 24 MeV incident projectile energy. We believe that these findings of Perey and Buck strongly support our result that there exists a nonlocal potential, which is not explicitly energy-dependent, which describes elastic nucleon scattering in a wide energy range. The theory presented in this paper may serve as a convenient tool in deriving such a potential. Actual calculation of an energy-independent optical-model potential as outlined in this paper is in progress. We are grateful to Professor A. Faessler, Professor A. Weiguny, Professor M. stingl, and Professor G. Vagradov for many helpful discussions. One of us (T. T.S.K.) wishes to thank Professor A. Faessler for his hospitality and assistance during his stay at Julich. We thank Professor G. E. Brown for a critical reading of the manuscript. One of us (T. T.S.K.) is an Alexander von Humboldt Foundation awardee. This work was partially supported by the U. S. Department of Energy under Contract No. EY -76-S-02-3001. (a Permanent address: state University of New York at Stony Brook, Stony Brook, N.Y. 11794. lH. Feshbach, Ann. Rev. Nucl. Sci. 8, 49 (1958). 2J. S. Bell and E. J. Squires, Phys.Rev. Lett. 3, 96 (1959); J. S. Bell, in Lectures on the Many-Eody-Problem, edited by E. R. Caianello (Academic, New York, 1962) . 3H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1968), and 19, 287 (1962). 4N. Austern, Direct Nuclear Reaction Theory (Wiley, New York, 1970). 5F. Villars, in Fundamentals in Nuclear Theory, edited by A. de Shalit and C. Villi (International Atomic Energy Agency, Vienna, 1967). 3D. J. Rowe, Rev. Mod. Phys. 40, 153 (1968). 7M. Oell-Mann and F. Low, Phys. Rev. 84, 150 (1951). 8T. T. S. Kuo, S. Y. Lee, and K. F. Ratcliff, Nucl. Phys. A176, 65 (1971). 9T. TTKuo and E. M. Krenciglowa, Nucl. Phys. A342, 454 (1980). This reference reports a similar equation-of-motion approach for the bound-state problems. lOJ. Shurpin, D. Strottman, T. T. S. Kuo, M. Conze, and P. Manakos, Phys. Lett. 69B, 395 (1977). llJ. P. Jeukenne, A. Lejeune, and C. Mahaux, Phys. Rep. 25C, 83 (1976). 12N. Vinh Mau and A. Bouyssy, Nucl. Phys. A257, 189 (1976). -13E. M. Krenciglowa and T. T. S. Kuo, Nucl. Phys. A235, 171 (1974). 14M. Johnson, Ann. Phys. (N.YJ 97, 400 (1976). 15F. O. Perey and B. Buck, Nucl:-Fhys. 32, 353 (1962).