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S Israel Atomic Energy Commission IA-1421 Israel Atomic Energy Commission AVAILABILITY Israel Atomic Energy Commission reports and bibliographies may be obtained from Technical Information Department Israel Atomic Energy Commission P.O.Box 7061, 61 070 Tel-Aviv, ISRAEL CONTENTS 1 MATHEMATICS, THEORETICAL PHYSICS AND THEORETICAL CHEMISTRY 1 II NUCLEAR ENGINEERING AND SAFETY 17 III PLASMA PHYSICS AND PLASMA CHEMISTRY 39 IV LASERS AND ATMOSPHERIC OPTICS 47 V SOLID STATE PHYSICS AND CHEMISTRY 61 VI MATERIALS SCIENCE 75 VII NUCLEAR PHYSICS 109 VIII GENERAL, PHYSICAL AND RADIATION CHEMISTRY 115 IX RADIOISOTOPES. LABELED COMPOUNDS AND BIOSCIENCES 141 X NUCLEAR SAFETY, RADIATION PROTECTION AND ENVIRONMENTAL STUDIES 171 XI INSTRUMENTATION AND TECHNIQUES 187 XII DOCUMENTATION 209 XIII AUTHOR INDEX 251 The studies connected with nuclear power plants are performed in cooperation and coordination with the Ministry of Energy and Infrastructure which has ministerial responsibility in this field. FOREWORD The Annual Report of the Israel Atomic Energy Commission presents, as in past years, a resume of the scientific research carried out by the staff of its nuclear research centers. The main thrust continues to be two­ fold: a long range, sustained effort in basic R&D and dynamic growth in the application of nuclear science and technology to securing benefits in various spheres of economic activity. Some examples of these activities include: - Development of a water permeable plastic membrane produced by a radiation*-1 induced grafting process to replace human or animal skin grafts used in the treatment of severe burns. - Development of new types of radiopharmaceuticals based on short-lived isotopes (e.g. an Os/Ir generator). * Development of contrast agents for medical nuclear magnetic resonance imaging. n Development of radiation sterilization of culture media for bacteriological testing in medicine and in the food industry. « Development of procedures for the radiation treatment of fruits, vegetables and spices. - Development of ion implantation techniques for surface modification of metals. - Comprehensive characterization of optical components, i.e. windows, lenses, mirrors, wedges, prisms, laser rods and curvature of focal length. In the field of mineral prospecting and recovery, a search for uranium resources throughout Israel was carried out. Novel processes for recovery of uranium from phosphates, as a by-product of the production of phosphoric acid, were developed. These processes can provide uranium at a price which is competitive with the present price of uranium on the international market. The knowledge and expertise gained in these endeavors strengthens the Israeli scientific and industrial infrastructure. Within this context, it is believed that the interaction between the research centers and industry will be mutually beneficial. To this end, suitable industrial parks are now being set up. In the field of nuclear power plants, the scope of activities related to Light Water Reactors for power generation has been narrowed. Israel is considering what may be termed a shift towards more emphasis on R & D and conceptual design of the coming generation of nuclear power reactors. Tel Aviv David Peleg (j June 1986 Acting Director General IAEC // V HIGH DENSITY PROPERTIES OF INTEGRAL EQUATION THEORIES OF FLUIDS: UNIVERSAL ANALYTIC STRUCTURE AND DETAILS FOR THE ONE-COMPONENT PLASMA [1 f2] Y. Rosenfeld We studied the analytic properties of the hypernetted chain (HNC) and soft-mean-spherical (SMSA) theories in the asymptotic high density limit (AHDL). The scaling properties of the inverse power potentials lead to the introduction of the SMSA-Ewald functions, which correspond to the "overlap-volume" functions for hard spheres. The HNC and SMSA theories for soft interactions, as well as the Percus-Yevick theory for hard spheres (FYHS), feature the same AHDL analytic structure of the pair correlation functions, which is dictated by the hard-sphere Ewald functions. Detailed results for the one-component plasma were also obtained. Implications for the analysis of the density functional theory, of dense matter, near its exact Thomas-Fermi limit were pointed out. REFERENCES: [1] Rosenfeld, Y., Phys. Rev. A 32, 183^ (1985). [2] Rosenfeld, Y., Phys. Rev. A 33, 2025 (1986). STATISTICAL THERMODYNAMICS OF CHARGED OBJECTS: GENERAL METHOD AND APPLICATIONS TO SIMPLE SYSTEMS* Y. Rosenfeld and L. Blum Real fluids are composed of molecules that are objects of complex geometries and charge distributions. In a previous note [1] we have shown that by studying the asymptotic high density limit (AHDL) and the asymptotic strong coupling limit (ASCL) one is able to reduce the problem of computing the thermodynamics and correlation functions of the system to a geometrical calculation involving overlap integrals between the objects. In previous work [2,3] a simple geometrical, physically intuitive meaning of the direct correlation functions (dcf) for point charges in a background (2,43 (as interactions between smeared charges) and hard spheres (as overlap volumes) within the mean spherical approximation (MSA) was given, thus also revealing the analytic structure of the solution to the model equations. As a result, the above calculation can be carried out completely for relatively simple systems (as e.g. the general ionic mixture of the multicomponent plasmas [4,5] using the MSA free energy functional which interpolates between the exact weak- (Debye-Huckel) and strong- ("Onsager-type") coupling bounds for the potential energy. Though featuring fewer "idealistic" features, in view of the higher complexity of the problem, this approach was successfully used to analyze the "isotropic"-"nematic" transition of line-charges [3,6] and the coupling of +This work was supported in part by PRF 15473 and the Office of Naval Research University of Puerto Rico, Rio Piedras, Puerto Rico, U.S.A. 3 the growth of micelles to their degree of alignment [6], In the present work we extended these methods to a much larger class of objects. The proposed approach is to write down an approximate free energy functional which has to be variational with respect to the pair functions. These would be either the indirect (hi-id"!?)) or direct (cii(ri?^ correlation functions. In order to get a convenient formalism, we have to use simple functions with physically motivated coefficients. Indeed, the direct correlation function in the asymptotic limits (AL = either AHDL, ASCL) provides such a simple instructive basis. The approximate solutions also provide exact bounds for the free energy of system. In the present work we considered a few simple systems. REFERENCES: [1] Rosenfeld, Y. and Blum, L., J. Phys. Chem. 819_, 5119 (1985). [2] Rosenfeld, Y., Phys. Rev. A 32, 1834 (1985). [3] Rosenfeld, Y. and Gelbart, W. M., J. Chem. Phys. 8l_, 4574 (1981). [4] Rosenfeld, Y., Phys. Rev. A 25, 1206 (1982). [5] Rosenfeld, Y., Phys. Rev. A 26, 3622 (1982). [6] McMullen, W. E., Rosenfeld, Y. and Gelbart, W. M., J. Chem. Phys., in press. IMPROVED REGULA FALSI METHOD FOR SOLVING THE SCHRODINGER EQUATION WITH A PIECEWISE CONSTANT POTENTIAL M. Friedman and A. Rabinovitch The solution of the 1-D Schrodinger equation is of major importance in quantum mechanics [1]. Many 3~D systems can be reduced to 1-D by standard techniques, such as the separation of variables. Moreover, quasi 1-D systems have recently attracted considerable attention [2]; localization problems and tunnelling are treated mainly in 1-D disordered lattices [3]. Since the number of cases for which analytic solutions are available is rather small, a general numerical scheme could be very helpful. A simple approach is to replace the potential V(x) of the Schrodinger equation by a piecewise constant function for which the solution is obtained by merging together the known solutions of each interval. In addition to being an approximation to the general case, it can simply yield the main qualitative features of any problem. In particular, if the actual potential is unknown but for its general form, the use of a stepped potential [4] brings out the relevant properties of the problem and permits understanding its physical nature. A numerical procedure designed to get the eigenvalues of the piecewise constant Schrodinger equation was outlined. Since it calls for the computation of the zeroes of a complicated function, special attention was given to reducing computing costs. A new improved regula falsi method was used. Only one calculation of the function per step is needed, but a Ben-Gurion University of the Negev, Beer-Sheva H quadratic convergence for the second and third iterations is still guaranteed. REFERENCES: [1] see e.g., Mattis, E. H. and Mattis, D. C., Mathematical Physics in One Dimension, Academic Press, New York, 1966. [2] Bernasconi, J. and Schneider, T., editors, Physics in one Dimension, Springer-Verlag, Berlin, 1981, p. 227 ff. [3] Erdos, P. E. and Hendon, R. C, Adv. Phys. 3X, 65 (1982). [H] see e.g., Rosenfeld, Y. and Thieberger, R., J. Chem. Phys. 6j3, 1875 (1975). ON THE CONVERGENCE OF THE TROTTER FORMULA [1] R. Thieberger In recent years there has been much interest in solving quantum statistical mechanics problems by a Monte-Carlo procedure [2], The approach is based on the path integral formulation due to Feynman. Intimately connected to this approach is the Trotter product formula [3]. Little is known about the nature of this formula. In this work the convergence of the Trotter formula for the one-dimensional harmonic oscillator was studied. Pade approximants improve the convergence. REFERENCES: [1] Thieberger, R., J. Phys. A, in press. [2] See e.g. De Raedt, H., Lagendijk, A. and Fives, J., Z. Phys. B £6, 261 (1982). [3D Suzuki, M. , Commun. Math. Phys. 51_, 183 (1976). THREE-DIMENSIONAL EFFECTIVE PHASESHIFTS IN THE PRESENCE OF ELECTRIC FIELDS [1] K. Thieberger, M. Friedman and A. Rabinovitch* A previously developed scattering theory method for one- dimensional problems [2] was generalized to treat three dimensional problems. The method permits calculating effective phase shifts in the presence of an electric field.

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