Israel Atomic Energy Commission IA-1364 MBSEAKCH

Israel Atomic Energy Commission IA-1364 MBSEAKCH \A 1 MATHEMATICS, THEORETICAL PHYSICS AND THEORETICAL CHEMISTRY 1 II REACTOR PHYSICS AND REACTOR SAFETY . 29 III PLASMA PHYSICS AND PLASMA CHEMISTRY 55 IV LASERS AND SPECTROSCOPY 73 V SOLID STATE PHYSICS 85 VI MATERIALS SCIENCE 105 VII NUCLEAR PHYSICS 135 vm CHEMISTRY 151 IX RADIATION CHEMISTRY 179 X RADIOISOTOPES, LABELLED COMPOUNDS AND BIOMEDICAL STUDIES 199 XI HEALTH PHYSICS AND ENVIRONMENTAL STUDIES 219 XII INSTRUMENTATION AND TECHNIQUES 235 XIII DOCUMENTATION 249 iY.\V AUTHOR INDEX 285 Israel Atomic Energy Commission * <AII.AIII.ITT Israel Atomic Energy Commission reports and bibliographies may be obtained on application to: TECHNICAL INFORMATION DEPARTMENT ISRAEL ATOMIC ENER6V COMMISSION P. O. 6. 17 12 0 TEL-AVIV, ISRAEL The studies connected with nuclear power plants are performed in cooperation and coordination with the Ministry of Energy and Infra structure which has ministerial responsibility in this field. MATHEMATICS, THEORETICAL PHYSICS AND THEORETICAL CHEMISTRY - 3 - ON REALIZATIONS OF GRADED LIE ALGEBRAS AND ON PROPERTIES OF d-POLYNOMIALSv ' Y. Ilamed (2—6) In previous papers we tried to understand intrinsic pro perties of polynomials that generalize the commutator and the anti- commutator in free associative algebras. In this work d-polynomials were defined that are noncommutative with noncommutative coefficients inserted between the variables. Realizations of graded Lie algebras were obtained using d-polynomials that are a natural extension of the usual symmetric and alternating polynomials. It was shown that d-poly nomials have a universal derivative property and that some d-polynomials may be used as an extension of the brackets of Nambu. As a result the following sets can be considered in a unified way as canonical sets of variables: i) n Heisenberg-Dirac canonical pairs, ii) the identity and n Heisenberg-Dirac canonical pairs, iii) the spin matrices of Pauli and iv) the octet matrices of Gell-Mann. REFERENCES: 1. Ilamed, Y., in Proceedings of the International Colloquium on Grouo Theoretical Methods in Physics, Cocoyoc, Mexico, 1980 2. Ilamed, Y., in Proceedings of the Fifth International Colloquium on Group Theoretical Methods in Physics, Montreal, 1976, Academic Press, New York, 1977, p. 623 3. Ilamed, Y., in Proceedings of the Sixth International Colloquium on Group Theoretical Methods in Physics, Tubingen 1977, Lecture Notes in Physics #79, Springer, Berlin, 1978, p. 494. 4. Ilamed, Y., in Proceedings of the Seventh International Colloquium on Group Theoretical Methods in Physics, Austin, 1978, Lecture Notes in Physics #94, Springer, Berlin, 1979, p. 446 5. Ilamed, Y., in Proceedings of the Eighth International Colloquium on Group Theoretical Methods in Physics, Kiryat Anavim, 1979, Israel Phys. Soc. Annals, #3, IPS, Jerusalem, 1980, p. 323 6. Ilamed, Y., Hadronic J. 3_, 327 (1979) REAL SPACE RENORMALIZATION GROUP AND CRITICAL DYNAMICS^1' Y. Achiam General aspects of the real space renormalization group (RG) approach to critical dynamics were considered. The RG transformation was applied directly to the master equation describing the time evolu tion of the probability distribution. The perturbation from equilib rium was taken in the linear response approximation, and only leading spin operators were included. We examined a wide family of models - '4 - based on generalization of the Glauber model. These models describe systems in one or two dimensions, having order parameters and energy which can be chosen to be conserved or not. The RG transformation was performed using several approximations. We found that these trans formations create memory effects and new dynamic modes which have not been included in previous models. We used two different sets of eigen-spin-operators, one to describe the static RG transformation and one to describe the transformation of the dynamic modes. Using these sets of eigenoperators we demonstrated the dynamic behavior of the models. REFERENCE: 1. Achiam, Y., in A. Jaffe, Statistical Mechanics and Quantum Fields; papers presented at the International Conference on Thermodynamics and Statistical Mechanics (STATPHYS-14), Edmonton,Canada,1980,in press. CRITICAL DYNAMICS OF THE ONE-DIMENSIONAL GENERALIZED KINETIC ISING MODEL^1' Y. Achiam A time-dependent real-space renormalization group was used to show that all the one-dimensional kinetic Ising models with transition rate that depends on nearest neighbors only belong to the same univer sality class of the critical dynamics. REFERENCE: 1. Achiam, Y., J. Phys. A 13, L93 (1980) CRITICAL DYNAMICS AND THE POTENTIAL MOVING APPROXIMATION^ Y. Achiam The real-space time-dependent renormalization group approach 'as applied to the study o'2 a square lattice. A decimation and a spin-block transformation were performed according to the potential moving trick suggested by Kadanoff. A value z « 2.2 was found for the dynamic index characterizing the two-dimensional lattice. REFERENCE: 1. Achiara, Y., J. Phys. A 13, 1355 (1980). - 5 - DIFFUSION IN THE ONE-DIMENSIONAL ISING MODEL*1' Y. Achiam The critical dynamics of the one-dimensional Ising system with conserved magnetization was studied by the real-space renormalization group approach. The relaxation of odd and even spin-operator pertur bations was calculated. The; critical exponent obtained by an exact transformation is z = 3 in agreement with the conventional theory. REFERENCE: 1. Achiam, Y., J. Phys. A 13, 1825 (1980). CRITICAL DIFFUSION IN A 2-D ISING MODEL*15 Y. Achiam A model for the critical relaxation in an Ising-like soin system with conserved magnetization was developed. This model generalizes (2) that of Kawasaki by allowing any two spins in the system to exchange values. The model was analyzed in two dimensions using the time de- (3) pendent real space renormalization group . In order to perform the calculation we used the potential moving approximation suggested by Kadanoff. We examined the relaxation of the even perturbations (energy like) , and showed that there are non-Markoffian corrections which have to be taken into account. We calculated the critical exponent z which characterize? the diffusion near the critical point and found the value z = 3.746. Using a near four dimension exoansion, (4) Halperin et al. showed that an exact value of z = 4-n, where n is the critical exponent of the correlation function, is expected. This result has been verified using similar exact time dependent renormalization group transformations in one dimension. The value we found in the present work is in excellent agreement with the expected value z = 3.75. REFERENCES: 1. Achiam, Y., Bull. Israel Phys. Soc, vol. 26, 1980, p. 38 2. Kawasaki, K., Phys. Rev. 145. 224 (1966) 3. Achiam, Y. and Kosterlitz, M. J., Phys. Rev. Lett. 41, 128 (1978) 4. Halperin, B. I., Hohenberg, P. C. and Ma, S. K., Phys. Rev. B 10_, 139 (1974). - 6 - UNIVERSALITY OF THE BRIDGE FUNCTIONS AND A SEMI-EMPIRICAL FREEZING CRITERION IN 2 AND 3 DIMENSIONS Y. Rosenfeld The. idea of universality of the bridge functions , B(v), has brought the theory of classical fluids (on the "pair" level) to within the accuracy of present day computer simulation studies for nearly every physically conceivable effective pair potential. Analysis of (2) the dense plasma statics and thermodynamics based on scaled direct correlation functions demonstrated that universality extends all the way to the origin (v=0), and proved very important for calculating enhancement rates of nuclear reactions. This analysis was extended to mixtures of "charged" particles interacting via relatively soft inverse power potentials. It thus became possible to express B(0), which is a structural quantity, directly in terms of the equation of state, and to find its physical meaning. In particular (and as a generalization of the Lindemann-Ross criterion) it was found that within the accuracy of the simulation studies, B(v=0) calculated along the freezing line is independent of potential" and is the same in 2 and 3 dimensions. REFERENCES: 1. Rosenfeld, Y., and Ashcroft, N. W., Phys. Lett. 73A, 31 (1979); Phys. Rev. A20, 1208 (1979) 2. Rosenfeld, Y., Phys. Rev. Lett. Vi_, 146 (1980) ALTERNATIVE DERIVATION OF THE FREE ENERGY IN THE MEAN-SPHERICAL APPROXIMATION Y. Rosenfeld The mean-spherical approximation (MSA) is emerging as a most important theoretical tool for studying plasmas. It is analytically solvable and yields results nearly identical to those of the hyper- netted-chain (HNC) approximation. As such it also provides an excellent starting point for the iterative solution of improved models. A detailed analysis , that views the hard-core portion of a potential as a perturbation on the whole, lends support to the "soft"-MSA (SMSA) (2) proposed by Gillan who imposed continuity of the pair function on the usual MSA. The condition of continuity was found to be rigorously equivalent to the maximization with respect to the effective hard-core - 7 - diameter of the free energy or potential energy functionals of the usual MSA. The thermodynamic functions in the SMSA were derived hv a new approach (3) that clarifies the special role olayed by potentials • (•J) that possess Fourier transforms. REFERENCES: 1. Rosenfeld, Y. and Ashcroft, N. W., Phys. Rev. A20, R162 (1979). 2. Gillan, M. J., J. Phys. <C7_, LI (1974). More recent applications are given by De Angelo et al., J. Phys. C13, 3649 (1980) and De Angelo, Phys. Lett. 78A, 75 (1980) 3. Rosanfeld, Y., J. Chem. Phys., in press UNIVERSAL STRONG COUPLING EQUATIONS OF

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