Nuclear cascade calculations of the Goldberger type have been performed using the MANIAC electronic computer. A three-dimensional relativistic treatment was used. The target nuclei were Al 27 , Cu 64 , Ru 100 , Ce 140 , Bi 209 , and U 238 . Incident protons and neutrons with energies between 82 and 365 Mev have been studied, but meson production was neglected in this energy range. Cascades initiated by about 1000 incident particles were followed in each case.The results have been compared with those of previous calculations of this type, as well as with experimental photographic-plate data and counter measurements reflecting the cascade stage of high-energy nuclear reactions. The agreement with experimental data is usually good.Tables and graphs are presented showing the frequency of occurrence of various residual nuclei, and data on the residual nuclear excitation energy after the cascade is over. A few comparisons with radiochemical data indicate over-all agreement with the general spallation pattern of copper with 340-Mev protons and good agreement with the Ni 64 (^>,w)Cu 64 reaction over the energy range 100-400 Mev. However, the calculated results for the Cu 66 (p,pn) Cu 64 reaction are low by almost a factor of two, although the energy dependence is approximately correct.

The nuclear cascade calculations described in the preceding paper have been extended to incident energies up to 1.8 Bev with the inclusion of pion production, scattering, and absorption processes. Again the MANIAC electronic computer was used. Several incident proton energies between 450 Mev and 1.8 Bev have been investigated, with Al 27 , Cu 64 , Ru 100 , Ce 140 , Bi 209 , and U 238 as target nuclei. Cascades initiated by pions of several energies up to 1500 Mev incident on Ru 100 have also been studied. The elementary cross sections used and the assumptions made about details of the inelastic nucleon-nucleon and pion-nucleon processes are presented. The results of the calculation are summarized in tables and graphs giving data on transparencies, on numbers, energy spectra, and angular distributions of emitted cascade nucleons and pions, and on frequencies of occurrence and excitation energies of residual nuclei. The computed number distributions, energy spectra, and angular distributions of emitted particles are compared with the results of several emulsion experiments with incident protons and negative pions. The agreement is generally satisfactory, but certain discrepancies are found, for example regarding spectra and angular distributions of emitted pions; some of these discrepancies are discussed in terms of details of the model used. The calculation predicts quite well the over-all yield distribution of spallation products of copper produced by 2-Bev protons; however, as at lower energies, the calculated cross sections for (p,pn) reactions are too low by factors of two or three. NUCLEAR MODEL AND INPUT INFORMATIONT HE nuclear cascade calculations described in the preceding paper 1 have been extended to the interval 0.4-1.8 Bev in incident nucleon energy. Pion production (single or double), pion scattering and charge exchange, and pion absorption have been included with varying degrees of completeness and accuracy. The angular distributions in nucleon-nucleon scattering, pion-nucleon scattering and charge exchange have also been taken into account. Cascades induced by incident pions have also been investigated. This appears to be the first extensive attempt to carry such calculations into the energy region in which pion effects are important. However, after the completion of the present computation, NikoPskii et al. 2 have published some results of a Monte Carlo cascade calculation involving 162-Mev ir~ mesons incident on emulsion nuclei.As in I, the calculations were performed relativistically in three-dimensional geometry by means of the MANIAC electronic computer at Los Alamos. The nuclear characteristics chosen for the target nuclei were the same as in I, with the radius parameter ro always taken as 1.3X10 -13 cm. Neutrons, protons, and the three types of pions were distinguished throughout. The mass of all the pions was taken as one-seventh of the nucleon mass. No nuclear or electrostatic potential was included for the pions, and Coulomb scattering was neglected for all particles.The behavior of each ...

The process of nuclear de-excitation by evaporation has been calculated by using a Monte Carlo method and fast electronic computers. The competition between the emission of neutrons, protons, deuterons, tritons, He', and He' has been studied as a function of various parameters and experimental conditions. A systematic survey is presented for a range of atomic numbers, mass numbers and excitation energy of initial nuclei. The nuclides studied extend from A =49 to A =239 with Z=Zg&3. The range of excitation energies for which computations are presented extends from 100 -700 Mev. Among the parameters aA'ecting the process the importance of the temperature correction of the Coulomb barrier and the level density parameters are considered in detail. The average properties of the process such as average numbers of the various particles emitted, the average number of nucleons, of charged particles, and of charges emitted are summarized in graphical and tabular form for various combinations of the parameters used in the computation. Energy spectra of the various emitted particles are also shown.The nuclei and parameters studied in this paper were chosen to illustrate the eGect of changing atomic number, mass number, excitation energy, level density parameter, and Coulomb barrier on the evaporation 4

The 3-J and 6-J Symbols The MIT Press 3j-6j-and 9j-symbols. The Clebsch-Gordan coefficients obey certain symmetry relations, like. ?j1j2 m1m2j1j2 jm?. = (?1)j1+j2?j?j2j1 m2m1j2j1 jm?. Catalog Record: The 3-j and 6-j symbols Hathi Trust Digital Library Abstract. We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that U111 Wigner 3-j, 6-j, 9-j Symbols Clebsch-Gordan, Racah W .-CMD Figure 34.2.1: Angular momenta j_r and projective quantum numbers m_ Figure 34.4.1: Tetrahedron corresponding to 6j symbol. Notation. 34.1 Special Images for The 3-J and 6-J Symbols 31 May 2002. Summary. This chapter contains sections titled: Introduction. Clebsch-Gordan coefficients. Wigner 3?j symbols. Wigner 6?j symbols. Reference. Semiclassical Mechanics of the Wigner 6j-Symbol For further information on these symbols, check out their respective Wikipedia pages: 3-j, 6-j and 9-j. For a calculator that can give exact values (not floating point DLMF: 34 3j, 6j, 9j Symbols 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in the coupling of three. Simplified recursive algorithm for Wigner 3j and 6j symbols. The 3-J and 6-J Symbols.

Equilibrium dissociation pressures for monovariant three-phase (icesolid clathrate-gas) systems were predicted for water clathrates with Ar, Kr, Xe, N2, 02, COz, and CH4 as the guest molecules. A Monte Carlo approach of statistically sampling the states available to the guest molecule inside the host water cage was used to evaluate the configurational properties including the free volume integral. The Lennard-Jones 6-12 potential adequately described the guest-host interaction for monatomic species, for example, Ar, Kr, and Xe, while the nonspherically symmetric Kihara potential with a fixed hard-core geometry was required for polyatomic guests. The simulated motion of the guest within the cell was consistent with the geometrical features of the host lattice. SCOPEWater clathrates are composed of an open network of host water molecules arranged to create several large void spaces or cages capable of entrapping guest molecules such as argon, methane, or carbon dioxide. Although there are no chemical bonds between the water hosts and the guests, the clathrate structure is stabilized by relatively weak van der Waals interactions. Clathrates are regarded as nonstoichiometric compounds since all available cages in a given unit cell need not be occupied by a guest.Since the size and chemical nature of the guest are critical in determining the feasibility of clathrate formation, their selectivity is usually very high. In recent years, water clathrates have been utilized in desalination processes involving propane and other hydrates (Barduhn et al., 1962). Knowledge of their behavior became important in preventing the stoppage of natural gas pipelines (Schaefer and Dorsey, 1962) as well as in the inhibition of clathrate formation in a direct contact butane freezing process for desalting (Wiegandt, 1967). Clathrate or inclusion compounds are used in a variety of other specialized separation processes, including the para-meta xylene separation, the recovery of vitamin A (Schaefer and Dorsey, 1962), and the separation and storage of gases (Miller and Strong, 1945). In addition to these practical applications, clathrates have been used to isolate molecules for fundamental studies of molecular motion and chemical kinetics (Davidson, 1971).In most cases of interest, the thermodynamic properties of the clathrate mmt be fully characterized. Several theoretical models have been proposed to predict these prop-J. W. Tester is a