Angular Approximations

OTF calculations using the S8 angular approximation result in a value of 1.0037 for keff of the extrapolated critical sphere, if treated as 94.8% Pu and 5.2% "Pu. When the indicated bias of 0.37% between calculation and experiment is applied, calculations yield 5425 g as the critical mass of Pu at 19.74 g/cm . The uncertainty in this value is stated to be %. 

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... 

The simplest case is a transition in a linear molecule. In this case there is no orbital or spin angular momentum. The total angular momentum, represented by tire quantum number J, is entirely rotational angular momentum. The rotational energy levels of each state approximately fit a simple fomuila ... 

Vector representation of momenta and vector coupling approximations 7.1.2.1 Angular momenta and magnetic moments... 

With axial-flow impellers, an angular off-center position may be used. The impeller is mounted approximately 15° from the vertical, as shown in Fig. 18-14. 

To approximate the flow, Stodola s theory assumes that the slip is due to the relative eddy. The relative eddy is eonsidered as a rotation of a eylinder of fluid at the end of the blade passage at an angular veloeity of—lu about its own axis. The Stodola slip faetor is given by... 

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