V. 1. Single particle motion -- v. 2. Nuclear deformations. / Originally published as 2 separate volumes. Title from ebook title screen. Includes bibliographical references (v. 2, p. 693-730) and index.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3760. Adviser: Rizwan Uddin. Includes bibliographical references (leaves 194-204) Available on microfilm from Pro Quest Information and Learning.

Two "collision biasing" schemes have been tested in a major production, Monte Carlo neutron and photon transport code MCNP. The intent is to reduce the variance that is inherent in all Monte Carlo calculations and increase the Monte Carlo efficiency in problems where the phase space is not sampled adequately. The first scheme, called collision biasing, already exists in the French code TRIPOLI. This method samples several post-collision coordinates and randomly selects one in proportion to an input importance function. The second scheme, called track biasing, is original and differs from collision biasing in that several particle tracks (trajectories) are sampled from one distance-to-collision calculation to the next distance-to-collision calculation, and one is chosen randomly in proportion to an input importance function. The effect of track biasing was found to be problem dependent. For transport along a long narrow cylinder the Monte Carlo efficiency increased, however for a deep penetration problem it decreased.

A Semi-Analytical Partial n'th Collision Source (SAPNCS) method that is fully compatible with the standard three-dimensional SN has been developed. The method generates a matrix operator that calculates scattering source for particles that have suffered n collisions in a selected number of mesh cells. Adopting this scattering source as distributed source, the standard three-dimensional SN method then calculates the remaining contribution to the flux. The sum of uncollided and collided fluxes yields total flux. Several tests for photon transport calculation in x-y-z geometry have been fully conducted and the illustrative results demonstrating the capability of the method to mitigate and eliminate the observable ray effects are presented.

Recent breakthroughs in effective interaction and effective operator techniques allow us to take a new look at this field that has seen limited progress in the past twenty years. A comparison of the old and new techniques will shed some new light on the use of effective interactions and effective operators in shell model calculations of light nuclei. Three different methods of calculating the effective interaction and effective operators are described and compared. A large model-space no-core shell-model calculation for ⁶Li is used as the basis for comparison. In the no-core calculation all nucleons are active in a model space involving all configurations with energies up to 8ħΩ. The second method is a perturbation expansion for the effective interaction and effective operators, using an inert ⁴He core and two valence particles. In particular, the electric quadrupole and magnetic dipole operators are studied to determine the effective charges to be used in connection with one-body operators in this shell-model space. The third method is a model-space truncation scheme, which maps operators in a large model space into operators in smaller, truncated model spaces. The effect of going to larger excitation spaces will be examined as well as the convergence trends regarding increases in the excitation space. The results from these three approaches are compared in order to gain new insight into the nature of effective interactions and operators in truncated model spaces. We find that by going to energies of 8ħΩ we can accurately reproduce the experimental values for the binding energy, excitation spectrum, electric quadrupole moment and magnetic dipole moment of ⁶Li and that there is a definite model-space dependence for these operators. To obtain results similar to the 8ħΩ ones in a truncated 2ħΩ model space we use effective operators and effective charges. Effective charges of approximately 1.1e for the effective proton charge and 0.3e for the effective neutron charge are obtained in the perturbation-expansion technique, while the model-space truncation calculations yield effective charges of 1.5e for the proton and.36e for the neutron. These values can be compared with empirically obtained values of eᵖ(eff) ≈ 1.5e and eⁿ(eff) ≈ 0.5e.

The angular dependence of the differential scattering cross section is typically represented as a truncated Legendre series expansion. If the scattering cross section is highly anisotropic, these expansions may result in negative regions in the -1 ≤ μ0 ≤ +1 interval, thus representing the cross section by negative values. These negative regions may cause negative components in the discrete ordinates scattering source, which are non-physical and which may adversely affect the iterative convergence of the exponential discontinuous spatial discretization scheme. Two methods are presented which produce a positive representation of the scattering cross section, and are designed to calculate a strictly positive scattering source. The first method constructs a scattering matrix from the exponential representation of the cross section derived from maximum entropy. Accuracy of these matrices is further improved by the application of SMART scattering theory. The second method adjusts the Legendre cross section moments with a constrained least squares algorithm. The adjustment is subject to constraints that the zeroth and first moment remain unchanged and that the resulting expansion is positive on all scattering angle cosines derived from a standard S N quadrature set. Extra moments from the maximum entropy representation of the cross section are also used to decrease the relative error of the modified moments. Numerical transport calculations using these two methods demonstrate consistent results with those using the standard truncated Legendre expansion of the cross section. The exponential discontinuous spatial scheme is shown to iteratively converged when these two methods are used. A comparison of these methods with results from multigroup and continuous energy Monte Carlo calculations are also shown to be consistent.

The no-core shell-model approach has proven to be extremely useful for the theoretical determination of the properties of light (A ≤ 12) nuclei. However, at present this method does not accommodate a three-nucleon interaction into the potential that it employs. The problem is introduced with a largely historical development of both the effective interaction formalism and three-nucleon interactions, placing the motivation in context. This work makes a first attempt to incorporate such a three-nucleon interaction into the no-core shell-model ansatz. To this end, a variant of the two-pion-exchange Tucson-Melbourne three-nucleon interaction has been chosen. A three-body translationally-invariant harmonic-oscillator basis is constructed, and matrix elements of the three-nucleon interaction in this basis are calculated. The majority of this is accomplished through standard angular-momentum algebraic techniques, with the most expensive component being the spatial one, as it requires a transformation of the basis set with computationally intensive transformation brackets. Given the ability to determine the matrix elements for the chosen Tucson-Melbourne force, the practicality of employing these in calculations is demonstrated, with calculations on the three-body nuclei ³H and ³He. These are simple calculations, where the Tucson-Melbourne matrix elements are added to those of the two-body effective potential (a slight inconsistency which future studies will aim to fix). The dependence of binding energies on the harmonic-oscillator parameter, hΩ, and the Tucson-Melbourne cutoff parameter, Λ are examined. The former is found to be small in the range of hΩ considered, while the latter is shown to be consistent with previous works that have explored this dependence using other methods. The convergence of the binding energy with increasing model space size is slow, but this is perhaps attributable to the unrenormalized nature of the three-body matrix elements. The ultimate aim of this research is to find a viable method for constructing a three-body effective interaction from a given "realistic" three nucleon interaction, for use in no-core shell-model calculations. The current work demonstrates that such a scheme is feasible, and should yield results more consistent with experiment. Such a three-body effective interaction should also achieve quicker convergence with model space size than shown here, as the three-nucleon matrix elements will be renormalized to account for the geometry of the model space. Thus, one will have constructed an ab initio method for calculations on light nuclei, that includes a three-nucleon interaction, and converges quickly in the determination of nuclear properties.

Critical calculations of unreflected cylinders filled with fissile solution were performed using the TWODANT code with the 118-isotope, 16-group Hansen-Roach neutron cross-section library. The benchmark experiments used were the France CRAC experiments. In these experiments unreflected 300mm and 800mm cylinders were used to contain the solution. The fissile solution was highly enriched (approximately 93%) uranyl nitrate solution of various concentrations. These concentrations varied from 21.4 g/l to 383 g/l in total uranium. The calculational results were compared to the experimental results and to calculations performed using the Monte-Carlo codes MCNP with a continuous-energy neutrons cross-section library and KENO V.a with a cross-section library based on the 16-group Hansen-Roach neutron cross-section set. The TWODANT and KENO V.a codes underestimated the calculated keff for most cases whereas MCNP in most cases showed a keff estimation much closer to unity. Dimension search performed using TWODANT show that the code is able to follow the trend in the measured critical height with a relatively constant bias of 8.96% of the measured height.

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