Thesis (Ph. D.)--University of Wisconsin, 1964. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The two theories of low energy nuclear reactions which are mainly used for the interpretation of experimental data are compared. The two theories of interest are the R-Matrix theory of Wigner and Eisenbud and the S-Matrix theory of Humblet and Rosenfeld. The two approaches to resonance reactions are quite different and the differences are discussed with reference to a variety of specific examples. A simple soluble model - the threshold resonances of scattering by a square potential well - is analysed in detail using the two approaches. The approximate formulae are then compared numerically with the exact solution. It proves necessary to modify the usual S-Matrix approach and to use expansions other than the Mittag-Leffler which was used in the development of the general theory. We discuss two alternate expansions. With the modification to the S-Matrix theory both approaches give very accurate approximate formulae. The theories give different interpretations of the position and width of the threshold level. If the level is unbound the R-Matrix interpretation is fully satisfactory. The S-Matrix interpretation is unsatisfactory because the level has the characteristics of a bound state but none exists. If the threshold level is bound the position is reversed. S-Matrix theory correctly locates the bound state but R-Matrix theory does not. For threshold resonances one R-Matrix level is involved but two S-Matrix poles (except for the 1-S state) give rise to the resonance cross section. The physical interpretations are consolidated by describing the cross section for n-p, n-l60 and n-208Pb scatterings. The slow neutron cross section of ¹³⁵Xe is discussed using both formalisms. This is an example of a narrow compound nucleus resonance very close to a channel threshold. The theories fit the data with different parameters and very near threshold they give quite different shapes to the cross section. The origin of this difference is traced to unitarity. S-Matrix theory, in this situation, fails to give the cross section the correct behaviour very near threshold, because its approximation to the collision matrix is not unitary. Two level interference is discussed. Artificial cross sections are constructed to illustrate the very different interpretations that the two approaches may give to an interference cross section. The (p, y) and (p, n) cross sectionsof ¹⁴C are analysed using both R-Matrix and S-Matrix formalisms. ¹⁵N* has two very wide ½+ levels near neutron threshold. Both approaches fit the data to very good accuracy. The level positions and widths are quite different but the partial widths are similar. An analytic method of relating the parameters of the two theories by a transformation is given with the necessary approximations noted. The accuracy of the method is confirmed by application to the ¹⁴C+p cross section parameters. The transformation is used to discuss some theoretical points. Unitarity is discussed and the unitarity of the R-Matrix collision matrix is demonstrated for all approximations. It is possible to satisfy the unitarity requirements explicitly in the S-Matrix theory in only the simplest situations and with poor approximations and the reasons for this are discussed. It is concluded that in most situations both theories are capable of fitting experimental data. The only situation in which there is a measurable (though small) difference is very near threshold. If one requires that unitarity be satisfied for all approximate formulae the S-Matrix theory is poor. Except for isolated resonances far from threshold the R-Matrix and S-Matrix theories give quite different values for the parameters of resonance levels. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis seeks simplifications to the formulation of the radiative three-nucleon reactions (i.e. direct capture, and partial and total photodisintegration) by means of group theory and other methods, similar to the simplifications to the three-nucleon Schroedinger equation made by other workers (e.g. Derrick and Blatt (1958)). Some useful results are derived for the S₃ group, the group of permutations of three things. In addition to the usual projection operators (e.g. Eichmann (1963))> operators are formed analogous to the operators J², J₂, and J± of the SU₂ group, and new methods of defining and generating permutation eigenfunctions, which transform according to the irreducible representations of S₃ are developed. Also, properties of the Derrick-Blatt (1958) addition coefficients which simplify their use are demonstrated, expressions are derived for permutations of product functions, a simplification is given for integration of permuted functions, and a Wigner-Eckart theorem for S₃ is derived, A new body-fixed coordinate system is derived which greatly simplifies the formation and use of Euler-angle functions. Three internal coordinate systems, each advantageous for a different problem, are defined, and their interconversions given. For each of them, necessary trigonometric formulae and expressions for integration are given. The Derrick-Blatt (1958) expansion for three-nucleon wave functions in permutation eigenfunctions is modified to take advantage of the new body-fixed coordinates, and relations between functions in the new and old expansions are derived. Expansions of bound states are discussed, and the continuum states of deuteron plus free nucleon and of three free nucleons are expanded in the new basis functions. Previous, erroneous attempts at similar expansions are discussed. The electric dipole and quadrupole and the magnetic-dipole orbital and spin-flip components of the interaction Hamiltonian representing an emitted or absorbed gamma ray are expressed in permutation-eigenfunction operators, using the long-wavelength and first-order-perturbation approximations, whose validity is discussed. Exact, closed, general forms are derived for matrix elements of the Hamiltonian in Euler-angle and spin-isospin variables, and the internal integrations are considerably simplified. Exact expressions, involving integrals over the three internal variables, are thus derived for matrix elements of the overall Hamiltonian between completely general initial and final states. Expressions are given for the cross section in terms of the matrix elements, and further simplifications are given for some of the reactions involved. A few numerical results are given, which show that the cross section depends sensitively on the wave functions used. The application of this work to the study of nuclear structure and interactions is discussed. Three-quark states are also expressed in the new formalism. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Triple correlation cross sections have been measured for the reaction T(He³,He⁴)np in a complete experiment at a He³ bombarding energy of 1.5 MeV. Three similar experimental geometries were used which allow the observation of low relative energies in the n-p system, and energies of 0.96 MeV in the He⁴-n system. Therefore the n-p singlet and He⁵ (g.s.) final state interactions were observed. Events from the two body reaction channel T(He³,d)He⁴ and overlapping kinematic contours were eliminated by particle identification. A least squares fit to the experimental triple correlation cross section for one geometry was made using two approximate theories for three body reactions. These were the Watson, and Phillips, Griffy and Biedenharn (P.G.B.) final state interaction theories. Both theories give the theoretical cross section to be proportional to a density of states (D.O.S.) function. The P.G.B. theory gives two forms for this function (P.G.B.1 and P.G.B.2). The D.O.S. functions for the state of He⁵ and Li⁵ were calculated using only the P.G.B. 1 and Watson forms. The P.G.B.1 form gives an inadequate description of both the n-p singlet and He⁵(g.s.) final state enhancements. The He⁵(g.s.) enhancement is well described by the Watson form of the D.O.S. function. The triple correlation cross section, for high proton energies, was dominated by a sequential breakup through the ground state of He⁵ and by direct three body breakup. No evidence for contributions from the states of Li⁵ or for any well defined contributions from the first excited state of He⁵ were observed. The Watson and P.G.B.2 forms of the singlet n-p D.O.S. function gave indistinguishable predictions of the n-p singlet enhancement. The P.G.B. 2 form was used, for seven values of the n-p singlet scattering length, to fit the experimental data. The value of the singlet n-p scattering length extracted in the fitting procedure was [formula omitted]. The large experimental errors assigned were caused by the sensitivity of the extracted value on the background terms included in each fit. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The (π, πn) reaction is studied theoretically, the specific case examined being 0¹⁶(π⁺, π⁺p)N¹⁵. Calculations of the differential cross sections for 1P ½ and 1P 3/2 protons are made at various incident pion energies. The remaining kinematic variables are specified by a geometry which emphasizes the behavior of the two-body pion nucleon interaction. The aim is to examine the influence of the nucleus on the two-body interaction. In particular, the influences of Pauli exclusion of the nucleon, the off-shell effect, and the effective polarization of the nucleon are examined. The computation is performed using the factorized distorted wave impulse approximation. By evaluating the distorted wave matrix element in coordinate space the localization of the knock-out reaction in the nucleus is determined. The Pauli exclusion of the nucleon is found to have the largest influence on the differential cross section at incident pion energies of 116 MeV. At higher energies the knock-out reaction occurs at the extreme edge of the nucleus and the effect of Pauli exclusion is minimal. At lower energies, the two-body interaction itself is less sensitive to Pauli exclusion. Off-shell effects were found to be very small. The polarization of the proton was found to have a large influence on the cross sections. Furthermore, it is noted that comparing the cross sections for 1P ½ and 1P3/2 protons will indicate the effective polarization of the proton in the nucleus. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014. / This investigation involves a survey of the fine structure phenomenon of the Isovector Giant Dipole Resonance (IVGDR) over a wide mass range of nuclei, from 27Al, 40Ca, 56Fe, 58Ni to 208Pb, using inelastic proton scattering at 200 MeV. Proton detection is accomplished using the recently commissioned zero-degree facility of the K600 magnetic spectrometer at iThemba LABS. Inelastic proton experiments at zero degrees are very selective to excitations with low angular momentum transfer, and therefore ideal for studies of the IVGDR. This is because such experiments simplify the analysis of the many contributions to the spectra due to the complex nature of the nuclear interaction. The ability to make precise measurements of the properties of the IVGDR demonstrated by this work opens up new challenges to both experimental and theoretical work in nuclear structure. This is a survey of the (p,p′) reaction at zero degrees as a probe to study properties of the GDR and also the low energy E1 strength with high energy-resolution. Such a data base will provide more stringent tests of nuclear theory and the progress is seen in the details obtained. These tests can only be described by microscopic models including complex degrees-of-freedom. This should lead to new insights into the underlying interactions responsible for the nature of the electric dipole strength in nuclei. In the present study, double-differential cross-sections were converted to equivalent photo-absorption cross-sections and their results compared to previously published photo-absorption data. An excellent correspondence in the excitation-energy region of the Giant Dipole Resonance (GDR) was noticed between the two data sets. The fine structure observed can be described using characteristic energy scales, arising mainly from Landau damping (even though the spreading width may also play a role). The extraction of these characteristic energy scales which are a signature for the decay process was achieved through the use of wavelet analysis. Furthermore, thanks to the recent advances in computational power and techniques, microscopic shell model-based calculations lead to new insights into the underlying properties of the nuclear interaction which are responsible for the collective behaviour evidenced by the existence and properties of the IVGDR. In addition to the extraction of characteristic energy scales, this study also provides level densities of J = 1− states. In order to extract nuclear level densities, there is need to eliminate instrumental background and other contributions to the spectra from (p,p′) scattering using the model-independent Discrete Wavelet Transform (DWT) method. Level densities of J = 1− states are determined using the fluctuation analysis technique and comparisons are made with the phenomenological Back Shifted Fermi Gas (BSFG) model predictions, calculations of the Hartree Fock- Bogoluibov (HFB) microscopic model and Hartree Fock-Bardeen-Cooper-Schrieffer (HF-BCS) predictions. Finally, this survey will simultaneously provide bench-marks on the capabilities and limitations of the new zero-degree facility important for planning of the future experimental work.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2016. / This study investigates the e ect of nuclear deformation on both the broad and ne structure of the Isovector Giant Dipole Resonance (IVGDR) in the rareearth region. The IVGDR is strongly excited at and close to zero degrees by virtual-photon Coulomb excitation. As such, the Zero-degree Facility of the K600 magnetic spectrometer of iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) was used with an incident proton beam energy of 200 MeV to measure high energy-resolution (p,p0) scattering on a range of neodymium isotopes from spherical 142 60Nd82 to the permanently deformed 150 60Nd90 and the correspondingly deformed 152 62Sm90 in the region of the IVGDR. It is important to note that for nuclei with 88 N 92, a detailed study of the IVGDR is of speci c interest since it is here that a transition from spherical to permanently deformed nuclei occurs. An extensive data analysis procedure was performed, which included cross section extraction and conversion to equivalent photo-absorption spectra for comparison with existing photo-absorption data and theoretical predictions. For the more deformed 150Nd and 152Sm nuclei, however, the data from this study lack the expected double-peaked structure resulting from the splitting of the IVGDR into K = 0 and K = 1 components, and display a signi cant reduction in the strength of the K = 0 component of the IVGDR in comparison to previously published photo-absorption spectra. This reduced strength near the neutron threshold agrees very well with recent photo-neutron experiments. A ne structure analysis was performed on all of the measured isotopes, that is, 142;144;146;148;150Nd and 152Sm through the use of techniques associated with ii the continuous wavelet transform. Characteristic energy scales for the present high energy-resolution data are extracted using the complex Morlet motherwavelet and compared to those obtained for the theoretically predicted B(E1) strength functions. Finally, conclusions regarding the suitability of the model predictions to the current data are drawn. / GR 2016