0 / SPK / specialcollections@tulane.edu

In the standard model the rare kaon decay 𝙆_𝐿 → 𝜇⁺𝜇⁻ is a highly suppressed, ``strangeness changing neutral current process'' that requires the exchange of two weak bosons with an accurately measured branching fraction 𝐵(𝙆_𝐿 → 𝜇⁺𝜇⁻) = (6.84 ∓ 0.11 ) ✕ 10⁻⁹ [1]. For this measurement to become an important short-distance test of the standard model, the competing 𝑂(𝛼²_𝙴𝙼𝐺_𝙵) two-photon contribution must be computed and removed from the total decay amplitude. While the imaginary part of this contribution can be obtained from the 𝙆_𝐿 → 𝜇⁺𝜇⁻ decay rate and the optical theorem, the real part must be computed in QCD [2]. Depending on a relative sign, a 10% calculation of the real part of the 𝑂(𝛼²_𝙴𝙼𝐺_𝙵) two-photon contribution would lead to a 6% or 17% test of the standard model. As a first step in developing a strategy for computing the two-photon contribution to the 𝙆_𝐿 → 𝜇⁺𝜇⁻ decay, we examine a simpler process 𝜋⁰ → 𝓮⁺𝓮⁻. Here no weak interaction vertex is involved and, more importantly, there is no intermediate hadronic state with a mass smaller than that of the initial pion. The sole complication arises from the presence of the two-photon intermediate state, only one of the difficulties offered by the 𝙆_𝐿 → 𝜇⁺𝜇⁻ decay. We show that the 𝜋⁰ → 𝓮⁺𝓮⁻ amplitude can be calculated with an analytic continuation method where the entire decay amplitude including the imaginary part is preserved. The real part involves non-perturbative QCD contribution and is of substantial interest, while the imaginary part of calculated amplitude can be compared with the prediction of optical theorem to demonstrate the effectiveness of this method. We obtain Re𝓐 = 18.60(1.19)(1.04) eV, Im𝓐 = 32.59(1.50)(1.65) e𝐕 and a more precise value for their ratio Re𝓐/Im𝓐 = 0.571(10)(4) from continuum extrapolation of two lattice ensembles, where 𝓐 is the decay amplitude, the error in the first parenthesis is statistical and the error in the second parenthesis is systematic. Next, we develop a computational strategy to determine the 𝙆_𝐿 → 𝛾 𝛾 decay amplitude. It involves the same hadronic matrix element as the 𝙆_𝐿 → 𝜇⁺𝜇⁻ decay as well as all the intermediate states whose energies are lower than or close to the initial kaon sate except for the |𝜋𝜋𝜇〉that is difficult to deal with. While the lattice QCD calculation is carried out in finite volume, the emitted photons are treated in infinite volume and the resulting finite-volume errors decrease exponentially in the linear size of the lattice volume. Only the 𝑪𝑷-conserving contribution to the decay is computed and we must subtract unphysical contamination resulting from single pion and eta intermediate states which grow exponentially (or fall slowly) as the time separation between the initial and final lattice operators is increased. Results from a calculation without disconnected diagrams on a 24³ ✕ 64 lattice volume with 1/𝛼 =1 Ge𝐕 and physical quark masses are presented.

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<p> The energy levels of Sm151 populated in the beta decay of Pm151 have been studied with the aid of magnetic spectrometers. The internal and external conversion spectra were examined with a π√2 spectrometer of 50 cm radius. A Gerholm-type double lens coincidence spectrometer was used to perform electron-beta, electron-electron, electron-gamma and gamma-beta coincidence experiments. In addition, precise measurements of the transition energies obtained by Geiger and Graham (1962) with the Chalk River π√2 iron-free spectrometer are included. A decay scheme based on these results is proposed and speculations are made concerning the possible interpretation of the levels on the basis of the Nilsson model. The results are also compared with other recently published data on this decay.</p> / Thesis / Doctor of Philosophy (PhD)

<p> The performance of a relative decay rate measurement technique was investigated. Determinations of the half-lives of the isotopes copper-64 and ruthenium-97 in various chemical states were attempted as illustrations of the use of the method. Applications of the technique are suggested.</p> / Thesis / Master of Science (MSc)

<p> The optimal temperature policy with time is sought which maximizes the total amount of reaction in a fixed time in a tubular reactor with uniform temperature and decaying catalyst for a single reversible reaction.</p> <p> A numerical procedure together with theoretical developments is used to solve this problem for two kinetic models. The problem is treated in the format of Pontryagin's Maximum Principle.</p> <p> Computer listings are given in the Appendix for the following cases A) Optimal policy for irreversible reactions 8) Optimal policy for isothermal irreversible reactions C) Optimal policy for reversible reactions.</p> / Thesis / Master of Engineering (MEngr)

<p> The alpha-activity of natural samarium has been studied using an ionization chamber. A gridless ionization chamber has been developed in order to obtain high resolution and high sensitivity. The half lives and the energies of the alpha decay of Sm147 and Sm148 were measured where as the alpha-activity of Sm149 and Sm146 could not be detected.</p> <p> Experiments were carried out in order to search for the existence of Particle stable neutron clusters in the range of Mass 6-10 as a component of a nuclear reactor flux and as the product of high energy proton spallation of heavy nuclei.</p> / Thesis / Doctor of Philosophy (PhD)

<p> The temperature policy with time is sought which maximizes a performance index for a fixed time in a tubular reactor with uniform temperature, decaying catalyst, and two first-order irreversible parallel reactions. </p> <p> For the case where the performance index is the total amount of desired product produced, an analogy between the optimization problems for a first-order reversible reaction and a parallel reaction first-order in both. paths is developed. </p> <p> A numerical procedure together with theoretical developments is used to solve the problem for a more general performance index which takes into account the cost of the reactant as well as the value of the desired product. The problem is· treated in the format of Pontryagin's Maximum Principle. </p> / Thesis / Master of Engineering (MEngr)

<p> The decay of 3.5 minute 89Kr to levels in 89Rb has been investigated with small and large volume Ge(Li) detectors used singly and in coincidence. A total of 160 gamma rays have been attributed to the nuclear process, 120 of which have been incorporated into a proposed decay scheme.</p> / Thesis / Master of Science (MSc)