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Item Asymptotic scattering wave function for three charged particles and astrophysical capture processes(Texas A&M University, 2006-08-16) Pirlepesov, FakhriddinThe asymptotic behavior of the wave functions of three charged particles has been investigated. There are two different types of three-body scattering wave functions. The first type of scattering wave function evolves from the incident three-body wave of three charged particles in the continuum. The second type of scattering wave function evolves from the initial two-body incident wave. In this work the asymptotic three-body incident wave has been derived in the asymptotic regions where two particles are close to each other and far away from the third particle. This wave function satisfies the Schrodinger equation up to terms O(1/3pa), where pa is the distance between the center of mass of two particles and the third particle. The derived asymptotic three-body incident wave transforms smoothly into Redmond??s asymptotic incident wave in the asymptotic region where all three particles are well separated. For the scattering wave function of the second type the asymptotic threebody scattered wave has been derived in all the asymptotic regions. In the asymptotic region where all three particles well separated, the derived asymptotic scattered wave coincides with the Peterkop asymptotic wave. In the asymptotic regions where two particles are close to each other and far away from the third one, this is a new expression which is free of the logarithmically diverging phase factors that appeared in the Peterkop approach. The derived asymptotic scattered wave resolves a long-standing phase-amplitude ambiguity. Based on these results the expressions for the exact prior and post breakup amplitudes have been obtained. The post breakup amplitude for charged particles has not been known and has been derived for the first time directly from the prior form. It turns out that the post form of the breakup amplitude is given by a surface integral in the six dimensional hyperspace, rather than a volume integral, with the transition operator expressed in terms of the interaction potentials. We also show how to derive a generalized distorted-wave-Born approximation amplitude (DWBA) from the exact prior form of the breakup amplitude. It is impossible to derive the DWBA amplitude from the post form. The three-body Coulomb incident wave is used to calculate the reaction rates of 7Be(ep, e)8B and 7Be(pp, p)8B nonradiative triple collisions in stellar environments.Item ??C(n,?) ??C as a Test Case in the Evaluation of a New Method to Determine Spectroscopic Factors Using Asymptotic Normalization Coefficients(2012-02-14) McCleskey, Matthew EdgarWith new radioactive isotope accelerators coming online in the next decade, the problem of extracting reliable nuclear structure information from reactions with unstable nuclei deserves considerable attention. A method has been proposed to determine spectroscopic factors (SFs) using the asymptotic normalization coefficient (ANC) to fix the external contribution of a nonperipheral reaction, reducing the uncertainty in the SF. The ??C[left right arrow]??C+n system was chosen as a test case for this new method. The direct neutron capture rate on ??C is important for a variety of topics of interest in astrophysics, and the ANC for ??C[left right arrow]??C+n was also used to calculate this reaction rate. The objective of the first part of this work was to find the ANC for ??C[left right arrow]??C+n. This was done in two independent experiments. First, the heavy ion neutron transfer reaction ??C(??C,??C)??C was measured at 12 MeV/nucleon. Second, the inverse kinematics reaction d(??C,p)??C was measured using the new Texas Edinburgh Catania Silicon Array (TECSA). The next phase of the experimental program was to measure a reaction with a non-negligible interior contribution, for which ??C(d,p)??C at 60 MeV deuteron energy was used. This reaction turned out to be more peripheral than anticipated, and as a result, the ANC for the ground state was extracted from this measurement as well. The final results for the three measurements are C?2s1/2 = 1.96?0.16 fm?? for the ground state and C?1d5/2 = (4.23?0.38)?10?? fm?? for the first excited state. Because the 60 MeV ??C(d,p)??C reaction turned out to have a very weak dependence on the interior, the SF could not be determined for the ??C+n ground state in ??C using the new method. A lower limit of 1.05 was found for the first excited state. It is possible that other reactions might turn out to be more suitable for this method, however, the difficulty encountered at this relatively high deuteron energy highlights a substantial problem likely to be seen in other applications. Using the ANCs determined in this work, the astrophysical ??C(n,?)??C reaction rate was calculated. The resulting value for the cross section for capture to the ground state at 23 keV was ?gs(23 keV)=5.1?0.4 ?b and to the first excited state was ?exc(23 keV)=0.2?0.02 ?b.