As energias e larguras de escape das Ressonâncias Gigantes, são calculadas utilizando-se técnicas de projeção visando incluir as ressonâncias de partícula-única nos cálculos de RPA (\"Random Phase Approximation\"). As equações de RPA obtidas são complexas, e as larguras de escape são interpretadas como sendo a parte imaginaria das soluções em energia. Os cálculos são feitos para a RGE1( O16 ) e RGE0 ( Zr90 ). Para o Zr90, os espectros das partículas emitidas pela RGE0, prótons e nêutrons, são calculados através do modelo híbrido. Devido à existência de mais do que um tipo de partícula sendo emitida, as analises são feitas dentro da aproximação de independência entre os canais de partículas no formalismo do modelo híbrido. / The energy and the escape of the Giant Resonances are calculated utilizing the projection to include the single-particle resonances in complex RPA (Random Phase Approximation) calculations. The escape widths are interpreted as the imaginary parts of the energy solution of the RPA equations. The Calculations are performed for the RGE1 ( O16 ) and RGE0 ( Zr90 ). For the Zr90 the spectra of the particles ejected by the RGE0, protons and neutrons, are calculated within the hybrid model. The analysis are made through the channels independence in the hybrid model formalism.

As energias e larguras de escape das Ressonâncias Gigantes, são calculadas utilizando-se técnicas de projeção visando incluir as ressonâncias de partícula-única nos cálculos de RPA (\"Random Phase Approximation\"). As equações de RPA obtidas são complexas, e as larguras de escape são interpretadas como sendo a parte imaginaria das soluções em energia. Os cálculos são feitos para a RGE1( O16 ) e RGE0 ( Zr90 ). Para o Zr90, os espectros das partículas emitidas pela RGE0, prótons e nêutrons, são calculados através do modelo híbrido. Devido à existência de mais do que um tipo de partícula sendo emitida, as analises são feitas dentro da aproximação de independência entre os canais de partículas no formalismo do modelo híbrido. / The energy and the escape of the Giant Resonances are calculated utilizing the projection to include the single-particle resonances in complex RPA (Random Phase Approximation) calculations. The escape widths are interpreted as the imaginary parts of the energy solution of the RPA equations. The Calculations are performed for the RGE1 ( O16 ) and RGE0 ( Zr90 ). For the Zr90 the spectra of the particles ejected by the RGE0, protons and neutrons, are calculated within the hybrid model. The analysis are made through the channels independence in the hybrid model formalism.

<p>&#65279;<p></p><p>Giant multipole resonances are a fundamental property of nuclei and</p><p>arise from the collective motion of the nucleons inside</p><p>the nucleus. Careful studies of these resonances and their properties provides</p><p>insight into the nature of nuclear matter and constraints</p><p>which can be used to test our theories. </p><p></p></p><p><p></p><p>An investigation of the Isovector Giant Quadrupole Resonance (IVGQR)</p><p>in ²⁰⁹Bi has been preformed using the High Intensity &gamma;-ray</p><p>Source (HI&gamma;S) facility. Intense nearly monochromatic</p><p>polarized &gamma;-rays were incident upon a ²⁰⁹Bi target producing</p><p>nuclear Compton scattered &gamma;-rays that were detected using the HI&gamma;S</p><p>NaI(Tl) Detector Array (HINDA). The HINDA array consists of six</p><p>large (10''x10'') NaI(Tl) core crystals, each surrounded by an</p><p>optically segmented 3'' thick NaI(Tl) annulus. The scattered &gamma;-rays</p><p>both parallel and perpendicular to the plane of polarization were</p><p>detected at scattering angles of 55&deg; and 125&deg; with</p><p>respect to the beam axis. This was motivated by the realization that</p><p>the term representing the interference between the electric dipole</p><p>(E1) and electric quadrupole (E2) amplitudes, which appears in the</p><p>theoretical expression for the ratio of the polarized cross sections,</p><p>has a sign difference between the forward and backward angles and also</p><p>changes sign as the incident &gamma;-ray energy is scanned over the E2</p><p>resonance energy. The ratio of cross sections perpendicular and</p><p>parallel to the plane of polarization of the incident &gamma;-ray were</p><p>measured for thirteen different incident &gamma;-ray energies between 15 and</p><p>26 MeV at these two angles and used to extract the parameters of the</p><p>IVGQR in ²⁰⁹Bi.</p><p></p></p><p><p></p><p>The polarization ratio was calculated at 55&deg; and</p><p>125&deg; using a model consisting of E1 and E2 giant resonances as</p><p>well as a modified Thomson scattering amplitude. The parameters of the E1 giant</p><p>resonance came from previous measurements of the Giant Dipole</p><p>Resonance (GDR) </p><p>in ²⁰⁹Bi. The finite size of the nucleus was</p><p>accounted for by introducing a charge form factor in the (modified)</p><p>Thomson amplitude. This form factor was obtained from</p><p>measurements of the charge density in inelastic electron scattering</p><p>experiments. </p><p></p></p><p><p></p><p>The resulting curves were fit to the data by varying the</p><p>E2 parameters until a minimum value of the &chi;² was found.</p><p>The resulting parameters from the fit yield an IVGQR in ²⁰⁹Bi</p><p>located at E_res=23.0&plusmn;0.13(stat)&plusmn;0.25(sys) MeV</p><p>with a width of &Gamma;=3.9&plusmn;0.7(stat)&plusmn;1.3(sys) MeV and a</p><p>strength of 0.56&plusmn;0.04(stat)&plusmn;0.10(sys) Isovector Giant</p><p>Quadrupole Energy Weighted Sum Rules (IVQEWSRs).</p><p></p></p><p><p></p><p>The ability to make precise measurements of the parameters of the</p><p>IVGQR demonstrated by this work opens up new challenges to both</p><p>experimental and theoretical work in nuclear structure. A detailed</p><p>search for the missing sum rule strength in the case of ²⁰⁹Bi should</p><p>be performed. In addition, a systematic study of a number of nuclei</p><p>should be studied with this technique in order to carefully examine</p><p>the A dependence of the energy, width and sum rule strength of the</p><p>IVGQR as a function of the mass number A. The unique properties of</p><p>the HI&gamma;S facility makes it the ideal laboratory at which to perform</p><p>these studies.</p><p></p></p><p><p></p><p>Such a data base will provide more stringent tests of nuclear</p><p>theory. The effective parameters of collective models can be fine</p><p>tuned to account for such precision data. This should lead to new</p><p>insights into the underlying interactions responsible for the nature</p><p>of the IVGQR. Furthermore, with the recent advances in computational</p><p>power and techniques, microscopic shell model based calculations</p><p>should be possible and could lead to new insights into the underlying</p><p>properties of nuclear matter which are responsible for the collective</p><p>behavior evidenced by the existence and properties of the IVGQR.</p><p></p></p> / Dissertation

Density functional theory is a preferred microscopic method for calculation of nuclear properties over the whole nuclear chart. Besides ground-state properties, which are calculated by Hartree-Fock theory, nuclear excitations can be described by means of Random Phase Approximation (RPA). The main objective of the present work is to give the RPA formalism for spherically symmetric nuclei, using the techniques of angular-momentum coupling. Various auxiliary topics, such as Hartree-Fock theory, Coulomb integral, center-of-mass corrections and pairing, are treated as well. RPA method is derived also for axially deformed nuclei. The derived formulae are then implemented in the computer code and utilized for calculation of some physical results. After thorough investigation of the precision aspects of the calculation, the following topics are treated as examples: toroidal nature of the low-energy (pygmy) part of the E1 resonance, giant resonances of various multipolarities in deformed nucleus 154Sm, and magnetic dipole (M1) transitions in deformed 50Cr. Powered by TCPDF (www.tcpdf.org)