The identification of energy scales in the region of Isoscalar Giant Quadrupole Resonance (ISGQR) is motivated by their potential use in understanding how an ordered collective motion transforms into a disordered motion of intrinsic single-particle degrees-of-freedom in many-body quantum systems. High energy-resolution measurements of the ISGQR were obtained by proton inelastic scattering at Ep= 200 MeV using the K600 magnetic Spectrometer at iThemba LABS. The nuclei 58Ni, 90Zr, 120Sn and 208Pb, associated with closed shells, were investigated. Both the Fourier transform and Wavelet analysis were used to extract characteristic energy scales and were later compared with the results from the theoretical microscopic Quasi-particle Phonon Model (QPM), including contributions from collective and non-collective states. The scales found in the experimental data were in good agreement with the QPM. This provides a strong argument that the observed energy scales result from the decay of the collective modes into 2p-2h states. The different scale regions were tested directly by reconstruction of measured energy spectra using the Inverse Fourier Transform and the Continuous Wavelet Transform (CWT), together with a comparison to a previously available reconstruction using the Discrete Wavelet Transform (DWT).

<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

Dans le cadre d'une approche Higher Tamm Dancoff Approximation notée HTDA, nous avons étudié les corrélations vibrationnelles de type quadrupole, avec et sans appariement. Le champ moyen a été déterminé dans le cadre d'une approche microscopique utilisant l'interaction effective de Skyrme. Une interaction résiduelle schématique de type delta plus quadrupole-quadrupole, tenant compte en particulier de l'appariement neutron-proton T=0 et T=1 a été utilisé. Les résultats obtenus pour la résonance géante quadrupolaire isoscalaire du noyau Ca40 ont été comparés aux données expérimentales et à d'autres résultats théoriques. Nous avons également étudié un gaz de fermions piégés dans un potentiel d'oscillateur harmonique à 2D, et à température nulle, en présence d'un champ magnétique uniforme. Les expressions exactes des quelques grandeurs thermodynamiques ont été dérivées à partir de la matrice densité de Bloch. / Within the framework of the so-called Higher Tamm Dancoff Approxiamtion (HTDA), we have studied the quadrupole vibrational correlations with and without pairing correlations. The mean field has been determined within a microscopic approach using the Skyrme effective interaction. A schematic residual interaction of the delta plus quadrupole-quadrupole type, allowing in particular neutron-proton T=0 and T=1 pairing, has been used. The results which have been obtained for the isoscalar quadrupole giant resonance of the Ca40 have been compared with the experimental data. A fermion gaz trapped in a 2D harmonic oscillator well at zero temperature and in the presence of a uniform magnetic field has been investigated. Exact expressions of some thermodynamic quantities have been derived from the Bloch density matrix.

Dans le cadre d'une approche Higher Tamm Dancoff Approximation notée HTDA, nous avons étudié les corrélations vibrationnelles de type quadrupole, avec et sans appariement. Le champ moyen a été déterminé dans le cadre d'une approche microscopique utilisant l'interaction effective de Skyrme. Une interaction résiduelle schématique de type delta plus quadrupole-quadrupole, tenant compte en particulier de l'appariement neutron-proton T=0 et T=1 a été utilisé. Les résultats obtenus pour la résonance géante quadrupolaire isoscalaire du noyau Ca40 ont été comparés aux données expérimentales et à d'autres résultats théoriques. Nous avons également étudié un gaz de fermions piégés dans un potentiel d'oscillateur harmonique à 2D, et à température nulle, en présence d'un champ magnétique uniforme. Les expressions exactes des quelques grandeurs thermodynamiques ont été dérivées à partir de la matrice densité de Bloch.