An Investigation of the Isovector Giant Quadrupole Resonance in 209Bi using Polarized Compton Scattering



Giant multipole resonances are a fundamental property of nuclei and

arise from the collective motion of the nucleons inside

the nucleus. Careful studies of these resonances and their properties provides

insight into the nature of nuclear matter and constraints

which can be used to test our theories.

An investigation of the Isovector Giant Quadrupole Resonance (IVGQR)

in ²⁰⁹Bi has been preformed using the High Intensity γ-ray

Source (HIγS) facility. Intense nearly monochromatic

polarized γ-rays were incident upon a ²⁰⁹Bi target producing

nuclear Compton scattered γ-rays that were detected using the HIγS

NaI(Tl) Detector Array (HINDA). The HINDA array consists of six

large (10''x10'') NaI(Tl) core crystals, each surrounded by an

optically segmented 3'' thick NaI(Tl) annulus. The scattered γ-rays

both parallel and perpendicular to the plane of polarization were

detected at scattering angles of 55° and 125° with

respect to the beam axis. This was motivated by the realization that

the term representing the interference between the electric dipole

(E1) and electric quadrupole (E2) amplitudes, which appears in the

theoretical expression for the ratio of the polarized cross sections,

has a sign difference between the forward and backward angles and also

changes sign as the incident γ-ray energy is scanned over the E2

resonance energy. The ratio of cross sections perpendicular and

parallel to the plane of polarization of the incident γ-ray were

measured for thirteen different incident γ-ray energies between 15 and

26 MeV at these two angles and used to extract the parameters of the

IVGQR in ²⁰⁹Bi.

The polarization ratio was calculated at 55° and

125° using a model consisting of E1 and E2 giant resonances as

well as a modified Thomson scattering amplitude. The parameters of the E1 giant

resonance came from previous measurements of the Giant Dipole

Resonance (GDR)

in ²⁰⁹Bi. The finite size of the nucleus was

accounted for by introducing a charge form factor in the (modified)

Thomson amplitude. This form factor was obtained from

measurements of the charge density in inelastic electron scattering

experiments.

The resulting curves were fit to the data by varying the

E2 parameters until a minimum value of the χ² was found.

The resulting parameters from the fit yield an IVGQR in ²⁰⁹Bi

located at E_res=23.0±0.13(stat)±0.25(sys) MeV

with a width of Γ=3.9±0.7(stat)±1.3(sys) MeV and a

strength of 0.56±0.04(stat)±0.10(sys) Isovector Giant

Quadrupole Energy Weighted Sum Rules (IVQEWSRs).

The ability to make precise measurements of the parameters of the

IVGQR demonstrated by this work opens up new challenges to both

experimental and theoretical work in nuclear structure. A detailed

search for the missing sum rule strength in the case of ²⁰⁹Bi should

be performed. In addition, a systematic study of a number of nuclei

should be studied with this technique in order to carefully examine

the A dependence of the energy, width and sum rule strength of the

IVGQR as a function of the mass number A. The unique properties of

the HIγS facility makes it the ideal laboratory at which to perform

these studies.

Such a data base will provide more stringent tests of nuclear

theory. The effective parameters of collective models can be fine

tuned to account for such precision data. This should lead to new

insights into the underlying interactions responsible for the nature

of the IVGQR. Furthermore, with the recent advances in computational

power and techniques, microscopic shell model based calculations

should be possible and could lead to new insights into the underlying

properties of nuclear matter which are responsible for the collective

behavior evidenced by the existence and properties of the IVGQR.