COMPARATIVE STUDY OF ANGULAR CORRELATION IN POSITRON ANNIHILATION (22Na) AND GAMMA CASCADE DECAY (60CO) USING NaI(Tl) SCINTILLATION DETECTORS

Abstract

This dissertation presents a detailed experimental investigation of angular correlations in coincident gamma-ray emissions from two distinct nuclear processes: positron annihilation in sodium-22 (22Na) and sequential gamma-ray cascade decay in cobalt- 60 (60Co). Using a dual-channel coincidence detection system equipped with high- resolution NaI(Tl) scintillation detectors, coincidence rates were recorded over a range of detector separations from ∘0 to ∘180. For 22Na, annihilation of a positron with an electron produces two back-to-back 511 keV photons. Measurements revealed a sharply peaked angular distribution with a maximum at ∘180, in agreement with momentum conservation in a two-body decay. In contrast, 60Co cascade decays displayed only a modest angular modulation of approximately 16 %, reflecting weaker correlations governed by nuclear spin and multipolarity selection rules. Energy spectra were calibrated using a linear relation E=a+b×channel, and Gaussian fits were applied to determine centroid energies, full width at half maximum (FWHM), and peak areas. Random coincidences were estimated and subtracted using 𝑅𝑟𝑎𝑛𝑑 ≈ 2 𝜏 𝑆1 𝑆2, where 𝜏 is the coincidence timing window and 𝑆1, 𝑆2 are singles rates. True coincidences were then obtained as with T the live acquisition time. The normalized angular correlation function was calculated as where ⟨Rtrue⟩ is the mean true-coincidence rate over all angles. Uncertainties were propagated using Poisson statistics and standard error-propagation formulas. pg. 3 The experimental results validate theoretical predictions of angular dependence and demonstrate the effectiveness of energy gating and timing methods. Beyond fundamental nuclear physics, the clear back-to-back correlation of 511 keV photons underpins medical imaging modalities such as Positron Emission Tomography (PET), while the weaker correlations in nuclear cascades provide insight into nuclear structure and transition multi-polarities.