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This paper introduces a novel line-of-sight (LoS) β−γ terahertz (THz) channel model that closely mirrors physical reality by considering radiation trapping. Our channel model provides an exhaustive modeling of the physical phenomena including the amount of re-radiation available at the receiver, parametrized by β, and the balance between scattering and noise contributions, parametrized by γ, respectively. Our findings indicate a nontrivial relationship between average limiting received signal-to-noise ratio (SNR) and distance emphasizing the significance of γ in THz system design. We further propose new maximum likelihood (ML) thresholds for pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) schemes, resulting in analytical symbol error rate (SER) expressions that account for different noise variances across constellation points. The results confirm that the analytical SER closely matches the true simulated SER when using an optimal detector. As expected, under maximum molecular re-radiation, the true SER is shown to be lower than that produced by a suboptimal detector that assumes equal noise variances.