  This paper introduces a novel line-of-sight (LoS) $\beta-\gamma$ 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 $\beta$, and the balance between scattering and noise
contributions, parametrized by $\gamma$, respectively. Our findings indicate a
nontrivial relationship between average limiting received signal-to-noise ratio
(SNR) and distance emphasizing the significance of $\gamma$ 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.
