The calculation of the decoherence effects on quantum tunneling can be a complex task and highly dependent on the specific system and the details of the environment causing the decoherence. Decoherence refers to the interaction of a quantum system with its surrounding environment, leading to the loss of quantum coherence and the emergence of classical behavior.
While physicists can study and model the effects of decoherence on quantum tunneling, obtaining precise quantitative predictions for a specific quantum object through a given barrier can be challenging. The calculation typically involves a combination of theoretical models and numerical simulations, and the results can vary depending on the specific system and the complexity of the environment.
One approach to studying decoherence in quantum tunneling is to employ methods from quantum open systems theory. This involves describing the system-environment interaction using mathematical models, such as density matrices or master equations. By incorporating the relevant decoherence mechanisms and solving the resulting equations, one can analyze the impact of decoherence on the tunneling probability.
However, it's important to note that decoherence can be a highly intricate phenomenon, influenced by various factors such as temperature, coupling strength, and the specific nature of the environment. Additionally, the complexity of the quantum system and the details of the barrier can also play a role in determining the extent of decoherence effects on tunneling.
In summary, while physicists can study the effects of decoherence on quantum tunneling, obtaining precise quantitative predictions for a specific system and barrier is a challenging task that requires sophisticated theoretical models and numerical calculations. The actual calculation and analysis would depend on the specific details and complexities of the system under consideration.