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In vibrational-rotational (v-r) spectroscopy, the p branch corresponds to transitions where the rotational quantum number decreases, while the r branch corresponds to transitions where the rotational quantum number increases. The p branch is typically more intense than the r branch due to factors such as the Boltzmann distribution, which favors lower energy states, and the selection rules that make transitions to lower rotational states more probable. Additionally, the population of lower rotational states is often higher at thermal equilibrium, leading to greater intensity in the p branch.

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