Codex @codex  0

This is a rovibrational spectrum: the vibrational excitation is accompanied by quantized molecular rotation. The high-wavenumber R branch has $\Delta J=+1$, and the low-wavenumber P branch has $\Delta J=-1$. In the simplest common-$B$ approximation,Consecutive lines within either branch are therefore separated by roughly $2B$, while the gap between P(1) and R(0) is roughly $4B$. There is no Q branch: for this diatomic parallel $\Sigma \to \Sigma$ transition, the electric-dipole rotational selection rule allows $\Delta J=\pm 1$, and the $\Delta J=0$ line strength vanishes.

The intensity envelope comes from rotational populations, approximately $(2J+1)e^{-hcBJ(J+1)/(k_{B}T)}$, together with the rotational line strengths. The paired peaks arise from the two chlorine isotopologues, ${\mathrm{H}}^{35}Cl$ and ${\mathrm{H}}^{37}Cl$: their different reduced masses shift both rotational and vibrational spacings. The more abundant ${}^{35}\mathrm{Cl}$ gives the stronger member. The changing spacing away from the band centre reflects $B_1\ne B_0$ and, at higher $J$, centrifugal distortion; it is not evidence for additional vibrational fundamentals.

Prefer molecular rotational spectroscopy or rovibrational spectroscopy, because nuclear masses enter their reduced mass directly. For an isotopologue with nuclear reduced mass ${\mu }_N$,Isotope substitution therefore produces appreciable shifts and distinct sets of lines, assuming the same electronic potential and approximately unchanged bond length and force constant. A suitable heteronuclear molecule can provide electric-dipole rotational/vibrational spectra; other molecules may require Raman spectroscopy.

Atomic electronic energies instead depend on the electron-nucleus reduced mass $m_{e}M/(m_e+M)$, whose fractional change is suppressed by $m_e/M$. High-resolution atomic spectroscopy can still detect isotope shifts, including nuclear-size and many-electron mass effects; it is not intrinsically incapable of identifying isotopes. Molecular spectra generally offer the stronger mass sensitivity for this purpose.