Diatomic molecules are normally in their lowest or ground state, which conventionally is also known as the  state. When a gas of diatomic molecules is bombarded by energetic electrons, some of the molecules may be excited to higher electronic states, as occurs, for example, in the natural aurora; high-altitude nuclear explosions; and rocket-borne electron gun experiments. Such excitation can also occur when the gas absorbs light or other electromagnetic radiation. The excited states are unstable and naturally relax back to the ground state. Over various short time scales after the excitation (typically a fraction of a second, or sometimes longer than a second if the excited state is metastable), transitions occur from higher to lower electronic states and ultimately to the ground state, and in each transition results a photon is emitted. This emission is known as fluorescence. Successively higher electronic states are conventionally named , , , etc. (but this convention is not always followed, and sometimes lower case letters and alphabetically out-of-sequence letters are used, as in the example given below). The excitation energy must be greater than or equal to the energy of the electronic state in order for the excitation to occur.
In quantum theory, an electronic state of a diatomic molecule is represented by the molecular term symbol
where  is the total electronic spin quantum number,  is the total electronic angular momentum quantum number along the internuclear axis, and  is the vibrational quantum number.  takes on values 0, 1, 2, ..., which are represented by the electronic state symbols , , ,....
For example, the following table lists the common electronic states (without vibrational quantum numbers) along with the energy of the lowest vibrational level () of diatomic nitrogen (N), the most abundant gas in the Earth's atmosphere. 
The subscripts and superscripts after  give additional quantum mechanical details about the electronic state. The superscript  or  determines whether reflection in a plane containing the internuclear axis introduces a sign change in the wavefunction. The sub-script  or  applies to molecules of identical atoms, and when reflecting the state along a plane perpendicualr to the molecular axis, states that does not change are labelled  (gerade), and states that change sign are labelled  (ungerade).
The aforementioned fluorescence occurs in distinct regions of the electromagnetic spectrum, called "emission bands": each band corresponds to a particular transition from a higher electronic state and vibrational level to a lower electronic state and vibrational level (typically, many vibrational levels are involved in an excited gas of diatomic molecules). For example, N - emission bands (a.k.a. Vegard-Kaplan bands) are present in the spectral range from 0.14 to 1.45 μm (micrometres). A given band can be spread out over several nanometers in electromagnetic wavelength space, owing to the various transitions that occur in the molecules rotational quantum number, . These are classified into distinct sub-band branches, depending on the change in . The  branch corresponds to , the  branch to , and the  branch to . Bands are spread out even further by the limited spectral resolution of the spectrometer that is used to measure the spectrum. The spectral resolution depends on the instruments point spread function.