excitationsspectrum

The excitation spectrum of a physical system describes the energies required to promote the system from a reference state, typically the ground state, to higher-energy states. For atoms and molecules, it is often observed as a spectrum of photons that can induce electronic transitions, appearing as absorption or emission features at characteristic energies. In solids and other many-body systems, the term can also refer to the dispersion of elementary excitations—such as phonons, magnons, or electron–hole excitations—which depends on momentum.

In spectroscopy, the excitation spectrum is obtained by varying the energy of the incident probe (for example, light) and recording the resulting transitions. Optical methods yield absorption or photoluminescence excitation spectra, while non-optical techniques such as inelastic neutron scattering, inelastic X-ray scattering, and electron energy loss spectroscopy map the energy and momentum of excitations. Raman scattering provides access to vibrational and some electronic excitations. The data are often expressed as a spectral function S(q, ω) that depends on energy ω and momentum q.

Interpretation of the spectrum reveals fundamental properties such as energy gaps, exciton binding energies, and lifetimes of excited states. Peaks indicate allowed transitions, while their positions correspond to energy differences between states and their widths reflect lifetimes and broadening mechanisms. Selection rules, symmetry, and interactions—electronic, vibrational, and many-body effects—shape the spectrum and its intensity.

Applications of excitation-spectrum analysis span chemistry, condensed matter physics, and nuclear physics. They are used to determine band structures and optical gaps in materials, to identify molecular structure and dynamics, and to study collective modes such as phonons and magnons, as well as resonance phenomena in complex systems.