Optical Spectra and Selection Rules
Optical spectra arise from radiative transitions between atomic energy levels, and selection rules—derived from conservation of angular momentum and parity—determine which transitions are allowed and how strong they are.
Definition
Optical spectra are the sets of discrete wavelengths an atom emits or absorbs as electrons make transitions between bound levels; selection rules are the conditions on quantum numbers, following from the symmetry of the transition operator, that determine whether a given transition is allowed.
Scope
This topic covers the interaction of atoms with light: spontaneous and stimulated emission and absorption, the Einstein coefficients, transition dipole moments and oscillator strengths, and the electric-dipole selection rules on the orbital, spin, and total angular-momentum quantum numbers. It also treats line strengths, lifetimes, and the distinction between allowed and forbidden transitions, providing the link between atomic structure and observed spectra.
Core questions
- What physical process produces a spectral line, and what sets its intensity?
- How are absorption, spontaneous emission, and stimulated emission related?
- Which changes in quantum numbers are allowed in an electric-dipole transition, and why?
- What distinguishes a forbidden transition from an allowed one?
Key concepts
- Spontaneous and stimulated emission
- Absorption and Einstein coefficients
- Transition dipole moment
- Oscillator strength and line strength
- Parity and angular-momentum selection rules
- Allowed versus forbidden transitions
Key theories
- Einstein coefficients
- Einstein introduced the A and B coefficients relating spontaneous emission, stimulated emission, and absorption rates, fixing their ratios from thermal equilibrium with blackbody radiation and anticipating stimulated emission decades before the laser.
- Electric-dipole selection rules
- Evaluating the transition dipole matrix element shows allowed electric-dipole transitions require Δl = ±1, Δm = 0, ±1, ΔS = 0, and a parity change, reflecting conservation of angular momentum carried by the photon.
Clinical relevance
Selection rules and transition strengths underpin quantitative spectroscopy used to identify and measure elements in laboratory and astronomical samples, the design of lamps and lasers, and the metastable forbidden transitions that serve as references in the most accurate optical atomic clocks.
History
The discreteness of spectral lines was catalogued spectroscopically through the nineteenth century, but their intensities awaited theory. Einstein's 1917 radiation paper introduced the coefficients linking emission and absorption, and the development of quantum mechanics and Dirac's radiation theory in the late 1920s derived selection rules from the symmetry of the transition operator.
Key figures
- Albert Einstein
- Paul Dirac
- Werner Heisenberg
Related topics
Seminal works
- einstein1917
- bransden2003
Frequently asked questions
- Does a forbidden transition never happen?
- No. 'Forbidden' means forbidden to leading (electric-dipole) order. Such transitions can still proceed via much weaker magnetic-dipole or electric-quadrupole mechanisms, giving very long-lived states whose narrow lines are valued for precision spectroscopy.
- Why does an electric-dipole transition require a parity change?
- The dipole operator is odd under spatial inversion, so the integral defining the transition strength vanishes unless the initial and final states have opposite parity; this is the origin of the Laporte rule.