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Spectral line
Spectral line
Spectral line
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Continuous spectrum
Continuous spectrum
Emission lines
Emission lines (discrete spectrum)
Absorption lines
Absorption spectrum with absorption lines

A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules. These "fingerprints" can be compared to the previously collected ones of atoms[1] and molecules,[2] and are thus used to identify the atomic and molecular components of stars and planets, which would otherwise be impossible.

Types of line spectra

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Continuous spectrum of an incandescent lamp (mid) and discrete spectrum lines of a fluorescent lamp (bottom)

Spectral lines are the result of interaction between a quantum system (usually atoms, but sometimes molecules or atomic nuclei) and a single photon. When a photon has about the right amount of energy (which is connected to its frequency)[3] to allow a change in the energy state of the system (in the case of an atom this is usually an electron changing orbitals), the photon is absorbed. Then the energy will be spontaneously re-emitted, either as one photon at the same frequency as the original one or in a cascade, where the sum of the energies of the photons emitted will be equal to the energy of the one absorbed (assuming the system returns to its original state).

A spectral line may be observed either as an emission line or an absorption line. Which type of line is observed depends on the type of material and its temperature relative to another emission source. An absorption line is produced when photons from a hot, broad spectrum source pass through a cooler material. The intensity of light, over a narrow frequency range, is reduced due to absorption by the material and re-emission in random directions. By contrast, a bright emission line is produced when photons from a hot material are detected, perhaps in the presence of a broad spectrum from a cooler source. The intensity of light, over a narrow frequency range, is increased due to emission by the hot material.

Spectral lines are highly atom-specific, and can be used to identify the chemical composition of any medium. Several elements, including helium, thallium, and caesium, were discovered by spectroscopic means. Spectral lines also depend on the temperature and density of the material, so they are widely used to determine the physical composition and condition of distant stars and other celestial bodies. Some of these data cannot be obtained or analyzed by other means, and so the field of spectroscopy has grown as astronomical and telescopic exploration has grown.

Depending on the material and its physical conditions, the energy of the involved photons can vary widely, with the spectral lines observed across the electromagnetic spectrum, from radio waves to gamma rays.

Nomenclature

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Strong spectral lines in the visible part of the electromagnetic spectrum often have a unique Fraunhofer line designation, such as K for a line at 393.366 nm emerging from singly-ionized calcium atom, Ca+, though some of the Fraunhofer "lines" are blends of multiple lines from several different species.

In other cases, the lines are designated according to the level of ionization by adding a Roman numeral to the designation of the chemical element. Neutral atoms are denoted with the Roman numeral I, singly ionized atoms with II, and so on, so that, for example:

Cu II — copper ion with +1 charge, Cu1+

Fe III — iron ion with +2 charge, Fe2+

More detailed designations usually include the line wavelength and may include a multiplet number (for atomic lines) or band designation (for molecular lines). Many spectral lines of atomic hydrogen also have designations within their respective series, such as the Lyman series or Balmer series. Originally all spectral lines were classified into series: the principal series, sharp series, and diffuse series. These series exist across atoms of all elements, and the patterns for all atoms are well-predicted by the Rydberg-Ritz formula. These series were later associated with suborbitals.

Line broadening and shift

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There are a number of effects which control spectral line shape. A spectral line extends over a tiny spectral band with a nonzero range of frequencies, not a single frequency (i.e., a nonzero spectral width). In addition, its center may be shifted from its nominal central wavelength. There are several reasons for this broadening and shift. These reasons may be divided into two general categories – broadening due to local conditions and broadening due to extended conditions. Broadening due to local conditions is due to effects which hold in a small region around the emitting element, usually small enough to assure local thermodynamic equilibrium. Broadening due to extended conditions may result from changes to the spectral distribution of the radiation as it traverses its path to the observer. It also may result from the combining of radiation from a number of regions which are far from each other.

Broadening due to local effects

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Natural broadening

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The lifetime of excited states results in natural broadening, also known as lifetime broadening. The uncertainty principle relates the lifetime of an excited state (due to spontaneous radiative decay or the Auger process) with the uncertainty of its energy. Some authors use the term "radiative broadening" to refer specifically to the part of natural broadening caused by the spontaneous radiative decay.[4] A short lifetime will have a large energy uncertainty and a broad emission. This broadening effect results in an unshifted Lorentzian profile. The natural broadening can be experimentally altered only to the extent that decay rates can be artificially suppressed or enhanced.[5]

Thermal Doppler broadening

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Main article: Doppler broadening

The atoms in a gas which are emitting radiation will have a distribution of velocities. Each photon emitted will be "red"- or "blue"-shifted by the Doppler effect depending on the velocity of the atom relative to the observer. The higher the temperature of the gas, the wider the distribution of velocities in the gas. Since the spectral line is a combination of all of the emitted radiation, the higher the temperature of the gas, the broader the spectral line emitted from that gas. This broadening effect is described by a Gaussian profile and there is no associated shift.

Pressure broadening

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The presence of nearby particles will affect the radiation emitted by an individual particle. There are two limiting cases by which this occurs:

  • Impact pressure broadening or collisional broadening: The collision of other particles with the light emitting particle interrupts the emission process, and by shortening the characteristic time for the process, increases the uncertainty in the energy emitted (as occurs in natural broadening).[6] The duration of the collision is much shorter than the lifetime of the emission process. This effect depends on both the density and the temperature of the gas. The broadening effect is described by a Lorentzian profile and there may be an associated shift.
  • Quasistatic pressure broadening: The presence of other particles shifts the energy levels in the emitting particle (see spectral band), thereby altering the frequency of the emitted radiation. The duration of the influence is much longer than the lifetime of the emission process. This effect depends on the density of the gas, but is rather insensitive to temperature. The form of the line profile is determined by the functional form of the perturbing force with respect to distance from the perturbing particle. There may also be a shift in the line center. The general expression for the lineshape resulting from quasistatic pressure broadening is a 4-parameter generalization of the Gaussian distribution known as a stable distribution.[7]

Pressure broadening may also be classified by the nature of the perturbing force as follows:

  • Linear Stark broadening occurs via the linear Stark effect, which results from the interaction of an emitter with an electric field of a charged particle at a distance , causing a shift in energy that is linear in the field strength.
  • Resonance broadening occurs when the perturbing particle is of the same type as the emitting particle, which introduces the possibility of an energy exchange process.
  • Quadratic Stark broadening occurs via the quadratic Stark effect, which results from the interaction of an emitter with an electric field, causing a shift in energy that is quadratic in the field strength.
  • Van der Waals broadening occurs when the emitting particle is being perturbed by Van der Waals forces. For the quasistatic case, a Van der Waals profile[note 1] is often useful in describing the profile. The energy shift as a function of distance between the interacting particles is given in the wings by e.g. the Lennard-Jones potential.

Inhomogeneous broadening

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Inhomogeneous broadening is a general term for broadening because some emitting particles are in a different local environment from others, and therefore emit at a different frequency. This term is used especially for solids, where surfaces, grain boundaries, and stoichiometry variations can create a variety of local environments for a given atom to occupy. In liquids, the effects of inhomogeneous broadening is sometimes reduced by a process called motional narrowing.

Broadening due to non-local effects

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Certain types of broadening are the result of conditions over a large region of space rather than simply upon conditions that are local to the emitting particle.

Opacity broadening

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Opacity broadening is an example of a non-local broadening mechanism. Electromagnetic radiation emitted at a particular point in space can be reabsorbed as it travels through space. This absorption depends on wavelength. The line is broadened because the photons at the line center have a greater reabsorption probability than the photons at the line wings. Indeed, the reabsorption near the line center may be so great as to cause a self reversal in which the intensity at the center of the line is less than in the wings. This process is also sometimes called self-absorption.

Macroscopic Doppler broadening

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Radiation emitted by a moving source is subject to Doppler shift due to a finite line-of-sight velocity projection. If different parts of the emitting body have different velocities (along the line of sight), the resulting line will be broadened, with the line width proportional to the width of the velocity distribution. For example, radiation emitted from a distant rotating body, such as a star, will be broadened due to the line-of-sight variations in velocity on opposite sides of the star (this effect usually referred to as rotational broadening). The greater the rate of rotation, the broader the line. Another example is an imploding plasma shell in a Z-pinch.

Combined effects

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Each of these mechanisms can act in isolation or in combination with others. Assuming each effect is independent, the observed line profile is a convolution of the line profiles of each mechanism. For example, a combination of the thermal Doppler broadening and the impact pressure broadening yields a Voigt profile.

However, the different line broadening mechanisms are not always independent. For example, the collisional effects and the motional Doppler shifts can act in a coherent manner, resulting under some conditions even in a collisional narrowing, known as the Dicke effect.

Spectral lines of chemical elements

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See also: Hydrogen spectral series
Absorption lines for air, under indirect illumination, so that the gas is not directly between source and detector. Here, Fraunhofer lines in sunlight and Rayleigh scattering of this sunlight is the "source." This is the spectrum of a blue sky somewhat close to the horizon, looking east with the sun to the west at around 3–4 pm on a clear day.

Bands

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The phrase "spectral lines", when not qualified, usually refers to lines having wavelengths in the visible band of the full electromagnetic spectrum. Many spectral lines occur at wavelengths outside this range. At shorter wavelengths, which correspond to higher energies, ultraviolet spectral lines include the Lyman series of hydrogen. At the much shorter wavelengths of X-rays, the lines are known as characteristic X-rays because they remain largely unchanged for a given chemical element, independent of their chemical environment. Longer wavelengths correspond to lower energies, where the infrared spectral lines include the Paschen series of hydrogen. At even longer wavelengths, the radio spectrum includes the 21-cm line used to detect neutral hydrogen throughout the cosmos.

See also

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Notes

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Spectral line

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from Grokipedia
A spectral line is a narrow, distinct bright or dark feature in an , appearing against a continuous background of and resulting from the emission or absorption of photons at precise wavelengths due to quantum transitions in atoms, ions, or molecules. These lines arise primarily from the quantized levels of electrons in atoms or molecules, as described by . In emission spectra, electrons excited to higher states release photons of specific energies when transitioning to lower states, producing bright lines at wavelengths given by the difference in levels, such as ΔE=hν\Delta E = h\nu, where hh is Planck's constant and ν\nu is the . Conversely, absorption lines form when photons from a continuum source are absorbed by cooler gas, exciting electrons and creating dark gaps in the spectrum at those same characteristic wavelengths. The exact positions and intensities of spectral lines depend on factors like the element involved, ionization state, , , and , leading to broadening effects such as Doppler, natural, or broadening. Spectral lines serve as unique signatures, or "fingerprints," for identifying chemical elements and molecules in various environments, from samples to distant astronomical objects. In astronomy, they enable precise measurements of composition, , , and radial velocities via Doppler shifts, which reveal motions such as galactic rotations or cosmic expansion through . Historically observed in as dark since the early 19th century, these features underpin modern , , and , facilitating applications in , plasma diagnostics, and fundamental tests of quantum theory.

Basic Principles

Definition and Characteristics

A spectral line is a narrow or broadened feature in the that corresponds to the emission or absorption of light at a specific due to transitions between quantized levels in atoms, ions, or molecules./05%3A_Radiation_and_Spectra/5.05%3A_Formation_of_Spectral_Lines) These lines appear as discrete peaks or dips in an otherwise uniform spectrum, reflecting the quantized nature of atomic and molecular energy states. Key characteristics of spectral lines include their position, intensity, sharpness, and occasional polarization. The position is defined by the precise wavelength λ\lambda or frequency ν\nu of the line, which directly relates to the energy difference ΔE\Delta E between the involved quantum levels via the equation E=hcλ,E = \frac{hc}{\lambda}, where hh is Planck's constant and cc is the speed of light. Intensity depends on the transition probability and the relative populations of the energy levels, determining the line's brightness or depth. In the ideal case, a spectral line is infinitely sharp, resembling a delta function δ(ν−ν0)\delta(\nu - \nu_0) at the central frequency ν0\nu_0, though observed lines exhibit finite width. Polarization may occur in lines influenced by magnetic fields or anisotropic conditions./05%3A_Radiation_and_Spectra/5.05%3A_Formation_of_Spectral_Lines) The historical observation of spectral lines dates to Newton's 1666 experiments, where he used prisms to separate into a continuous color without resolving discrete features. In 1814, first identified dark lines in the solar , cataloging over 500 such features and establishing them as standards for wavelength measurement. These observations laid the groundwork for . Spectral lines differ fundamentally from continuous spectra, which display a smooth distribution of all wavelengths without gaps. Lines originate from discrete quantum transitions in sparse gases or low-density media, whereas continuous spectra arise from thermal emission in hot, dense bodies () or free-free processes like in plasmas./05%3A_Radiation_and_Spectra/5.05%3A_Formation_of_Spectral_Lines)

Formation Mechanisms

Spectral lines form through atomic and molecular processes involving the absorption or emission of photons at discrete wavelengths corresponding to transitions. In the emission process, atoms or molecules in excited states return to lower energy states, releasing photons with energies equal to the difference between the levels. This occurs via , as seen in where light excites atoms, leading to visible re-emission, or in thermal incandescence of low-density gases where collisions populate excited states. In contrast, absorption lines arise when photons from a continuum source interact with atoms or molecules in their , exciting them to higher levels and removing specific wavelengths from the , producing dark lines against a bright background. This mechanism requires a cooler, intervening gas relative to the hotter continuum source, such as in stellar atmospheres where photospheric absorption imprints lines on the emerging continuum radiation. Temperature plays a key role by determining the population of excited states through the Boltzmann distribution, with higher temperatures increasing the fraction of atoms in upper levels and thus enhancing emission line strengths. Density influences collision rates, which can excite atoms to higher states in hot, dense environments or de-excite them via inelastic collisions in higher-density regimes, affecting the overall line formation efficiency. These processes are codified in Kirchhoff's laws of spectroscopy, formulated in 1860, which relate spectral types to source conditions: a hot, dense body like a solid or liquid produces a continuous spectrum; a hot, low-density gas yields bright emission lines; and a cooler gas overlying a hot continuum source results in absorption lines. The relative populations of upper (nun_u) and lower (nln_l) energy levels in thermal equilibrium follow the Boltzmann equation: nunl=guglexp⁡(−ΔEkT)\frac{n_u}{n_l} = \frac{g_u}{g_l} \exp\left( -\frac{\Delta E}{kT} \right) where gug_u and glg_l are the degeneracies of the upper and lower levels, ΔE=Eu−El\Delta E = E_u - E_l is the energy difference, kk is the Boltzmann constant, and TT is the temperature. To derive this, consider a system of non-interacting atoms in local thermodynamic equilibrium under Maxwell-Boltzmann statistics. The probability of an atom occupying a specific quantum state with energy EE is proportional to exp⁡(−E/kT)\exp(-E / kT), reflecting the entropic maximization of configurations at fixed energy. For discrete energy levels, each level ii has degeneracy gig_i, the number of accessible states at energy EiE_i, so the population nin_i is ni∝giexp⁡(−Ei/kT)n_i \propto g_i \exp(-E_i / kT). Normalizing to the total population and taking the ratio for two levels yields the equation, assuming the partition function cancels out. This distribution underpins line intensities, as emission or absorption rates scale with nun_u or nln_l.

Classification and Types

Emission Lines

Emission lines manifest as bright, discrete features superimposed on a predominantly dark spectral background, arising from the emission of photons during atomic or ionic transitions in excited media. These lines are primarily produced through , where electrons in higher energy states decay to lower states, releasing photons of specific wavelengths, or via in the presence of a field. Such processes commonly occur in low-density plasmas or gases, where collisional de-excitation is minimal, allowing radiative decay to dominate. Prominent observational examples include the of , which features emission lines in the resulting from transitions to the n=2 principal quantum level. The most intense of these is the H-alpha line at 656.3 nm, appearing as a vivid red feature in spectra from ionized regions. In astrophysical contexts, such as the , emission spectra reveal forbidden lines—like those from doubly ionized oxygen ([O III]) at 495.9 nm and 500.7 nm—which are characteristic of low-density environments where densities are below approximately 10^6 cm^{-3}, suppressing collisional of metastable states. The intensity of an emission line is directly proportional to the population of atoms or ions in the upper and the transition probability, quantified by the Einstein A (AulA_{ul}), which represents the rate in s^{-1}. The radiative transition rate, determining the line's emitted photon flux per unit volume, is expressed as Γ=Aul Nupper,\Gamma = A_{ul} \, N_{\rm upper}, where NupperN_{\rm upper} is the of particles in the upper state; this relation underpins quantitative analysis of spectral data. Emission lines find critical applications in plasma diagnostics, enabling inference of physical parameters like and from line ratios, as well as in laser spectroscopy for real-time characterization of excited in plasmas.

Absorption Lines

Absorption lines manifest as dark features superimposed on a continuum spectrum, arising when photons from a background source are absorbed by atoms or ions in cooler intervening material. This absorption occurs at discrete wavelengths corresponding to quantum transitions from lower to upper levels, selectively removing those specific frequencies from the incident . The excited atoms subsequently re-emit the energy isotropically or through cascades to other levels, leading to a net reduction in intensity at the original wavelength rather than a directional continuum contribution. In stellar spectra, absorption lines form primarily in the cooler outer layers of a star's atmosphere, where gas temperatures allow population of ground or low-lying states that intercept the continuum radiation emerging from the hotter interior. A classic example is the observed in sunlight, first cataloged in the early ; prominent among them are the calcium H and lines at approximately 396.8 nm and 393.4 nm, respectively, produced by resonance transitions in singly ionized calcium (Ca II). These lines probe the solar photosphere and , with their depths reflecting local abundance and temperature conditions. Similarly, interstellar absorption lines appear in the spectra of distant stars, where foreground neutral or ionized gas along the absorbs continuum light; common features include the Ca II H and lines and sodium D lines (Na I at 589.0 nm and 589.6 nm), which trace diffuse interstellar clouds and their column densities. The strength of an absorption line is quantified by its depth and , which together indicate the amount of absorbing material. The line depth represents the fractional reduction in continuum intensity at the line center, while the WλW_\lambda, defined as the integral of the normalized absorption profile over , equals the width of a hypothetical rectangular dip with the same total absorbed flux. For optically thin lines, Wλ≈σλNfW_\lambda \approx \sigma_\lambda N f, where σλ\sigma_\lambda is the wavelength-dependent absorption cross-section, NN is the column of absorbers (N=∫n dlN = \int n \, dl, with nn the and dldl the path length), and ff is the of the transition, a measure of its intrinsic probability. This relation allows astronomers to infer atomic abundances and physical conditions from observed spectra, though saturation effects in stronger lines require the full -of-growth analysis to accurately recover NN. Absorption lines are observed across diverse contexts, including stellar atmospheres where they reveal elemental compositions and velocity fields; planetary atmospheres, such as those of or exoplanets, which imprint signatures on transmitted ; and laboratory , where controlled conditions enable precise measurements of atomic parameters. The underlying absorption process is described by the monochromatic absorption αν=hν4πBlunlϕ(ν)\alpha_\nu = \frac{h\nu}{4\pi} B_{lu} n_l \phi(\nu), where hh is Planck's constant, ν\nu the , BluB_{lu} the Einstein for absorption, nln_l the in the lower , and ϕ(ν)\phi(\nu) the normalized line profile function with ∫ϕ(ν) dν=1\int \phi(\nu) \, d\nu = 1. Integrating αν\alpha_\nu along the yields the , which governs the observed line profile. These features contrast with emission lines formed in the same transitions but under conditions favoring net addition, such as in hotter, optically thin plasmas.

Band Spectra

Band spectra in molecular consist of series of closely spaced spectral lines arising from simultaneous changes in vibrational and rotational quantum numbers during electronic, vibrational, or pure rotational transitions in molecules. Unlike the discrete, isolated lines observed in atomic spectra, these lines form shaded or banded regions due to the dense packing of rotational levels within each vibrational transition, often appearing as continuous bands at lower resolution. The internal structure of a molecular band typically features P, Q, and R branches, corresponding to rotational changes of ΔJ = -1, 0, and +1, respectively. The P branch forms on the low-wavenumber side of the band origin, the R branch on the high-wavenumber side, and the Q branch, when allowed, clusters near the origin; in many diatomic cases, such as Σ–Σ transitions, the Q branch is absent due to selection rules. Vibrational progressions manifest as sequences of bands from Δv > 0 transitions, where higher vibrational levels produce successively weaker bands approaching the dissociation limit. The energy levels determining these bands for diatomic molecules are described by the anharmonic oscillator with rotation, with wavenumber given by σ(v,J)=ωe(v+12)−ωexe(v+12)2+BJ(J+1)\sigma(v, J) = \omega_e \left(v + \frac{1}{2}\right) - \omega_e x_e \left(v + \frac{1}{2}\right)^2 + B J(J+1) where ωe\omega_e is the harmonic vibrational frequency, ωexe\omega_e x_e the anharmonicity constant, vv the vibrational , BB the rotational constant, and JJ the rotational ; centrifugal and other corrections may apply for precision. Prominent examples include the Swan bands of the C₂ molecule (d³Π_g – a³Π_u electronic system), observed in carbon-rich stars and flames with strong features around 5165 and 4737 , revealing molecular abundance and temperature. The violet system (B²Σ⁺ – X²Σ⁺) appears in cometary atmospheres and stellar spectra, exemplified by the (0,0) band near 3883 , aiding in diagnosing excitation conditions. Band widths depend on the rotational temperature, which governs the of J levels and thus the extent of populated branches, while high-vibrational bands truncate near molecular dissociation energies.

Theoretical Foundations

Quantum Mechanical Basis

The quantum mechanical basis of spectral lines originates from the quantization of atomic and molecular energy levels, which replaced classical models with discrete states leading to sharp emission or absorption features. In 1913, introduced a semi-classical model for the , postulating that electrons occupy stationary orbits with quantized L=nℏL = n \hbar, where nn is a positive integer and ℏ=h/2π\hbar = h / 2\pi, preventing continuous energy loss via radiation. Transitions between these levels were assumed to emit or absorb photons with energy ΔE=hν\Delta E = h \nu, explaining the discrete lines in spectra. Although successful for , the failed for multi-electron atoms and lacked a relativistic or wave description, paving the way for full . The foundational quantum mechanical treatment of atomic energy levels came from solving the time-independent for the in 1926, yielding exact discrete energy eigenvalues En=−13.6 eVn2E_n = -\frac{13.6 \, \text{eV}}{n^2} for n=1,2,…n = 1, 2, \dots, with bound states below the ionization threshold at E=0E = 0 and a continuum above it. These levels arise from the radial and angular solutions of H^ψ=Eψ\hat{H} \psi = E \psi, where H^=−ℏ22μ∇2−e24πϵ0r\hat{H} = -\frac{\hbar^2}{2\mu} \nabla^2 - \frac{e^2}{4\pi \epsilon_0 r} for μ\mu and potential. For multi-electron atoms, the exact many-body becomes intractable due to electron-electron interactions, so the Hartree-Fock method approximates the wavefunction as a of single-particle orbitals, solving self-consistent field equations variationally to obtain approximate energy levels that capture exchange effects and correlate well with observed spectra for light atoms. In molecules, energy levels are more complex due to nuclear motion, addressed by the Born-Oppenheimer approximation in , which exploits the mass disparity between electrons and nuclei to separate the total wavefunction into electronic, vibrational, and rotational parts: the electronic Hamiltonian is solved for fixed nuclear positions to yield surfaces, on which nuclei vibrate and rotate. This yields discrete electronic transitions split into vibrational (via anharmonic potentials) and rotational (via levels) substructure, forming band spectra rather than isolated lines. Above the dissociation or ionization limit, levels merge into continua, analogous to atomic cases. Spectral lines emerge from transitions between these discrete levels induced by electromagnetic perturbations, described by . The transition rate from initial state ∣i⟩|i\rangle to a continuum of final states ∣f⟩|f\rangle is given by : Γ=2πℏ∣⟨f∣H^′∣i⟩∣2ρ(Ef)\Gamma = \frac{2\pi}{\hbar} |\langle f | \hat{H}' | i \rangle|^2 \rho(E_f), where H^′\hat{H}' is the interaction Hamiltonian (e.g., operator −μ⃗⋅E⃗-\vec{\mu} \cdot \vec{E}
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