9: Oscillator Strengths and Related Topics
- Page ID
- 6705
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 9.1: Introduction, Radiance, and Equivalent Width
- This page explains radiance in hot gases, illustrating its presentation as discrete emission lines in a spectrograph. It differentiates between radiance and intensity, describing how radiance of an emission line correlates with atomic column density.
- 9.2: Oscillator Strength. (die Oszillatorenstärke)
- This page covers oscillator strength in atomic absorption through classical electromagnetic theory, explaining how an atom's loosely bound electron interacts with oscillating electric fields. It presents equations for determining equivalent widths, vital for deriving atomic densities in stellar spectra.
- 9.3: Einstein A Coefficient
- This page covers oscillator strength and Einstein \(A\) coefficients linked to atomic transitions, differentiating their applications for absorption and emission lines. It explains atomic transitions, radiation emission, and the relationships governing transition rates and lifetimes. Measurement techniques for oscillator strengths are discussed, along with the definition and significance of transition probabilities.
- 9.4: Einstein B Coefficient
- This page explores atomic transitions by discussing oscillator strengths, Einstein coefficients, and their relationships to absorption and emission processes. It defines key concepts like absorption oscillator strength, emission oscillator strength, and generalized weighted oscillator strength. The text clarifies the complexities of Einstein \(B\) coefficients, induced transitions, and atomic level populations.
- 9.5: Line Strength
- This page explores line strength in spectroscopy, defining its intensity and theoretical significance. It contrasts emission (Einstein coefficient) and absorption (oscillator strength) parameters, detailing the calculation of line strengths, especially for hydrogen-like atoms. The relationship between line strengths, transition moments, and their symmetry in emission and absorption is examined.
- 9.6: LS-coupling
- This page covers the calculation of transition moments and line strengths in LS-coupling, detailing the challenges of determining absolute values and introducing key formulas. It differentiates between two types of multiplets based on changes in angular momentum and highlights the strongest main lines versus weaker satellite lines.
- 9.7: Atomic hydrogen
- This page discusses the oscillator strength of the \(\text{H}\alpha\) line, which encompasses various transition components, including multiplets and splits. By using the hydrogen atom's wavefunction, one can calculate these strengths and determine the overall \(\text{H}\alpha\) strength. Additionally, it highlights the significance of the weighted oscillator strength \(ϖf\) in understanding transition probabilities, specifically for the Lyman and Balmer series.
- 9.8: Zeeman Components
- This page explores the strengths of Zeeman components in spectral lines, detailing how the relative strengths depend on the angular momentum quantum numbers \(J\) and magnetic quantum numbers \(M\). It provides formulas for calculating these strengths and includes examples demonstrating the normalization process. The section distinguishes between resolved and unresolved component strengths across varying Zeeman patterns.
- 9.9: Summary of Relations Between f, A and S
- This page provides an overview of the Einstein coefficients \(A\) and \(B\) in emission spectroscopy, detailing definitions, applications, and relevant symbols. It explores the relationships between electric dipole radiation properties and includes equations linking radiation energy density with the coefficients.