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Exercise 3.2 - Show that the integral under the absorption cross-section in Eq. (3.18), $\sigma = \frac{|q_a|^2}{\epsilon_0 m_a c \gamma} \frac{(\gamma/2)^2}{(\gamma/2)^2 + (\omega_0 - \omega)^2}$, from a detuning, $(\omega_0 - \omega)$, of $-\infty$ to $+\infty$ is independent of the line width of the resonance.

          Exercise 3.2 - Show that the integral under the absorption cross-section in Eq.
(3.18),
$\sigma = \frac{|q_a|^2}{\epsilon_0 m_a c \gamma} \frac{(\gamma/2)^2}{(\gamma/2)^2 + (\omega_0 - \omega)^2}$,
from a detuning, $(\omega_0 - \omega)$, of $-\infty$ to $+\infty$ is independent of the line width of the
resonance.

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Exercise 3.2 - Show that the integral under the absorption cross-section in Eq.
(3.18),
σ = (|qa|^2)/(ϵ0 ma c γ)((γ/2)^2)/((γ/2)^2 + (ω0 - ω)^2),
from a detuning, (ω0 - ω), of -∞ to +∞ is independent of the line width of the
resonance.

Added by Montserrat M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ameer Said

Step 1

Start with the absorption cross-section equation given in Eq (3.18): σ_abs = (Y/2)^2 ∫ emc(y/2 + √(y^2 - 4)) dy Show more…

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Exercise 3.2 - Show that the integral under the absorption cross-section in Eq (3.18), (Y/2)^2 âˆ« emcyy/2+(=2 resonance.

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