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Download Molecules and clusters in intense laser fields by Jan Posthumus PDF

By Jan Posthumus

This ebook presents a radical advent to the physics of molecules and clusters in excessive laser fields. It provides either theoretical and experimental features of the topic, and covers new study within the sector of clusters in extreme laser fields. The e-book discusses femto moment pulse construction and diagnostics, and covers diatomic and polyatomic molecules, in addition to coherent regulate. This booklet could be of curiosity to graduate scholars and researchers in atomic, molecular and optical physics. it is going to even be appropriate as a reference textual content for complicated physics classes.

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120). If s ≤ 2 + 3 the integral diverges and the first term in the effective range expansion is no longer defined. 138) only converges for large r if s > 2 + 5 and consequently if s ≤ 2 + 5 the second term in the effective range expansion is not defined. 139) and so on for higher terms in the effective range expansion. An important example of long-range potentials occurs in elastic electron scattering by an atom in a non-degenerate s-wave ground state such as atomic hydrogen or the inert gases.

The radial Schrödinger equation then has the asymptotic form ( + 1) A d2 − − 2 + k 2 u (r ) = 0, 2 2 dr r r r ≥a. 150) which has the solution λ = − 12 ± 1 2 (2 + 1)2 + 4A 1/2 . 149) reduces to the standard form d2 λ(λ + 1) − + k 2 u (r ) = 0, dr 2 r2 r ≥a. 152) where λ is in general a non-integral quantity. 151) so that λ → in the limit A → 0. 155) which defines the K -matrix K λ (k). 155). 156) where τ = 12 π( − λ) . 157) It follows that when A = 0 then = λ and K (k) = K λ (k). 118) by relating K λ (k) to the R-matrix on the boundary r = a.

120) that the low-energy s-wave cross section σ0 = 4πa02 1 4π 4π 2 = sin δ (k) = . 127) The zero-energy cross section is thus 4πa02 . Also, when an s-wave bound state occurs at zero energy then the scattering length and hence the cross section is infinite. We now determine the behaviour of the cross section when an s-wave bound state occurs close to zero energy. 26) that T (k) = S (k) − 1 = 2i . 128) Hence a pole in the S- and T -matrices occurs when cot δ (k) = i. However, we saw in Sect. 3, see Fig.

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