The Franck—Condon Principle in Bound‐Free Transitions

Heavy Rydberg Photo-dissociation Cross-section Calculations and Experimental Progress Towards Cold Collisions in Lithium

“…One such normalization is an energy normalization [15] which may on occasion generate exact analytical results. A second method involves placing the system in an infinite potential well, box normalization [16], such that states at all energies are bound, with states in the previously continuous regime becoming discretized due to the box. Any results found using this method will converge towards the correct value for an increasing radius of confinement; the case as the radius of confinement approaches infinity is that of the unbound system.…”

Bound→free and bound→bound multichannel emission spectra from selectively excited Rydberg states in the ZnAr and CdAr van der Waals complexes

“…It has to be emphasized however, that in any of the above Rydberg-state studies emission spectra in MRg complexes have not been observed, except one investigation. For the HgAr, Duval et al [4] recorded dispersed emission bound→bound spectra using the C 3 1(7 3 S 1 ), 𝜐 ′ = 3 → A 3 0 + (6 3 P 1 ), 𝜐′′, C 3 1, 𝜐 ′ = 14,19 → a 3 0 − (6 3 P 0 ), 𝜐′′ and C 3 1, 𝜐 ′ = 2,4,14 → b 3 2(6 3 P 2 ), c 3 1(6 3 P 2 ), d 3 0 − (6 3 P 2 ), 𝜐′′ transitions, as well as long bound→free undulated CID reflection [20] patterns using the 𝐶 3 1, 𝜐 ′ = 3, 11 → a 3 0 − , C 3 1, 𝜐 ′ = 2, 10 → A 3 0 + , B 3 1 and C 3 1, 𝜐 ′ = 3, 14 → b 3 2, c 3 1, d 3 0 − transitions; it allowed to probe and determine lower-lying state potentials including their repulsive branches.…”

Elucidating Fermi's golden rule via bound-to-bound transitions in a confined hydrogen atom

“…a radial wavefunction with zero amplitude) and show that multiplication by ρ(W ) (which is infinite) gives energy-normalized finite-amplitude wavefunctions satisfying Eq. (10). The left hand side of this equation takes the form…”

“…The first method uses a particular form of normalization for the continuum states called energy-normalization, 9 which we introduce below. The second method involves placing the system in an infinite well (box normalization) 10 which causes all states to be bound so that states in the previously continuous regime become discretized, allowing the familiar techniques from a bound-to-bound approach to be used to perform bound-to-continuum calculations.…”

“…(10) to the asymptotic form of the radial wavefunction, and these result in wavefunctions that when multiplied by r tends to an oscillatory function with constant amplitude of a 2 0 π 2 W Ry −1/4 for large r. 10 Note that for W = − Ry n 2 the functional form of Eq. (12), which contains 1 F 1 (a; b; z), the confluent hypergeometric function, 23 reduces to that of the well-known generalized Laguerre polynomials for hydrogenic bound states.…”