Semiclassical calculation of matrix elements

More, R.M.; Warren, K.H.

doi:10.1016/0003-4916(91)90060-l

Cited by 40 publications

(10 citation statements)

References 22 publications

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“…In astrophysical plasmas of compact objects and laboratory inertial confinement fusion plasmas, many authors have investigated the screened interaction potentials to study the effect of the plasma environment upon the process of electron-ion collisional excitations in weakly coupled plasmas using the Debye-Hückel interaction potentials. [6][7][8]11 This Debye-Hückel potential describes the properties of a low-density plasma and corresponds to a pair correlation approximation. The plasma described by the Debye-Hückel model is called ideal plasma, since the average energy of interaction between plasma particles is small compared to the average kinetic energy of the particle.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical inelastic electron-ion collisional excitations in nonideal plasmas

Yoon

2000

Physics of Plasmas

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Semiclassical electron-hydrogenic ion collisional excitation cross sections for 1s→2s and 1s →2p 0 in nonideal plasmas are obtained. An effective pseudopotential model taking into account the plasma screening and collective effects is applied to describe the electron-ion interaction potential in a classical nonideal plasma. The semiclassical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the total inelastic scattering cross section as a function of the projectile energy, nonideal plasma parameter, and Debye length. It is found that the transition probabilities in ideal plasmas described by the Debye-Hückel potential model are greater than those in nonideal plasmas described by the pseudopotential model. The maximum position of the transition probability gets closer to the target core as the projectile energy increases. It is also found that the scaled cross section decreases when the nonideal plasma parameter (␥) is increased, i.e., the nonideality of plasmas reduces the electron-ion collision cross section.

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Section: Introductionmentioning

confidence: 99%

Semiclassical inelastic electron-ion collisional excitations in nonideal plasmas

Yoon

2000

Physics of Plasmas

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“…With the semiclassical wave function at hand and using the restricted interference approximation [21] one can now calculate the transition matrix elements which enter the transition rates in Equation 15.31. Upon inserting these transition rates into the time evolution Equation 15.29, an expansion in powers ofh can be performed, where one has to keep in mind, however, that for energies near the barrier top reflection and transmission probabilities are of order 1, particularly with T (E = V b ) = R(E = V b ) = 1/2.…”

Section: Escape Over a Potential Barriermentioning

confidence: 99%

Tunneling of Ultracold Atoms in Time-Independent Potentials

Arimondo¹,

Wimberger²

2011

Dynamical Tunneling

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“…For the calculation of the matrix elements they replaced the quantum numbers n and l in the hydrogenic wave equation by n D n nl and l D l nl . Here Lebedev and Beigman (1998) summarize alternative methods for the calculation of radial integrals especially suitable for highly excited (Rydberg) atoms and ions: semiclassical (J-W-K-B) (Sobel'man 1992) for hydrogenic atoms, (Davydkin and Zon 1981) for nonhydrogenic atoms, asymptotic (Oertel and Shomo 1968;Picart et al 1978;Edmonds et al 1979), and saddle point (J-W-K-B) (More and Warren 1991). The semiclassical expression for the radial matrix element involves Anger functions (Abramowitz andStegun 1964/1972).…”

Section: Bound-bound Processesmentioning

confidence: 99%