Zero-range Potential Approximation Research Articles

Positron scattering by the Ar2 and Xe2 dimers

Positron scattering by Ar2 and Xe2 dimers are studied for low incident energies. The Zero Range Potential approximation is used and the dimer is modeled as two independent atoms under an internuclear distance constraint. The scattering calculations are performed within the fixed nuclei and the rigid rotor formulations. For the fixed nuclei approximation, analytical expressions are obtained for the positron-dimer scattering length and for the elastic cross section. In the rigid rotor treatment, an analytical expression is obtained for the rotational excitation cross sections. The main results obtained in this investigation are that the short-range interaction between the positron and the molecular dimer is the dominant mechanism for rotational excitation in this energy range. Such effect is explained by the small values of the quadrupole moments of the Ar2 and Xe2 dimers.

Zero range potential approximation in quantum scattering problems

This article presents the Zero Range Potential (ZRP) approximation as an alternative to treat quantum scattering problems. The main focus is to provide an undergraduate-level derivation of the ZRP boundary condition that describes the interaction between an electron and a potential, using the spherical-potential-well analytical solutions. The validity of the approximation is discussed qualitatively and quantitatively. Finally, the ZRP approximation is applied to the scattering of an electron by an atom, comparing the results obtained with modern experimental measurements.

Spatial distribution of a hole localized on a magnetic acceptor in cubic crystals

The wave-function of a hole localized on a magnetic ion (Mn) in GaAs is considered. The calculations are based on the zero-range potential approximation. The obtained hole density spatial distribution is in good agreement with the experimental data of STM imaging. The influence of the exchange interaction between a hole and 3d 5-electrons is analyzed. It is predicted that at room temperature this interaction does not change the hole density spatial distribution. The proposed method allows us to take into account additional factors such as deformation and chaotic electrical fields, external magnetic fields, quantum size confinement etc.

Cold Bose gases near Feshbach resonances

The lowest order constrained variational method [Phys. Rev. Lett. 88 (2002) 210403] has been generalized for a dilute (in the sense that the range of interatomic potential, R, is small compared with inter-particle spacing r 0) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na( F=1, m F =1) atoms near the B 0=907 G Feshbach resonance. It is shown that at high densities na 3⪢1, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform condensate for the case of negative scattering length.

Final-state-interaction effects on one- and two-photon detachment ofH−in the presence of a static electric field

We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green's function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.

Quantum proximity resonances

Abstract The zero-range potential approximation is used to show that quantum proximity resonances discussed recently by Heller [Phys. Rev. Lett. 77 (1996) 4122] may also occur in the absence of single-scatterer resonances. It is argued that for two identical scatterers a resonant structure appears in the Σ u -wave rather than in the P -wave partial cross section.

Associative detachment and vibrational excitation in the e--HF system

The electron-HF interaction is formulated in an effective range formalism which takes into account both the long-range dipolar and short-range forces. This formalism extends a previous one of Gauyacq's (1982) in the zero-range potential approximation and allows for an exact treatment of the interaction between the nuclear vibration and the electron motion, in the associative detachment and vibrational excitation processes. The relevant parameters are extracted from the ab initio results of Segal and Wolf (1981) and the corresponding predictions are compared with experimental results. Discussions are presented on the effect of short-range and long-range forces on the peculiarities of the system and on the validity of the adiabatic approximation for nuclear vibration.

On the impact parameter dependence of detached electron energy spectra in H--He collisions

The impact parameter dependence of the energy spectra of neutral atoms produced in H--He collisions has been measured in the collision energy range from 126 to 500 eV using the time of flight (TOF) method. The TOF spectra reproduce the energy spectra of detached electrons, the impact parameter dependence of which are thus established. Excellent agreement with theoretical results in the zero-range potential approximation is obtained.

Nascent product vibrational state distributions of ion–molecule reactions: The H+F−→HF(v)+e− associative detachment reaction

The nascent product vibrational state distribution is obtained for the thermal energy associative detachment reaction H+F−→HF(v?5)+e−, ΔH = −57.0 kcal/mol. The relative vibrational populations are as follows: Nv = 10 = 0.00±0.06; Nv = 20 = 0.23±0.04; Nv = 30 = 0.27±0.03; Nv = 40 = 0.29±0.03; and Nv = 50 = 0.21±0.03. Arguments are presented that suggest that Nv = 00 = 0. The average fraction of the total energy deposited in product vibration is <fv≳ = 0.64±0.03. The release of the very light electron as one of the reaction products places severe angular momentum constraints on the reaction system. A simple kinematic model predicts a highly non-Boltzmann HF rotational state distribution which increases with increasing J up to some cutoff level. The high degree of vibrational excitation in the HF product has been accounted for by theoretical calculations of Gauyacq using the zero-range potential approximation.

Theoretical study of the detachment process in the zero-range potential approximation. H--He collisions

Theoretical study of the detachment process in the zero-range potential approximation. H--He collisions

Theoretical study of the detachment process in the zero-range potential approximation. H--He collisions

A theoretical study of the detachment process in H--He collisions is presented for the 1-103 eV collision energy range. The outer electron of the colliding system is described in the zero-range potential approximation, the relevant parameters of which are extracted from an ab initio calculation of the (HHe)- molecular ion. This enables an exact treatment of the bound-state-continuum transitions induced by the nuclear motion. A very efficient approximation is also proposed to solve the collision problem. A detailed picture of the final state of the system is thus obtained (differential cross sections, total cross sections, spectra of ejected electrons, isotope effect) and compared with experimental data when available.

Electron detachment in low-energy H--Ne collisions: evidence of a purely dynamical phenomenon

The problem of electron detachment in low-energy D-(H-)-Ne collisions (below 30 eV) is studied in a molecular framework: the molecular ion (HNe)- and neutral (HNe) ground states are computed by standard ab initio techniques that provide the input data for the treatment of collisional detachment in the zero-range potential approximation. It is found that the molecular negative ion energy is always below the energy of the neutral molecule, so that the detachment can occur only via direct dynamical transitions from the bound state to the continuum. The present results are found to reproduce fairly well the experimental findings of Champion et al. (1976).