Bound states of a charged particle in a dipole field

Crawford, Oakley H.

doi:10.1088/0370-1328/91/2/303

Cited by 230 publications

(93 citation statements)

References 9 publications

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“…To obtain this critical dipole value, we investigate Eq. (3.8) with Table 4 for large N. The values obtained in this Table agree with those already reported long ago by Crawford in [10]. …”

Section: Pure Dipole Interactionsupporting

confidence: 92%

Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

Alhaidari

2008

Annals of Physics

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We relax the usual diagonal constraint on the matrix representation of the eigenvalue wave equation by allowing it to be tridiagonal. This results in a larger solution space that incorporates an exact analytic solution for the non-central electric dipole potential 2 cos r θ , which was known not to belong to the class of exactly solvable potentials. As a result, we were able to obtain an exact analytic solution of the three-dimensional timeindependent Schrödinger equation for a charged particle in the field of a point electric dipole that could carry a nonzero net charge. This problem models the interaction of an electron with a molecule (neutral or ionized) that has a permanent electric dipole moment. The solution is written as a series of square integrable functions that support a tridiagonal matrix representation for the angular and radial components of the wave operator. Moreover, this solution is for all energies, the discrete (for bound states) as well as the continuous (for scattering states). The expansion coefficients of the radial and angular components of the wavefunction are written in terms of orthogonal polynomials satisfying three-term recursion relations. For the Coulomb-free case, where the molecule is neutral, we calculate critical values for its dipole moment below which no electron capture is allowed. These critical values are obtained not only for the ground state, where it agrees with already known results, but also for excited states as well.

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“…To obtain this critical dipole value, we investigate Eq. (3.8) with Table 4 for large N. The values obtained in this Table agree with those already reported long ago by Crawford in [10]. …”

Section: Pure Dipole Interactionsupporting

confidence: 92%

Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

Alhaidari

2008

Annals of Physics

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“…Some of these critical dipole moments are shown in table 2; they agree with the values obtained by Fermi and Teller [27] and Crawford [28]. The condition µ > µ crit guarantees binding by either a point-like or finite dipole.…”

Section: Angular Equationsupporting

confidence: 84%

Effect of dipole polarizability on positron binding by strongly polar molecules

Gribakin

Swann

2015

J. Phys. B: At. Mol. Opt. Phys.

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Abstract.A model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron-positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including the polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies for a range of polar organic molecules and hydrogen cyanide. The model also agrees with the linear dependence of the binding energies on the polarizability inferred from the experimental data [Danielson et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 235203]. The effective core radii, however, remain unphysically small for most molecules. Treating molecular polarization nonperturbatively leads to physically meaningful core radii for all of the molecules studied and enables even more accurate predictions of binding energies to be made for nearly all of the molecules considered.

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“…in going from the neutral to the HF anion. This, 2 in turn, causes a more localized dipole-bound electron and increased importance of ⌬ E M P 2 . Due to…”

Section: žmentioning

confidence: 99%

Energies of dipole-bound anionic states

Gutowski

Skurski

Jordan

et al. 1997

Int. J. Quant. Chem.

102

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Ž. Dipole-bound anionic states of CH CN, C H , and HF were studied using highly 3 3 2 2 correlated electronic structure methods and extended one-electron basis sets. The electron detachment energies were calculated using the coupled cluster method with single, double, and noniterative triple excitations. Geometrical relaxation of the molecular framework upon electron attachment and the difference in the harmonic zero-point vibrational energies between the neutral and the dipole-bound anionic species were calculated at the MP2 level of theory. We demonstrate that the dispersion interaction between the loosely bound electron and the electrons of the neutral molecule is an important component of the electron binding energy, comparable in magnitude to the electrostatic electrondipole stabilization. The geometrical relaxation upon electron attachment and the change in the zero-point vibrational energy is important for the weakly bound HF dimer. The predicted values of the vertical electron detachment energies for the dipole bound states of CH CN and C H of 112 and 188 cm y1 , 3 3 2 respectively, are in excellent agreement with the recent experimental results of 93 and y1 Ž. y 171 " 50 cm , respectively. For HF , the predicted value of adiabatic electron 2 detachment energy is 396 cm y1 , whereas the experimental vertical detachment energy is 508 " 24 cm y1. The possibility of formation of the neutral dimer in an excited vibrational state is considered.

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Bound states of a charged particle in a dipole field

Cited by 230 publications

References 9 publications

Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

Analytic solution of the wave equation for an electron in the field of a molecule with an electric dipole moment

Effect of dipole polarizability on positron binding by strongly polar molecules

Energies of dipole-bound anionic states

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