Structure of Resonances in Electron Scattering by Hydrogen Atoms

Abstract

A study of the structure of resonances just below the n = 2 excitation threshold in electron scattering by hydrogen atoms is carried out by utilizing an approximate method adopted from the projection-operator formalism. Analytic expressions for the level width near the threshold are obtained for both the singlet-and triplet-compound-state series with zero total angular momentum. It is found that the level widths behave like the level spacings in that they decrease exponentially as the levels approach the threshold. Nevertheless, the ratio between the level spacings and widths remains a constant less than 1. It is then concluded from the study that within the approximations adopted in the method, neither the singlet nor triplet series of the compound states become overlapping near the threshold. However, the Lamb shift may, by removing the degeneracy in the n -2 levels, cut off these infinite sequences of compound states, thereby restricting the number of allowed resonances. The interference between potential and resonance scatterings is also examined.

Observation of a triplet D-wave resonance below the H excitation threshold in electron - hydrogen scattering

“…These resonances have also been confirmed in various experiments (Sanche and Burrow 1972, Williams 1976, Warner et al 1986. A couple of other resonances, including the triplet S-wave 3 S e and the singlet P-wave 1 P o , have also been found below this threshold by various authors (see, for example, Seiler et al 1971, Chen 1967, Sadeghpour 1992 and other references therein). However, no triplet D-wave resonance ( 3 D e ) has been seen in any list of the resonances observed.…”

Resonant Charge Exchange of the Negative Ions in Slow Collisions with Atoms

“…where Fj w (#>^) ar e the normalized spherical harmonics, and r 0 is the effective range of the atomic potential" On the sphere S 2 (R»r) the radial part of the function ^(fj can be represented in the form B 1 (r 1 )=/e 1 U + AR)=/2 1 (/2) e 0rCOsa , (14) where /3 = y + (A^) _1 ln[l + (AR/R)], Ai?=-rcos6>, and for R»\AR\,…”

“…(13), (14), and (17), we have ( \ m i r or i\ h \f~lV 2 im \W , ( + v (-) l \ 2L+1) (1, + mJl e ^ * l(r i } = 72^T)TT L 2~~ (Z^mJlJ "(2^ be multiplied by a factor P $ which is just the square of the corresponding Clebsch-Gordan coefficient. When one electron is captured and the atomic core has spin zero, the spin factor P s is R^R) sin l Br l e^ /R l .…”

Low-Energy e-He(21L) Scattering Calculations

“…(14) in I), but they depend on the en ergy of the lowest lying bound state in the cor responding dipole potential Vy (see e.g. Chen [12]), which in our case is not known. Besides, since for small 12 values the internal region is important, and there Vy deviate considerably from their asymptotic form, we calculate the corresponding § matrix ele ments by a matching procedure, without making use of (14) from I.…”