By Philip George Burke

Commencing with a self-contained evaluate of atomic collision concept, this monograph offers fresh advancements of R-matrix idea and its functions to a wide-range of atomic molecular and optical techniques. those advancements contain electron and photon collisions with atoms, ions and molecules required within the research of laboratory and astrophysical plasmas, multiphoton methods required within the research of superintense laser interactions with atoms and molecules and positron collisions with atoms and molecules required in antimatter reviews of clinical and technologial significance. uncomplicated mathematical effects and common and conventional R-matrix machine courses are summarized within the appendices.

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Also the sign of the potential strength A is chosen so that it is positive for attractive potentials and negative for repulsive potentials. We show in Fig. 124) for three different potential strengths. The first example, shown in Fig. 5, the second example, shown in Fig. 3b, corresponds to a weak attractive potential which does not support a bound state where a0 = −1 and the third example, shown in Fig. 3c, corresponds to a stronger attractive potential which supports one bound state where a0 = 2.

4 Effective Range Theory 23 which we assume is energy independent. 107), where the non-resonant background scattering is zero. Case (c) with q = 0 corresponds to a window resonance where the background scattering has its maximum value allowed by unitarity. Finally, cases (b) and (d) are intermediate cases where the resonance shapes are asymmetric. When several resonance poles lie in the lower half k-plane and close to the positive real k-axis their effects on the cross section may overlap. 111) where the position of the jth pole is E = E j − 12 iΓ j .

5, is that it does not tend to nπ radians at threshold energy. This is in contrast to the phase shift for scattering by neutral targets which tends to a multiple of π radians as the scattering energy tends to zero. 70) is effective, even for nonzero angular momenta. 197) to be non-zero at threshold. When the Coulomb potential Uc (r ) is repulsive, which is the situation when electrons scatter from negative ions or positrons scatter from positive ions, the scattered electron or positron is kept away from the target at low energies and the phase shift vanishes rapidly as the energy tends to zero.