Weakly bound states

Molecular adsorbates usually cover a substrate with a single layer, after which the surface becomes passive with respect to fiirther adsorption. The actual saturation coverage varies from system to system, and is often detenumed by the strength of the repulsive interactions between neighbouring adsorbates. Some molecules will remain intact upon adsorption, while others will adsorb dissociatively. This is often a frinction of the surface temperature and composition. There are also often multiple adsorption states, in which the stronger, more tightly bound states fill first, and the more weakly bound states fill last. The factors that control adsorbate behaviour depend on the complex interactions between adsorbates and the substrate, and between the adsorbates themselves. 

A weakly bound state is necessarily nonrelativistic, v Za (see discussion of the electron in the field of a Coulomb center above). Hence, there are two small parameters in a weakly bound state, namely, the fine structure constant a. and nonrelativistic velocity v Za. In the leading approximation weakly bound states are essentially quantum mechanical systems, and do not require quantum field theory for their description. But a nonrelativistic quantum mechanical description does not provide an unambiguous way for calculation of higher order corrections, when recoil and many particle effects become important. On the other hand the Bethe-Salpeter equation provides an explicit quantum field theory framework for discussion of bound states, both weakly and strongly bound. Just due to generality of the Bethe-Salpeter formalism separation of the basic nonrelativistic dynamics for weakly bound states becomes difficult, and systematic extraction of high order corrections over a and V Za becomes prohibitively complicated. 

Danby, G. and Tennyson, J. (1988). Positron-HF collisions prediction of a weakly bound state. Phys. Rev. Lett. 61 2737-2739. 

V. Efimov, Weakly-bound states of three resonantly-interacting particles, Sov. J. Nucl. Phys. 12 (1971) 589 [Yad. Fiz. 12 (1970) 1080],... 

In some cases when electron trapping leads to formation of the weakly bound state, S- (it may also takes place in reaction with hot electrons), reaction e+ +S —> Ps becomes possible and should be taken into account. On the contrary, in the case of a strongly bound electron and sufficient affinity of S to the positron, this reaction may lead to e+S complex formation and, therefore, decreased Ps yield. 

The low energy elastic scattering cross section may become quite large if there is a weakly bound state or a nearby virtual state. For a nonpolarizable... 

In the period 1940-1946, Ogg (132) developed the first quantitative theory for the solvated electron states in liquid ammonia. The Ogg description relied primarily on the picture of a particle in a box. A spherical cavity of radius R is assumed around the electron, and the ammonia molecules create an effective spherical potential well with an infinitely high repulsive barrier to the electron. It is this latter feature that does not satisfactorily represent the relatively weakly bound states of the excess electron (9,103). However, the idea of a potential cavity formed the basis of subsequent theoretical treatments. Indeed, as Brodsky and Tsarevsky (9) have recently pointed out, the simple approach used by Ogg for the excess electron in ammonia forms the basis of the modem theory (157) of localized excess-electron states in the nonpolar, rare-gas systems. [The similarities between the current treatments of trapped H atoms and excess electrons in the rare-gas solids has also recently been reviewed by Edwards (59).]... 

Bethe region (A Z 7). This interesting feature persists for a non-quasiclassical Morse well (see Section 4) and can be also seen in the results of accurate numerical calculations for a system with a reahstic potential (see Section 6). Of course, the prerequisite of these effects is an existence of a weakly bound state. 

Note that this ratio does not depend onT, that is on the energy of a weakly-bound state. We also see that depending on k, the low-energy (M l) VR cross section can be suppressed or enhanced compared to the quasiclassical cross section The... 

Two liming expressions for B(k) correspond to a pure repulsive potential (k ,—>0) and a potential that supports a single weakly-bound state (Ak ,=k ,-1/2 1)... 

N2, NH3, NO, CO, and O2.—Considerable success has resulted from the application of sophisticated techniques to the study of these small molecules. Changes of morphology on Pt single crystal spheres have been observed during oxidation of NH3, CaHs, and CO. A weakly bound state appears in N2 adsorption on Fe(lll), but not on Fe(lOO), and there are similarities observed between N on Fe(lOO) at 6 0.5, and Fe4N. Reconstruction of Fe(lll) occurs on covering the surface with N and this can be related to work by Boudart et al, on small particles. N2 weakly bound states have been observed for polycrystalline Fe and Kishi and Roberts have related this to the mechanism of adsorption and dissociation. No evidence for weakly bound N2 on Pt(lll) at r > 165 K has been found. 

The addition of hh to Zi in equation (20) accounts for the lack of Wh electrons in the empty bound states. The number of holes not only determines the total number of electronic states, but also how many of them are bound. As decreases, the outer bound orbitals merge into the continuum, without appreciably varying their spatial shape. This means that the screening by a low-lying orbital in the continuum is very similar to that of a weakly bound state. 

If, on the contrary, anharmonicity is weak ( A particle states. But inside the band of two-particle states, as shown by Pitaevsky (38), only weakly bound states of biphonons are formed (even for the smallest value of A it is necessary, of course, that the value of the binding energy of the biphonon be greater than the width 6 of the phonon level regarding the feasibility of observing the states discussed by Pitaevsky(38), see below). 

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