Inner bound states

Unlike iNOS and nNOS, the eNOS protein is post-translationally modified by the attachment of fatty acids, myristate or palmitate. This modification is important because the fatty acids help to attach the enzyme, in an inactive form, to the inner face of plasma membrane of endothelial cells or platelets. Several mechanisms serve to release eNOS from its membrane bound state and thus activate the enzyme. 

Indirect photodissociation involves two more or less separate steps the absorption of the photon and the fragmentation of the excited complex. Resonances, which mirror the quasi-bound states of the intermediate complex in the upper electronic state, are the main features. They have an inherently quantum mechanical origin. If we consider — in very general terms — the inner region, before the fragments have obtained their identities, as the transition state, then the resolution of resonance structures in the absorption spectrum manifests transition state spectroscopy in the original sense of the word (Foth, Polanyi, and Telle 1982 Brooks 1988). 

Figure 24 Model cases for the potential energy curve crossing between a bound and dissociative state, (a) The potential energy curves cross approximately at right angles. This is often the case when the dissociative state intersects the bound state on its outer limb, i.e., at bond distances longer than its equilibrium internuclear separation, (b) Bound and dissociative state exhibit similar slopes and cross on the inner limb of the bound state, (c) The dissociative state crosses the bound potential both on the inner and outer limbs.

When the nuclear charge changes due to radioactive decay and/or an inner-shell vacancy is produced, the bound electrons in the same atom or molecule experience the sudden change in the central potential and have a small but finite probability to be excited to an unoccupied bound state (shakeup) or ejected to the continuum (shakeoff). We calculated the shakeup-plu.s-shakeoff probabilities accompanying PI and EC using the method of Carlson and Nestor [45]. 

An inner-shell electron can be excited by photoabsorption to a bound state below the ionization threshold. From such an excited state Auger electrons are also emitted. This makes the structure of Auger spectra simple because the spectra are free from the shake-off peak due to multiple ionization. Aksela et al. [26] have studied F KVV Auger spectra emitted from a series of fluorides by use of the synchrotron radiation. Spectra taken from LiF and KF are shown in Figs. 14 16 as typical examples. 

Fig. 1 Conceptual energy landscapes for bound states c confined by sharp activation barriers. Oriented at an angle 9 to the molecular coordinate x, external force / adds a mechanical potential — (/cos 6)x that tilts the landscape and lowers the barrier. For sharp barriers, the energy contours local to barriers—transition states s —are highly curved and change little in shape or location under force, (a) A single barrier under force, (b) A cascade of barriers under force. The inner barrier emerges to dominate kinetics when the outer barrier is driven below it by k T.

The one-dimensional potential depicted in Fig. 7(a) provides an illustration of this effect. The Schrodinger equation can be solved with the method used for the square-well case above. Each well gives rise to a nearly independent progression of states. For fi = 2p = 1 and other potential parameters indicated in Fig. 7 one finds that the system has two bound states and a resonance state at 9.46 — i 0.11 localized above the deep outer well. There is also another resonance in the system, E = 9.8 - i 0.002. Its width is very small because this state belongs to the shallow inner well, which is separated from the continuum by a potential barrier. Suppose that we force — by varying a parameter in the Hamiltonian — the narrow state (denoted n) in the shallow well to move across the broader resonance (b) belonging to the deep minimum. The relative positions of the two states can be, for example, controlled by shifting the infinite wall at the... 

A quantitative compaiison of our theory with existing measurements of the energy loss of antiprotons [13] (which unlike protons carry no bound states) in a variety of target materials can be achieved by combining our first-principles calculations of the Zj (linear-response) stopping power with Zj corrections in a FEG. Nevertheless, a comparison with experiment still requires the inclusion of losses from the inner shells, xc effects, and higher-order nonlinear terms. Work in this direction is now in progress. 

Recapitulation will be discussed in more detail in section 3.4. As n increases, the number of nodes also increases and, as n — oo, the inner nodes coincide with those of a continuum functions. In fact, the positions of the nodes determine the phase of the continuum function (which is oscillatory) at threshold. There is a simple relation between the phase shift above threshold and the quantum defect of the bound states, which will be explained in chapter 3. If the eigenfunctions recapitulate, i.e. the positions of the nodes are nearly constant, then it follows that the... 

Recapitulation is an important property because it provides us with an immediate interpretation of the physical meaning of the quantum defect p for large enough n, the bound state wavefunctions possess an oscillatory inner part which defines a phase, and is nearly independent of energy if p is nearly constant in energy. A change in the value of p corresponds to a shift in the radial position of all the nodes. As one tends to the series limit, the oscillatory part grows. Continuum functions, of course, become... 

The SCF potential is well represented by a Morse potential in the inner well (see fig. 5.10) we obtain an analytic form for the wavefunction of the bound state, and we can compare the analytic wavefunction with the numerical solution. It is apparent from the figure that they agree excellently. Since the Morse potential has no outer well, the properties of the collapsed orbital are entirely determined by the inner well and, since 0.6, it is clear that the binding condition is satisfied in the case of La. 

In this way, we may picture orbital contraction as a purely quantum-mechanical effect, which arises from the existence of a short range well within the atom. The binding strength of this well increases with atomic number and, as a result, the critical condition for the appearance of the first bound state is satisfied around Z = 56. The condition for two bound states to occur inside the inner well is satisfied in a similar way at the onset of the 5/ period, giving rise to the actinide sequence. 

As shown by Berry [220], the phase shift increases by % at each shape resonance for positive energies above threshold. When the 4/ function drops into the inner well, 5/ moves to occupy the position of 4/ before collapse, 6/ moves to play the role of 5/, etc [201]. As far as QDT is concerned, p relates to the Rydberg energy formula applied in the outer well. Thus, if p = n—v is written with n obtained by node counting, there will be an error of 1, because in fact one should use p = n—l — v when the resonance drops below the bound states. Consequently, Seaton s theorem becomes... 

Fig. 5.14. Quantum defect plots for the centrifugally distorted nf series in Ba+ (a) shows the ordinary QDT plot, while (b) shows the plot obtained from the same experimental data using the generalised theory in the text. Note that the lowest point in the nf channel lies off the graph this is normal, since it has no node except at the origin and the corresponding wavefunction lies mostly in the non-Coulombic part of the potential (c) shows how the energy of the bound state can also be obtained by fitting a Morse potential to the Hartree-Fock potential of the inner well (after J.-P. Connerade [217]).

---