Free-bound transitions

Bound-free transitions, due to photo-ionization of H-like ions of oxygen etc. ... 

We note that line shape calculations may be reduced to near trivial proportions if the basic line profile is approximated by one of the better model profiles mentioned in Chapters 5 and 6. This is generally possible, even advantageous, if the van der Waals bound-bound and bound-free transitions do not shape the spectra significantly. In such a case, the spectra are constructed by a simple superposition of the model line profiles, which is done in seconds even if small (desktop type) computers are used. The simplified line shape calculation has been used successfully on many occasions. Early examples are shown in Figs. 3.11, 3.13, and 3.33, but many more are known [58],... 

A. Bound-Free Transitions into Excited States... 

Stationary spectroscopy on the C and D states of Na3 already indicated the onset of photoinduced fragmentation. Fragmentation becomes more important as the cluster size increases. As a result, nondissociative electronic excitation processes have not yet been observed for free metal clusters larger than trimers [20]. An alternative to conventional spectroscopy of such bound-free transitions was provided by depletion spectroscopy [2]. A deep insight into the dynamics of such photoinduced cluster fragmentation, however, is obtained with ultrafast observation schemes. The principle of such an... 

Figure 19. Excitation scheme for probing bound-free transitions. Initially the photoion of the mother molecule appears. After dissociation, however, the relating fragment ion is observed.

Figure 23. Pump and probe spectra of a two-color experiment probing bound-free transitions in K (3 < n < 9). For At < 0, Epump = 1.47 eV and Eprobe = 2.94 eV for At > 0, Epump — 2.94 eV and Eprobe = 1.47 eV [23],...

First, we describe briefly the calculation of the absorption spectrum for bound-bound transitions. In order to keep the presentation as clear as possible we consider the simplest polyatomic molecule, a linear triatom ABC as illustrated in Figure 2.1. The motion of the three atoms is confined to a straight line overall rotation and bending vibration are not taken into account. This simple model serves to define the Jacobi coordinates, which we will later use to describe dissociation processes, and to elucidate the differences between bound-bound and bound-free transitions. We consider an electronic transition from the electronic ground state (k = 0) to an excited electronic state (k = 1) whose potential is also binding (see the lower part of Figure 2.2 the case of a repulsive upper state follows in Section 2.5). The superscripts nu and el will be omitted in what follows. Furthermore, the labels k used to distinguish the electronic states are retained only if necessary. 

In Section 2.1 we derived the expression for the transition rate kfi (2.22) by expanding the time-dependent wavefunction P(t) in terms of orthogonal and complete stationary wavefunctions Fa [see Equation (2.9)]. For bound-free transitions we proceed in the same way with the exception that the expansion functions for the nuclear part of the total wavefunction are continuum rather than bound-state wavefunctions. The definition and construction of the continuum basis belongs to the field of scattering theory (Wu and Ohmura 1962 Taylor 1972). In the following we present a short summary specialized to the linear triatomic molecule. 

A linear approximation of the potential is certainly too sweeping a simplification. In reality, Vr varies with the internuclear separation and usually rises considerably at short distances. This disturbs the perfect (mirror) reflection in such a way that the blue side of the spectrum (E > Ve) is amplified at the expense of the red side (E < 14).t For a general, nonlinear potential one should use Equations (6.3) and (6.4) instead of (6.6) for an accurate calculation of the spectrum. The reflection principle is well known in spectroscopy (Herzberg 1950 ch.VII Tellinghuisen 1987) the review article of Tellinghuisen (1985) provides a comprehensive list of references. For a semiclassical analysis of bound-free transition matrix elements see Child (1980, 1991 ch.5), for example. 

In the time-independent formulation, the absorption cross section is proportional to (4>/(.R .E) i(R] E )) 2. Approximate expressions may be derived in several ways. One possibility is to employ the semiclas-sical WKB approximation of the continuum wavefunction (Child 1980 Tellinghuisen 1985 Child 1991 ch.5). Alternatively, one may linearly approximate the excited-state potential around the turning point and solve the Schrodinger equation for the continuum wavefunction in terms of Airy functions (Freed and Band 1977). Both approaches yield rather accurate but quite involved expressions for bound-free transition matrix elements. Therefore, we confine the subsequent discussion to a merely qualitative illustration as depicted in Figure 6.2. 

Tellinghuisen, J. (1985). The Flranck-Condon principle in bound-free transitions, in Photodissociation and Photoionization, ed. K.P. Lawley (Wiley, New York). 

Thus the excitation pulse can create a superposition of i), 2) consisting of two states of different reflection symmetry. The resultant superposition possesses no symmetry properties with respect to reflection [78]. We now show that the broken symmetry created by this excitation of nondegenerate bound states translates into a nonsymmetry in the probability of populating the degenerate , n, D ), , n, L ) continuum states upon subsequent excitation. To do so we examine the properties of the bound-free transition matrix elements ( , n, q de,g Ek) that enter into the probability of dissociation. Note first that although the continuum states , n, q ) are nonsymmetric with respect to reflection, we can define symmetric and antisymmetric continuum eigenfunctions , n, s ) and , n, a ) via the relations... 

Bound—Free Transitions in Weakly Bound Metal Aggregates... 

Supersonic expansions have been used to form small metal aggregates, (2 < n < 4). Emphasis is placed on the analysis of bound-free transitions in these small metal clusters. Discussion focuses on the characterization of variously produced sodium supersonic expansions and the analysis of laser Induced atomic fluorescence resulting from the photodissociation of triatomic sodium clusters. We will consider (1) the nature of observed "fluctuation" bands corresponding to bound-free transitions involving a repulsive excited state which dissociates to yield (Na-D line) sodium atoms and ground state,, ... 

Given the fact that we have observed photodissociation from "hot bands" of the sodium trlmer, it should be possible to alleviate this hot band structure and in this way obtain photodissociation spectra which result only from the pumping of bound-free transitions involving cooled sodium trlmer. 

The intensities of the 83/2 and Pi/2 fluctuation bands in Figure 8 are in the ratio 2 to 1, virtually a statistical distribution however, the relative Intensity distributions for the Pi/2 and Pa/2 fluctuation bands differ notably. Much more pronounced differences are observed for the "hot bands" depicted in Figures 6 and 7 where the P3/2/ Pi/2 ratio varies with exciting frequency and in many instances approaches 8/1. This difference in intensity ratio must reflect very different geometries for the lower discrete states from which pumping occurs in bound-free transition. Again such a result would appear to correlate well with the theoretical analysis of the sodium trimer surface. Martin and Davidson predict that a linear symmetric conformation lies only 1050 cm above the ground... 

Further studies indicate that the phenomena characterized here can be extended to the study of other bound-free transitions, furnishing a means of mapping the repulsive states which characterize small metal clusters (51). This may have significant importance for the characterization of photocatalytic processes. Further it appears that one can make use of the shallow nature of the bonding potentials characterizing many metal clusters and supersonic expansions in general to obtain "hot band" structure... 

By optical excitation with argon and krypton laser lines, continuous laser oscillation on A -> X and B -> X transitions of Li Na2 and K molecules can be achieved dimer lasers show such interesting features as multiline emission, extremely low threshold pump intensities and forward-backward amplification asymmetry. Basic principles, operating conditions and applications of these lasers will be discussed. The dimer lasers operate between bound electronic states, resulting in the emission of discrete lines. To achieve tunable laser oscillation, continuous emission bands from bound-free transitions have to be considered. Some possibilities for alkali dimers are outlined and recent spectroscopic investigations on UV excited diffuse bands are reported. 

LIF from Brj excited by 158 nm radiation (F2 laser) has been observed and interpreted. Oscillatory continuum emission, involving three bound-free transitions, dominates in the region 210—440 nm. Collisional interstate transfer in the presence of SF< Nj, and He was found to be efficient and was discussed in terms of a possible optically pumped Bra laser. 

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