By Aldo Ghizzetti (auth.), Aldo Ghizzetti (eds.)
A. Ghizzetti: a) Lezioni sui procedimenti di quasilinearizzazione e applicazioni. b) Nozioni fondamentali sulle equazioni alle differenze e sulle frazioni continue.- P. Wynn: 4 lectures at the numerical software of endured fractions.- W. Gautschi: power and weak point of three-term recurrence relation.- F.L. Bauer: Use of endured fractions and algorithms regarding them.
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Extra info for Alcune questioni di analisi numerica
Kr+ is only different by one electron from Rb+. Thus, the properties of KrF~' are very close to those of the ionic RbF molecules. A number of other useful analogies exist as weIl. For instance, the rare gas excited states, such as Kr* have low ionization potentials and as a result the chemistry of Kr'~, both kinetically and generically, is very sirnilar to that of Rb. The simplified potential curves shown in Fig. 1 do not illustrate the other ionic excited states, which lie very c10se to the ionic 2~l/2 state.
In general, it is true that the longer pulse, larger volume, highest efficiency excitation schemes place the most stringent constraints on the intrinsic aspects of the laser medium. For example, there is one very important difference in the required laser kinetics of an allowed UV or visible laser transition excited by an E-beam stabilized discharge for a large volume device, contrasted to a short pulse, small scale discharge. As noted above the coupling efficiency of a large scale, very efficent laser improves _with long excitation pulses, t'> 300 ns.
Apriori calculations show that a substantial amount of mixing occurs between the n = 1/2 states, and as such the 2~ notation given in Fig. 1 is an over simplification.  Emission from the higher ionic states has been observed. [5, 8,13] In fact,· the broad bands are probably super positions of emission from the 2~1/2 and the 2 n3 /2 states to the repulsive 2n. Note the high quantum efficiency that is intrinsic to the rare gas monohalide lasers. Assuming the process begins with production of an excited meta stable , such as Kr~', quantum efficiencies of order 50% can be achieved.