Cumulative excitation

CUMULATIVE EXCITATION. An excited atom, in the metastahle slate, may receive a further increment of energy by collision, as with an electron, and thus be raised to a still higher energy state. This process by which an atom is raised by collision from one excited stale to higher states is known as cumulative excitation. In fact, it is possible for an atom in the mctastable slate to receive sufficient energy by this process to be ionized and this process is designated as cumulative ionization. 

For a fixed value of the first time delay r, the amplitude of the Hahn echo is determined by the thermal polarization and the cumulative excitation bandwidth of the detection pulses. While in a two-level system (5 = 1/2) the thermal polarization continuously grows with decreasing measurement temperature, in a multilevel system, as it is the case for Gd(iii) centres (5=7/2, eight levels), the polarization of a pair of levels, of which none corresponds to the lowest energy in the multiplet, would attain its maximum at a certain non-zero temperature. Below that temperature the polarization decreases as both levels get depopulated. For instance, for the l/2><-> -Fl/2> transition of Gd(iii) the optimum... 

L. Mandelstam and N. Papalexi performed an interesting experiment of this kind with an electrical oscillatory circuit. If one of the parameters (C or L) is made to oscillate with frequency 2/, the system becomes self-excited with frequency/ this is due to the fact that there are always small residual charges in the condenser, which are sufficient to produce the cumulative phenomenon of self-excitation. It was found that in the case of a linear oscillatory circuit the voltage builds up beyond any limit until the insulation is ultimately punctured if, however, the system is nonlinear, the amplitude reaches a stable stationary value and oscillation acquires a periodic character. In Section 6.23 these two cases are represented by the differential equations (6-126) and (6-127) and the explanation is given in terms of their integration by the stroboscopic method. 

For X = Br, Cl and F, the observed retentions are 73%, 33% and 5% respectively. Simultaneous with the decrease of retention, the (CgH5)2PoX2 increased. Since no y transition occurs, this series clearly must reflect the influence of the halogen electronegativity on the cumulative electron excitation and the shakeoff. Evidently fluorine is least able to compensate for shakeoff and thus preserve the original structure ... 

This expression gives the cumulative density of absorbing states between energies 0 and E (note the change of sign in front of e). This expression can be used to estimate the total excited state absorption by computing... 

In the last equation Hi(x) is the th Hermite polynomial. The reader may readily recognize that the functions look familiar. Indeed, these functions are identical to the wave functions for the different excitation levels of the quantum harmonic oscillator. Using the expansion (2.56), it is possible to express AA as a series, as has been done before for the cumulant expansion. To do so, one takes advantage of the linearization theorem for Hermite polynomials [42] and the fact that exp(-t2 + 2tx) is the generating function for these polynomials. In practice, however, it is easier to carry out the integration in (2.12) numerically, using the representation of Po(AU) given by expressions (2.56) and (2.57). 

Each burst of imagery would last about fifteen minutes and subside then we would take another hit of the caapi smoke. The cumulative effect persisted for a couple of hours. We triggered it repeatedly, and excitedly discussed it as an example of the sort of thing that sophisticated shamanic technicians must have been whipping up for each other s amazement since the late paleolithic. 

T. Schork and R Fulde, Calculating excitation-energies with the help of cumulants. Int. J. Quantum Chem. 51, 113 (1994). 

To summarize the theory dynamic correlations are described by the unitary operator exp A acting on a suitable reference funchon, where A consists of excitation operators of the form (4). We employ a cumulant decomposition to evaluate all expressions in the energy and amphtude equations. Since we are applying the cumulant decomposition after the first commutator (the term linear in the amplimdes), we call this theory linearized canonical transformation theory, by analogy with the coupled-cluster usage of the term. The key features of the hnearized CT theory are summarized and compared with other theories in Table II. 

A further point is of interest in the formal discussion of the canonical transformation theory. So far we have assumed that the reference function is fixed and have considered only solving for the amplitudes in the excitation operator. We may also consider optimization of the reference function itself in the presence of the excitation operator A. This consideration is useful in understanding the nature of the cumulant decomposition in the canonical transformation theory. 

To understand this more clearly, consider a simpler model where A consists of single excitations, only single-particle operators are retained in the effective Hamiltonian, and we choose the reference function iho to be a single determinant. Then, from a cumulant decomposition of the two-particle terms, the effective Hamiltonian becomes... 

Isomeric states are denoted by the symbol "m after the mass number and are given in the order of increasing excitation energy. The 235U thermal fission products, with fractional cumulative yields>10, are italicized in the table. The information on fission products is taken from the ENDF/B—VI fission products file [8],... 

In conclusion, we believe that our ability to observe higher atropisoraeric excesses from Irradiations of BN in cholesteric mesophases than from thermal lsomerlzations can be traced to the larger interaction energies associated with the excited state species and its environment. The cumulative effect of these Interactions is manifested more specifically on a reactive solute when the solvent molecules are uniquely ordered than when they are isotropically dispersed. 

Let us evaluate the positions where the lines pt-( 0) branch off the ,0 axis, that is, where NIR takes place at an infinitesimal excitation. In Ref. 22 it was shown that this regime can be described in terms of cumulants Qk of the equilibrium distribution function. Carrying out this adiabatic treatment, one finds that the branchoff points in the fcth order are the zeros of... 

This being the case, the coherence among energy levels, hence the time dependence of the initial state, has no influence whatsoever on the product yield. This implies, for example, that in the weak-field regime, the product yield obtainable with a subfemtosecond laser pulse with frequency spectrum 1(a)) is exactly equal to the sum of a set of, for example, microsecond pulses with an appropriate set of frequen-cies and intensities that have the same cumulative I(co). Shorter pulses alter the. product probabilities only to the extent that they excite a larger number of states, as the frequency spectrum broadens with diminishing pulse duration. Clearly, am observation of increased yield of a particular product upon use of a shorter pulse is then due solely to the fact that the shorter pulse encountered some states with at preference for a particular product. ... 

Fig. 18.6. Example for ADAS error analysis. Shown here is the cumulative statistical error (see text) being built up for an excited level of He I by the interactive code ADAS2f6...

It Is of Interest to note that subsequent cycling of the epoxy sample In Figure 6 results In a gradual Increase of the "stable" dry and wet state tan 6 values. This cumulative Increase In network mobility continues with moisture cycling because the sample Is never allowed a macroscopic network relaxation. Recovery of original dry state properties at least requires thermal excitation of the system to temperatures near the glass transition point (3). 

The DANTE pulse sequence is shown in Figure 20b. A peak that is exactly on-resonance or an integral multiple of l/d2 Hz off-resonance, experiences the cumulative effect of the n pi pulses. Other resonances see a random excitation that effectively sums to zero. In exchange experiments, a variable delay (vd) is inserted between the end of the DANTE pulse train and the read pulse, p2. During vd, magnetization is transferred between exchanging sites. 

In addition to a suitable environment, appropriate pigments, whose cumulative light-absorbing properties determine the range of wavelengths over which photosynthesis occurs, a reaction center where the excited pigments emit... 

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