Excitation functions

Figure 1.15 Time domain representation of a hard rectangular pulse and its frequency domain excitation function. The excitation profile of a hard pulse displays almost the same amplitude over the entire spectral range.

Figure 1.16 Time domain representation and frequency excitation function of a soft pulse. The soft pulse selectively excites a narrow region of a spectral range and leads to a strong offset-dependent amplitude of the excitation function.

A Fourier Transform Relationship between Time-Domain and Frequency-Domain Excitation Functions. 

Indeed, several identifiable resonance fingerprints in experimental observables were found.26-31 Concurrent theoretical simulations and analyses not only confirmed the experimental conjectures, but also provided deeper insights into the nature of this resonance state. For the integral cross-sections, a distinct step for Ec < 1 kcal/mol was observed in the reactive excitation function (i.e. the translation energy dependence of the reactive cross-section) for the HF+D product channel, whereas it is totally absent for the other DF+H product channel.26 Anomalous collision energy dependence of the HF vibration branching was also observed.28 For Ec < 1 kcal/mol more than 90% of the HF products are populated in the v = 2 state. However, as the energetic threshold for the formation of HF( / = 3) from... 

F(2P3/2) + HD, which occurs at Ec = 1.16kcal/mol, is reached, a sudden drop (growth) of the v = 2 (v = 3) branching was observed. In fact, the vibration state-specific excitation functions displayed two distinctive features a steplike feature span from 0.2 to 1 kcal/mol was detected for... 

The molecular beam experiments of Liu and co-workers65,66 employed the Doppler profile time-of-fiight technique that allowed the ready observation of the excitation function (i.e. the total reactive ICS summed over... 

Fig. 3. The normalized excitation functions in A2 versus collision energy for the two isotopic channels for the F+HD reaction. The solid line is the result of quantum scattering theory using the SW-PES. The QCT simulations from Ref. 71 are plotted for comparison. The experiment, shown with points, is normalized to theory by a single scaling factor for both channels. Also shown in (a) is the theoretical decomposition of the excitation function into direct and resonant contributions using the J-shifting procedure.

Fig. 9. The excitation function in A2 for the reaction F + p-H2 —> H + HF versus collision energy. The solid line is the result of quantum scattering calculations done with the SW-PES and the points are the molecular beam experiments.

Fig. 2. Excitation functions of 95Mo(p, xn)-processes leading to the formation of 94mTc, 94 Tc, 93mTc and 93m>gTc [11]. Some data of other authors are included (X, x). The unit in the ordinate mb = 10 31 m"2...

An excitation function of "Tc(p, 3n) 97Ru up to 100 MeV was determined by a Russian group [16]. The product nuclide 97Ru can be used in nuclear medicine. 

Fig. 3. Excitation functions of 95Mo(p, n) 95m Tc reactions. Open circles and triangles are taken from the data of Skakun et al. The unit in the ordinate mb = 1CT31 mJ. (Reprinted with permission from Ref. 13. Copyright (1991) Elsevier Science Ltd)...

Johnston, R. E. (1975) Sexual excitation function of hamster vaginal secretion. Anim. Learn. Behav. 3, 161-6. 

Here, Flffl are matrix elements of a zeroth-order Hamiltonian, which is chosen as a one-electron operator in the spirit of MP2. is an overlap matrix The excited CFs are not in general orthogonal to each other. Finally, Vf)(i represents the interaction between the excited function and the CAS reference function. The difference between Eq. [2] and ordinary MP2 is the more complicated structure of the matrix elements of the zeroth-order Hamiltonian in MP2 it is a simple sum of orbital energies. Here H is a complex expression involving matrix elements of a generalized Fock operator F combined with up to fourth-order density matrices of the CAS wave function. Additional details are given in the original papers by Andersson and coworkers.17 18 We here mention only the basic principles. The zeroth-order Hamiltonian is written as a sum of projections of F onto the reference function 0)... 

The principles of pulse and phase-modulation fluorometries are illustrated in Figures 6.5 and 6.6. The d-pulse response I(t) of the fluorescent sample is, in the simplest case, a single exponential whose time constant is the excited-state lifetime, but more often it is a sum of discrete exponentials, or a more complicated function sometimes the system is characterized by a distribution of decay times. For any excitation function E(t), the response R(t) of the sample is the convolution product of this function by the d-pulse response ... 

The convolution integral appearing in this equation can be easily understood by considering the excitation function as successive Dirac functions at various times t. 

Phase-modulation fluorometry The sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. 6.9) of the pulse response by the sinusoidal excitation function, is sinusoidally... 

Relationship between harmonic response and rt-pulse response It is worth demonstrating that the harmonic response is the Fourier transform of the d-pulse response. The sinusoidal excitation function can be written as... 

Numerous nuclear reactions have been employed to produce astatine. Three of these are particularly suited for routine preparation of the relatively long-lived isotopes with mass numbers 209, 210, and 211. The most frequently used is the ° Bi(a,xn) At (a = 1-4) reaction, in which bismuth 44, 74,120) or bismuth oxide (7,125) is bombarded by 21-to 40-MeV a-particles. The ° Bi(He, xn) At reaction can also be used to produce isotopes of astatine 152), the nuclear excitation functions (62) favor a predominant yield of ° At and °At. The routine preparation of astatine is most conveniently carried out through the ° Bi(a,xn) At nuclear reactions, from which a limited spectrum of astatine nuclides may be derived. The excitation functions for these nuclear reactions have been studied extensively (78, 89, 120). The... 

Excitation Eunctions of O2 and 02-Doped Ar Eilms. Resonances can be best identified by the structures they produce in excitation functions of a particular energy-loss process (i.e., the incident-electron energy dependence of the loss). Fig. 7 is reproduced from a recent study [118] of the electron-induced vibrational and electronic excitation of multilayer films of O2 condensed on the Pt(lll) surface and shows the incident electron energy dependence of major losses at the indicated film thickness and scattering angles. Also shown in this figure is the scattered electron intensity of the inelastic background... 

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