Single-particle resonance

Although the adiabatic pathway appears unlikely, we note that the shape resonance or single particle resonance at low energy ca. 0-7 eV) have several interacting pathways, including vibrational. 

Fig. 6. A potential curve V(r) and collision energy E for which potential (i.e. single-particle) resonances exist.

Consider first the case of a potential, or single particle resonance which results from one-dimensional lunnelling through a potential barrier (see Fig. 6). T, the probability of tunnelling through the barrier, is given by40... 

Here we used the approximation Eq> E. The function (4.34) corresponds to the so-called valence nucleon model, which may be of some importance in the vicinity of the single particle resonance corresponding to eqs. (4.33) and (4.34). 

Here we assume that the compound resonance total widths are equal to F Fq and Fq are the total widths of the two single-particle p-wave resonances Upp, = ImVpp, in eq. (4.11) Dq is the distance between single particle p-wave resonances. 8, = F )ID is a neutron strength function, where (F ) is an average reduced neutron width of p-wave compound resonances. It should be noted that, for the case of s- and d-single particle resonances, the value of A[Pg.102]

Temporary anion resonances can be broadly classified according to two criteria. First, does the electron attach to the ground state of the molecule M, or is M excited in the process If M remains in its ground state, then the resonance is classified as a single-particle resonance, since excitation of M s electrons can be ignored in a quaHtative treatment. In contrast, a core-excited or target-excited resonance involves electronic excitation of M, for example. 

A wide variety of measurements can now be made on single molecules, including electrical (e.g. scanning tunnelling microscopy), magnetic (e.g. spin resonance), force (e.g. atomic force microscopy), optical (e.g. near-field and far-field fluorescence microscopies) and hybrid teclmiques. This contribution addresses only Arose teclmiques tliat are at least partially optical. Single-particle electrical and force measurements are discussed in tire sections on scanning probe microscopies (B1.19) and surface forces apparatus (B1.20). 

Fig.3. Single particle density of a characteristic surface resonance state on the W((X)1) surface shown in the (110) plane perpendicular to the surface (after Ref. 21).

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

The electrodynamic balance (EDB) is a modern version of the Millikan oil drop apparatus in which a charged particle is levitated in an electric field [20]. By using quadrupole focusing, it is possible to suspend a single particle in a controlled environment virtually indefinitely. The size of a levitated particle can be measured by a variety of methods, the most precise of which uses the information contained in the resonant structure of light... 

A single-particle effect that adds features in the X-ray absorption spectrum of molecules not present in that of atoms is the shape resonance (74, 75). (In the case of solids this effect, caused by a modification of the density of states due to the presence of the other atoms in the molecule, is automatically accounted for in band calculations.) Localization of the excited electron inside the molecule in states resulting from an effective potential barrier located near the electronegative atoms in the molecule causes strong absorption bands in free molecules and near the inner-shell ionization limits of positive ions in ionic crystals (74). Consequently, molecular inner-shell spectra depart markedly from the corresponding atomic spectra. The type of structure of an inner-shell photoabsorption spectrum depends on the geometry of the molecule, the nature of its ligands, etc., and can sometimes be used to determine the structure of the molecule. 

It is also important to notice that plasmon characteristics of particle plasmons typically represent those of single particles, because particles tend to aggregate at high concentration at which interparticle interaction starts to appear for an ensemble of particles and particle plasmon resonance is affected additionally by particle... 

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