Nuclear excitons

In a nuclear resonant scattering experiment all resonant levels of the Mossbauer nuclei in the sample are simultaneously excited by a short pulse of synchrotron radiation, creating the nuclear exciton. The time dependence of the delayed intensity emitted upon de-excitation of the nuclear exciton in forward direction is the time spectrum of nuclear forward scattering (NFS). 

From (1.32) it is obvious that in the presence of diffusion an effective broadening of the nuclear resonant line via rd(q) takes place leading to an accelerated decay of the nuclear exciton. The intuitive picture is that due to the diffusive motions of resonant atoms the spatial coherence between the scattered wave trains is partially destroyed, leading to increasing destructive interferences at latter times after the excitation. 

Figure 1.24 shows time spectra of nuclear forward scattering from a single crystal of FeAl measured at the indicated temperatures [85,86,90]. With increasing temperature one clearly observes an accelerated decay of the nuclear exciton. The maximal values of the diffusion coefficient D determined by this method are limited by the accessibility of early times after the excitation within which the fast decay can be observed. Assuming start time for the time spectra at 20 ns sets an upper limit for D < 10 m s. ... 

Nuclear excitation and nuclear resonant scattering with synchrotron radiation have opened new fields in Mossbauer spectroscopy and have quite different aspects with the spectroscopy using a radioactive source. For example, as shown in Fig. 1.10, when the high brilliant radiation pulse passed through the resonant material and excite collectively the assemblies of the resonance nuclei in time shorter than the lifetime of the nuclear excited state, the nuclear excitons are formed and their coherent radiation decay occurs within much shorter period compared with an usual spontaneous emission with natural lifetime. This is called as speed-up of the nuclear de-excitation. The other de-excitations of the nuclei through the incoherent channels like electron emission by internal conversion process are suppressed. Synchrotron radiation is linearly polarized and the excitation and the de-excitation of the nuclear levels obey to the selection rule of magnetic dipole (Ml) transition for the Fe resonance. As shown in Fig. 1.10, the coherent de-excitation of nuclear levels creates a quantum beat Q given by... 

With tlie development of femtosecond laser teclmology it has become possible to observe in resonance energy transfer some apparent manifestations of tire coupling between nuclear and electronic motions. For example in photosyntlietic preparations such as light-harvesting antennae and reaction centres [32, 46, 47 and 49] such observations are believed to result eitlier from oscillations between tire coupled excitonic levels of dimers (generally multimers), or tire nuclear motions of tire cliromophores. This is a subject tliat is still very much open to debate, and for extensive discussion we refer tire reader for example to [46, 47, 50, 51 and 55]. A simplified view of tire subject can nonetlieless be obtained from tire following semiclassical picture. 

The absolute configuration of the 9,10-dihydrodiol metabolite was established to be 9R,10R both by nuclear magnetic resonance spectroscopy and by the structures of the hydrolysis products formed from the svn and anti 9,10-dihydrodio 1-7,8-epoxides which were synthesized from the same 9,10-dihydrodiol enantiomer (13). The absolute configuration of a BaP trans-9.10-dihvdrodiol enantiomer, after conversion to a tetrahydro product, can also be determined by the exciton chirality method (Figure 2) (19.20). 

Coherent optical phonons can couple with localized excitations such as excitons and defect centers. For example, strong exciton-phonon coupling was demonstrated for lead phtalocyanine (PbPc) [79] and Cul [80] as an intense enhancement of the coherent phonon amplitude at the excitonic resonances. In alkali halides [81-83], nuclear wave-packets localized near F centers were observed as periodic modulations of the luminescence spectra. 

In the strong coupling case, the transfer of excitation energy is faster than the nuclear vibrations and the vibrational relaxation ( 10 12 s). The excitation energy is not localized on one of the molecules but is truly delocalized over the two components (or more in multi-chromophoric systems). The transfer of excitation is a coherent process9 the excitation oscillates back and forth between D and A and is never more than instantaneously localized on either molecule. Such a delocalization is described in the frame of the exciton theory10 . 

Figure 2.2. Scheme of nuclear potentials in the ground electronic state E°(Q) and the excited electronic state E (Q). In the excited state, the frequency changes (i20->S2r) and the equilibrium point is shifted. The classical relaxation energy to the new nuclear configuration in the excited state is the Franck-Condon energy Efc and characterizes the linear exciton-vibration coupling. 

Figure 18 Models from which the excitonic coupling between pairs of peptide groups were calculated (a) The direction and location of the transition dipole of the amide I mode (118,123) from which the coupling between two peptide groups is calculated according to a dipole-dipole interaction term [Eqaution (28)] (b) The nuclear displacements, partial charges, and charge flow of the amide I normal mode obtained from a DFT calculation on deuterated N -methylacetamide (all experiments were performed in D2O) (42). With this set of transition charges, the multipole interaction is computed, avoiding the limitations of the dipole approximation.

In the case of erythro-1,2-glycols, the determination of AC is more difficult. If the two groups R1 and R2 are identical, the glycol is a meso-isom c and hence achiral. If they are different, the glycol is chiral. In general, the exciton CD Cotton effects of erythro-diester are weak and depend on the equilibrium of the rotational conformations. Therefore, the assignment of ACs needs the further conformational analysis by other methods, for example, nuclear overhauser effect (NOE).73... 

Dynamics. Cluster dynamics constitutes a rich held, which focused on nuclear dynamics on the time scale of nuclear motion—for example, dissociahon dynamics [181], transihon state spectroscopy [177, 181, 182], and vibrahonal energy redistribuhon [182]. Recent developments pertained to cluster electron dynamics [183], which involved electron-hole coherence of Wannier excitons and exciton wavepacket dynamics in semiconductor clusters and quantum dots [183], ultrafast electron-surface scattering in metallic clusters [184], and the dissipahon of plasmons into compression nuclear modes in metal clusters [185]. Another interesting facet of electron dynamics focused on nanoplasma formation and response in extremely highly ionized molecular clusters coupled to an... 

For computing the wavefunction of a localized exciton the adiabatic approximation (see (20), 28,29) can be used. The first step in this approximation consists of establishing the wavefunction x and the corresponding eigenenergy U for the electronic subsystem assuming that the positions of atomic nuclei are fixed. Thus, denoting by r the set of electronic coordinates and by R the set of nuclear coordinates, we have x = x(R), U = U(R), i.e. the wavefunction x and the energy U depend on R treated as parameters in this approximation. 

The frequencies of intramolecular vibrations are approximately by order smaller than the frequencies of pure electronic transitions in the considered spectral region, and the quantities (cpf, cp[j) decrease rapidly with increasing n. Therefore one can read off from (3.174)22 that the sum of oscillator strengths for vibronic transitions in this approximation equals the oscillator strength for pure electronic transitions by the assumption, that nuclear vibrations are neglected. Now the question arises, to what extent is this approximation valid for vibronic transitions in crystals. Further examination of this question requires a detailed study of the nature of excitonic states in molecular crystals, which appear when electronic states of the crystal interact with intramolecular vibrations. 

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