Dipole photoabsorption strength

Figure 7.5 Dipole photoabsorption strength for the cluster Na2i in the diffuse jellium model after averaging over the thermal ensemble of and shape fluctuations at T = 480 K. The experimental strength from [79] is also shown for comparison (upper panel). The potential energy surfaces for P2 and deformation compared with the thermal energy atT = 480 K are displayed in the lower panel...

The dipole oscillator strength is the dominant factor in dipole-allowed transitions, as in photoabsorption. Bethe (1930) showed that for charged-particle impact, the transition probability is proportional to the matrix elements of the operator exp(ik r), where ftk is the momentum transfer. Thus, in collision with fast charged particles where k r is small, the process is again controlled by dipole oscillator strength (see Sects. 2.3.4 and 4.5). 

The advantage of this reformulation is that in the limit q- 0, i.e., expanding exp(i -r ) in eq. (4) and taking the leading non-zero term, df q,AE)/d(AE) corresponds to the dipole oscillator strength encountered in photoabsorption. 

Figure 1. Photoabsorption cross section for the dipole plasmon in axially deformed sodium clusters, normalized to the number of valence electrons N - The parameters of quadrupole and hexadecapole deformations are given in boxes. The experimental data [39] (triangles) are compared with SRPA results given as bars for RPA states and as the strength function (49) smoothed by the Lorentz weight with A = 0.25 eV. Contribntions to the strength function from p =0 and 1 dipole modes (the latter has twice larger strength) are exhibited by dashed curves. The bars are given in eVA. ...

The dipole response in real time gives access to the response in frequency domain by Fourier transfrom D (a)), from which one can extract the strength function S(n>) = cA b yf and the power spectrum P( ) = I)(a/) 2. The strength function is the more suited quantity in the linear regime, where it can be related to the photoabsorption cross section [31], while the power spectrum better applies for spectral analysis in the non linear regime [24],... 

Excitation and ionization energies derived from photoabsorption (PA) or dipole (e,e) spectroscopy (simulating PA) and also from multiphoton ionization (MPI) work (which is not accounted for in the following) are reported in the chapters on electronically excited states (p. 144) and on ionization potentials (p. 149). The absolute photoabsorption oscillator strength df/dE and cross section a, related via a(in Mb)=109.75 df/dE(in eV" ), were obtained from gas-phase dipole (e,e) spectroscopy [1, 2] and are shown for a large range of photon energies. 

In the following we are going to relate the dipole-strength function given in eqn (55) to the photoabsorption cross section photoabsorption cross section is derived in ref. 23 for a monochromatic electric field. If the calculational method contains all frequencies, e.g. as in refs. 13, 24 and 25, we have to sum over all excited states n. Furthermore, in experiments the molecules are randomly oriented. Therefore, we take the sum of all directions of the matrix elements ... 

From eqn (57) we see, that the dipole-strength function is directly proportional to the photoabsorption cross section. 

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