Spectroscopy two photon

Two-photon Spectroscopy.—Papers dealing with the theory of simultaneous two-photon absorption processes are covered in Section 4 of this chapter. Two-photon absorption processes are of great interest in that the selection rules differ from those for single-photon events, thus permitting excitation of new features in absorption spectra. There is also considerable current interest in the use of two- 

Leuliette-Devin, R. Locqueneux, and J. Tillien, Chem. Phys. Letters, 1975, 30, 109. 

Tajiri, and M. Hatano, Chem. Phys. Letters, 1974, 28, 197 N. Teramae, K. Yazawa, T. Matsui, and S. Tanaka, Chem. Letters, 1974, 581. 

Bowman, R. Evans, and A. Schreiner, Chem. Phys. Letters, 1974, 29, 140. 

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One very important aspect of two-photon absorption is that the selection ndes for atoms or synnnetrical molecules are different from one-photon selection ndes. In particular, for molecules with a centre of synnnetry, two-photon absorption is allowed oidy for g g or u u transitions, while one-photon absorption requires g-f u transitions. Therefore, a whole different set of electronic states becomes allowed for two-photon spectroscopy. The group-theoretical selection ndes for two-photon spectra are obtained from the synnnetries... 

An interesting aspect of two-photon spectroscopy is that some polarization infonnation is obtainable even for randomly oriented molecules in solution by studymg the effect of the relative polarization of die two photons. This is readily done by comparing linearly and circularly polarized light. Transitions to A states will absorb linearly polarized light more strongly than circularly polarized light. The reverse is true of transitions to B ... 

Doppler-free two-photon spectroscopy spect A version of Doppler free spectroscopy in which the wavelength of a transition Induced by the simultaneous absorption of two photons is measured by placing a sample In the path of a laser beam reflected on itself, so that the Doppler shifts of the Incident and reflected beams cancel. dap-lor fre tu fO,tan spek tras-ka-pe j... 

The two-photon transition operator is a tensor whose components may be nonzero. Thus an important reason for doing two-photon spectroscopy is that it allows us to observe the transitions directly as allowed transitions instead of indirectly as forbidden transitions as are all one-photon spectra of transition metal ions. 

In single beam two-photon spectroscopy, an intense laser beam having a frequency hv = l/2(fi2 -E )is passed through the crystal, and the attenuation of the beam is measured. To measure attenuation directly is extremely difficult and it is better to measure the proportional quantity, while the fluorescence maybe the most useful. Two-photon spectroscopy has not been used so far in the luminescence of minerals field, but many relevant centers have been studied in artificial compounds, such as Cr ", Mn, Cu, Ni, Eu (McClure 1990). 

For many years, this hydrogen maser measurement remained the most accurate experiment in modern physics. Only recently the accuracy of the Doppler-free two-photon spectroscopy achieved comparable precision [34] (see the result for the IS — 2S transition frequency in (12.7)). 

As shown by Fig. 14.15, the resonances occur near zero field, and it is easy to calculate the small Stark shifts with an accuracy greater than the linewidths of the collisional resonances. As a result it is straightforward to use the locations of the collisional resonances to determine the zero field energies of the p states relative to the energies of the s and d states. Since the energies of the ns and nd states have been measured by Doppler free, two photon spectroscopy,22 these resonant collision measurements for n = 27, 28, and 29 allow the same precision to be transferred to the np states. If we write the quantum defect dp of the K np states as... 

Fig. 16.1 Schematic diagram of the experimental arrangement for two photon spectroscopy of Rb Rydberg states (from ref. 5).

The measurements of 2s — Is transitions in magnetically trapped hydrogen have achieved a relative accuracy of one part in 1012 [21] by means of two-photon spectroscopy which eliminates the first-order Doppler broadening. It is hoped that this technique will allow the measurement of the Is — 2s transition with the accuracy limited only by the shape of the transition line dictated by quantum electrodynamics, i.e. to a few parts in 1015. Further, if the center of the Is — 2s line could be determined with the accuracy of a few parts in 103 of its width, the relative accuracy for this transition would increase to a few parts in 1018. 

A special case in the uranyl spectroscopy is formed by Denning s extensive work on the UO + group in Cs2U02Cl4C ([65], and papers cited therein). Later this work was extended to two-photon spectroscopy, a powerful method for a complex with inversion symmetry [66]. Excited state spectroscopy followed soon after [67], The latter experiments show a progression in the excited-state absorption spectrum of the UO + complex in a frequency of 585 cm-1. This is the U-O stretching frequency in the second excited state. In the first excited state it is at 715 cm-1. In this way it is possible to determine that the U-O distance expands from 1.77 A in the ground state to 1.84 A in the first and 1.95 A in the second excited state. This work has been reviewed recently [68]. 

Another possible means of distinguishing electronic from vibronic lines is two-photon spectroscopy. The relevant matrix element for a single beam two-photon transition is... 

Chu, S., Mills Jr., A.P. and Hall, J.S. (1984). Measurement of the positronium 13Si-23Si interval by Doppler-free two-photon spectroscopy. Phys. Rev. Lett. 52 1689-1692. 

L. Wunsch, F. Metz, H. J. Neusser, E. W. Schlag, J. Chem. Phys. 66, 386 (1977). Two-Photon Spectroscopy in the Gas Phase Assignments of Molecular Transitions in Benzene. 

Naphthalene, Anthracene, and Linear Polyacenes Linear polyacenes possess two low-lying excited states, which in the Platt notation used in spectroscopy, are labeled as La and Lb the former is Biu and the latter is 1 B2u (7,19). The Biu state is a monoionic state, while B2U is a covalent excited state, which as in benzene, is dipole forbidden, but can be accessed by two photon spectroscopy. In naphthalene and anthracene, is the second excited state, but in higher acenes, becomes the first excited state (16,19). We will now show how to construct and conceptualize this excited state. Already at the outset, we encounter here a problem of choice, namely, that the set of covalent Rumer VB structures involves many structures (e.g., 42 in naphthalene), and one has to restrict the VB structure set in order to understand the constitution of these... 

Figure 7.6c shows that the vibrational mode b2u interchanges the Kekule structures K and Kr. Since the excited state is made only from these Kekule structures, then by analogy to benzene, one will expect that the frequency of this mode will be larger in the B2u excited state than in the Ag ground state, which is indeed what is observed by two-photon spectroscopy (16,24). Another analogy... 

Fig. 1. Setup for Doppler-free two-photon spectroscopy of the hydrogen IS — 2S transition...

The two-photon spectroscopy described above had made it possible to study three characteristic features of Bose-Einstein condensation condensation in real space, condensation in momentum space (Fig. 5) and the mapping the phase boundary (Fig. 6) [9]. 

In high precision two-photon spectroscopy of hydrogen the large natural width of the 2P level is avoided by measuring nS—n S, D transitions [47,48,49]. In He+... 

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