Second order Doppler effect

Fig. 10. Extrapolation of the half maximum center (o) and of the line position corrected for the light-shift, second order Doppler effect and 8D hyperfine structure ( ) versus the light power P in the case of the 2 >i/2 (F = 1) — 8D5/0 transition of deuterium...

Abstract. This paper deals with high resolution spectroscopy of hydrogen and deuterium atoms. The 1S-3S and 2S-6S/D transitions have been used to determine the ground state Lamb shift with an accuracy of 46 kHz. The aim of the present experiment is to make an absolute frequency measurement of the 1S-3S transition. We present in this paper the improvement on the experiment and the developpment of a new method to compensate the second order Doppler effect by the application of a magnetic field. 

Secondly, in the atomic frame, it comes with a motional electric field E = V x B hydrogen atom are specially sensitive to this field. As this electric field is proportional to v, the corresponding shift of the S level due to the interaction with a near P level, is quadratic with v. Moreover, since the nearest level (P1/2) is below the S one, this motional electric field can give a positive frequency shift of the transition Av able to compensate the negative shift due to the second order Doppler effect. 

We have improved the signal to noise ratio of the experiment by a factor 15, this allows us to determine very precisely the 1S-3S transition frequency with a reasonnable integration time. The preliminary results for the second order Doppler effect are very stimulating. We plan to make more precise measurements of this effect. The frequency chain to make an absolute frequency measurement is in preparation in the Laboratoire Primaire du Temps et des Frequences. The determination of the absolute frequency of the 1S-3S transition is planed within one year. 

In both atomic hydrogen and deuterium we have studied the three transitions 2S - 8Da/z, 2S1/s- 10D3/z and 2S1/g- 12D3/2. The frequencies measured, corrected for hyperfine splittings and for the second-order Doppler effect, are reported in Table I. 

Besides the IS there exists a shift of the Mossbauer lines due to the second-order Doppler effect (i3, 14). This shift is given by... 

The thermal shift 6j of the Mdssbauer spectrum is the sum of a contribution due to the second-order Doppler effect (6sod) and a possible contribution due to an intrinsic dependence of the isomer shift (8j) on temperature. The second-order Doppler shift is proportional to the mean square velocity of the Mdssbauer nucleus. For the purpose of a comparison with thermodynamic data, the SOD shift may be described in terms of the Debye approximation,6... 

K. Upon increasing the temperature the isomer shift decreases, consistent with expectations based on the second-order Doppler effect. Electron density maps of the complex support the E2g ground state with an electronic configuration of (d y) (d. z.d3iz) (dz2) Another... 

Mossbauer Spectroscopy. Mdssbauer spectroscopy has been used as a powerful technique to probe the electronic structure of the five- and six-coordinate ferrous nitrosyl porphyrins. The isomer shifts of both types of complexes (5 0.35 mm s ) are similar and show temperature dependences that are consistent with a second-order Doppler effect, but are slightly smaller than those of most other iron(II) porphyrin complexes (5 0.45 mm Unlike the isomer... 

The first term represents the absorption frequency coq = Ek — Ei) of an atom at rest if the recoil of the absorbing atom is neglected. The second term describes the linear Doppler shift (first-order Doppler effect) caused by the motion of the atom at the time of absorption. The third term expresses the quadratic Doppler effect (second-order Doppler effect). Note that this term is independent of the direction of the velocity v. It is therefore not eliminated by the Doppler-free techniques described in Chaps. 2-5, which only overcome the linear Doppler effect. 

The Mossbauer measurements makes it possible to study a variety of interesting effects that may be brought about by the introduction of impurity in the lattice as also the modifications brought about by imperfection in the crystal lattice, since the nuclei must be bound in a crystal for this study of resonant emission (or absorption) of y-rays. Three dynamical quantities of interest, which are possible in the Mossbauer studies, are (i) Zero-phonon absorption cross-section giving the Lamb-Mossbauer factor, (ii) One-phonon absorption cross section yielding the time information as well as the information of the localized modes and through this the information on the force constant between impurity and the host atom, (iii) the second order Doppler effect yielding information about the mean square velocity of the Mossbauer probe. 

The thermal shift of Mossbauer lines arises from the second-order Doppler effect (Pound Rebka, 1959). If is the mean-square velocity of the Mossbauer nucleus in the crystal, then the relative shift in energy of the Mossbauer line will be given by AE/Eq= — /2c. In the Debye model approximation this leads to AE... 

Residual Doppler broadening, in particular the second-order Doppler effect (due to the time dilatation effect (1-j/2/c2)1/2 in (9.16), which is present irrespective of the direction of motion. 

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