Recoil limit

All the symbols have their usual meanings. In the non-recoil limit, the motion of the nucleus is neglected and its finite mass enters only as a reduced mass of the electron. The additional terms arising from the dynamical effects of the nucleus, namely the recoil corrections and radiative-recoil corrections, have been omitted from equation 1 and will not be considered here. For more detailed discussions of the theory, see the review by Sapirstein and Yennie [3] and more recently [4,5,6], The expansion in (Za) is now carried out by expressing F and H as power series in (Za) and ln(Za) 2, as shown below in equations 2 and 3, where a is the ratio of the electron mass to its reduced mass. 

Nonrelativistic Hamiltonian of the helium atom in the non-recoil limit (m/mN 0) is... 

The lower limit for the achieved temperature is given by the recoil energy that each atom acquires when it emits or absorbs a photon. This recoil limit is reached when the thermal energy kT equals the recoil energy p /2M = h k /2M... 

The recoil limit can be overcome by a recently discovered cooling scheme called Raman cooling (Fig. 9.29). Here a stimulated Raman scattering process is used, which traverses from level 1 via a virtual level down to level 3. If the levels 1 and 3... 

J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, C. Cohen-Tajmoudji Three-dimensional laser cooling of helium beyond the singlephoton recoil limit. Phys. Rev. Lett. 75, 4194 (1995)... 

The two methods of demonstrative character considered above should be supplemented with the classical Doppler-cooling method for forbidden transitions with a very small radiative broadening 7. In the first experiments of this kind (Katori et al. 1999) with an ensemble of Sr atoms, a 3D-cooling temperature that was close to a single effective recoil was obtained, that is, the alternative cooling pathway shown on the left of Fig. 5.4 was realized. Moreover, in the case of polychromatic excitation, there is even a possibility of reaching a temperature below the recoil limit (Wallis and Ertmer 1989). 

Reasonable estimates of ultimate sensitivity and depth resolution in ERDA can hardly be given because of the large range of projectiles and energies (from He ions of several MeV up to 200-MeV Au ions), and the use of different detection systems. In addition, stability of the sample under irradiation (which, of course, depends on the target material) is also important in the discussion of sensitivity and detection limits. The sensitivity is mainly determined by the recoil cross-section, the solid an-... 

There are four naturally occurring isotopes of Ra " " Ra (ti/2 = 5.8 a) and " Ra (3.7 d) in the Th series, (1600 a) in the series, and Ra (11.7 d) in the series (Table 1). The data for Ra are more limited, since it is generally present in low concentrations due to the low abundance of The differences in half lives and the connections across the different decay series have been used to infer a variety of groundwater and water-rock interaction features. For the short-lived Ra isotopes, the dominant input term to groundwater is recoil, rather than weathering, and steady state concentrations are often achieved (see Section 2.2). 

High ratios in groundwaters can be generated where U is concentrated in secondary phases and weathering is limited. For example, U can be precipitated when groundwaters become anoxic since reduced is much more insoluble. Therefore, concentrations are greatly lowered, and ratios increase due to efficient recoil from precipitated... 

There are various parameters and assumptions defining radionuclide behavior that are frequently part of model descriptions that require constraints. While these must generally be determined for each particular site, laboratory experiments must also be conducted to further define the range of possibilities and the operation of particular mechanisms. These include the reversibility of adsorption, the relative rates of radionuclide leaching, the rates of irreversible incorporation of sorbed nuclides, and the rates of precipitation when concentrations are above Th or U mineral solubility limits. A key issue is whether the recoil rates of radionuclides can be clearly related to the release rates of Rn the models are most useful for providing precise values for parameters such as retardation factors, and many values rely on a reliable value for the recoil fluxes, and this is always obtained from Rn groundwater activities. These values are only as well constrained as this assumption, which therefore must be bolstered by clearer evidence. 

Polyalphaolefin Hydraulic Fluids. Polyalphaolefm hydraulic fluids have properties comparable to the most effective components in mineral oil and are used in applications identical to mineral oil hydraulic fluids (Chrisope and Landry 1993 Papay 1993 Shubkin 1993 Wills 1980). Polyalphaolefins are more expensive than mineral oil, and this may limit their use in industry. In addition, polyalphaolefin hydraulic fluids are used in military applications such as aircraft and missile hydraulic systems, tank recoil and hydraulic systems, and aerospace test stands (Shubkin 1993). 

---