Differential cross section helium

Figure 11. Doubly differential cross sections (DDCS — 2m> dufdv ) f°r the electrons emitted after the single ionization of helium by 3.6-MeV/amu Au53+ ions, plotted for the electron s longitudinal momentum distributions for increasing transverse momenta. Here only one very small cut has been made in the electron s transverse momenta (pf < 0.04 a.u.). Experimental data and theoretical results are from Schmitt et at. [50],...

Calculations using the CDW-EIS model [38] are shown to be in good accord with 40-keV protons incident on molecular hydrogen and helium, and at this energy both theory and experiment show no evidence of any saddle-point enhancement in the doubly differential cross sections. However, for collisions involving 100-keV protons incident on molecular hydrogen and helium the CDW-EIS calculations [39] predict the existence of the saddle-point mechanism, but this is not confirmed by experiment. Recent CDW-EIS calculations and measurement for 80-keV protons on Ne by McSherry et al. [41] find no evidence of the saddle-point electron emission for this collision. 

Figure 11 A Platzman plot, the ratio of the experimental single differential cross section for electron emission from helium by 1-MeV protons to the corresponding Rutherford cross sections plotted as a function of RjE. The experimental cross sections are from Ref. 54 and the differential oscillator strength is taken from Ref. 43.

Figure 12 The ratio of the measured single differential cross section for ionization of helium by protons to the corresponding Rutherford cross sections plotted as a function of the ejected electron energy. The solid line represents the expected high-energy behavior of the ratio it should approach the number of electrons in the atom. The measurements are from Manson et al. [54].

Figure 18 shows differential cross sections measured using the helium plasma jet described in Section III.A.6. It is surprising that so much structure is still resolved, even though the velocity resolution of the beam is only 30%. No fit has so far been attempted for these data. 

L. Malegat, P. Selles, A.K. Kazansky, Absolute differential cross sections for photo double ionization of helium from the ab initio hyperspherical R-matrix method with semiclassical outgoing waves, Phys. Rev. Lett. 85 (2000) 4450. 

Starting in a manner similar to the treatment of single photoionization described in Section 2.1, double photoionization in helium caused by linearly polarized light will be treated first with uncorrelated wavefunctions. A calculation of the differential cross section for double photoionization then requires the evaluation... 

Figure 4.43 Energy- and angle-resolved triple-differential cross section for direct double photoionization in helium at 99 eV photon energy. The diagram shows the polar plot of relative intensity values for one electron (ea) kept at a fixed position while the angle of the coincident electron (eb) is varied. The data refer to electron emission in a plane perpendicular to the photon beam direction for partially linearly polarized light (Stokes parameter = 0.554) and for equal energy sharing of the excess energy, i.e., a = b = 10 eV. Experimental data are given by points with error bars, theoretical data by the solid curve.

The matrix element Mfi derived so far for the differential cross section of double photoionization in helium is based on uncorrelated wavefunctions in the initial and final states. For simplicity the initial state will be left uncorrelated, but electron correlations in the final state will now be included. The significance of final state correlations can be inferred from Fig. 4.43 without these correlations an intensity... 

Fig. 8.12. Differential cross section for the 1 S, 2 S and 2 P states of helium and electron impact coherence parameters (8.40) for the 2 P state at Eo=50 eV. Experimental data for differential cross sections are 1 S, Register, Trajmar and Srivastava (1980) 2 S,2 P, Cartwright et al. (1992). Experimental data for electron impact coherence parameters are crosses, McAdams et al. (1980) squares, Beijers et al. (1987) plus signs, Eminyan et al. (1974). Solid curves, coupled channels optical (equivalent local) (McCarthy et al., 1991) broken curve, distorted-wave Born (Cartwright et al, 1992). From McCarthy et al (1991).

Fig. 10.2 shows that the plane-wave impulse approximation is as good for relative helium differential cross sections at different energies as it is for hydrogen. Here p) is the Hartree—Fock orbital. For helium there is an absolute experiment by van Wingerden et al. (1979) for 0 = 0 in symmetric kinematics at different total energies. Fig. 10.3 shows that the plane-wave impulse approximation using the Ford T-matrix element is consistent with the experiment. 

Fig. 10.3. The differential cross section for electron—helium ionisation at < = 0 in symmetric kinematics, plotted against total energy (van Wingerden et al., 1979). Full curve, distorted-wave impulse approximation broken curve, plane-wave impulse approximation. From McCarthy and Weigold (1988).

Fig. 10.6. Relative differential cross section for the ionisation of helium (Pan and Starace, 1991). Ef = Eg = 2 dV, (f> = 0, the polar angle is Of = n+Og. Open circles, Schlemmer et al. (1989) solid triangles, Selles, Huetz and Mazeau (1987) full curve, distorted-wave calculation including the screening effect of the final-state electron-electron interaction broken curve, distorted-wave Born approximation.

Fig. 10.12. Primary-electron double differential cross section for electron-helium ionisation. Experimental data are due to Muller-Fiedler et al. (1986) (open circles) and Avaldi et al. (1987a) (full circles). Full curves, distorted-wave Born approximation (McCarthy and Zhang, 1989). Cases illustrated are (a) Eq = 100 eV, Ef = 73.4 eV(A), 71.4 eV(B), 55.4 eV(C) (b) Eq = 300 eV, Ef = 235.4 eV (cross section multiplied by 100) (A), 271.4 eV(B) (c) Eq = 500 eV, Ef = 471.4 eV(A), 435.4 eV(B). From McCarthy and Zhang (1989).

Fig. 11.6 shows the noncoplanar-symmetric differential cross sections at 1200 eV for the Is state and the unresolved n=2 states, normalised to theory for the low-momentum Is points. Here the structure amplitude is calculated from the overlap of a converged configuration-interaction representation of helium (McCarthy and Mitroy, 1986) with the observed helium ion state. The distorted-wave impulse approximation describes the Is momentum profile accurately. The summed n=2 profile does not have the shape expected on the basis of the weak-coupling approximation (long-dashed curve). Its shape and magnitude are given quite well by... 

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