Berlin 2001 – wissenschaftliches Programm

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A: Atomphysik

A 6: Spectroscopy

A 6.12: Vortrag

Dienstag, 3. April 2001, 18:30–18:45, H1028

Does the Heisenberg angle quantization exist? — •Yuri V. Popov¹ and Lorenzo Ugo Ancarani² — ¹Nuclear Physics Institute, Moscow State University, Moscow 119899 Russia — ²LPMC, Institut de Physique, 1 Bd Arago, Technop/"ole 2000, 57078, Metz, France

Recent (e,3e) coincidence experiments on different atomic targets (He, Ar, Ne, Mg) clearly demonstrate that simple many–body wave–functions, used with success for calculations of elastic and inelastic scattering, are not necessarily satisfactory to describe the details of many–electron ionization processes. This motivated us to develop rigorous mathematical studies of the many–body Schrödinger equation (SE) with long–range potentials. In the report we consider the SE for the helium ground state.

Several well known scientists have investigated the SE formal solutions for He bound states (Hylleraas, Bartlett, Conroy, Fock etc.). Nevertheless, remains the difficulty of building probing many–electron wave–functions which, on one hand, are as close as possible to the formal solution and, on the other, are practical for numerical calculations. Generally speaking, most approximate constructions have incorrect asymptotic and/or origin behaviours.

In the report we present the exact form of the helium bound state wave–function at small and large hyperradii, including the technique for its numerical evaluation [1]. It was found, in particular that if both bound electrons No-dqmoveNo-dq far form the nucleus their mutual angle is a constant of motion.

To observe and probe the behaviour of the wave function at large distances from the nucleus, one needs experimental situations where the transferred momentum is small. We examined a recent set of experiments. Among them are the (e,3e) measurements at high impact energies (3-8 keV) and small momentum transfers of the Freiburg [2] and the Paris [3] groups, many (γ,2e) coincidence measurements with relatively small energies above threshold [4], and quite different experiment [5] of the Frankfurt group, in which they has measured the angular distribution of fragments of the reaction p+He → H+e+He⁺⁺ using the COLTRIMS technique. The latter experimental conditions suggest that one of helium electrons is resonantly captured by the proton (v_e ≈ v_p).

All the experimental evidence presented above seem to indicate that, at large distances from the nucleus, the angle separating the two electrons is somehow fixed at a given value in the range 120⁰−150⁰. Since in the independent electrons model such property does not appear it can then be identified as a signature of their correlation. No No-dqtraditionalNo-dq wave function proposed or used so far predicts such a behaviour.

Further investigations to fully understand this property is under way. For the moment, we may say that coincidence measurements such as those described above illustrate that it may be necessary to reconsider the simple atomic models used up to now, and to accept the idea of an "asymptotic angularNo-dq quantization pointed out by Heisenberg (history one finds in [6]).

References

1. -3pt Yu.V.Popov and L.U.Ancarani. Phys.Rev.A 62, 42702 (2000)
2. A.Dorn et al., Phys. Rev. Lett. 82, 2496 (1999).
3. A.S.Kheifets et al., J.Phys.B 32, 5047 (1999);
4. J.S.Briggs and V.Schmidt, J. Phys. B 33, R1 (2000).
5. V.Mergel et al., Many-particle spectroscopy of atoms, molecules, clusters and surfaces, J.Berakdar and J.Kirschner eds (2001).
6. G.Tanner et al., Rev.Mod.Phys. 72, 497 (2000) (Chap.2)