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In Figure 7 b the diameter of the multitarget tube at the impinging electrons amounts to 4 mm and at the end of the tube 6 mm in order to receive a connection of the solid curve with the dashed curve of the standard target according to Figure 4 b. Therefore, some interesting consequences result from Figures b. A very practical aspect appears to be the construction of an ideal scanning machine in radiotherapy. In a paper [22] the bremsstrahlung of 6 MeV is applied, and a rather small scanning beam comparable to CT in diagnostics performs a rotation around an iso-center.

However, in a conventional technique one has to use multi-leaf collimators in order to protect some critical areas. By using the technique according to Figure 4 a and exploiting the improved yield of bremsstrahlung the whole procedure is much more efficient, and the intensity of radiation can be steered by the electron current impinging the multi-target.

Even by restriction to small-angle reflection at the tungsten wall and neglect of an additional magnetic field for focusing one receives superior results than by a target according to Figure 4 b without flattening filter. In a fundamental paper dealing with photon scatter based on the Dirac equation [23], which is referred to as Heisenberg-Euler scatter, it has been pointed out that the areas of the cross-sections have to be as small as possible.

In order to achieve this requirement, the multitarget system Figure 8 a must not have any divergence, and the diameter of the tungsten plates is restricted to 3 mm - 4 mm. By that, an extremely high density of the photon fluence is obtained. An essential technical requirement would be a vacuum equipment for the both multiplate targets, inclusive the beam propagation to the detector array.

In order to gain an optimum cross-section of the photon beams, the angle between the them should be kept as small as possible. The configuration at the right-hand side seems to be more suitable to realize the task because of the size of the apparatuses. In both figures, we have omitted that the low-energy electrons leaving at the ends of the multi-target channels must be deflected by additional magnets in order to prevent disturbing effects at the detector arrays.

The Heisenberg-Euler scatter is not a first-order effect in relativistic quantum theory. Figure 8 b is the analogue to the preceding Figure 5 and Figure 6. A significant improvement of the present configuration of Figure 3 and Figure 4 with regard to the detection of Heisenberg-Euler scatter and with regard to the 9 GeV case in the next section, is received by the prolongation of the focusing magnetic field, which should already be active before the electron beam impinges the first subplate of the multitarget.

By that, the intensity profile can be reduced to the boundary of the order 3 mm. Molecular rotation and vibration spectra were understood and the electron's spin was discovered, leading to the confusion of half-integer quantum numbers. Max Planck introduced the zero point energy and Arnold Sommerfeld semiclassically quantized the relativistic hydrogen atom. Hendrik Kramers explained the Stark effect.

Bose and Einstein gave the correct quantum statistics for photons. The Sommerfeld extensions of the solar system Bohr model of the hydrogen atom showing the addition of elliptical orbits to explain spectral fine structure. Kramers gave a prescription for calculating transition probabilities between quantum states in terms of Fourier components of the motion, ideas which were extended in collaboration with Werner Heisenberg to a semiclassical matrix-like description of atomic transition probabilities.

Heisenberg went on to reformulate all of quantum theory in terms of a version of these transition matrices, creating matrix mechanics. In , Louis de Broglie introduced the wave theory of matter, which was extended to a semiclassical equation for matter waves by Albert Einstein a short time later.

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