Coulomb field, nuclear

It is not obvious how a stable nuclear atom can be rationalized in terms of a static charge distribution in a Coulomb field, where the force between two charges is given by... 

Z is the nuclear charge in units of e (or the number of protons in the nucleus), — e is the charge on the electron, s0 is the permittivity of vacuum, r is the distance from the electron to the center of mass, and V2 is the Laplacian30 operator. The first term of Eq. (3.5.1) is the kinetic energy operator the second is the potential energy operator (Coulomb field). We will show below that the solution to the time-independent Schrodinger equation... 

Owing to rapid experimental progress in the field of laser physics, ultra-short laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach or even exceed the strength of the static nuclear Coulomb field. If an atomic system is placed in the focus of such a laser pulse one observes a wealth of new phenomena [240] which cannot be explained by perturbation theory. In this case a non-perturbative treatment, i.e., the solution of the full TDKS equations (39)-(41) is mandatory. The total external potential seen by the electrons is given by... 

In the R-BO scheme, the stationary electronic wave function drives the nuclear dynamics via the setup of a fundamental attractor acting on the sources of Coulomb field [11]. The nuclei do not have an equilibrium configuration as they are described as quantum systems and not as classical particles. The concept of molecular form (shape) is related to the existence of stationary nuclear state setup by the electronic attractor and their interactions with external electromagnetic fields. 

In Eq. (IV.55), part (a) is identical with the Hamiltonian operator of the electrons if moving in the Coulomb field of the non-rotating nuclear frame. Part... 

From the values given in the table below it is obvious that the finite nucleus and QED corrections contribute with the same order of magnitude to the Lamb shift in a heavy atom. The uncertainty in the theoretical value comes not only from yet uncalculated very high order QED contributions (estimated to be less few tenths of an eV) but also from less well known nuclear parameters of uranium that can amoimt to an uncertainty of about 0.3 eV. Up till now the best experimental value for the Is Lamb shift in obtained at the GSI [5] is 468 13 eV. This value is still an order of magnitude too imprecise to allow QED to be tested in high Coulomb fields where Za is not a small parameter. 

The field of force of the core of an atom is, at a sufficiently great distance, a Coulomb- field of force. In the case of the neutral atom it corresponds to the effective nuclear charge Z=l, in the case of the 1-, 2-. . . fold ionised atom Z=2, 3. . . respectively. The orbits of the radiating electron at a large distance are therefore similar to those in the case of hydrogen. They differ from the Kepler ellipses only by the fact that the perihelion executes a slow rotation in the plane of the orbit. The semi-axes and parameter of the ellipses are, by (9), (10), and (11) of 22,... 

Electrons and photons scatter through a Coulomb field interaction. Therefore, scattering experiments with these particles are studying the distribution of protons. The possibility exists that neutrons and protons do not have the same distribution in nuclei. Unfortunately, there are no convenient weak interactions of a neutron which would be useful for studying the spatial distributions of neutrons. As is discussed in the section on form factors (Sect. 7) it is not simple to interpret in terms of nuclear radii those measurements which are made with particles which interact strongly with neutrons and protons. Whether neutrons and protons have the same density distributions may be answered by theoretical developments rather than experimental advances. 

Since the electron motion is very rapid compared with the nuclear motions, the procedure is to assume that the nuclei are at rest a distance R apart from each other with the single electron moving in their Coulomb fields. Next, one can treat R as a variable and consider both the electron energy and the internuclear Coulomb repulsion energy, as a fimction of the internuclear separation. The total energy of the system is the sum of these two energies, and the system will be bound if the total energy E exhibits a minimum at some value of internuclear separation. 

The atomic shell phenomena (electrons in a central Coulomb field) can be successfully treated with quantum-mechanical methods. In the case of atomic nuclei, the situation is more complicated, because here there is no well-defined central field, the average field of nucleons substantially differs from the well-known Coulomb field (the nuclear forces are very complicated), and there are two different types of nucleons in nuclei (p and n). 

Coulomb field of Scattering, slowing- Nuclear reaction, chemical changes... 

Here, emphasis is given to the application of few-state models in the description of the near-resonant vacancy exchange between inner shells. It is well known that the quantities relevant for inner-shell electrons may readily be scaled. Therefore, the attempt is made to apply as much as possible analytic functional forms to describe the characteristic quantities of the collision system. In particular, analytic model matrix elements derived from calculations with screened hydrogenic wave functions are applied. Hydrogenic wave functions are suitable for inner shells, since the electrons feel primarily the nuclear Coulomb field of the collision particles. Input for the analytic expressions is the standard information about atomic ionization potentials available in tabulated form. This procedure avoids a fresh numerical calculation for each new collision system. 

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