Nucleus/nuclear finite

The electrostatic interaction of s-electrons with a nucleus of finite dimensions produces shifts in the nuclear energy levels. Since nuclear charge distributions generally vary from one nuclear state to another, the magnitude of the shift will also depend on the nuclear state. It may be shown (5) that a gamma ray photon emitted in a transition from an excited state e > to the ground state g > will be shifted in energy by an amount... 

We have already seen above that the choice of a point-like atomic nucleus limits the Dirac theory to atoms with a nuclear charge number Z < c, i.e., Zmax 137. A nonsingular electron-nucleus potential energy operator allows us to overcome this limit if an atomic nucleus of finite size is used. In relativistic electronic structure calculations on atoms — and thus also for calculations on molecules — it turned out that the effect of different finite-nucleus models on the total energy is comparable but distinct from the energy of a point-like nucleus (compare also section 9.8.4). 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

The first term in (4.6), Jp (r)r dr, depends only on the radial distribution of the nuclear charge. This term represents the so-called nuclear monopole moment, note that it is related to the extended finite size of the nucleus. ... 

Before formally developing the tensor it is perhaps worthwhile to discuss the various types of interactions which contribute to it. The coupling between nuclear and electron magnetic moments are conveniently divided into those which are isotropic and those which depend on orientation. The former is the result of the impaired electron having a finite probability of being at the nucleus. This type of interaction is termed the contact interaction, and is described by the constant,... 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

Due to the finite size of the nuclear charge distribution, the relative distance between the nucleus and the electron is not constant but is subject to additional fluctuations with probability p r). Hence, the energy levels experience an additional shift... 

It is much more difficult to take into account the influence of finite dimensions and form of the nucleus (volume effect) on the atomic energy levels, because we do not know exactly the nuclear volume, or its form, or the character of the distribution of the charge in it. Therefore, in such cases one sometimes finds it by subtracting its part (22.35) from the experimentally measured total isotopic shift. Further on, having the value of the shift caused by the volume effect, we may extract information on the structure and properties of the nucleus itself. For the approximate determination of the isotope shift, connected with the differences dro of the nuclear radii of two isotopes, the following formula may be used [15] ... 

The principle of small nuclear changes was given a theoretical basis by George Gamow. In 1928 he derived a successful theory of alpha decay, in which the nucleus is quantized and only small particles, such as protons or alpha particles, have a finite probability of tunneling through the nuclear barrier and escaping the nucleus. That... 

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