Symmetry energy effective field theory

Recently the density dependence of the symmetry energy has been computed in chiral perturbation effective field theory, described by pions plus one cutoff parameter, A, to simulate the short distance behavior [23]. The nuclear matter calculations have been performed up to three-loop order the density dependence comes from the replacement of the free nucleon propagator by the in-medium one, specified by the Fermi momentum ItF... 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

We intend in this chapter to consider the manner in which the symmetry of the chemical surroundings of an ion determines the effect of this environment on the energy levels of the ion. In the crystal field and ligand field theories we often wish to regard the effect of the environment as a small perturbation on the states of the free ion. For the benefit of readers not acquainted with certain general features of the electronic structures of free atoms and ions, a brief resume of the subject is given in this section. 

The rules have been accounted for in terms of ligand field theory, taking Q°l (see Figure 6) to be the reactive state.35 36 Figure 7 illustrates the energy level orderings of the one-electron -orbitals and the electronic states for [CrX(NH3)5]2+ complexes of effective C4v symmetry. The lowest quartet... 

As pointed out by Clark, the Ti(H20) ion has an important historical connection with ligand field theory. In a perfect octahedral field of O symmetry, the ground term of titanium(III) is split into a lower term and an upper Eg term. The broad, quite asymmetric band at ca. 20100cm in the visible spectrum of Ti(H20)i arises from the Eg- Tig transition. The energy of this transition for a complex is a direct measure of the ligand field strength. The splitting of the Eg term is a consequence of the Jahn-Teller effect. 

In the crystal-field-theory formulation of a metal complex, we consider the ligands as point charges or point dipoles. The crystal-field model is shown in Fig, 9-8. The point charges or point dipoles constitute an electrostatic field, which has the symmetry of the complex. The effect of this electrostatic field on the energies of the metal d orbitals is the subject of our interest, /... 

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