Spin-down configuration

The normalisation factor is assumed. It is often convenient to indicate the spin of each electron in the determinant this is done by writing a bar when the spin part is P (spin down) a function without a bar indicates an a spin (spin up). Thus, the following are all commonly used ways to write the Slater determinantal wavefunction for the beryllium atom (which has the electronic configuration ls 2s ) ... 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The simplest expression for T consists of a single configuration, in which each electron is assigned to an orbital with spin up (a) or spin down (p). If two electrons with opposite spin occupy the same orbital, /,-, it is notationally more convenient to denote this orbital occupancy by replacing / // with T . 

Table 55 Ionization energies of atoms Li-Ne, shewing the ground-state election configuration and (underlined) the electron first ionized arrows represent spin-up1 and spin-down electrons, with ms= +1 and-1, respectively.

We consider first a three iron cluster with three equivalent metal sites in the "singly reduced", Fe(II)/Fe(III)/Fe(III) formal oxidation state. In the high spin configurations, the first five d-electrons on each site are aligned in a parallel fashion, say spin-up. We form three basis configurations by allowing the final d-electron (which must be spin-down) to reside in turn on each of the three sites. We have worked out the matrix elements of the... 

The simpler wavefunctions for helium atom, for example (8.5), can be interpreted as representing two electrons in hydrogenlike s orbitals, designated as a configuration. Pauli s exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers, requires the two s electrons to have different spins one spin-up ora, the other spin-down or A product of an orbital with a spin function is called a spinorbital. For example, electron 1 might occupy a spinorbital which we designate... 

TMR [5] is calculated on the basis of the difference of height of the effective barrier 8q> for spin-up and spin-down electrons, e.g. the magnetic molecular field V Estimates of 5

ideal structure FeCo/MgO/FeCo [6]. It leads to dcp 0.45 eV. In real structures containing intermediate silicon layer and the Schottky barrier the difference between barriers is reduced to 0.02-0.1 eV. 

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