Multipolarity

Bell R J 1970 Multipolar expansion for the non-additive third-order interaction energy of three atoms J. 

Larsen B, Rasaiah J C and Stell G 1977 Thermodynamic perturbation theory for multipolar and ionic fluids Mol. Phys. 33 987... 

For efficient transmission of ions, multipolar guides provide a means of reducing ion losses during their transit from one part of a mass spectrometer to another. It is useful to understand some of the reasons for ion losses. 

The lshi2uka cell (39—41), another multipolar cell that has been ia use by Showa Titanium (Toyama, Japan), is a cylindrical cell divided ia half by a refractory wall. Each half is further divided iato an electrolysis chamber and a metal collection chamber. The electrolysis chamber contains terminal and center cathodes, with an anode placed between each cathode pair. Several bipolar electrodes are placed between each anode—cathode pair. The cell operates at 670°C and a current of 50 kA, which is equivalent to a 300 kA monopolar cell. 

Eor specific models of the nucleus, it is possible to compute theoretical wave functions for the states. Eor a model that assumes that the nucleus is spherical, the general properties of these wave functions have been used to compute theoretical estimates of the half-hves for y-rays of the various multipolarities. Some values from the Weisskopf estimate of these half-hves are shown in Table 7. These half-fives decrease rapidly with the y-ray energy, namely, as and, as Table 7 shows, increase rapidly with E. This theoretical half-life applies only to the y-ray decay, so if there are other modes of... 

Parent nucHde y, keV Multipolarity ICC" xX IPECX7 xlO" Total transition probabihty, %... 

Fig. 5. Decay scheme of showing the energies, spins, and parities of the levels populated in the daughter nucleus, Xe, and the energies in keV, emission probabihties (in %), and multipolarities of the y-ray transitions. There is a strong dependence of the y-ray lifetime on the y-character. The Ml + E2 y-ray of 177 keV has a half-hfe of 2.1 ps the half-hfe of the 164-keV M4 y-ray is 1.03 X 10 s.

A sample of theoretical conversion coefficients is given ia Table 12, iUustrating the great range of values. The most common case where two multipolarities compete is Ml + E2. For example, the for Ml and E2 are nearly equal at Z = 60 and E = 150 keV. It is, however, relatively easy to determine the fraction of each of these components that is present if the relative iatensity of the three E conversion fines can be measured. For the E2 portion the three fines are almost equal, = 0.035, = 0.050, and = 0.048, whereas for the Ml portion they change by factors of 10, namely,... 

In addition to the possible multipolarities discussed in the previous sections, internal-conversion electrons can be produced by an EO transition, in which no spin is carried off by the transition. Because the y-rays must carry off at least one unit of angular momentum, or spin, there are no y-rays associated with an EO transition, and the corresponding internal-conversion coefficients are infinite. The most common EO transitions are between levels with J = = where the other multipolarities caimot contribute. However, EO transitions can also occur mixed with other multipolarities whenever... 

The Alcan process has been used commercially by Osaka Titanium Co. ia Amagasaki, Japan. Multipolar ceUs of 1000 t/yr capacity are ia operation. Energy consumption is about 9.5—10 kWh/kg of magnesium metal (111). 

Vielling, m. Cryat.) multiple twin. Viellinienspektrum, n. many-line spectrum, viellinig, a. many-line, multilinear, viel-mal, adv. many times, -mehr, adv. much more, more. — conj. rather, -phasig, a. polyphase, multiphase, -polig, a. multipolar. 

Let us reconsider the four-level system shown in Fig. 4.1(6), which has two doublets in the spectrum split by 2A and 2e (Fig 4.4(a)). Since diagonal elements of G,kjm are the same in impact and Markovian theories we assume that F , = 0 without any restriction of generality. This is actually the case for any electric multipolar interaction and hence Ac0 = 0. The non-zero elements of the perturbation... 

In the Hamiltonian conventionally used for derivations of molecular magnetic properties, the applied fields are represented by electromagnetic vector and scalar potentials [1,20] and if desired, canonical transformations are invoked to change the magnetic gauge origin and/or to introduce electric and magnetic fields explicitly into the Hamiltonian, see e.g. refs. [1,20,21]. Here we take as our point of departure the multipolar Hamiltonian derived in ref. [22] without recourse to vector and scalar potentials. 

In a molecule-fixed coordinate system, the multipolar Hamiltonian of ref. 

Hohenau, A., Krenn, J. R., Schider, G., Ditlbacher, H., Leitner, A., Aussenegg, F. R. and Schaich, W. L. (2005) Optical nearfield of multipolar plasmons of rodshaped gold nanopartides. Europhys. Lett., 69, 538-543. 

For the sake of simplicity and a more instructive description, we shah restrict ourselves to the case of unpolarized single line sources of 7 = 3/2v / = 1/2 magnetic dipole transitions (Ml) as for example in Fe, which has only a negligible electric quadrupole (E2) admixture. It will be easy to extend the relations to arbitrary nuclear spins and multipole transitions. A more rigorous treatment has been given in [76, 78] and [14] in Chap. 1. The probability P for a nuclear transihon of multipolarity Ml (L=l) from a state I, m ) to a state h, m2) is equal to... 

In those cases where we are dealing with nuclear transitions which are a mixture of multipolarity Ml and E2 with a mixing parameter 5 defined by = ((/i E2 h))l ((/i I M111/2)) (positive or negative), one obtains the extended relation... 

The Maximum Entropy (abbreviated MaxEnt) method has been used in the field of accurate charge density studies for some time now (see Section 2.2) it has the potential to overcome some of the limitations of traditional multipolar modelling, but great care must be taken not to apply it outside the range of validity of its own foundations. 

Model bias in multipolar charge density studies... 

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