CGS Gaussian units

Useful Conversion Factors and Units (All calculations made in Gaussian cgs units) g = 4.S X 10 state c = 3 X 10 cmsec ... 

The quantity H) is called the magnetic coherence length of the nematic. Taking as typical values (in Gaussian cgs units)... 

Table D.2 Conversion factors for common quantities [132, 206]. These allow simple conversions from Gaussian cgs units into standard SI units and vice-versa, c == 2.998 X 10 represents the numerical value of the speed of light in SI units. The abbreviations used are poise (P), gauss (G), oersted (Oe), newton (N), pascal second (Pa s), tesla (T), ampere (A), volt (V), coulomb (C), joule (J). This quantity was formerly known as specific gravity it is the density of the material divided by the (maximum) density of water (given by 1 g cm , equivalent to 1000 kg m ).

The system of quantities usually associated with cgs units is called the Gaussian system that associated with SI is often called 4D. 

Theory and Applications of Molecular Paramagnetism," Wiley-Interscience, New York, NY (1976). [These give a detailed discussion and factors for converting the classical Gaussian cgs-emu parameters to the mksA S.I. units.] Note ... 

The abbreviation au stands for atomic units , which is a system of units meant to simplify the equations of molecular and atomic quantum mechanics. The units of the au system are combinations of the fundamental units of mass (mass of the electron), charge (charge of the electron), and Planck s constant. By setting these three quantities equal to unity one gets simpler equations. The au system has a simple relation to the SI and Gaussian (cgs) systems of units. For example, 1 au of length = aQ (Bohr radius) = 5.29 x 10"9 cm =... 

Equations (10)-(17) are given in the MKSA system, although it is still usual practice to quote experimental values in the Gaussian cgs sj stem (in which these equations have a slightly different form). Furthermore, it is common to attribute to magnetic fields II the units of gauss (instead of oersted). 

Table 1.2-11 deals with the relationship between CGS units and SI units, and lists those CGS units that were assigned special names. In the field of mechanics, the CGS system of units was built upon three quantities and their corresponding base units the centimeter, the gram, and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can be done in different ways, this led to the establishment of several different systems, for example the CGS electrostatic system, the CGS electromagnetic system, and the CGS Gaussian system. In those three systems, the system of quantities used... 

Two unit systems are commonly employed in describing NLO properties the SI (MKS) and the Gaussian (cgs) systems. One should note that many equations have a different form when written in these two systems of units, and that conversion between these two systems is frequently cumbersome. One should also be aware that definitions of hyperpolarizabilities and susceptibilities may differ between different authors because of the lack of general agreement whether the complex field amplitude in Eq. (2) should include a factor of 1/2 and whether the multiplying degeneracy factors [such as those in Eq. (3)] should be included in the hyperpolarizabilities. 

Quantity Gaussian (c units) SI units Conversion fiictor (cgs to SI)... 

The electric and magnetic fields appearing in Sections 2.3.1 and 2.3.2 have been described in terms of the SI system of units. The Gaussian system of cgs units has frequently been employed in the theory of liquid crystals when magnetic fields are discussed. Gaussian units are considered by many to be natural units for the calculation and measurement of magnetic field effects in liquid crystals. Since much of the literature contains results in both Gaussian units and SI units, it seems appropriate at this point to make some comments on the conversion from one system of units to the other. A comprehensive account of the points touched upon here may be found in Jackson [132] or Moskowitz [206]. Readers should also be famihar with derived SI units. 

The assumptions made in tlie development of Eq. 12.6.1 are (1) tlie plume spretid lias a Gaussian distribution in both tlie horizontal and vertical planes witli standard deviations of plume concentration distribution in the horizontal and vertical of Oy and respectively (2) tlie emission rate of pollutants Q is uniform (3) total reflection of tlie plume takes place at tlie eartli s surface and (4) tlie plume moves downwind with mean wind speed u. Altliough any consistent set of units may be used, tlie cgs system is preferred. 

A short digression on units is perhaps appropriate here. We shall use either Gaussian rrrrits in this book or, much more frequently, Hartree s atomic units. Gaussian units, as far as we are concerned, are identical with the old cgs system of units with the added proviso that charges are measured in unnamed electrostatic units, esu. The value of e is thus 4.803206808 X 10 esu. Keeping this number at hand is all that will be required to use Gaussian rmits in this book. 

We shall use mainly the cgs Gaussian system of units. This is a mixed system with electrical quantities measured in cgs electrostatic units (esu) and magnetic quantities measured in cgs electromagnetic units (emu). 

The two common unit systems employed for the description of nonlinear optical properties are the SI (or MKS) and Gaussian (or cgs) systems (Boyd24 mentions an alternative system of SI units that are not discussed further in this article, as it has not been used with organometallic complexes). In the Gaussian system, properties are described in units of esu. 

Still, units can be a nuisance. One difficulty is that much serious theoretical work is still done in centimeter-gram-second (cgs) or "Gaussian" units such is the case with the Level 3 derivations in this text. Most students learn applications in meter-kilogram-seconds (mks) "SI" or "Systeme International" units. Happily, practical formulae for... 

The first, permanent-dipole term is important only at zero frequency in the summation over imaginary sampling frequencies f . The relaxation time r is big enough that for f =i the permanent-dipole term in a is effectively zero this term counts only at zero frequency. In both mks (SI or Systeme International) and cgs ("Gaussian") units, the dipole moment //.dipole = qd for charges q separated by distance d. [See table S.8 and Eq. (L2.171) in Level 2.]... 

Material polarization coefficient or dielectric susceptibility such that polarization density P = soxmks E in mks ("SI") units or /cgs E in cgs ("Gaussian") units. 

Dielectric" designates the response of material to an electric field applied across it 0Si or Sia, Greek di or dia means "across"). Recall that a "dielectric constant," e, is a coefficient of proportionality relating a constant electric field E in a material to the electric polarization P of the material in response to that field (note the use of cgs Gaussian units here). 

The system of units most frequently employed in nonlinear optics is the Gaussian (or cgs) system. Sporadically, the SI unit system is used. It is important to be able to convert between the two systems. However, not only do the units need to be con-... 

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