Gaussian units

Zeeman displacement spect The separation, in wave numbers, of adjacent spectral lines in the normal Zeeman effect in a unit magnetic field, equal (in centimeter-gram-second Gaussian units) to e/4innc, where e and m are the charge and mass of the electron, or to approximately 4.67 x 10 (centimeter) (gauss) . za man di.splas-mant ... 

Readers may be aware that the equations and numerical values of a magnetic field change with the system used. It thus becomes necessary to review the basics of unit systems here. The units in magnetics have always been somewhat confusing. Both SI and Gaussian unit systems are widely used in the literature. This state of affairs may be understood in terms of the following ... 

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. 

Note that capital letters indicate multi-electron operators and that—in contrast to the previous sections—all quantities are expressed in atomic emits. (However, Gaussian units may easily be recovered if each squared spin expression is multiplied by fr and each linear expression by h.)... 

In Gaussian units, Jackson [Ref. 7, pp. 220-223] shows that Maxwell s four equations (vacuum form) can first be reduced to a set of two coupled equations... 

So far we have employed gaussian units, which are more common in theoretical discussions. However, experimental results are generally discussed in terms of practical units. Since conversions between different systems of units can sometimes be confusing we include here an example. Consider R. In gaussian units E and are in statvolt/cm (for this is called gauss ), j in... 

Table A.5 allows one to convert an equation from SI units to Gaussian units the quantities in the SI column are replaced by those in the Gaussian column. For example, Coulomb s law in SI units is...

In 1960, the eleventh General Conference on Weights and Measures recommended the International System of Units (Systeme International d Unites), abbreviated as SI units, for use in science SI units are essentially the rationalized mks system of units. Relations between SI units and Gaussian units are given in Table A.4 of the Appendix. Table A.5 allows one to convert equations from SI to Gaussian units. 

All equations are in Gaussian units where charge is measured in esu, potential in statvolts and distance in centimetres. 

The classical electromagnetic force acting on a particle of charge q is the Lorentz force (in Gaussian units)... 

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). 

In terms of the irrational susceptibility (ir), which is often used in connection with the older esu, emu, and Gaussian unit systems (see section 7.3 below), this equation becomes... 

But note the use of the esu or Gaussian unit irrational displacement is being quoted, D(ir)... 

But note in practice susceptibilities quoted in the context of emu or Gaussian units are always ... 

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