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LETTERS TO THE EDITOR 647g, the root-mean square error of the function, are com-puted by the methods of James and Coolidge. The unit oflength is a~/9.aCK~ (ev)6~ (ev)~

e minimized0.3803.191.001620.049(2.884) 21.0640.017 &q &0.071

P minimized0.36753.1071.000660.064(2.828) 21.0550.023 &q &0.081Minimization of 5, it will be noted, is rather ineffective inreducing this quantity, and is associated with a relativelymuch larger increase in e.From the computed value of p and the observed hyper-fine splitting of the state one can compute, according tothe formulas of Breit and Doermann, the magnetic momentof the Li nucleus. Using the observational results ofGranath' and the first value of p we obtain for Li' themagnetic moment 3.28~0.03 nuclear magnetons, whilewith the second value of p we obtain 3.305~0.03. (Theestimated uncertainties arise principally from the uncer-tainties in p, as discussed by Breit and Doermann. ) Thesevalues are to be compared with the value 3.265~0.016given by the 'new and completely independent method ofI&abi and his co-workers. 'These results indicate that an attempt to improve theaccuracy of the determination of the nuclear magneticmoment of Li by the h. f.s. method should be based on thedetermination of a more accurate wave function by theconventional variational method, rather than by minimiza-tion of 6'.

HUBERT M. JAMESF. L. YosTDepartment of Physics,Purdue Vniversity,Lafayette, Indiana,October 1, 1938.~ H. M. James and A. S. Coolidge, Phys. Rev. Sl, 860 (1937).~ G. Breit and F.W. Doermann, Phys. Rev. 36, 1732 (1930).3 L. P. Granath, Phys. Rev. 42, 44 (1932).4 I. I.Rabi, J.R. Zacharias, S.Millmann, and P. Kusch, Phys. Rev.53, 318, 495 (1938).

refers, of course, to the normal state in which there are nofree electrons. After the ionization of an atom, the electroncan be described as moving freely in the surroundingmedium consisting of neutral polarizable atoms and in thefield of the remaining positive ion. Since this field isscreened by the polarization of the surrounding atoms,the ionization energy must be decreased in the ratio e .. 1where e is the electronic component of the dielectric con-stant (i.e., the square of the refractive index n for ordinarylight).In an external field 8 this energy is further decreasedby a mechanism similar to that of the Schottky effect inthe thermoelectronic emission from metals. In Fig. 1 the

Fu'. 1. Potential energy as a function of distance from the positiveion. Full line, without an external field, dotted line in the presence ofthe field.full line represents the normal potential energy of theelectron as a function of the distance from the positive ionwhile the dotted line represents the same quantity in thepresence of the field. The height of the potential barrier islowered in the field by the amount6U= eZr p+e'/cr p,where r p, the distance to the maximum from the ion, isgiven by e'/~r p' eB. Thus r p= (e/ATE) l and

6U= 2eBr p 2e(eB/c) '.Now if, in the absence of the electric field, the number offree electrons due to the thermal ionization of the atoms,is proportional to exp (Up/2k T), where Up is theionization energy (decreased in the ratio e . 1 comparedwith an isolated atom), the electrical conductivity in thepresence of the field will be proportional to

On Pre-Breakdown Phenomena in Insulators and Elec-tronic Semi-Conductors We thus obtainexp tUpU) /2kT j.

It is well known that insulators and electronic serni-conductors display in high electric fields B (over 10'volts/cm for the:former and a few thousand volts/cm forthe latter) an increase of electrical conductivity whichfinally leads to breakdown, and which is approximatelyrepresentable by 0'=Ope~@ (Poole's law). The fact that theillumination of an electronic semi. conductor results in anadditional increase of the conductivity independent of Bshows that the increase of electrical conductivity inintense fields is due to the increase of the number of freeelectrons, and not of their mobility.This phenomenon can be explained very simply if thedielectric (or semi-conductor) is described not as a systemof free electrons moving in a self-consistent periodic heldof force, but simply as a system of neutral atoms. This

0 =Op exp P(e'8/e}&/kT),differing from Poole's law by the substitution of E& for E.This is in excellent quantitative agreement with theexperiments of P. Granovskaja' on the electrical conduc-tivity of mica in intense fields (over 10' volts/cm') as wellas with the (still unpublished) experiments of Joffe on thepre-breakdown phenomena in electronic semi-conductors(up to field strengths of the order of 50,000 volts/cm). Itis interesting that on the above theory the effect of thefield is reduced by the elevation of the temperature, just asis observed experimentally. It should be mentioned thatwith 8= 10' volts/cm, and n = 2, the distance rp is of theorder of 30A; i.e., about ten times the interatomicdistance. At smaller distances the electron is therefore still

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LETTERS TO THE EDITORattached to the parent ion, just as if there were no neutralatoms between them.It can be shown that the mechanism of facilitatedthermal ionization described above is more effective, bothfor dielectric and semi-conductors, than the mechanism ofelectrostatic ionization, which gives an additive (and nota multiplicative) effect proportional to

exp $ (2m)l Uo&/heB$

unless the temperature falls below 500'K for insulators,or below a few degrees for semi-conductors. Further detailsof the theory will be published in Technical Physics of theU. S. S. R. J. FRHNKELLeningrad, U. S.S. R.August 10, 1938

~ P. Granovskaja, Physik. Zeits. der Sowjetunion.