9914714240

I

.Reprinted fioui The Physical Kotew, Vol. 73, Ko. 3, 2S8-2S9, Fcbruaiy 3. 3943

Pnntcd in U. S. A.

/,?

On the Phase Shift Approxiination in the Theory of Pressure Broadening of Spectra! Lines

At.R.KANDER Jaolońses

Physics Departmcr.t, Nicholas Coptrnuus Umversily. Toruń. Polond :z----—    Auir&st 11. 1947

A (w,-) — A («,) =¹

instead of

Jo ^dTi ^T, T„ is obtained instead cf Foley’s

Tc?

I-W7V

"rp HFcólliltdn dam ping' theory ćf broadening cf spectra!

X lines is still widely used in discussions of experi-mental rcsults. Lately, sotnc ncw contributions to this theory have been published.^{2 1} Formcr attenipts to give a ąuantum-mcchanical foundarion to the collision damping theory were discussed in a previous paper.¹ A new attempt in this linę Las bcen madę rcccntly by Foley.¹ According to Foley the wave mechanical theory proposed by the ~ present writer¹ leads to.the Lorentz linę form for the cor.di-.tions assumed in collision damping theories (phase shift approzimation). Unfortuualely, Foley's argument is liable

large CoTlision paramerers (smali phase shifts) are also taken into consideration. Clearly, the Inst typc of collisions must contribute consićerably to the intensity in the core of che linę.

Sotr.e further remarks should be added. According to Foley, “any linę broadening theory which consideis a single perturbing atom and then avcrages over-alI transi-tions of this system will aiways yield a lilie form which diverges at the center.” Actually, the asyiuptotic distribution (Kuhns distribution) obtained in the above way in the previous paper¹ divcrges at the linę center. Ho\vcver, the disćusśion of applicability ćf this distribution¹ shows tbat it does so only owing to tac approximations madę by its derivau’on. The same discussion shows that its applica-bility is not rcstricted to high cuncentrations of perturbing atoms, a3 suppesed by Foley. I: can be used up to the Iow-est conccr.trations if utlier factors do not cause its failure.

On the whole tbc situation remains as it was before the publication of Foley's paper. One has either to demon strato rigorously tlu: the Lorentz formula can be obtained from the quanluin-mechanical theory proposed by the writer or to modify (or to reject) one of thesc theories.

The subseąuent notę by Dr. Foley obviousiy contains not only modifications of some of the assumptions on which his original calculations were based (T.-Ri/r with R< variableand r = cor.st., instead of T; = R₀/v withi?₀-con3t. and v variable, is intrcduced), but aiso a modif.cation of the present wnter’s theory itself (in the original theory a Container with a coiistant radius R₉ was ccnsidcrcd). The writer sees no physical grounds for intrcduction of such assuraptions, and, besides, is unablc to sce how Dr. Folcy's new partition formula can be snown to be compatible with the conventional theor/ of fłuctuaticns. As to the other points of disagrccrr.ent the writer should like to refer Ctf the original papers (cf., H. M. Foley, reference 3, p. 618 lef: column and page 627 left column).

» F.g . J. H. Var. V.«± and V. F. Wcisłlcopf. Rev. Mod. Thys. 17. 227 (194S).

»A. Jabłoujki. Phys. Rev. 68. U (1945).

^ł H. M. Foley. Kr/a. Rev. 69. 616 (1916;.

•Soch x ritaribution derived from Max\vdi’a Iow would be

*    Sce rcfcrcncc 3. Eq. (35).

•Tbc Lut cxiirc»ign for A(<¹0 fe, zs it must bc. dimcmionicss. «b^ ząuzrc of i: dcnotintr peebabiiity.

i Ji/JE-jRi/rłUlE)'-7i/rh (cf.. A. JsbłoTiski. rcfaeiicc 2).

■ A ZYir.dcpcmieat factor is omitted m thU cxp:wsion.

•    Cf., A. Jabloiiski. reference 2.

1

validate Dr. Foley's results.

But even if this incorrect distribution be adopted, further calculations, if carried out correctly, lead to rc-suits differing from thos? of Foley. Because of the dropping of a "numeriral factor” (normalization factor, which, as inspcction shows, deper.ds on 7\1), the cvaluation of ”overlap” integral in phase shift approximation leads Foley to the expression

sinaijFi ¹

w '

sin w 7\ ‘

<«T< •

If the ccrrccted expression for A (u,) is used and another factor, the density of trauslational energy IeveIs^T (also omitted by Foley) taken into account, the integral

-_ sin^iiTi e~^T'^lr1 log(l +W7V)¹

87W

■ sińⁱuiTte~^T>^,7» dTi--:--——

w

IIowevcr, the "overlap” integra! in Foley’s approxima:ion may be useful in the calcnlations of the intensity ćistribu-lion in the core of the broadened linę, if "collisions” with

2

—-tc-critrcism—I^iey adopts tbe^strilmtionnr^^/To '»n' tkc parameter 7<-R¹/v, in which Ra is the radius of the Container, v tbc velocity of gas molecules, T_D=Ro/c, and u their average vdocity. This distribution does not result frora MaxweU'$ distribution !aw< and fhus does not corre-tpom¹ to tbe real distribution. This alone sufńces to in-