The angular distributions of neutral mesons produced by 170-MeV bremsstrahlung on carbon, aluminum, copper, cadmium, and lead have been obtained through the coincident detection of the decay photons by a scintillation counter system. The experimental data have been analyzed by means of a Monte Carlo prediction based on an impulse-approximation elastic coherent production model. The nuclear density distributions which were used in the synthesis of those predictions which were in best agreement with the experimental data from this experiment have been compared to the charge density distributions inferred from electron scattering experiments. The values of the rms radii of nuclear matter obtained in this experiment are, within the limits of error of the experiment (about 2X10~1 4 cm), consistent with the values of charge distribution radii obtained in electron scattering.The spin-independent part of the neutral meson photoproduction cross section used in the synthesized predictions is obtained using the dispersion theory of Chew, Low, Goldberger, and Nambu. The dependence of the cross section on the meson-nucleon phase shifts used is investigated and a set of phase shifts is presented that results in a correct prediction of the absolute cross sections observed in this experiment; however, this particular set of phase shifts is not unique. 3 E. L. Goldwasser, L.

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A u seful analyti c expression for the form fa ctor F (q) = f p (r)e iq . ·r(P.· of the F ermi di stribution p(r) = Po[l + e(r-c)/"l -l is de riv ed. This expre ss ion con s is ts of a sim p le te rm with elementary fun ction s plu s a rapidl y conve rge nt infinit e seri es with term s of alt e rn at.in g sign. Tables of th e form fa ctor a s a fim c tio n of q for several valu es of th e pa ra met.e rs c and a, as we ll a s t.h e numeric al valu es of the normalization co ns ta nt po a nd th e rm s radiu s co rres pondin g to th ese va lu es of th e paramete rs, are al so giv en. Key W ord s: An alyti c, fe rmi di s tributi on , form fac tor , mom e ntum tra n sfe r, no rm ali za ti o n co ns ta nt , roo t-m e a n-squ a re radiu s.In th e calc ulati on of a cross sectio n in th e Born approxim ati on th e s pati al di s tributi on of th e interac ti on may b e re prese nte d by th e inclu sio n of a form fac tor whi c h is its F ouri er tra nsform.The r e action ampJitud e for a di stribute d interacti on is th e n th e fo rm factor F tim es th e reacti o n amplitude for a p oint inter ac ti o n. Th e form facto r s qu ar ed thu s e nters ex pressions for th e cross section. Th e co n ce pt of th e form fa c tor has been utilize d in a to mi c ph ysics fo r so me tim e a nd no w is used wid ely in nucle ar a nd particle physics to c hara cterize th e e ffec ts of th e s pati al di s tributi on of th e inter ac ti on.Th e form factor F is ge nerally give n as a fun cti on of th e mo me ntum q tra nsfe rre d by th e incide nt particle (r e prese nte d by a pl ane wave) to th e interac tin g parti cle. If the s ph eri cally symmetri c s pati al di s tributi o n of the inter actin g parti cle is giv en by p(r), the n th e form factor as sociate d with it is gi ve n by th e Fouri er trans form of p(r) : F( q)= f p(r)e;q "cflr = 4; fox p (r)r sin qr d r .(1)The de nsit y is normalize d s_ o thatfrom whichThere are se veral collecti ons of form factors for vari ous models of th e s patial di stribution (for example , de nsity di s tributio ns in nu clei) in th e lite rature [1 , 2, 3, 4].One of the mos t widely used models is not include d in most collections of form tactors. It is de fine d by the spatial di stributio n:wher e th e normalization c onstant po is chosen so that (2) is satisfied. The parameters a and c d e termin e the s hape of the spatial distribution. 85