h=lem, FWHM =:=8.5 cm geht facto, the g,’s ———C UNKNOWN sok set pi = KNOWN —-— REAL DISTRIBUTION = to the eo C is knoy > 40k secrete for 5 Oo <a | > 30+ sufficient q i° | a nimize ti, The prot | 4 ' 30 DISTANCE (cm) ft 40 | ! 50 | { 60 Fic. 71.—Variations in f(z) eaused by previous knowledge of C, kh = 1 cm Thiejtotal amount of activity C can also be measured variable, and (c) 44-54 em, where the density of ac- ontrol the olld think that prior knowledgeof the total activity C (a,b), an vould lead to a more accurate determination of f(x) liers, ‘Tht! or the net activities in certain subintervals of (a,b). does not yield better results; whereas when h = 4 (see ecurately by independent methods.” Intuitively one he weight!’ “ever, according to our mathematical method, the the abort! priori” condition ee furthe b [ f(z)dz=C ion of th (5) s desirable only if (1) C is known to a high degree of (4peocuracy, and (2) the best experimental choice of quadrature (the interval A between two readings) can- hot be made priori. In our calculations, we have elected to use the Simpson rule for quadrature and to take readAn: of g(x) at equally spaced intervals of length h = (hs ~~ a)/n. | [n Figures 71 and 72 are plotted the distributions () as computed in turn with C unknown and known, tovether with the actual f(z), respectively for h = lem IRS aud 2 = 4 em in the cases of K(z,x’) with FWHM = of Radin § em; Figure 73 gives the integrated activity over the three following intervals of the distribution: (a) 0-14 es C alcn, where the density of activity is constant and low, 3 A(b (4-44 em, where the density of activity is widely tivity is constant and high. From Figures 71 and 73 we see that for 1 < A — 3 em,previous knowledge of C Figure 72) one can clearly obtain improved results with such knowledge. These implieations are also confirmed by using two other collimators whose point response functions have FWHM11.0 cm and 15.0 cm respectively (Figure 74). B. The FWHMof K(2,2) The same distribution of activity was measured, us- ing the three different point response functions K (x,x') with FWHMI of 15.0 em, 11.0 cm, and 8.5 cm, respectively, plotted together in Figure 75. We assumed that K(a,2") = K(\x — 2’|), ie., K constant and symmetric for every position x of the point source. This approximation is true if there is no absorber material between the distribution and the crystal, and if the backscatter- ing due to the wall of the lead enclosing the entire apparatusis uniform all along the length of the distribution f(z). The three computed values of the distribution f(z) are plotted in Figure 76 together with the real distribu- tion. The statistical errors are between 5%-10% in all cases for both g(z) and K(x,x’). In Figure 74 are given