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

Select target paragraph3