The advantages and limitations of using a small computer to analyze Ge(Li) radiation spectra are studied. The computer has to: (1) find the spectrum peaks, (2) determine the count rate in the photopeaks, and (3) relate the count rate to known gamma transitions to find the amount of each radionuclide present. Results show that tasks one and two may be done by the computer but task three must be done by an experimenter or a larger computer

Mcdermott, W. E.

English

NASA Technical Reports Server

GE(LI) DATA REDUCTION USING SMALL COMPUTERS
W.E. MCDERMOTT
1155 T.O.S., MCCLELLAN AFB , CA.
I. INTRODUCTION
The introduction of lithium-drlfted
germanium detectors for use in X-ray and
gamma ray spectroscopy has made it possible
to measure accurately the relative abun-
dances of radionuclides present in a
mixture directly, without the use of chem-
ical separation techniques. Events depos-
iting differing amounts of emergy into
the crystal result in pulses of varied
height,which are then sorted using a pulse
height analyzer. Having accumulated a
spectrum, three steps are required for its
analysis. The peaks in the spectrum must
be found, the count rate in the photopeaks
determined, and this count rate related
through a knowledge of machine efficien-
cies to known gamma transitions to find
the amount of each radionuclide present.
Since 4096 channels of data are usually
involved, this process has often been
accomplished on a remote computer. With
the introduction of small , relatively
inexpensive computers it has become pos-
sible to interface these devices with the
Ge(Li) detector in such a way as to allow
the experimenter to maintain an inter-
active control not only of the experimen-
tal parameters, but also of the data inter-
pretation. This latter approach also has
the desirable advantage of providing real-
time information on the progress of the
experiment.
There are essentially two approaches
which are used to produce an interactive
system. In the first, the small computer
is interfaced directly to the ADC and a
portion of the computer memory provides
the storage area for the data! whereas in
the second, the computer is interfaced to
the analyzer memory in which the data is
stored. The analyzer memory thus appears
to the central processor as a bulk storage
device. We have pursued the latter appro-
ach.
2. ANALYZER/COMPUTER COMBINATION
The system used in this study was a
commerlcally made 50/50 S_stem , obtained
from NUCLEAR DATA. It includes a i00 MHz
ADC with 8192 resolution and a 4096 word,
24 bit analyzer memory. Also part of this
system was a 12K PDP 8/I computer produced
by DIGITAL EQUIPMENT CORP. Other equipment
included a display scope, high speed
punch/reader unit, teletype, and interface
units. Machine language instructions were
provided to control all major functions
of the analyzer under computer control,as
well as allowing acess through the computer
accumulator to any memory location within
the analyzer or direct access to the ADC
output.
Various computing languages are
available to program the PDP 8/l;includ-
ing assembly languages, FORTRAN, and
FOCAL ( a conversational language ). The
assembly languages are most efficient
from the point of view of speed and pro-
gram size,however,programs are long and
tedious to write. FOCAL requires the
compiler to reside in core and is there-
fore wasteful of core memory. FORTRAN
programs allow easier design and modifi-
cation and also eliminate training oper-
ators in the assembly languages. Further-
more, FORTRAN programs are available from
a variety of sources including the excel-
lent text by Bevlngton ( ref. i ). Our
approach was to utilize FORTRAN programs
with a number of FORTRAN-callable routines
which provide control over the major
functions of the aru_lyzer.
3. LIMITATIONS OF FORTRAN
There are several limitations placed
on the FORTRAN program by the construction
of the central processor. The PDP 8/1
memory is divided into 4096 word units
called fields . Each field is further di-
vided into 128 word blocks called Da_es.
There are 32 pages in a field. The FORTRAN
loader requires 3 pages in the first field
(field 0), and one page each in the remain-
ing fields. Some locations in the first
page in each field are also required leav-
ing 27 pages available in field 0 and 30
in each of the remaining fields. The
FORTRAN library subroutines_ including
subscripting,square root,read,write,add,
subtract, etc. requires another 25 pages.
The exponentlation routines are not in-
cluded and would require another 6 pages.
Without the latter, in a 12K computer,
this leaves 62 free pages or about 8K for
operator programs.
4. SERVICE ROUTINES
Four service routines were written
to facilitate analysis of the Ge(Li) spec-
trum. These are listed on Slide i. The
routines ANAL and TYME are in the same
package and occupy 2 pages of core, as
does each of the other routines.
5. METHODS OF ANALYSIS
The general problem in the analysis
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of Ge(Li) spectra is to determine the area
of the full energyphotopeakafter subtrac-
tion of the background,whichis due to
Comptoninteractions producedby higher
energy gammas.Themain portion of the
photopeakis a gaussianfunction, modified
on the low energyside by tailing. A close
examination of well defined photopeaks,such
as the one shownon Slide 2, also reveals
the existence of a step function-like con-
tribution, the higher level of which is
again on the low energyside of the photo-
peak. Theactual situation is not as bad as
shownas the scale is semi-logarithmic.
In the caseof isolated photopeaks,the
photopeakarea is simply what is left over
after the backgroundis subtracted so the
problemreducesto a determination of the
form of the background. Onepossible
approach is to define a region on either
side of the peakand drawa least square
straight llne through it. Thephotopeakis
defined as anything abovethat line. A more
pleasing solution might be to Join the two
regions on either side of the peak by a
smoothfunction suchas ( I - err(x) ).
With a small computer,however, it is more
practical to use the former method.The
error resulting from using this methodis
about 1%.
Whenphotopeaksare not isolated, then
there is a secondproblem- that of deter-
mining howmuchof the total peakarea is
due to a specific gammaray. For this it is
necessary to usean expression for the in-
dividual peakshapesand an iterative pro-
cedure to minimize the weighted squared
error ( chisquare ). Theerror in this type
of determination is proportional to the
product of chisquare and the error expected
from Poisson statistics alone. Either of
these types of analysis can be coded in
FORTRAN and run on the 50/50 system descri-
bed earlier.
6. ANALYSIS PROGRAM
A flow chart of a typical peak loca-
tion and analysis program is shown on the
next slide. An initial set of parameters
is read in from the high speed paper tape
reader. These include smoothing coeffici-
ents for the peak finding routine,gain,zero,
and estimates of the peak width as a func-
tion of channel number. The teletype is
then used to define the region to be anal-
yzed, the minimum separation between iso-
lated peaks, and the number of channels to
be used in the background region. The
photopeaks are then found by the subroutine
FIND which examines the behavior of the
smoothed first derivative of the spectrum
using an algorithmn similar to that used
in the GASPAN program ( ref 2 ). When all
peaks have been found, the first (highest
energy ) peak is checked against the second
to determine if they are resolved. If so,
the specified number of channels are ex-
tracted from the analyzer and the limits of
the peak determined. The program looks on
either side of the peak for three
successive increases in the smoothed chan-
hal contents such that the difference be-
tween the first and third values are at
least twice the square root of the first.
The first channel in this group is taken
to be the limit of the peak on that side.
The remaining channels are then used to
calculate a least square line to be used
as the background and the resulting peak
area and centroid calculated.
If the peak was found not to be iso-
lated, then the region to be analyzed
includes that second peak and any other un-
resolved peaks. After calculating the total
peak area in the same manner as for an iso-
lated peak, a non-llnear least square fit
using the functional form,
4
y = a + bx + _ c I exp( - s2( x-d i )2 )
1
is used and the total area for each peak
calculated from the area previously cal-
culated and the relative peak amplitude.
The form of the functional fit may be varied
by using different calculation subprograms.
The next slide shows a memory map of this
program to give some idea of the size of
each subprogram.
7. CONCLUSION
In conclusion, I feel that a small
computer can perform the first two steps
necessary in the analysis of a Ge(Li) spec-
trum. The last step, that of correlating
the photopeak intensities and determining
the amount of each radionuclide present
must be taken either by the experimenter
or a larger computer.
REFERENCES
i. Bevington,P.R. , Data Reduction and
Error Analysis for the Physical Sciences.
McGraw-Hill (1969)
2. Barnes, V.s IEEE Trans.Nucl. Sci. NS-15,
no 3 (1968)
745
SLIDE 1 FORTRAN S_VICE ROUTINES
Name Calling S_atement
ANAL CALL ANAL (CTS,CHAN,N) Lead into the vector CTS, starting at
CTS(1), _e contents of the N analyzer
locations beginning with CHAN, Conwrt
24 bit word to fl_ting point.
Tn_ X=T_m(T) Load contents of ana_er channel 0
_to X after converting to f!oat_
point and multiplying by the constant
T.
F_IL CALL FNDIL (X,Y)
CAUS X = GAUS (T)
Find _he upper channel, X, and the
lower channel, Y_ of the analog
intensified region on the display scope.
Compute EXP(- T2). If T is greater in
magnitude than 5, GAUS (T) = O.
INPUT
IS Nth pEAK
NO CROM N+I st ?RESOLVE_____ES
_ULTIPLET
N =N+I
I
IFIND PEAK(S I
- ...... L
NO i ISOLATED PEAK ._S
_OE MNEA_ LEAST I _S
QUARES ROUTINE I
4
I -
$L,_6 5
COUNTS
iO5
,O4
,?
102
(o
o,., ,,,,
• °
,o ,.Do e,
o., •
C_ANNEL
SLIDE 2
MEMORY MAP
FIELD 0 PlELD I FIELD 2
FORTRAN (3)
FORTRAN
LIBRARY
SUBROUTINES
(2_)
ANAL (2)
GAUS (Z)
(i)
MAIN (25)
DERV (_)
CALC (6)
NON-LINEAR
LEAST SQUARE
FITTING ROUTIN]
(16)
FIND (7)
SLIDE 4
746


Ge(Li) data reduction using small computers

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