Graphical analysis of neutron line spectra

NUCLEAR

INSTRUMENTS

AND

METHODS

72

(i969)

205--209;

©

NORTH-HOLLAND

PUBLISHING

CO.

G R A P H I C A L ANALYSIS OF N E U T R O N LINE SPECTRA * R. G. N I S L E

ldaho Nuclear Corporation, Idaho Falls, ldaho 83401, U.S.A. Received 17 M a r c h 1969 A graphical m e t h o d o f analysis h a s been used successfully to reduce recoil-proton c o u n t e r d a t a to a n e u t r o n s p e c t r u m f r o m eL p r o t o n s p e c t r u m o f discrete sources. A c o m p u t e r generated synthetic curve is m a t c h e d visually on a c a t h o d e ray oscilloscope display to the experimental curve a n d the p a r a m e t e r s o f the c o m p u t e r curve are t a k e n to be t h o s e of the experimental curve w h e n a m a t c h is obtained. T h e p a r a m e t e r s used are source

energy a n d intensity, a n d i n s t r u m e n t resolution. T h e i n s t r u m e n t response to a m o n o e n e r g e t i c source is a s s u m e d to be G a u s s i a n a n d the source width is a s s u m e d to be negligible c o m p a r e d with the i n s t r u m e n t resolution. T h e source intensity, m e a s u r e d in this way, c o r r e s p o n d s to the area used in area analysis m e t h o d s for evaluating the results o f cross-section m e a s u r e m e n t s .

1. Introduction

intensities pertain to the source; and the resolution width pertains to the instrument, i.e., the recoil-proton counter system. The analysis equipment used in this work consisted of the following units:

The analysis of neutron flux data taken with a recoil-proton proportional counter usually depends on tJhe differentiation of the integral data. But differentiation, as such has certain disadvantages. To overcome them, various alternative approaches have been investigated. An analytical approach using Polynomial Transforms was described in a previous paper1). Another approach that is particularly applicable to a spectrum of discrete sources, i.e., a line spectrum of sources which are much narrower than the resolution of the instrument, is described in this paper. The analysis of a neutron line spectrum seeks to evaluate three parameters: a. The energy, Eo of the line; b. The relative amplitudes, i of the lines which are proportional to the intensities of the sources; c. The resolution width. Thus, the resolution width as a function of energy for the recoil-proton proportional counter can be obtained directly from a neutron line spectrum such as a neutron beam containing several discrete sources. The method has been used to measure the spectrum of neutrons in a scandium filtered beam from the Materials Testing Reactor (MTR).

a. PDP-9 a programmed data processor with standard peripherals; b. 339 programmed buffered display;

TELEPRINTER KEYBOARD

I

I

I

PROGRAMINTERRUPTANDSTATUSCONTROL

PAPERTAPEREADER I IINITIATE DISPLAY

PARAMETERINPUT

DATAINPUT

SCALEANDSTORE DATA

NUMBERENERGYCHANNELS SOURCEENERGYCHANNEL CHANNELWIDTH REFERENCELEVEL RESOLUTIUNWIDTH SOURCEINTENSITY

1

2. Description of the method

'The method consists of a visual matching process bel:ween a computer generated synthetic curve and the experimental curve of recoil-proton integral data. The values of the parameters required to generate the matching curve are then taken to be the values of these same parameters pertaining to the neutron source and to the instrument. The energy, E0 and the relative * W o r k p e r f o r m e d u n d e r the auspices o f the U.S. A t o m i c Energy C o m m i s s i o n .

205

SYNTHETIC SOURCE

I 339 C]SPLAY

INTEGRATEAND I NORMALIZESOURCE l

SCALEANOSTORE [

Fig. 1. Block d i a g r a m o f c o m p u t e r p r o g r a m .

I

206

R.G.

NISLE

...... ~ : : . . : ] . . . . . .

Fig. 4. Integral data from a line spectrum o f two sources are shown with the generated integral displaced below the reference count level of the lower energy line.

Fig. 2. The integral of the synthetic source shown displaced eight energy channels from the data in the direction o f higher energy.

...........

::

. . . . .

• . . . . ° . ° . .°° °

". "'

Fig. 3. The integral data and the generated integral are shown in register, i.e., equal values o f E0.

.'10o~o.**.

Fig. 5. The generated integral is shown in register with the integral data o f the lower energy line. The data of the higher energy line has been discarded.

GRAPHICAL

A N A L Y S I S OF N E U T R O N

207

LINE SPECTRA

TABLE 1 S u m m a r y o f results (scandium filtered beam).

H~ p r o b e

CH4 probe (A)

CH4 (B)

Energy range

14 to 100 keV

32 to 250 keV

61 to 400 keV

54 to 450 keV

93 to 700 keV

250 to 500 keV

Channel width

0.900 (keV)

1.984 (keV)

4.077 (keV)

3,578 (keV)

5.813 (keV)

5.505 (keV)

Eo

Averages

cr i

27.9 3.50 8.215

27.9 3.50 8.215

Eo cr i

42.3 6.00 3.875

42.3 6.0 3.875

Eo i

63.9 2.25 2.077

63.5 3.5 2.077

63.7 2.9 2.077

Eo a i

75.6 2.75 2.077

75.4 3.5 2.077

75.5 3.1 2.077

Eo G

i

125.0 3.8 0.900

i

•40.9 6.5 1.038

Eo

178.6

Eo O"

i

Eo O"

i

130,5 9.0 0.900

125.2 9.0 0.900

179.4 8.0 0.514

171,7 10.5 0.650

216.3 5.0 0.277

212.0 10.5 0.278

203.9 12.5 0.350

330.2 10.5 0.141

325.6 14.5 0.150

i

Eo G

i a Average of other values in same row. b Relative intensities scaled to this value.

125.7 10.2 0.900 140.9 6.5 1.038

5.0 1.108

Eo

122.1 19.0 0.900 b

180.2 25.0 0.662

•77,7 •2.6 0.758 210.7 9.3 0.302

319.7 25.0 0.132

314.2 27.5 0.141 a

322.4 19.4 0.141

456.8 16.5 0.020

456.8 16.5 0.020

208

R . G . NISLE

c. DM-09A (a drum memory with associated handlers). Basic software 2) associated with this equipment consisted of the usual program assembly, editing, transfer and compiling routines. A block diagram of the program written to accomplish the necessary operations is shown in fig. 1. The analysis program consists of three parts: a. Main p r o g r a m - interrupt routine, teletype print and read routines, c o m m a n d routines, display routines; b. Synthetic source g e n e r a t o r - calculation of assumed Gaussian and its integration; c. Normalization and scaling of assumed source to input data. Both PDP-9 machine language and Fortran IV, adapted to linking the latter to the former, were used in writing these programs. The analysis procedure, then, is as follows: a. Read-in from the teletype keyboard the pertinent parameters - number of energy channels, channel width and background count; b. Read-in first guesses of line energy, resolution width and line intensity; c. Read-in from paper tape the integral data obtained from the recoil-proton proportional counter; d. Calculate integral and display it with integral data; e. Reassign values to source energy, resolution width, and intensity until a match is obtained between input data and calculated integral curve. The cathode ray oscilloscope photographs shown in figs. 2-5 illustrate the application of the method. The left hand trace in fig. 2 is the integral data from a 2 keV source. The right hand trace is the integral generated from the synthetic source, displaced eight channels in the direction of higher energies. Fig. 3 shows the two curves in register (equal values of Eo) and illustrates the nature of the match obtained. The upper trace in fig. 4 is the integral data from a spectrum containing two lines. The lower trace is the synthetic integral displaced below the reference count level of the left hand line. Fig. 5 shows the two curves in register with the data from the right hand (higher energy) line discarded. Measurements of neutron line spectra of a scandium filtered beam were made with a recoil-proton proportional counter 3) in the energy range from 1 keV to 1 MeV. Three different probes operating in overlapping energy ranges were used. One was an H2 unit,

1" dia. with an active length of 3" and filled to a pressure of 200 cm Hg; the second was a CH4 unit, of the same dimensions filled to a pressure of 380 cm Hg [CH4(A) in table 1]; the third was also a CH4 unit, ~-" dia. with an active length of 1.5" and filled to a pressure of 621 cm Hg [CH4(B) in table 1]. 3. Results and discussion It was found that a Gaussian source function

G(E)

= (2~z)-~ exp

[-½(Eo-E)Z/a2],

(1)

when integrated provided a function that fits the data very well over a large range of energies as may be seen from the photographs in figs. 2-5. Spectral lines measured in the range from 27 keV to 456 keV for the scandium filtered beam are listed in table 1 with their Gaussian widths and relative intensities. With a few exceptions the line energies and relative intensities, i of the various spectral lines as measured by different probes operating in different energy ranges agree very well. TABLE 2

Comparison of intrinsic widths (all values in keV). Line energy

27.9 42.3 63.4 75.5 125.7 140.9 177.7 210.7 322.4 456.8

Measured Calculated width width

3.5 6.0 2.9 3.1 10.2 6.5 12.6 9.3 19.4 16.5

2.1 2.7 3.6 4.0 6.2 6.9 8.3 9.5 14.4 19.4

C h a n n e l width

0.9 0.9 0.9, 0.9, 1.98, 1.98 1.98, 1.98, 3.58, 5.51

1.98 1.98 3.58, 4.08, 5.81 3.58, 4.08, 5.81 3.58, 4.08 4.08, 5.81

The Gaussian widths, however, vary as a function of energy according to a formula given by Bennett'). A comparison between "intrinsic widths", as calculated by that formula, and measured Gaussian widths is shown in table 2. The channel widths of the pulse height analyzer used are also given to show the degree of agreement between the measured and calculated values as compared with instrument channel width. A "mechanical width" of 8% at 600 keV was used in these calculations. The values given in table 2 are "intrinsic widths" and are not subject to error, due to the slope-taking interval, introduced by differen-

GRAPHICAL

ANALYSIS

OF N E U T R O N

tiation. Neither are the relative intensities subject to differentiation error and for the same reason, namely, the integral data are dealt with directly and the differenl:iation step is dispensed with. Large Gaussian widths cause some lines to be ,;hadowed by adjacent lines, which accounts for the missing lines in table 1. The intensities shown in table 1 were obtained from the factor by which the normalized Gaussian had to be multiplied to cause the integrated Gaussian to fit the data. This factor and a are independent parameters. The use of intensities derived in this manner thus constitutes a form of area analysis for finding relative source amplitudes among the various spectrum lines. The 2 keV line is not shown because there were no energy ranges that overlapped the 2 keV and 27.9 keV lines. Furthermore, there were no lines of sufficient magnitude between these two energies such that they could be used to scale the intensities among the various ranges. Manganese bath experimentsS), however, indicate that the flux in the 2 keV line constitutes about ~- of the flux in the total beam. On this basis the 2 keV line would have a relative intensity of about 38, In view of the agreement between measured and cap culated widths mentioned above, it is possible to compare relative intensities of lines measured with different recoil-proton counters by use of Bennett's formula. Usable data in the energy range above 400 keV were

LINE

SPECTRA

209

obtained in but one instance. For the other probes and ranges the counting statistics were too poor. These p o o r statistics may account for the p o o r agreement among the energies of the 330 keV line. 4. Conclusion A graphical method for analyzing neutron line spectrum data taken with a recoil-proton proportional counter has been described. It has the advantage over differentiation methods that the "slope-taking interval" error has been eliminated. This method, applied to the neutron spectrum of a scandium beam is shown to be useful for measuring the resolution width of a recoil-proton proportional counter, and the relative intensities among the various spectrum lines.

The author would like to make special acknowledgment of the work of J . W . Rogers who made the measurements and supplied the data used in this analysis, and of C. W. Richardson who provided parts of the PDP-9 programs. References 1) R. (3. Nisle, Nucl. Instr. and Meth., to be published. '~) Digital Equipment Corporation, Advanced software system, DEC-9-A-GUAA-D, MAAO-D, AM9A-D, AF40-D (1968). ~) J. E. Powell, USAEC Report IN-1054 (1968). 4) E. F. Bennett, Nucl. Sci. Eng. 27 (1967) 16. .5) j. R. Smith, unpublished.