Tsoulfanidis N. Measurement and detection of radiation

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488

MEASUREMENT AND DETECTION

RADIATION

The evaluation of the derivative in Eq. 14.32 is performed by numerical

techniques, since it is not the spectrum M(E) that is measured but its "binned"

equivalent,

I;+'M(E) d~

(14.33)

where Mi is the number of counts in channel

of the spectrometer. Several

investigator^'^-'^

applied least-squares fit techniques to numerically perform the

differentiation of Eq. 14.32. Usually, each Mi is assigned the energy correspond-

ing to the midpoint of the channel and an Mth-order polynomial is least-squares

fit to that point and the preceding and following

points [this is an Mth-order,

1)-point fit]. The derivative of the polynomial at the mid-point is used as

the derivative [dM(E)/dE],. This method has the disadvantage that it slightly

hardens the unfolded spectrum.

improved differentiation technique1' consists of first smoothing the true

spectrum @(E) to obtain a "smoothed" true spectrum

+s(E),

given by

where G(E, E') is a smoothing function normalized to

Substituting Eq. 14.32

into Eq. 14.34, one obtains1'

where

is the number of channels,

Mi is given by

Eq.

14.33, and the

assumption is made that the quantity [E1/a(E')]G(E, E') approaches zero at

both limits of integration of Eq. 14.34. Results obtained with Eq. 14.35 and a

Gaussian smoothing function show no spectrum hardening.

14.5.2

The FERDOR

Unfolding

Method

The unfolding code FERDOR based on the work of ~urrus'~ is described in

several

article^.'^^^^

The measured spectrum given by Eq. 14.28 is written in the

form

where

Ei+

AEi

width of the spectrometer channel at energy

number of spectrometer channels

The functions ki(E), which represent the detector response, can be measured at

selected energies or can be

c~mputed.~'

NEUTRON

DETECTION

AND

SPECTROSCOPY

489

The code FERDOR, instead of obtaining +(El, calculates the quantities S,

given by

where W,(E)

window function, chosen by the observer

number of window functions

There are many interpretations of Eq.

14.38,

all equally valid:

If W,(E) is taken as the response of an "ideal" detector, then the S,'s are the

elements of an "ideal" measured spectrum.

The functions W,(E) are smoothing functions for the true spectrum 4(E).

The Sk7s are linear functions of the true spectrum +(El that have to be

calculated. For example, if W,(E) is a cross section, the corresponding Sk is a

reaction rate; if W,(E) is a flux-to-dose conversion factor, then S, is the dose

rate; or if Wk(E)

then S, is the integral spectrum.

The functions Wk(E) used by FERDOR are Gaussians with a standard

deviation given by

where

rk/Ek, and its value is set by the user. The code calculates the S,'s

and their uncertainties based on the values of ki(E), Mi, and the statistical

errors of Mi, using a constrained least-squares method.

Experience has shown that the proper values of w, depend on both the

shape of the neutron spectrum and the statistical errors of Mi, and that small

changes in the

w, cause large changes in the errors of the result.23 This effect

has been mitigated in the code

FORIST,~~

which is a modification of FERDOR.~

In FORIST, the value of

is obtained by an iterative process in terms of the

desired statistical error of the result S,. Choosing the widths w, by this method

improves the resolution of the unfolded spectrum, for a fixed desired statistical

error.

14.5.3

Proportional Counters Used as Fast-Neutron Spectrometers

Proportional counters filled with hydrogen or methane are used for the mea-

surement of neutron spectra in the energy range

keV

MeV. Neither

hydrogen nor methane are equally useful over the full energy range. Hydrogen-

filled counters are used for En

100

keV. For higher neutron energy, greater

stopping power is needed, and for this reason, methane is used instead of

hydrogen. Methane-filled counters do not give good results for E,

100 keV

because of spectrum distortion from carbon recoils.

t~he codes FERDOR and FORIST are available through the Radiation Shielding Information

Center

Oak Ridge National ~aboratory.~~~~~

490

MEASUREMENT

AND

DETECTION

RADIATION

The efficiency of a proportional counter, like that of any other gas counter,

depends on its size, the composition and pressure of the gas, and the energy of

the incident neutrons. Knowledge of the neutron cross section for interactions

with hydrogen and carbon over the energy range of interest is necessaq for

efficiency calculations. The hydrogen cross section is known to better than

percent for neutron energies between 0.2 and 22 MeV. The carbon cross section

is less accurately known for En

2 MeV. In addition to elastic scattering, other

carbon reactions, such as (n, n'), (n,

a),

and (n,

p),

are important for En

4.8

MeV and should be included in the response function of the counter. Table 14.3

gives hydrogen and carbon cross sections for 0.2

20 MeV.

The relationship between the neutron spectrum and the measured pulse-

height distribution is given by Eq. 14.28. The response function k(E, En) (Eq.

14.29) may be measured or calculated. In either case, the following effects have

to be taken into account in obtaining

k(E, E~):~~-~~~~~~~~

Wall-and-end effects.

Tracks of protons generated close to the wall or close to

the ends of the counter have a high probability for incomplete energy deposition

and collection of ionization. Proton-recoil tracks close to the wall are truncated

by collisions with the wall material before the struck proton deposits all its

energy in the counter. Protons being produced close to the end of the counter

Table

143

Total Hydrogen and Carbon Cross Sections

for 0.2

M~v~'

NEUTRON DETECTION

AND

SPECTROSCOPY

491

and moving toward either end enter into a region of lower electric field where

there is little or no gas multiplication and where there is, consequently, incom-

plete collection of the charge produced.

As a result of wall-and-end effects, lower energy pulses are generated that

tend to increase the response function toward the lower energies (Fig. 14.11).

Corrections for this effect have been

~alculated,"~~~ but unfortunately each

calculation applies only to a specific geometry.

The magnitude of wall-and-end effects increases as the size of the counter

decreases. It also increases as the neutron energy increases. In fact, for neutrons

in the MeV range, the distortion of the spectrum due to these effects becomes

so significant that it sets the upper energy limit

MeV) for the use of a

proportional counter as a spectrometer.

Electric field distortion.

The gas multiplication in a proportional counter de-

pends on the intensity of the electric field. Close to the ends of a cylindrical

counter, the strength of the electric field becomes gradually less intense than in

most of the counter volume. This effect produces lower pulses from proton

recoils at the ends of the counter. Detectors with large length-to-diameter ratio

are less affected by this problem. Theoretical corrections of this effect have

been developed and successfully

applied.17

Effect of carbon recoils.

Neutrons detected by methane-filled counters collide

not only with hydrogen nuclei but also with carbon atoms. The ionization

produced by carbon recoils is indistinguishable from that produced by protons.

However, carbon recoils produce pulses that are smaller than those from

protons because of differences in both kinematics and ionization ability. The

maximum fraction of neutron energy that can be imparted to a carbon nucleus

in one collision is

0.28

(versus

for a hydrogen nucleus), and the relative

ionization efficiency of a carbon to a proton recoil is about 0.5." Thus, the

effect of carbon recoils is to add pulses at the low-energy region of the response

Heavy-atom recoils

Wailandend effects

Response obtained without

Figure

14.11

Distortion of the response function because of wall-and-end effects and heavy-atom

recoils.

492

MEASUREMENT

AND

DETECTION OF RADIATION

function (Fig. 14.11). Carbon-recoil effects are so significant for En

100 keV

that methane-filled counters are not usable below this energy.

Variation of energy needed to produce one ion pair.

The measured spectrum

may differ from the proton-recoil spectrum because of nonlinearity in the

relationship between proton energy and ionization produced. That relationship

is expressed by the quantity w(E), defined as the energy needed by a proton of

energy

to produce one electron-ion pair. To be able to use a counter as a

spectrometer, the value of w(E) should be accurately known for the gas of the

counter for all energies below the maximum neutron energy measured. Experi-

ments have shown that the value of w(E) is essentially constant for hydrogen

for neutron energies about

20 keV. Below that energy, w(E) changes slightly

with energy.'7'28 For methane, w(E) seems to be essentially constant between

100

keV and

M~v.~~

Gamma-ray discrimination.

Proportional counters used in a mixed neutron-

gamma field detect both types of radiation. Discrimination of y-ray pulses has

been accomplished

utilizing the fact that the Compton electrons produced by

the gammas have longer range than proton recoils. The

time-of-rise method,

which is now almost universally used, takes advantage of the faster risetime of

the proton pulse relative to that of the electrons. Proton range is so much

shorter than electron range that all the ions produced by the proton arrive at

the anode at about the same time and generate a pulse with a fast risetime. On

the other hand, ions produced by electrons along their path arrive at the anode

over a period of time and generate a pulse with a slower risetime. Thus, using

appropriate electronics, the pulses from gammas can be rejected.

Finite resolution of proton detector.

The resolution of a proportional counter

for monoenergetic protons is derived from two factors. One is a statistical

broadening that depends on the number of ion pairs produced. The other is a

"mechanical" broadening due to imperfections in the design of the counter and

impurities in the filling gas. At an energy of 615 keV, the energy resolution is of

the order of 4 percent, but it deteriorates to about 60 percent at

keV.

Response functions of proportional counters have been measured and

calculated by several people. Verbinski and

GiovanniniZ8 gave a critical study of

response functions of gas-filled counters as well as a comparative study of the

different codes used to unfold their spectra. Figures 14.12 and 14.13 show

measured and calculated response functions for methane- and hydrogen-filled

proportional counters.

Coarse calibration of proportional counters is achieved by using

3~e and Nz

as additives in the gas of the counter and employing the reactions

NEUTRON DETECTION

AND

SPECTROSCOPY

493

Measured

Calculated

lonization, KeV

(a)

800

Measured

Calculated

600

400

200

0~"'"'

200 400 600

lonization, KeV

(b)

Figure

14.12

Measured and calculated response functions for a methane-filled proportional counter

(1.5 in diameter,

3.5

atm pressure).

(a)

At 75°C. 1772 keV.

(b)

At 75°C 592 keV. (From Ref. 28;

dN/dI

is the proton ionization spectrum.)

Measured

Calculated

20 30 40 50

lonization, keV

(a)

(

Measured

Calculated

20 40 60 80 100 120

lonization, keV

(b)

Figure

14.13

Measured and calculated response functions for a cylindrical hydrogen-filled propor-

tional counter (1.5 in diameter, 2.6 atm pressure,

5 percent

N,).

(a)

Electric field distortion,

45T,

keV;

(b)

45T,

100

keV. (From Ref. 28;

dN/dI

is the proton ionization spectrum.)

494

MEASUREMENT AND DETECTION OF RADIATION

Fine calibration is obtained by placing the detector inside neutron filters made

of aluminum, NaC1, and ~eflon.~' The filters generate dips in the unfolded

spectrum, which coincide with the energies of cross-section resonances of the

corresponding isotope. Fine calibration is achieved when the energies of the dips

of the unfolded spectrum coincide with the energies of the resonances.

14.5.4

Organic Scintillators Used as Fast-Neutron Spectrometers

Organic scintillators have proven to be excellent fast-neutron detectors because

they have high and known efficiency, good energy resolution, and low sensitivity

to gammas. The high efficiency is due to their hydrogen content (1.1 hydrogen

atoms per carbon atom, density about

lo3

kg/m3

g/cm3), the relatively

high hydrogen cross section (2.5 b for 2.5-MeV neutrons), and the ability to

make and use them in large sizes. Organic scintillators are the main detectors

used for neutron spectroscopy from

10 keV to 200 MeV.

excellent review

of organic scintillator properties is given in Ref. 31.

Stilbene scintillators were used as early as 1957. Stilbene as a crystal is very

sensitive to mechanical and thermal shock and shows an anisotropic response to

neutrons-i.e., neutrons incident from different directions, with respect to the

crystal lattice, produce different light output. Liquid organic scintillators have

none of these problems; in addition, they have higher H/C ratio, and light

production from carbon recoils relatively lower than in stilbene. For all these

reasons, liquid organic scintillators are almost exclusively used for detecting fast

neutrons.

The NE seriest of organic scintillators has been studied in detail and used

in particular NE 213. The NE 213 scintillator, which is most

commonly used, consists of xylene, activators, the organic compound

POPOP (as

a wavelength shifter), and naphthalene, which is added to improve light emis-

sion. The density of NE 213 is about 870 kg/m3 (0.87 g/cm3), and its composi-

tion is taken to be CH,,,,.

As the size of an organic scintillator increases, the efficiency increases, the

energy resolution deteriorates, and the background increases. The optimum size

for MeV neutrons seems to be a scintillator with a volume

lop4

m3 (100 cm3),

i.e., a cylinder 50 mm in diameter and 50 mm tall. The efficiency of the NE 213

scintillator has been determined by Verbinski et a1.22 using a combination of

measurements and Monte Carlo calculations for 20 neutron energies between

0.2 and 22 MeV.

The response of an organic scintillator to monoenergetic neutrons depends

on effects similar to those discussed in the previous section for proportional

counters, with the exception of electric field distortions. The most important

cause of a response different from the ideal rectangular distribution shown in

Fig. 14.9 is the nonlinear relation between the energy of the proton and the

amount of light produced by the scintillation process. For organic scintillators,

'Manufactured

Nuclear Enterprises, Winnipeg, Ontario, Canada.

NEUTRON

DETECTION

AND

SPECTROSCOPY

495

the light production by protons and heavier ions is essentially proportional to

the

power of the energy deposited22 in the energy range

0.3

MeV

MeV, and linear for lower energies.33 The light production by electrons varies

almost linearly with energy33 (Fig. 14.14).

Response functions for the NE 213 organic scintillator were first obtained

by Verbinski et a1.22 These authors measured the

213 response for 20

energies between 0.2 and 22 MeV and then normalized the spectra to Monte

Carlo calculations. One additional response was constructed at 10 MeV from

Monte Carlo calculations and from interpolation of the measured responses at

and 12 MeV. These 21 neutron response functions are included in the FER-

DOR/COOLC but they constitute an insufficient response matrix.

Ingersoll and

~ehrin~,~~,~~ using an interpolation scheme, expanded these data

into an 81-column matrix, and used it successfully to unfold neutron spectra up

to 20 MeV. This expanded matrix, along with a measured gamma-ray response

function,34 is included in the FORIST code package.26 Figure 14.15 shows

typical response functions for monoenergetic neutrons up to 8.12 MeV. Figure

14.16 shows a pulse-height distribution and an unfolded spectrum. Two other

unfolding methods can be found in Refs. 37 and

38.

Neutron-gamma discrimination is essential for satisfactory performance of

an organic scintillator as a neutron spectrometer. Fortunately, rejection of

gamma pulses can be achieved by electronic means. The method is called

pulse-shape discrimination (PSD) and is based on the difference in scintillator

response to gamma- and neutron-associated events. The electrons, which are

produced by gammas, cause scintillations at a rate faster than that due to

protons produced by neutrons. Thus, the electron pulses, which are associated

with photon interactions, have a faster risetime than the proton pulses associ-

ated with neutrons. There are many

PSD

circuits.

All

of them generate a pulse

with amplitude dependent upon the fast and slow components of the scintilla-

tion. The PSD circuit used by Burrus and verbinski20 produces a large positive

pulse for neutrons and a small positive or large negative pulse for gammas.

10'

Electrons

Figure

14.14

Light response of

NE 110

(plastic)

and

213 scintillator as a function

electron

Electron or proton energy, MeV

and proton energy (from

Ref.

35).

496

MEASUREMENT AND DETECTION

RADIATION

Cross

section

Figure

14.15

Response functions of

213 spectrometer. The curves represent

the

quantity

ki(E),

Eq.

14.37 (from Ref. 20).

Johnson et al.36 used a time-to-amplitude converter to generate a signal propor-

tional to the risetime of the pulses produced in the scintillator (Fig. 14.17).

Organic scintillators can be used in time-of-flight measurements because

they have shown timing resolution less than

ns3' (see Sec. 14.8).

14.6

DETECTION OF FAST NEUTRONS USING THRESHOLD

ACTIVATION REACTIONS

Detection of fast neutrons

threshold activation reactions (or threshold

detectors) is based on the existence of an energy threshold for certain reactions

of neutrons with nuclei. Thus, if one activates a foil made of such nuclei, the

activity of the foil will give a measure of the neutron

flux

above the threshold.

Consider, for example, the (n,

and (n,2n) cross sections of

27Al

46~i

shown in Fig. 14.18. If

and Ti foils are irradiated, the activity produced

(activity of 24~a and 45~i) will be a measure of the neutron

flux

above

MeV

and

13 MeV, respectively.

NEUTRON

DETECTION

AND

SPECTROSCOPY

497

Channel number

-10

8 10 12 14 16 18

Energy, MeV

Figure

14.16 Pulse-height distribution and un-

folded neutron spectrum obtained with a 46-

46.5-mm diameter

213

organic scin-

tillator (from Ref. 20).

The main advantages of this technique, over the use of other spectrometers,

are

follows:

The foils have

small volume and

low cross section; therefore, they do not

disturb the neutron field.

The foils are almost insensitive to gammas.

Their small size makes the location of foils possible in places where no other

spectrometer would fit.

The counting equipment does not have to be carried to the radiation area.

As shown in Sec.

14.4,

the saturation activity

of a foil is given by