Tsoulfanidis N. Measurement and detection of radiation

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528

MEASUREMENT

AND

DETECTION OF RADIATION

15.4 SOURCES OF RADIATION

Intensities, energies, and special characteristics of the various radiation sources

are briefly discussed in this section.

15.4.1 Sources

Neutrons

Neutron sources include nuclear reactors, accelerators, and isotopic sources.

Nuclear reactors are, by far, the most frequently used irradiation facilities. They

provide high fluxes [upper limit

1018 neutrons/(m2. s)] of mostly thermal

neutrons

eV). Fast neutrons in the keV range are also available, but at

lower

flux

levels.

When short-lived isotopes are involved, a higher activity is produced by

irradiating the sample in a reactor that can be pulsed (see Lenihan et al.). Such

a reactor producing a high flux of about

lo2'

neutrons/(m2. s) for a short

period of time (milliseconds) is the TRIGA reactor, marketed by General

Atomic.

Accelerators produce fast neutrons as products of charged-particle reac-

tions. The most popular device is the so-called neutron generator, which

operates on the reaction

+:H

+in +;He

17.586

MeV

The cross section for this exothermic reaction peaks at a deuteron kinetic

energy of about 120 keV with a value of about

b. The neutrons produced have

an energy of about

MeV. (The neutron kinetic energy changes slightly with

the direction of neutron emission.) The maximum neutron flux provided by a

neutron generator is of the order of 1012 neutrons/(m2

s).

Neutrons with an average energy of about

2.5

MeV are produced

the

(d, d) reaction

The cross section for this reaction peaks at about 2-MeV bombarding deuteron

energy with a value of about 100 mb. At acceleration voltages normally used in

neutron generators

150 kV), the cross section is about 30 mb. The (d, d)

reaction offers neutron fluxes of the order of

lo9

neutrons/(m2. s). It is

important to note that both the (d,

and the (d, d) reactions produce essen-

tially monoenergetic neutrons.

Isotopic neutron sources are based on

(a,

n) and (y, n) reactions, and on

spontaneous fission ('"~f). They all produce fast neutrons. The

(a,

n) and

(y, n) sources produce the neutrons through the reactions

ACTIVATION

ANALYSIS

529

The isotope 252~f is the only spontaneous fission

(SF)

source of neutrons easily

available. It provides fission spectrum neutrons with an average of 2.3 MeV. The

characteristics of isotopic neutron sources are given in Table 15.4.

15.4.2

Sources of Charged Particles

Apart from certain a-emitting radioisotopes, accelerators are the only practical

sources of charged particles. They can provide almost any charged particle or

ion for bombardment

the target for a wide range of energies. The particles

most commonly used as projectiles are protons, deuterons, alphas, tritons, and

3~e nuclei. The beam current of the accelerator is related to particles per

second hitting the target by the equations33

where

the beam current in mA

the charge of the accelerated particle in units of the electronic charge

Knowing the number of particles per second hitting the target and the cross

section for the reaction, one can calculate the reaction rate.

15.4.3

Sources of Photons

The sources of photons include radioisotopes, nuclear reactions, and brems-

strahlung radiation.

There are many radioisotopes that emit gamma rays. The most useful ones

are as follows:

Na with a 15-h half-life emitting y's with energy 1.37 and 2.75 MeV

2. 60~o with 5.3-year half-life emitting y's with energy 1.17 an 1.33 MeV

124

Sb with a 60-d half-life emitting y's with energy 1.71, 2.1, and 2.3 MeV

Table

15.4

Isotopic Neutron sourcest

Average Half-life of

neutron isotope

Source

Reaction Yield

energy

(MeV)

involved

la6

Ra-Be

(a, n)

10' neutrons/s.g

(Ra)

-4

1,600

Po-Be (a, n)

101° neutrons/s.g (Po) -4 138.4 d

239

Pu-Be (a,

1.0

lo5

neutrons/s-g

(Pu)

-4 24,131

Am-Be

(a, n)

lo6

neutrons/s*g

(Am)

-4 432

la4

Sb-Be

(7,

n) 1.0

10'" neutrons/s-g

0.024 60.2

Cm-14' Am-Be

(a, n) 1

10'" neutrons/s-g (Cm)

4 162.8 d

(14' Cm)

lS2

(SF)

10" neutrons/s.g 2.3 2.646

t~rom Lenihan, Thornson, and Guinn.

530

MEASUREMENT

AND DETECTION OF RADIATION

4. "Na with a 2.6-y half-life emitting a gamma with energy 1.275 MeV ("Na

being a positron emitter is also a source of 0.511-MeV gamma rays)

Photons of extremely high energy may be produced by nuclear reactions.

Examples are

H(p, y)4~e

19.8 MeV

Li(p,

-y

18~e

14.8 and

17.6

MeV

B(~, y)12c

11.7 and 16.1 MeV

Unfortunately, the gamma fluxes generated by these reactions are very small,

relative to neutron fluxes produced by reactors.

Bremsstrahlung is produced with the help of electron accelerators. The

electrons are accelerated to a certain energy and then are allowed to hit a solid

target. The radiation produced has a continuous energy spectrum, extending

from zero energy up to the maximum electron kinetic energy. Large photon

fluxes are produced, and may be used for activation of rather large samples.

15.5

IRRADIATION OF

THE

SAMPLE

Depending on the selected reaction, irradiation of the sample may take place in

a reactor, in an accelerator, or with an isotopic source. After the selection of an

irradiation facility, the next step is a decision about the irradiation time. If the

sample contains known isotopes at approximately known amounts, it is easy to

estimate the proper irradiation time. If, on the other hand, the sample is

completely unknown, one irradiates the sample for an arbitrary time, checks

some of the isotopes present (from the emitted radiations), and then irradiates

the sample again for a time that will provide enough activity for proper isotope

identification with the desired accuracy.

Since neutrons are, by far, more frequently used for activation analysis than

other particles, neutrons will be assumed to be the projectiles for the equations

discussed next. However, it should be noted that the same equations apply when

some other radiation is used as the bombarding particle.

The equation that gives the activity produced after irradiating the sample

for time

is (for derivation, see Sec. 14.4)

where

mass of the element of interest in the sample

weight fraction (abundance) of isotope with atomic mass Ai (Ai is

an isotope of the element with mass

the element of interest)

A,,

decay constant of the radioisotope produced

ACTIVATION

ANALYSIS

531

cross section for the reaction that makes the isotope with atomic

weight

radioactive

particle

flux

[particles/(m2

s)]

Avogadro's number

Equation

15.2

is valid

(see Sec.

14.4)

The number of target nuclei stays essentially constant, i.e.,

a,&

The radioisotope produced has such a small reaction cross section that

hi+

&'i+

The

flux

is uniform throughout the target.

If the half-life of the radioisotope is much shorter than

to (to

6~~/2),

saturation activity

(A,,,)

is obtained, given by

Equation

15.3

indicates that, for a particular isotope, the activity increases by

irradiating a larger mass

in a higher

flux

The size of the sample (mass m) is dictated by four factors:

The maximum activity that can be safely handled under the conditions of the

laboratory (i.e., shielding of source and detector, existence of remote control,

automated remote handling of samples).

The size of the sample holder.

The self-absorption of the radiation emitted by the sample. This is particu-

larly important if the radiation detected is betas or soft X-rays.

The size of the detector. Little, if anything, is gained by using a sample much

larger than the detector size.

The flux

is determined by the limitations of the irradiation facility. At the

present time, the maximum flux is about 10" neutrons/(m2

s) (thermal neu-

tron flux).

15.6

COUNTING OF THE SAMPLE

After irradiation is completed, the sample is counted using an appropriate

system. The qualitative and quantitative determination of an isotope is based on

the analysis of the energy spectrum of the radiations emitted by the radioisotope

of interest. Sometimes it may be necessary to use information about the half-life

of the

isotope(s). In such a case, counting may have to be repeated several times

at specified time intervals.

The counting system depends on the radiation detected. Modern activation

analysis systems depend on the detection of gamma rays and X-rays and very

532

MEASUREMENT AND DETECTION OF RADIATION

seldom on detection of other particles. For this reason, the discussion in the rest

of this chapter is based on the assumption that the irradiated sample emits

photons.

A basic counting system for activation analysis consists of a detector

[Ge or

Si(Li)], electronics (i.e., preamplifier, amplifier), and a multichannel analyzer

(MCA). Modern MCAs do much more than record the data. They are minicom-

puters or are connected to computers that store and analyze the recorded data.

Examples are the

ADCAM architecture offered by EG

G ORTEC and the

Genie-ESP VAX-based Data Acquistion and Analysis System offered by Can-

berra.

15.7

ANALYSIS

THE RESULTS

The analysis of an activation analysis spectrum is based on the procedures

described in Sec. 12.7.3. It is performed either by the MCA itself, if that

instrument has such capability, or by a digital computer. Several computer codes

have been written for that

p~rpose.~~-~'

Activation analysis may be qualitative or quantitative. In a qualitative

measurement, only identification of the element is involved. This is accom-

plished, as shown in

Sec. 12.7.3, from the energies and intensities of the peaks of

the spectrum. In a quantitative measurement, on the other hand, in addition to

identification, the amount of element in the sample is also determined. To

illustrate how the mass is determined and what the errors and sensitivity of the

method are, consider the energy spectrum of Fig. 15.1 as an example.

Assume that the mass of an element in the sample will be determined from

the full-energy peak at

E,.

Using the notation of Sec. 14.4, the mass

is given

by (see Eq. 14.22)

where

net number of counts under the peak (determined by one of the

methods described in Sec. 12.7.3)

E(E,)+

absolute full-energy peak detector efficiency at energy

probability that a photon of energy

is emitted per decay of the

isotope (also known as intensity of this gamma)

counting time

The error in the value of

depends on the errors of the quantities that

comprise Eq. 15.4, such as

P,,

a,, and

In the most general case, the

standard derivation

'In activation analysis, the efficiency is determined in such a way as to include the solid angle

and the other correction factors

F(E,)

discussed in Chap.

ACTIVATION

ANALYSIS

533

200 300

400

500

600

700

800 1000 1100 1200 1300

Channel

Figure

15.1

typical Ge(Li) energy spectrum. The element will be identified using the main peak at

channel

888.

In practice, certain errors are always negligible when compared to others. The

quantities

Ai,

e,,

and

are known very accurately for most isotopes. Also,

the flux

and the efficiency

can be determined with a known but small error.

The error in the times

and

can be negligible. Thus, the major contribution

to the error of

comes from the error of

P,,

i.e., the error of the area under

the peak. Assuming that

upk

is the only important error, the standard error of

or the relative error (using Eq. 15.4) is

Thus, the relative error of

equal to the relative error of

P,,

in this case.

It should be emphasized that only one well-identified peak, and not the

whole spectrum, is needed for quantitative determination of an element in the

unknown sample. The other peaks, if used, should give results consistent with

the one chosen for the analysis, and they should also be utilized as additional

534

MEASUREMENT

AND

DETECTION

RADIATION

check points to remove any doubts in the identification of the unknown. For

example, if the

peak leads to the identification of isotope

other peaks in

the spectrum should agree, in energy and intensity, with additional gammas

emitted by isotope

In practice, the objective of the measurement is often to identify the mass of

a particular trace element in the sample. Then the unknown mass is determined

in a simpler way

irradiating, along with the unknown, a standard sample with

a known mass of the trace element and counting both samples with the same

counter. If

is the mass of the standard and

the mass of the unknown,

using Eq. 15.4, one obtains

where the times

and

are different for the standard and the unknown, but in

both cases,

Use of Eq. 15.8 constitutes a relative method, in

contrast to the use of Eq. 15.4, which represents an absolute method.

15.8

SENSITIVITY OF ACTIVATION ANALYSIS

Sensitivity of the activation analysis method for a particular element refers to

the minimum mass of that element that can be reliably detected. The minimum

detectable mass is determined from

Eq.

15.4 by assuming the most favorable

conditions for the measurement and by setting an upper limit for the acceptable

error of the result. The process is similar to the determination of the minimum

detectable activity discussed in

Sec. 2.20.

Assuming that the observer is willing to accept a maximum error

such

that

sfm

(15.9)

and that the only error in the determination of the mass comes from the

error in the number of counts under the peak, a limiting counting rate can be

defined as follows. If one defines a net counting rate

rk as

then, using Eqs. 2.101, 15.7, and 15.11, one obtains for the minimum acceptable

counting rate

rk,

'~ote that both

and

refer to gross counts and background of the peak

and not the

whole spectrum.

ACTIVATION

ANALYSIS

535

Example

15.1

What is the minimum mass of gold that can be detected by

neutron activation analysis under the conditions listed below?

1016 neutrons/(m2

0.30

t,=2h t,

5 min

0.50 t,

125 min

0.2 counts/min

For gold,

197,

99 b, and

TI,,

2.7 days.

Answer

Using

Eq.

15.12, the minimum acceptable counting rate is

Using Eqs. 15.10 and 15.11,

r,T

0.93(120)

111.12 counts

Since the half-life of lgs~u is 2.7 days,

and the exponential factors

Eq.

15.4 become

exp (-Ai+ ,to)

exp

[(

2.971

10-6)2(3600)1

0.979

exp(-Ai+,t,)

exp [(-2.971

10P6)300]

0.999

exp

(-A,+

,t2)

exp

[(

-2.971

10-6)125(60)]

0.978

Equation 15.4 gives

Example

15.2

What is the absolute minimum mass of an element that can

be detected under the most favorable conditions?

536

MEASUREMENT AND DETECTION OF RADIATION

Answer

The absolute minimum mass will be determined if one assumes

Efficiency 100 percent

Intensity 100 percent (e,

Saturation activity (1

eA'0

Maximum thermal neutron

flux

[

1018 neutrons/(m2

s)]

Then

Eq.

15.4 takes the form

Factors that may further affect the result given by

Eq.

15.13 depend on the

background of the counting system and the maximum acceptable error (both

background and acceptable error affect the minimum acceptable value of

P,).

15.9

INTERFERENCE REACTIONS

One source of error in activation analysis is interference reactions. These are

reactions that produce the same isotope as the one being counted, through

bombardment of a different isotope in the sample.

an example, assume that a

sample is analyzed for magnesium by using fast-neutron activation. The reaction

of interest is 24~g(n, p)24Na. Therefore, the activity of 24~a will be recorded,

and from that the amount of 24Mg can be determined. If the sample con-

tains 23~a and 27~, two other reactions may take place which also lead to 24~a.

They are

Na(n

y )24~a

ANn,

)24~a

If this is the case and the investigator does not consider these last two reactions,

the mass of

24~g

will be determined to be higher than it is.

Interference reactions are discussed in detail in many activation analysis

books (see Rakovic, and Nargolwalla

Przybylowicz).

few representative

examples are given below:

68~n(n, y)69m~n and 69~a(n, p)69m~n and 72~e(n, a)69m~n

32~(n, p)32~ and 31~(n, y )32~ and 35~l(n, a)32~

O(n, a)14c and 13c(n, y)14c and 14N(n, p)14c

Tc(n,

and 98~o(n, y)99~o

P-

99m~c

~(n, y)32~ and 30~i(n, y)31~iP+31~(n, y)

55~n(n, y )56~n and 54~r(n,

-y

)55~rp-

5s~n(n, )56~n

lgF(n, 2n)18~ and I70(p, y )18F and 180(p, n)18F

ACTIVATION

ANALYSIS

537

In the last two reactions, the proton is produced by the incident fast neutrons

interacting with the target nuclei.

15.10

ADVANTAGES AND DISADVANTAGES OF THE

ACTIVATION

ANALYSIS

METHOD

One of the greatest advantages of activation analysis is its ability to detect most

of the isotopes with an extremely high sensitivity. Other advantages are that the

method

Is nondestructive (in most cases)

Needs a sample with a very small mass

Can detect more than one element at a time

Identifies different isotopes of the same element

Provides results rapidly

Is not affected by the chemical form of the element of interest

The greatest disadvantage of the method is that it requires expensive

equipment, and the analysis of the results is not trivial. Also, activation analysis

does not provide information about the chemical compound in which the

nuclide of interest belongs.

Overall, activation analysis is a very powerful technique, as demonstrated by

its wide use in so many different

fields-i.e., chemistry, biology, medicine,

forensic medicine, industry, archaeology, and environmental research. For de-

tails regarding these special applications, the reader is referred to Refs.

3-33

and to the bibliography of this chapter, in particular, to the books by Nargol-

walla and Przybylowicz, and by Rakovic.

PROBLEMS

15.1

Traces of manganese are suspected in an unknown sample that has been irradiated for 30 min

in a

flux

of 1016 neutrons/(m2. s). Counting started 5 min after the irradiation ended. The 0.8-MeV

gamma of "~n was detected by a counter with a

percent efficiency (F.e.0). The sample gave 500

counts in 5 min, while the background was 30

1 counts/min. Based on this information, calculate

the mass of manganese in the sample and the standard error of this measurement. For "Mn,

b. For 56~n, T,,,

2.58 h.

15.2

What should the minimum activity of a sample be if it is required that in the worst case

0.8r, and the sample is counted in a system for which

0.50, and the background is 100

counts/min. The sample can only be counted for 1 min.

153

In a neutron activation analysis experiment, a 10-percent-efficient Ge(Li) detector with

0.1 counts/min background is used for the measurement of 0.6-MeV y's emitted by the

sample. If the counting time is 5 min,

(a) What is the minimum acceptable counting rate if the maximum acceptable error is

percent?