Крючков Фундаменталс оф Нуцлеар Материалс Пхысицал Протецтион 2011

should be as simple as possible. In the event of a complex spectrum, there are “inactive” high-energy lines that create the ba ckground in the region of measured X-rays or even interfere with these.

Table 5.10 gives the values of the Pu and U X-ray energy and yields.

						Table 5.10
Values of the Pu and U transition energies and X-ray yields
Line	Transition	Uranium, %		Plutonium, %
Kα1	K-L3	98.44	(100)	103.76		(100)
Kα2	K-L2	94.66	(61.9)	99.55	(62.5)
Kβ1	K-M3	111.31 (22.0)		117.26		(22.2)
Kβ3	K-M2	110.43(11.6)		116.27		(11.7)
Lα1	L3-M5	13.62	(100)	14.28	(100)
Lα2	L3-M4	13.44	(10)	14.08	(10)
Lβ2	L3-N5	16.43	(20)	17.26	(20)
Lβ1	L2-M4	17.22	(50)	18.29	(50)

To observe representative peaks, one needs to choose the proper measurement geometry. Observations may be hampered by the background created by the quanta resulting from the source’s Compton radiation scattering.

The i-th element X-ray quanta detection rate nфi relates to the content of this element Ni in the sample and the quantum yield of its radiation

IiX through the following:

n

= N

i

× I X ×W X

× eX

,

(5.15)

Φ i

i

i

i

where Wi X

is the X-ray excitation function which is the product of the

photoeffect

cross-section

σ Fi (E)

and

the source quanta flux onto the

sample Фγ (Е); and εiX

is the efficiency of X-ray detection:

]× dE ,

W X =

∞siФ(E) ×Ф

γ

(E) × dE = (Z

)5

× ∞[Ф

γ

(E) /(E - E )3

(5.16)

i

∫

i

∫

i

Ei

Ei

where Еi is the threshold energy of photoeffect on the respective electron shell (K or L) of the i-th element, and Zi is the atomic number of the i-th element.

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Obviously, excitation function depends strongly on the Z element and the more, the closer is the energy of the excitation source to the photoeffect threshold energy (the electron binding energy on the shell).

Radioactive gamma sources have small dimensions. They are also simple to handle and fit for many XFAs. The major deficiency involved in these is disintegration thereof over time and the requirement to have them periodically replaced. There is also a transportation problem. As the power of such sources is over 1 mCi, handling them requires shielding of both personnel and the detector. An XFA facility layout is shown schematically in Fig. 5.13.

As with passive gamma measurements, the XFA data accuracy may be limited by the absorption inside the sample. This effect is to be taken into account both for the characteristic radiation measured and for the exciting radiation of the external source. The absorption in large-size and solid samples is so great that XFA is not appropriate for analyzing such samples. So it is used to control liquid homogeneous samples.

The source radiation absorption is more intensive as the radiation energy exceeds the absorption threshold for the NM analyzed. Attenuation depends also on the material and the thickness of the container walls. An XFA to study L-radiation requires using plastic rather than metallic containers.

The XFA measuring system is calibrated using a set of reference solutions with different NM concentrations in containers, these being of the same type as used for the solutions under examination.

57Co source

Removable uranium foil

Detector shielding

Solution sample

Lead

Aluminum

Fig. 5.13. Schematic of an XFA facility

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X-ray generator has more power than radioactive sources. It generates 1012 photons/s and more. The major complications involved in using generators are the requirement to keep high stability of the parameters thereof and relatively large dimensions that make it difficult to move them.

X-ray fluorescence measurements help determine the relation of NM concentrations in a solution. Fig. 5.14 gives the spectrum of a solution with a content of uranium and plutonium.

		98.44
		UKα1
	94.66				111.30
	UKα2				UKβ1
			110.43
			UKβ3

Count

103.73 Pu Kα1

Channels

Fig. 5.14. Fluoresecence spectra of uranium and plutonium solutions

The U/Pu weight relation can be found from the areas of the XKα1 peak for uranium (SU) and the XKα1 peak for plutonium (SPu):

U / Pu =	AU	×	S U	×	ε Pu	×	1	,	(5.17)
	APu		S Pu		ε U		RU / RPu

where AU and APu are the atomic masses of uranium and plutonium, (εPu/εU) is the relative efficiency of uranium and plutonium detection; and (RU/RPu) is the factor allowing for the difference in the probabilities of uranium and plutonium radiations being excited using the given source.

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Neutron measurements of NM

There are three processes causing neutron irradiation of NM samples:

∙spontaneous NM fission;

∙induced NM fission;

∙(α, n) – a reaction induced by NM α-radiation.

Neutrons are highly penetrating particles. They go out from all over the sample and pass easily through the walls of the container with the sample.

Spontaneous fission is most likely for isotopes with an even mass number (238Pu, 240Pu, 242Pu and others). The relative probability of 240Pu

fission with emission of a different number of neutrons is shown in Fig. 5.15. The average number of neutron/fission is about 2. Altogether, there are 473 spontaneous fissions per second occurring in 1 g of 240Pu.

Fission

fraction

0.4

0.3

0.2

0.1

0.0

0

1

2

3

4

5

6

Number of neutrons

Fig. 5.15. Relative probability of fissions with emission of different neutron numbers

The number of neutrons generated by one fission is called multiplicity. In total, 1 g of 240Pu has 473 spontaneous fissions per second taking place therein.

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The technique based on detection of spontaneously emitted neutrons is called passive.

Handling of passive neutron measurement results often includes the notion of “effective” 240Pu which is believed to account for all neutron radiation of a plutonium sample:

240Pueff=2.52× f238+f240+1.68×f242,

(5.18)

where fi is the fraction of the i-th plutonium isotope in the sample.

Induced fission is most likely for fissile isotopes (235U, 239Pu, 241Pu). Induced fission generates 0–8 neutrons per fission. In the event of 239Pu, the average number of these is about 3. The neutron measurement method using an external source is called active.

More neutrons may be generated in spontaneous or induced fission as the result of the multiplication thereof in the sample. The (a,n)-reaction is an extra source of neutrons that hampers neutron measurements of NM. Radioactive decays of uranium and plutonium isotopes are commonly accompanied by emission of a-particles. The energies of the emitted a- particles are from 4 to 6 MeV. A major source of a-particles is also 241Am.

Alfa-particles emitted by uranium and plutonium react with 11 elements with a small atomic number Z, including oxygen, fluorine, carbon and aluminum.

One neutron is generated as the result of the (a, n)-reaction. Cases of single ((a,n)-reactions) and multiple (spontaneous and induced fission) neutron generations may be divided by detecting time coincidences of neutrons.

Helium counters are commonly employed to detect neutron in NM test measurements. The reaction taking place in such counters is the (n, p)- reaction:

3He + n ® 3H + 1H + 765 keV

(5.19)

The 3He(n,p) reaction cross-section for thermal neutrons reaches 5330 barns and varies in a broad energy range (10-2 to 105 eV) according to the

law 1/ E .

For higher efficiency of fast neutron counting, the counter has a moderator made around it. The 3He-counter is normally placed in a 10-cm thick polyethylene block.

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3He-counters are fit for neutron measurements in strong g-fields. They

are highly reliable, stable and durable.

Active analyses for the contents of fissile isotopes (235U, 239Pu, 241Pu) in samples require a source of neutrons with the energy below the fission thresholds of even-even isotopes (238U, 240Pu). Such neutrons are emitted by 241AmLi-sources. Fig. 5.16 shows the neutron spectrum of a 241AmLisource. The power of 241AmLi-sources used for nondestructive assays is 104–10 5 n/s.

Real cases generally give an excessive number of the sample-emitted background neutrons from (α, n)-reactions, this making it impossible to find the NM content by counting single neutrons. Active analyses have the same intensive background created by neutrons from the (α, n)-reactions inside the source.

As noted, one can separate the neutrons generated by the fission of isotopes in the NM sample from the neutrons of (α, n)-reactions by detection of time-coinciding pulses.

If the number of neutrons emitted in a fission equals n, the probability of detecting k neutrons is given by the equation:

	P(n, k ) =	n!		×ε k × (1	- ε )n−k .	(5.20)
		(n - k )!k!

N(E)

0

0.5

1.0

1.5

Energy, MeV

Fig. 5.16. Neutron spectrum for a 241AmLi-source

If two neutrons have been emitted, the probability Р(2,0) of no neutrons to be detected is equal to 0.64; the probability Р(2,1) of detecting one neutron is 0.32; and the probability Р(2,2) of having two neutrons detected

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is 0.04. Therefore, the probability of detecting an actual coincidence of two neutrons from one fission is relatively small. A great deal of coincidences observed in a sequence of pulses will be random and caused by coincidences between the neutrons of (α, n)-reactions, the neutrons of (α, n)-reactions and fission neutrons or neutrons from different fissions.

To identify and determine the number of real and random coincidences, Rossi-alpha distribution is used. This distribution is obtained when the timer is started at the instant the pulse arrives. The timer counts the time and each subsequent pulse is memorized in the cell that matches its arrival time. When the preset time of counts is over, the timer stops and is switched on again as the new pulse launches the counting. Fig. 5.17 presents a Rossi-alpha distribution. The probability of the coincidence count after the fission event is decreased exponentially over time. Where neutrons of (α, n)-reactions or background neutrons coincide, the probability of such random coincidences in any time interval is the same.

Number of cases

t = 0

exp(-t/τ)

R

A A

P G D G

Time

Fig. 5.17. Rossi-alpha distribution represents the number of neutron detection cases as the function of the time that has elapsed after the first fission neutron was detected

The number of true double coincidences is found by the formula:

= [(R + A)count - Acount ] ×exp(G ×T )

R [ ] [ ] , (5.21) exp(-P /τ ) × 1- exp(-G / τ ) × 1- exp(-(D + G) / τ )

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where R is the number of true coincidences; A is the number of random coincidences; P is the time of the pulse count delay, G is the coincidence count time; D is the long delay; τ is the time of the neutron life in the detector, and D >>τ; Т is the total neutron count rate.

A neutron coincidence counting circuit is shown in Fig. 5.18.

In

Predelay

Gate

Long delay

Gate

P

G

D

G

			СС					СС
General
counter
			R+A					A
			counter					counter

Fig. 5.18. Separation of fission neutron coincidences

Practical uses of such circuits are confined to count rates of below 20– 30 kHz as large corrections are required to take into account dead time of electronics. Further evolutions of measuring technology were based on using a shift register.

A shift register comprises a set of timer-controlled triggers. The sequence of pulses coming in for the time G is memorized. Each subsequent pulse opens its own gate so there is no need to wait for one gate to close to have another gate opened. It makes it possible to operate count rates of hundreds of kHz and more. Coincidences start to be detected not straight away but just in a short interval after the pulse P arrives (preliminary delay). During this time (3–6 µs), the coincidence source rate is distorted due to overlapping pulses and the electronics dead time. Following the preliminary delay, the shift register opens the R+A gate, the width of which is normally 32–64 µs. True and random coincidences are detected during this time. Then, after the long delay D, the gate А opens. As the quantity D is normally equal to 1000 µ, which exceeds considerably the neutron lifetime in the detector (30–100 µs), the scaler А detects only random coincidences.

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A simplified shift register circuit is given in Fig. 5.19.

In

	Predelay	Shift register for R+A-
		gate

UP-DOWN (bidirectional) counter

R+A		A
counter		counter

Long delay

Fig. 5.19. A shift register circuit

Measurements using the above shift register can produce only two quantities: random and true double coincidences. Some contaminated or heterogeneous samples require one more quantity, triple coincidence (triplet) count rate, to be measured.

Measurements of single neutrons, doublets and triples may help determine the quantity of the 240Pu effective mass, the neutron multiplication factor in the sample and the yields of (α, n)-neutrons without the need to calibrate the measuring system.

Instrumentation for NM neutron measurements

There is a variety of measuring systems for a range of applications fit to analyze different types of samples, including containers with PuO2 powder, pellets and rods filled with mixed uranium-plutonium fuel, metal slugs, intact fuel assemblies, and drums with scrap and waste. Unlike chemical analyses where the sample is adapted to the instrument, nondestructive assays have equipment adapted to the sample.

Neutron analysis is used to control highly dense NM with results thereof having the potential of depending greatly on the matrix material.

Coincidence count results are used to determine the NM quantity in samples in passive and active neutron measurements.

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Passive neutron methods are employed extensively to test plutonium samples which emit their own neutrons as the result of spontaneous fission and during (α, n)-reactions (Table 5.11) in different forms: in fuel slugs, rods, powders, granules, scrap, waste and PuO2+UO2 mixtures. To interpret such measurement results, one needs to know the plutonium isotopic

composition (spontaneous fission occurs largely in even isotopes such as Pu: 238Pu, 240Pu and 242Pu).

Active neutron methods serve to control uranium samples for the content of 235U as the uranium isotope spontaneous fission rates are low. Use of an AmLi-source in the sample causes induced fission with the number of fissions found by counting neutron coincidences. High penetrating power of neutrons enables determination of the total 235U content in the entire volume.

					Table 5.11
		Yield of NM-emitted neutrons
	Spontaneou	Yield of	α-decay	Yield of	α,n yield in
	s fission	spontaneoeus-
Isotope			period,	α-particles,
	period,	fission neutrons,			oxide, n/s×g
			years	α/s×g
	years	n/s×g
238U	8.2×1015	1.36×10-2	4.47×109	1.2×104	8.3×10-5
238Pu	4.77×1010	2.59×103	87.74	6.33×1011	1.34×104
239Pu	5.48×1015	2.18×10-2	2.41×104	2.3×109	3.81×101
240Pu	1.16×1011	1.02×103	6.56×103	8.4×109	1.41×102
242Pu	6.84×1010	1.72×103	3.76×105	1.4×108	2.0

Passive coincidence count is based largely on the following principles:

∙the NM sample is placed in a cavity surrounded by neutron counters;

∙coincidences of pulses generated by spontaneous-fission neutrons are detected;

∙the coincidence count rate is directly proportional to the mass of the fissile material:

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