SALVAGUARDIAS Y NO PROLIFERACIÓN
Uranium Enrichment Determination of the InSTEC Sub Critical Ensemble Fuel by Gamma Spectrometry
Determinación
del grado de enriquecimiento del combustible nuclear del conjunto subcrítico
del INSTEC por espectrometría gamma
José L .
Borrell Muñoz, Neivy López Pino, Oscar Díaz Rizo, Katia
D´Alessandro Rodríguez, Fátima Padilla Cabal, Yunieski Arbelo
Peña, Aczel R. García Ríos, Ernesto L. Quintas Muñoz,
Amaya O. Casanova Díaz
Instituto Superior
de Tecnologías y Ciencias Aplicadas (InSTEC)
Ave. Salvador Allende, esq. Luaces, Ciudad de La Habana, Cuba
Centro de Estudios Aplicados al Desarrollo Nuclear (CEADEN)
odrizo@ins tec.cu
ABSTRACT
Lowbackground gamma
spectrometry was applied to analyze the uranium enrichment of the nuclear fuel
used in the InSTEC Sub Critical ensemble. The enrichment was calculated by two
variants: an absolute method using the Monte Carlo method to simulated detector
volumetric efficiency, and an iterative procedure without using standard sources.
The results confirm that the nuclear fuel of the ensemble is natural uranium
without any additional degree of enrichment.
RESUMEN
Se analiza el grado de enriquecimiento del uranio del combustible nuclear usado en el Conjunto Subcrítico del InSTEC mediante espectrometría gamma de bajo fondo. El enriquecimiento se calcula tanto por vía absoluta, simulando la eficiencia del detector por Monte Carlo, como por un procedimiento iterativo que no requiere del empleo de muestras estándares. Los resultados confirman que el combustible nuclear es uranio natural sin ningún grado de enriquecimiento adicional.
Key words: isotope separation, gamma spectroscopy, Monte Carlo method, subcritical assemblies, nuclear fuels
INTRODUCCIÓN
Gamma-ray spectrometry
is a non-destructive passive analytical method utilized in the uranium enrichment
determination. If secular equilibrium exists between the progeny radionuclides
and the long-lived parents
and
,
then the rates of gamma-rays emitted by the progeny will be proportional to
the amounts of the uranium isotopes. Secular equilibrium is obvious for an early
daughter in the decay series, where the radioactive half-lives leading to and
including this daughter are very short compared with that of the parent.
The determination
of the amounts of uranium isotopes
and
present can be performed by gamma-ray spectrometry exploiting either a set of
uranium isotopic standards [1], or a set of radionuclide gamma-ray standards
used to calibrate the detection efficiency of the gamma-ray detector [2,3].
In the latter approach, the radioactivity of a parent nuclide is measured by
the calibrated detector, and hence its number of atoms is determined from the
gamma-ray emission probability and the parent half-life. Recently, an analytical
method for the absolute gamma spectrometric determination of uranium enrichment
without using calibration standards was described [4].
This «simple
method” is based on finding the separation between two “detection
efficiency curves”, one derived from gamma-rays of
within the 143.76 - 205.31 keV energy range and the other from gammarays of
(granddaughter in equilibrium with
)
in the 258.26 - 1001.03 keV range, assuming a similar amounts of
and
nuclides. Then, the enrichment is calculated from the curve’s separation,
applying an iterative procedure to find the “true efficiency curve”.
The InSTEC Sub
Critical Ensemble is a neutron multiplier facility for teaching proposes, made
in the former USSR and installed in Cuba at the end of the 60´s of last
century. It is an ensemble of 165 fuel elements using light water as moderator.
According to the fabricant [5], each fuel element is composed by 8 “natural
uranium” pellets with enrichments between 0.714 and 1.0%. As well known,
natural uranium is defined as uranium-containing materials in which the isotopic
composition of
in uranium atoms is equal to natural isotopic abundance (0.72%). This value
differs with the enrichment reported by the ensemble fabricant.
Taking into the
account the actual IAEA Safeguard Regulations, the main objective of the present
work was
to measure the real isotopic composition of the InSTEC Sub Critical ensemble
fuel elements by gamma spectrometry. Two analytical methods are used: (1) an
absolute method, using a set of point radionuclide gamma-ray standards and a
Monte Carlo Simulation to evaluate the efficiency curve of measurement geometry
(fuel pellet - gamma-ray detector), and (2) the “simple method” without
the utilization of standards source.
Materials and
Methods
Absolute Method:
The uranium enrichment (
), expressed in %, is defined as:
where N( )
and N (
)
are the nuclide number of
and
,
respectively. Generally the amount of
is very small compared with the other two uranium isotopes and usually is neglected
in above equation.
The enrichment
can be expressed as a function of the activity values of
and
.
Starting from the activity definition:
where A is the
activity, N-the number of radioactive nuclei and –
the half-life, and the amounts in mass unit of both isotopes are:
where A()
and A(
)
are the corresponding activity values;
(
)
= 2,5706.
years and
(
)
= 1,633.
years are their half-lives [6] and N A is the Avogadro’s constant. Using
the formulae (1-4), the enrichment of a sample containing uranium can be computed
as:
where k = A ()
A (
)
and
is the corresponding decay constant for each nuclide. The activity values for
the nuclide j can be computed according to the formula:
where
is the ith photopeak area for the nuclide j, t the counting time,
the absolute emission probability corresponding to the ith gamma-ray
for the nuclide j and
is the detection efficiency of the full-energy absorption peak considered, where
is the energy corresponding to the ith gamma-ray for the nuclide j.
The
nuclide emits both alpha and gamma-rays.
is practically a pure alpha emitter, with negligible gamma-ray emissions; however,
his granddaughter
(
;
= 1.17 min, i.e., in secular equilibrium) have several important gamma-ray emissions.
The
and
gamma-rays main characteristics are present in table 1.
The experimental
determination of the detector efficiency for volumetric samples is not a simple
problem. A set of volumetric certified gamma sources (with density, composition
and gamma energy range similar to the samples of interest) is needed. An alternative
way to find the energy-dependent volumetric efficiency (
(
)) is starting from the detector efficiency using a set of point standard sources
(for example,
,
,
,
and
),
compute the point (
(
))
and volumetric (
(
)) energydependent solid angles by Monte Carlo Simulations [9] or a Semiempirical
Method [10], and calculate the volumetric efficiency as follow:
“Simple Method”: This method is an original variant of the Absolute Method. Reordering and applying natural logarithm to Eq. (6) we obtain
As ln (
)
can be expressed as function of the energy logarithm,
,
Eq. (8) becomes:
For fixed experimental conditions every nuclide has the same efficiency curve. In a sample containing uranium we obtain:
where x is any
nuclide in the sample. In the cases of
and
,
for a given energy, Eq. (9) can be written as follows:
Then, plotting
the experimental curves of
versus ln(
)
for
and
using the energies given in table 1, we obtain two parallel curves (see figure
1) separated by ln k. This can be easily verified by subtracting, for a given
energy, Eqs. (11) and (12), taking Eq. (10) into account. Then, we can calculate
the uranium enrichment (Eq. (5)) using the experimental k values.
For ln k
calculation, the set of four experimental points obtained applying Eq. (11)
to
and the set of
four experimental points obtained applying Eq. (12) to
are fitted by means
of a polynomial by least squares. With the selected polynomial using x = ln
(table 1), eight values of
are calculated.
The sum of the squares from the residuals is calculated as follows:
A value of 0.001
is added to the experimental points of the ordinates of
and eight new points are obtained, four points with coordinates
=
+ 0:001,
and four points of
without modification.
These eight points
are fitted again and a new t is calculated. This process of increasing
ordinates in 0.001 and calculating t is repeated until a minimum value of t
is obtained. The resulting curve is the best fit for Eq. (12), giving ln k =
0.001.n, where n is the number of iterations. The value of 0.001 was chosen
taking into account the ln k values [4].
There is only one
condition to use this method: in the sample the radioactive chain
must be in secular equilibrium. If this is true we have:
Sample characteristics
like density, geometric shape, medium (liquid or solid) and type of detector
employed are not a restriction to use this method [4].
Sampling:
Randomly, 17 fuel elements (10.9% of the total) from the internal, middle and
external zones of the Sub Critical Ensemble (see figure 2) and 14 additional
uranium pellets (no used in the current ensemble configuration) were taken for
the analysis. The uranium pellets were fabricated as 1 mm thickness aluminium
cylinder (120 mm large,=
31 mm) refilled with a compacted
powder (2.1 kg total weight) [5].
Gamma spectrometry
of uranium pellets: The gamma spectra of 150 uranium pellets were acquired
in the Low-Background Chamber (LBC) of the Nuclear Analytical Lab at InSTEC,
using an n-type closed-end coaxial high-purity germanium detector (DSG, NGC-3018,
130
, FHWM = 2.04 keV for 1332 keV
gamma line) equipped w ith a 8192 channel multichannel analyzer (webMASTER TARGET
coupled to PC). The gamma spectra were processed using the Gamma-W version 18.03
code (Dr. Westmeier Gesellschaft für Kernspektrometrie mbH). The energy
and efficiency calibrations were carried out using point standard sources (
,
,
,
and
),
produced by AEA Technology QSA GmbH. Fuel elements pellets were placed at 10
cm from the detector to minimize true coincidence summing [11] and measured
during one hour. The LBC is a detector shielded with 55 mm thickness of lead,
35 mm thickness of a steel frame, and an internal graded shielding consisting
of 12 mm thickness of cadmium, 17 mm of cooper and 9 mm of aluminium. The inner
dimensions of the LCB are 800 mm depth ´ 718 mm width ´ 736 mm height.
Monte Carlo simulation:
Monte Carlo (MC) Simulations were carried out to compute the point (
(
)) and volumetric (
(
))
energy-dependent solid angles of Eq. (7). The MCNPX 2.5 was used as simulation
code [12]. It has been used widely to estimate the efficiency curve of HPGe
detectors for volumetric samples [13-17]. The sample - detector configuration
were exactly reproduce in the MC simulation, taking as data the dimensions,
density and chemical elemental composition of the uranium pellets found in Sub
Critical Assemble documents [5], as well as the detector specifications (Ge
crystal dimensions, dead layer and Al thickness, distance Ge crystal to Al end
cap) provided by detector supplier.
Results and
Discussion
A typical fuel
element uranium pellet gamma-ray spectra measured in the InSTEC LBC is presented
in figure 3. The
and
analytical lines (table 1) are remarked. Due to the high count rate in one hour
of measurement, the obtained peak area statistical error was less than 1% for
all analytical lines.
Figure 4 shows the efficiency curves for point sources located at 30 cm of height (experimental), and for the uranium pellets at 10 cm. The last curve was obtained computing the energy-dependent solid angles by MC simulations and taking the 30 cm point efficiency as reference (Eq. 7). Strong gamma rays self-absorption inside the pellets is clearly observed. These curves were well described (using Origin 6.1 code) by the following polynomials:
Table 2 lists the
final results of the uranium enrichment of the 17 ensemble fuel elements and
14 additional uranium pellets determined by gamma spectrometry. Absolute method
shows bigger dispersion and deviation for the expected reference value (0.72%)
than the “simple method”. This agreed quiet well with the dispersion
(9.10%) and deviation for the expected values (-4.90%), obtained for Absolute
method during an international exercise for uranium enrichment measurements
celebrated in 2000 [18]. On the other hand, the precision and accuracy of the
«simethod” results are excellent. The last one confirms the small
dependence of sample characteristics like density and geometric shape of this
method.
Independently of
mentioned above criteria, the results obtained by both methods confirm that
the InSTEC Sub Critical ensemble nuclear fuel is natural uranium. Considering
the enrichment range reported in the 60’ by the ensemble fabricant (0.714
- 1.0%) [5], an idea about a possible small
enrichment degree must be inferred, i.e., an enrichment higher than considered
as “natural” by actual IAEA Safeguard Regulations. The high resolution
gamma spectrometry carried out with modern HPGe detector rejects this possibility.
References
[1] NIR-EL Y. Isotopic
analysis of uranium in U 3 O 8 by passive gamma-ray spectrometry. Applied Radiat.
Isot. 2000; 52(3) 753-757.
[2] LUCA A. Experimental determination of the Uranium enrichment ratio. Rom.
Jour. Phys. 2008; 53 (1-2): 35-39.
[3] SHOJI M, HAMAJIMA Y, TAKATSIKA K , et. al. A convenient method for discriminating
between natural
and depleted uranium by g-ray spectrometry. Applied Radiat. Isot. 2001; 55(2):
221-227.
[4] KOROB RO, BLASIYH NUÑO GA. A simple method for the absolute determination
of uranium enrichment by
high-resolution g spectrometry. Applied Radiat. Isot. 2006; 64(5): 525-531.
[5] Documentación Técnica del Conjunto Subcritico. Laboratorio
del Conjunto Subcritico del InSTEC, 1968 (en Ruso).
[6] FIRESTONE RB. Table of Isotopes. Eighth edition. Wiley Interscience, 1996.
[7] SCHMORAK MR. Nuclear Data Sheets Update for A =235. Nuclear Data Sheets.
1993; 69(2): 375-428.
[8] AKOVALI YA. Nuclear Data Sheets for A = 234. Nuclear Data Sheets. 1994;
71(1): 181-259.
[9] VIDMAR T, AUBINEAU-LANIECE I, ANAGNOSTAKIS MJ, et. al. An intercomparison
of Monte Carlo codes used
in gamma-ray spectrometry. Applied Radiat. Isot. 2008; 66(6-7): 764-768.
[10] LEPY MC, ALTZITZOGLOU T, ARNOLD D, et. al. Intercomparison of efficiency
transfer software for gamma-ray spectrometry. Applied Radiat. Isot. 2001; 55(4):
493-503.
[11] GILMORE G, HEMINGWAY J. Practical Gamma-ray Spectrometry. Wiley, Chichester,
1995, pp. 137-138,
148-159.
[12] PELOWITZ DD. MCNPX TM User's manual. Version 2.5.0. Report LA-CP-05-0369.
Los Alamos National
Laboratory. 2005.
[13] RÓDENAS J, MARTINAVARRO A, RIUS V. Validation of the MCNP code for
the simulation of Ge-detector
calibration. Nucl. Inst. and Meth. in Phys. Res. 2000; A450(1): 88-97.
[14] KARAMANIS D. Efficiency simulation of HPGe and Si(Li) detectors in ã-
and X-ray spectroscopy. Nucl. Inst.
and Meth. in Phys. Res. 2006; A505(1-2): 282-285.
[15] MARQUES SALGADO C, CONTI CC, BECKER PHB. Determination of HPGe detector
response using MCNP5 for 20-150 keV X-rays. Applied Radiat. Isot. 2006; 64(6):
700-705.
[16] RODENAS J, GALLARDO S, BALLESTER S, et. al. Application of the Monte Carlo
method to the analysis
of measurement geometries for the calibration of a HP Ge detector in an environmental
radioactivity laboratory. Nucl. Instr. and Meth. B. 2007; 263(1). doi:10.1016/j.nimb.
2007.04.210.
[17] SAEGUSA J. CREPT-MCNP code for efficiency calibration of HPGe detectors
with the representative point method. Applied Radiat. Isot. 2008; 66(6-7): 774-779.
[18] MOREL J, HILL C, BICKEL M, et. al. Results from the international evaluation
exercise for uranium enrichment measurements. Applied Radiat. Isot. 2000; 52(3):
509-522.
Recibido: 12 de
Julio de 2008.
Aceptado: 14 de mayo de 2009.