University of Ljubljana

Faculty of Mathematics and Physics

Aljaž Kolšek

Utilization of Thermal Neutrons

Seminar IV

Abstract:

The neutrons produced in the fission reactions emerge with the average

energy being around 2MeV, therefore neutron moderation is required to

achieve well thermalized neutron flux. Their usage is spread over various

science fields with applications exploiting several physical processes like

neutron capture, elastic and inelastic scattering, upscattering, etc. The

MCNP Monte Carlo neutron transport code is used to calculate the

neutron fluxes and spectra in the TRIGA Mark-II MCNP model.

MENTOR: doc. dr. Andrej Trkov

CO-MENTOR: dr. Luka Snoj

Ljubljana, 2012

Contents

1 Introduction 2

1.1 Neutron Thermalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Moderating Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Utilization of Thermal Neutrons 4

2.1 Neutron Activation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Physical Aspect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.3 Calculating Element Concentration . . . . . . . . . . . . . . . . . . . . 5

2.1.4 FT-TIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Neutron Scattering Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Elastic Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2 Inelastic Neutron Scattering . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Ultracold Neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Designing of the Irradiation Device 12

3.1 The Irradiation Device Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Conclusion 13

References 14

1

1 Introduction

The study of thermal neutrons is a very important part of reactor physics. As the

neutrons are produced in neutron induced fission of a fissile material, they have to be

slowed down to the thermal energies due to the absorption cross section being inversely

proportional to the velocity. This property makes them suitable for measuring the

cross sections of the different isotopes. Their usage is spread over various science fields

with applications exploiting several physical processes like neutron capture, elastic and

inelastic scattering, upscattering, etc. Neutron moderators, such as light water, heavy

water and graphite, are used for neutron thermalization to achieve well thermalized

neutron flux, required for these applications.

1.1 Neutron Thermalization

The neutrons produced in the fission reactions emerge with a distribution (Figure

1) of energies, with the average fission neutron energy being around 2MeV. This

distribution depends on incident neutron energy and nuclear isotope involved, however

it also differs for prompt and delayed neutrons. On Figure 1 is function χ(E) defined

so that χ(E)dE is the fraction of the prompt neutrons with energies between E and

dE.

0 1 2 3 4 5 60,0

0,1

0,2

0,3

0,4

[E]

E [MeV]

Figure 1: Fission spectrum for thermal neutron induced fission in 235U

As we can see most of the fission neutrons are produced in the fast region, but the

fuel absorption cross section has 1/v dependence in the low-energy region (Figure 2).

Therefore neutron thermalization is desirable to sustain nuclear chain reaction in nu-

clear reactors. Neutron thermalization is the process that utilizes inelastic collisions in

the fuel and elastic collisions in the moderator to slow down high energy (fast) neutrons

to thermal equilibrium with the moderator nuclei. The spectrum of the thermal neu-

trons is Maxwellian characterized by the moderator temperature. Their temperature

is around ET = 0.025 eV) at room temperature 293K and velocity 2.2 · 105 cm/s.[1]

2

Cro

ss S

ecti

on [

b]

Energy [MeV]

Figure 2: Energy dependence of the absorption cross section.[14]

1.2 Moderating Power

Some applications and experimental methods require high thermal to fast neutron

flux ratio, therefore neutron moderation is necessary. Cross sections are highly depen-

dant on the type of nuclide in the moderator. The number of collisions necessary to

slow down a neutron to thermal energies is inversely proportional to ξ, which is defined

as the mean lethargy gain per collision. Lethargy is defined as

u = lnE0

E, (1.1)

where E0 is chosen to be maximum energy that neutrons can achieve in the problem.

Better moderators will thus have larger values of ξ. Moderating or slowing down power

of a moderator is defined as ξΣs. This definition does not take into account neutron

absorption, therefore more appropriate quantity is moderating ratio ξΣs

Σa.

Table 1: Slowing down parameters of typical moderators.[1]

Moderator ξ No. of collisions from 2MeV to 1 eV ξΣs[cm−1] ξΣs

Σa

H2O 0.920 16 1.35 71D2O 0.509 29 0.176 5670C 0.158 91 0.060 192

238U 0.008 1730 0.003 0.0092

The moderating ratio and moderating power is given for few materials in Table 1. In

this comparison it is apparent that D2O is better moderator than others. Its advan-

tage is a very low neutron absorption with still sufficiently large moderating power.

However, using heavy water as a moderator is also very expensive with prices being

around $300/kg.[1]

3

2 Utilization of Thermal Neutrons

Thermal neutrons are invaluable tools for applications in fundamental, engineer-

ing and medical science, as their physical properties allow scientists to conduct non-

destructive testing techniques. They have wavelength similar to atomic distances in

crystal lattices, which means these neutrons can produce interference patterns and give

information about material structures. Penetration can be deep into the material, as

they have no electric charge and the neutron-matter interaction is weak. Presence of

the neutron magnetic moment can also help with the research on magnetic structures

of magnetic materials. Moreover, testing of the lattice vibrations can be conducted,

as thermal neutrons have kinetic energy similar to vibration energy of atoms in solids

and liquids.[16]

2.1 Neutron Activation Analysis

Neutron Activation Analysis is a sensitive analytical technique used for quantitative

and qualitative multi-element analysis of major, minor, trace and rare elements in

different types of samples.

2.1.1 Physical Aspect

The sample is bombarded with neutrons, causing one of the most common neutron-

matter nuclear reactions (n,γ) or neutron capture, where a neutron interacts with the

target nucleus via non-elastic interaction and compound nucleus is formed in an excited

state. The excitation energy of the compound nucleus is due to the binding energy of

the neutron with the nucleus.

The compound nucleus almost instantaneously de-excite into a more stable nucleus

through emission of characteristic prompt gamma rays with short half lives in the

order of milliseconds. Frequently can this new configuration also include radioactive

nucleus which also de-excites and emits characteristic delayed gamma rays, but with

much longer half lives that can ranger from part of a second to several years. Therefore

Neutron Activation Analysis splits into two categories: Prompt Gamma-Ray Neutron

Activation Analysis (PGNAA) and Delayed Gamma-Ray Neutron Activation Analysis

(DGNAA).[17]

2.1.2 Detection

Measurements of gamma rays are usually performed with semiconductor detectors,

associated electronics and a computer-based multi-channel analyser. Typical semi-

conductor detector is HPGe (intrinsic germanium) which operates at liquid nitrogen

temperatures (77 degrees K) by mounting the germanium crystal in a vacuum cryo-

stat, thermally connected to a copper rod. Most frequently used type of detector can

4

measure gamma-rays with energies from 60KeV to 3.0MeV. Figure 3 shows typical

gamma-ray spectra from an irradiated pottery specimen.[17]

Most common and efficient neutron sources are nuclear reactors, that can produce

thermal neutron flux of around 1012 − 1014 neutrons/cm2s at maximum power. Highly

sensitive analysis is possible, because the cross section of neutron activation is high

in thermal region for the majority of the elements. However, interfering reactions

must also be considered, as there is a wide distribution of neutron energy in nuclear

reactor. To take this reactions into account, the neutron spectrum in the channels of

irradiation should be known exactly. For this application, mostly thermal neutron flux

is desired.[19]

Figure 3: Gamma-ray spectrum showing several short-lived elements measured in asample of pottery irradiated for 5 seconds, decayed for 25 minutes, and counted for 12minutes with an HPGe detector.[17]

2.1.3 Calculating Element Concentration

The usual procedure to calculate concentration (in units ppm) of an element in the

unknown sample is to irradiate the unknown sample and a comparator with known

amount of the element of interest together in the reactor. If the activities of sample and

standard are measured on the same detector, it is necessary to correct the difference in

decay between the two. Measured counts are usually corrected for both samples using

the half-life of the measured isotope. Equation 2.1 is used to calculate the mass of an

element in the unknown sample relative to the comparator standard.

Asam

Astd

=msam(e

−λTd)sammstd(e−λTd)std

(2.1)

where A is the activity of sample (sam) and standard (std), m is mass of the element,

λ equals decay constant for the isotope and Td is decay time.

5

Table 2: Estimated Detection limits for NAA using decay gamma rays. Assumingirradiation in a reactor neutron flux of 1013 neutrons/cm2s.[17]

Sensitivity [picograms] Elements1 Dy, Eu

1− 10 In, Lu, Mn10− 100 Au, Ho, Ir, Re, Sm, W100− 103 Ag, Ar, As, Br, Cl, Co, Cs, Cu, Er, Ga, Hf, I, La,

Sb, Sc, Se, Ta, Tb, Th, Tm, U, V, Yb103 − 104 Al, Ba, Cd, Ce, Cr, Hg, Kr, Gd, Ge, Mo, Na, Nd, Ni,

Os, Pd, Rb, Rh, Ru, Sr, Te, Zn, Zr104 − 105 Bi, Ca, K, Mg, P, Pt, Si, Sn, Ti, Tl, Xe, Y105 − 106 F, Fe, Nb, Ne

107 Pb, S

The sensitivity of Neutron Activation Analysis is dependent on the irradiation parame-

ters (neutron flux, irradiation and decay times), measurement conditions (measurement

time, detector efficiency) and nuclear parameters of the elements being measured (iso-

tope abundance, neutron cross-section, half-life and gamma-ray abundance). Table 2

lists the approximate sensitivities for determination of elements assuming irradiation

in a reactor flux of 1013 neutrons/cm2s and interference free spectra.[17]

2.1.4 FT-TIMS

Fission Track-Thermal Ionization Mass Spectrometry (FT-TIMS) is ultra-sensitive

particle analysis technique that uses high thermal flux from nuclear reactors for sample

irradiation. Firstly, particles are removed from a filter or a swipe by ultra-soneration.

Collodion is added to the suspension in ethanol and all the particles are spread on

polycarbonate disks (Lexan). Each disk is covered with a solid state nuclear track

detector made of another Lexan disk. Well thermalized neutron flux is then applied

that activates fissile atoms and their tracks can be revealed after chemical etching of

the detector. Largest fission tracks correspond to the biggest particles or the highest

enrichment in 235U or 239Pu. Figure 4 shows 100µm tracks that come from 1µm

particles and contain a few picograms of uranium or plutonium.[9]

Figure 4: Fission tracks for uranium particles in Lexan after 1 min irradiation.[9]

6

2.2 Neutron Scattering Techniques

Neutron scattering referring to the experimental technique is a scattering of free

neutrons by matter. It is used in biophysics, physics, chemistry, crystallography, ma-

terials research and many other areas. Depending on the neutron-matter interaction,

two main physical processes are used: neutron diffraction (elastic scattering) for deter-

mining structures and inelastic neutron scattering for the study of atomic vibrations

and other excitations.

The Fermi Golden Rule (Equation 2.4) is a base for single-scattering theory that

describes the s-wave scattering. The result applies to elastic, quasielastic and inelastic

scattering. If the spin coupling term is included in the interaction potential, Eq. 2.2

can also be applied for magnetic scattering.

d2σ

dEdΩ=

kski

∣

∣

∣

⟨

s∣

∣

∣

( m

2π~2

)

V (Q)∣

∣

∣i⟩∣

∣

∣

2

δ(E − Es + Ei), (2.2)

with m being the neutron mass, Es and Ei are the energy states of the nucleus after

and before the scattering and V(Q) is the Fermi pseudo-potential formed of a series of

Dirac Delta functions due to the short-ranged neutron-nucleus interactions.

V (Q) =

(

2π~2

m

) N∑

j

bje−i ~Q~rj , (2.3)

with bj being the scattering length for nucleus j and N is the number of scattering

nuclei in the sample.

2.2.1 Elastic Neutron Scattering

Elastic Neutron Scattering consists of measuring the scattered intensity with vary-

ing scattering angle. This is a way of solving the scattering Equation 2.4

Q =4π

λsin

Θ

2(2.4)

with Q being~Q = ~ks − ~ki, (2.5)

λ is the neutron wavelength and Θ is the scattering angle. Angle variation is performed

by step-scanning or using a position-sensitive detector. Two main types of neutron

scattering methods are used: Neutron Diffraction is using mostly single scattering

events, while Neutron Reflectometry operates in the refraction mode and it involves

a large number of incremental scattering events that completely reflect the incident

neutron beam.

One of the most used techniques is SANS or Small-Angle Neutron Scattering that

uses elastic neutron scattering at small angles from 0.2 to 20 to investigate structures

7

from the near Angstrom sizes to the near micrometer sizes. Figure 5 shows four

basic steps used in this technique. Monochromation is performed mostly by using a

velocity selector, collimation is achieved through the use of source and sample aperture

placed far apart, scattering is done mainly on liquid or solid samples and detection is

performed using a neutron area detector inside an evacuated scattering vessel.

Figure 5: Schematics of the SANS technique.[5]

SANS advantage over other small-angle scattering methods (like small-angle x-

ray scattering) is the deuteration method. This method is done by using deuterium

labelled components in sample in order to enhance their contrast, so SANS can measure

density fluctuations and also composition fluctuations. However, low neutron flux is

the disadvantage comparing to the SAXS (Small-Angle X-Ray Scattering).[5]

Figure 6: Single crystal diffraction pattern obtained from highly packed silica particlesunder gentle shear and in D2O.[5]

Figure 6 shows highly packed silica particles in D2O solution with a 6-fold symmetry

pointing to a body centered cubic structure. Four orders of diffraction spots are visible

before the instrumental smearing becomes overwhelming.[5]

8

2.2.2 Inelastic Neutron Scattering

Inelastic Neutron Scattering techniques are used for the study of thermodynamical,

optical, dielectrical and magnetic properties of materials, which are closely related to

lattice vibrations and crystal field excitations. Equations 2.6 and 2.7 are energy and

momentum conservation equations for one phonon process:

~Q = ~K0 −~K ′ = 2π ~K ± ~q (2.6)

E0 − E ′ = ±hν (2.7)

where E0 and E ′ are respectively the incident and scattered neutron energy, ~K0 ( ~K ′)

is the incident (scattered) wave vector, ~Q is the momentum transfer vector, m is the

mass of the neutron, ν is the frequeny and ~q is the propagation vector of the normal

mode to which the phonon belongs and ~K is the reciprocal lattice vector. The plus or

minus sign refers to creation or annihilation of the phonon.[6]

Most common application utilizing and measuring one-phonon inelastic scattering

is Triple Axis Spectrometry (TAS), shown on Figure 7.

Figure 7: Triple Axis Spectrometer (TAS).[11]

Triple Axis Spectrometer is neutron application, where thermal neutrons from the

reactor core pass through the primary collimator and are reflected on the monochro-

mator crystal (first axis) according to the Bragg Law. Monoenergetic neutrons then

fall on sample (second axis) and are inelastically scattered through an angle Φ. Anal-

yser crystal (third axis) is used as the energy analyser for the inelastically scattered

neutrons and also diffracts neutrons to the position sensitive detector.[6]

9

2.3 Ultracold Neutrons

Ultracold Neutrons (UCN) are those neutrons which have an energy lower than the

average Fermi potential (Eq. 2.9) formed by the scattering length density of constituent

nuclei in matter.[8] They experience special physical properties comparing to the cold,

thermal or fast neutrons under certain velocities, so UCN can be totally reflected at any

angle of incidence from surfaces of most materials. The behaviour of ultracold neutrons

can be described as gas, filling the available volume in material. Their trajectories are

parabolic due to the small kinetic energy and the effect of the potential energy in

Earth’s gravitational field.

Energy of the ultracold neutrons is usually below 300 neV. That corresponds to a

maximum velocity of a few metres per second or a minimum wavelength of a few tens

of nanometres. If their velocity exceeds the critical velocity (i.e. threshold velocity of

a material, over which UCN are no longer totally reflected on the materials surfaces),

neutrons can escape from the traps. However, because the cross section is inversely

proportional to the neutron velocity (Subsection 1.1) and becomes huge for the UCN

energy range, escaped neutrons would be absorbed in a few nanometres of a surface.[20]

Figure 8: Ultracold Neutron Traps.[20]

Figure 8 shows simple schematic of the two different types of ultracold neutron

traps, one using the total reflection mentioned in the paragraph above, and the second

one with the magnetic trap. In a magnetic trap the magnetic field increases in all

directions from its center, thus forcing neutrons with their magnetic moment in the

direction parallel to the magnetic field gradient. A magnetic barrier of 1T completely

reflects the neutrons with velocities below 3.4m/s.[13]

Equation 2.8 represents the customary definition of ultracold neutrons as neutrons

with energies E lesser than effective potential V in the medium.

E < V =2π~2

m

∑

i

Niai ± ~µ · ~B (2.8)

where Ni is the number density of nuclei of type i in the material, ai is the coherent

scattering length of a type i nucleus, and V is the effective potential for the neutrons

in the medium. In practical units the effective potential V can be written as

10

V =157 · ρg/cm3 · afm

A± 6.03 · Bkilogauss [neV ] (2.9)

where ρg/cm3 is the density in g/cm3, a and B are measured in fm and kG, respectively,

and A si the atomic mass of the element in the medium.[7]

2.3.1 Production

Fission neutrons are produced with energies around 2MeV, so they have to be

cooled down for about 13 orders of magnitude to achieve ultra-cold region. First, their

energy is reduced by reactor moderator usually being light or heavy water. The process

is called thermalization, as they reach thermal equilibrium with their environment.

Thermal neutrons can then be cooled down by entering solid methane at temperature

around 45K and become cold neutrons. At the end they enter solid deuterium, where

some of neutrons loose all of their kinetic energy at once. This type of resonance effect

happens when the kinetic energy of the neutron matches one of the possible excitation

energies of the deuterium crystal. Neutron excites the molecules of solid deuterium

and becomes ultracold with reduced energy by five orders of magnitude. UCN effective

temperature is about 1mK in comparison to the solid deuterium temperature of 5K,

so they have to be extracted as quickly as possible, or else they can be heated back up

by next collision.[20]

2.3.2 Utilization

Ultracold neutron storage experiments have improved the production, transporta-

tion and storage of UCN and thus broaden their usefulness on many scientific fields.

Studies of condensed matter utilize ultracold neutrons in reflection and tunneling stud-

ies (UCN Reflectometry), elastic scattering, inelastic scattering and also upscattering.

Absorption cross section vary as 1/v for low energy neutrons, thus making UCN perfect

for measuring absorption in rare isotopes or for making high-accuracy measurements

of absorption cross sections.

Due to the total reflection at any angle of incidence and UCN trapping capabilities,

ultracold neutrons can also be used for measuring neutron lifetime and neutron β-decay

observables to provide fundamental information on the parameters characterizing the

weak interaction of the nucleon. Results can be used to extract a value for the CKM

quark-mixing matrix element Vud, the spin content of the nucleon and tests of the

Goldberger-Treiman relation.[4]

The observation of a non-zero neutron electric dipole moment would provide the

first evidence for Time-Reversal violation and related CP violation as an explanation

for the matter-antimatter asymmetry observed in the universe. This violation is a result

of a photon interaction with the permanent electric dipole moment of the neutron, as

it violates both parity and T invariance.[12]

11

3 Designing of the Irradiation Device

The TRIGA Mark II research reactor at the Jozef Stefan Institute features sev-

eral ex-core irradiation facilities that can be used for different applications, e.g. neu-

tron radiography, radiation damage studies, etc. Recently a few test irradiations were

performed for the Fission Track-Thermal Ionization Mass Spectrometry (FT-TIMS)

method, which requires a well thermalized neutron spectrum for sample irradiation.

The percentage of fast neutrons must be very low, in the range of 0.01% and the

thermal neutron fluence should be about 1015 neutrons/cm2. The MCNP Monte Carlo

neutron transport code is used to calculate the neutron fluxes and spectra in the major

TRIGA ex-core irradiation facilities (Figure 9).

The Radial Beam Port (RBP) and the Radial Piercing Port (RPP) extend radially

from the outer and inner boundaries of the graphite reflector, while the Tangential

Channel (TangCh) and the Elevated Piercing Port (EPP) are tangential to the reactor

core. EPP is marked on Fig. 9 with the dashed line, as it’s not on the same level as

other three. The Thermal Column, a graphite stack that extends from the graphite

reflector to the outer concrete wall of the reactor, thermalizes the neutrons leaking

from the reactor core.

The results of MCNP calculations and data visualization are used in diploma thesis,

that consists of the designing and optimization of an irradiation device, placed in one

of the TRIGA reactor’s ex-core irradiation facilities. Calculations of neutron flux and

energy spectra were made in the irradiation facilities to optimize the position of the

device. Optimal conditions were found in the thermal column, while the irradiation

channels can’t be used for this application.

Figure 9: TRIGA Mark-II top view.

12

3.1 The Irradiation Device Design

The irradiation device is placed in the thermal column. The design consists of an

aluminium vessel filled with heavy water and with the opening for sample insertion.

Inside the vessel is cylindrical opening where the polyethylene capsule can be placed.

Irradiation facilities, several neutron tracks and the irradiation device on Figure 10 are

visualized with Amira, software platform for visualizing and manipulating data.

Figure 10: Side view of the canister filled with heavy water and the capsule placement.

4 Conclusion

Nuclear research reactors such as TRIGA Mark-II are ideal as a source of thermal

neutron flux used in many different applications presented in the seminar. Current

results of MCNP calculations show that with minor modifications sample irradiation for

desired application can be possible. Using the proposed irradiation device, approximate

700:1 thermal to fast neutron ratio was calculated with thermal neutron fluence of

1015 neutrons/cm2.

13

References

[1] J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, 1976

[2] J. R. Lamarsh and A. J. Baratta, Introduction to Nuclear Engineering, Prentice Hall, 2001

[3] G. I. Bell and S. Glasstone, Nuclear Reactor Theory, Van Nostrand Reinhold Company, 1970

[4] A. Frei et al., First Measurement of the Neutron β Asymmetry with Ultracold Neutrons, PhysicalReview Letters 102, 012301, 2009

[5] B. Hammouda, Probing Nanoscale Structures - The SANS Toolbox, National Institute of Stan-dards and Technology

[6] A. A. Z. Ahmad, Thermal Neutron Scattering: Principles & Applications, BRAC UniversityJournal, Vol. I, No. 1, 2004

[7] R. Golub, Ultracold neutrons: Their role in studies of condensed matter, Reviews of ModernPhysics, Vol. 68, No. 2, 1996

[8] Y. Masuda, Ultra-cold neutron production with superfluid helium and spallation neutrons, Nu-clear Instruments and Methods in Physics Research A 440, 2000

[9] S. Baude, M.C. Larriere, O. Marie, R. Chiappini, Micrometric particle’s isotopics: An ultra-

sensitive tool to detect nuclear plant discharge in the environment, Radioprotection-Colloques,Vol. 37, C1, 2002

[10] R. Golub, J. M. Pendlebury, Ultra-cold Neutrons, Rep. Prog. Phys., Vol. 42, 1979

[11] M. C. Rheinstaedter, Triple-Axis Spectrometry, CINS Summer School 2011

[12] R. Alarcon, Fundamental physics with cold and ultracold neutrons, Revista Mexicana de FisicaS53 (3) 125-127, 2007

[13] V. F. Ezhov et al., First Ever Storage of Ultracold Neutrons in a Magnetic Trap Made of Per-

manent Magnets, Journal of Research of the National Institute of Standards and Technology,Volume 110, Number 4, July-August 2005

[14] http://atom.kaeri.re.kr/cgi-bin/endfplot.pl

[15] http://www.coursehero.com/file/1251057/ch3neutrons/

[16] http://www.ndt.net/article/v07n08/guidez/guidez.htm

[17] http://archaeometry.missouri.edu/naa_overview.html

[18] http://www.ne.ncsu.edu/nrp/naa.html

[19] http://www.reak.bme.hu/Wigner_Course/WignerManuals/Budapest/NEUTRON_ACTIVATION_

ANALYSIS.htm

[20] http://www.ne.ncsu.edu/nrp/ucns.html

14