Measurement of Thermal Neutron Flux
and
Measurement of Thermal Neutron Radiative Capture Cross Section
Purpose: The purpose of this experiment is to measure the flux of thermal neutrons in a water moderator
using irradiation of foils and then, in this flux of neutrons to measure the thermal neutron
radiative capture cross section on another nuclide.
Method: Thin foils of known composition (e.g., indium) will be placed in a field of thermal neutrons
whose flux in a neutron/cm2 / sec will be assumed to be time-independent. (In the case of
indium, this will be naturally-occurring indium and therefore its composition will not be isotopically
pure. The nuclei in these foils when placed in this neutron flux will, with some probability, capture
neutrons via the radiative capture process (n,) producing radioactive isotopes of indium. These isotopes
will decay via known decay processes and known lifetimes and emissions from the decays can be
detected allowing one to measure the number of decays detected in a given time period. Working
backward, it will be possible to calculate the neutron flux in which the foil was placed so as to produce
the measured number of counts.
Once this thermal neutron flux has been measured, it will be used as the source of neutrons for a
radiative capture (n,) cross section measurement. The assumption that the flux is time-independent is
important because some time will elapse (e.g., 1 week) between when the flux measurement is made and
when the cross section measurement is made.
To understand the method, it is necessary to understand the characteristics of the thermal neutron flux
field. This is understood to be best described as an ideal gas of neutrons whose (kinetic) energy spectrum
is determined by one parameter, the absolute temperature of the “gas” T. (In fact, given the short range
of the nuclear force by which the neutrons scatter, this is likely one of the most perfect “ideal” gas
examples. Therefore, the distribution of neutron velocities is described by a Maxwell-Boltzmann
distribution. (A separate write-up describes this in more detail.)
It is important to understand, however, that the means by which the neutrons are created in this “source”
is by a nuclear reaction 9Be(,n)12C. The source of the alpha particles is the radioacative decay of 239Pu
 235U. The 239Pu is mixed with 9Be placing the 9Be in proximity to 239Pu nuclei so as to be able to
capture the emitted -particle. These sources are known as PuBe sources and each of the 5 we have emits
~16 x 106 neutrons/sec. The neutrons emitted have an initial range of energies that are considered “fast”
neutrons, e.g., 4-9 MeV in kinetic energy. However, via elastic collisions with the hydrogen nuclei in the
water environment they quickly lose energy, passing through the “epithermal” neutron energy range
(~100 eV – 100 keV) and eventually into the thermal neutron energy range (0.0 - ~100 eV). At any given
time, the foil will be exposed to neutrons of all energy ranges in some unknown composition or mixture.
The cross section for capture of “fast” neutrons on indium is vanishingly small compared to the capture
rate for thermal neutrons. This is not the case for epithermal neutrons whose capture rate is much
smaller than thermal neutrons, but is not negligible and therefore, we will need to account for the effects
of epithermal neutrons so as not to include their activations (captures) with the ones from thermal
neutrons when determining the flux of thermal neutrons (only).
If a thin foil is exposed to the neutron flux for a known time, t o , the saturation activity of the foil can be
obtained from the following relation: i
As 

C  B

  t t    t t 
 1 e t o 1 e  1 o  1 e  2 o 
 





(1)
In this equation, the following definitions apply:

 is the decay constant for the radioactive nuclide formed by the capture of a thermal neutron.
C is the observed number of counts measured from time t1 to t2.
B is the measured number of background counts obtained for the same time interval t 1 to t2.
 is the overall efficiency for the detection system used to measure the radiation emitted from the
radioactive nuclide. This factor should include corrections for the intrinsic efficiency of the
detector for the specific radiation detected at that particular energy, and corrections for the
counting geometry which will give the number of counts expected per disintegration of the
nuclide in the foil.
to is the total time of irradiation and the time at which the foil is removed from the neutron field.
to is measured from the time the foil is inserted in to the neutron field taken to t = 0.
t1 is the time the count of radiations emitted from the activated foil is begun. t 1 – to is the elapsed
time between the time the foil is removed from the neutron field and the time the count is
begun.
t2 is the time the count is stopped. t2 – t1 is the net time for the counting.
The activity obtained using the equation (1) for the bare foil in the neutron field is due to the capture of
the thermal neutrons and to the capture of neutrons of higher energies. This total activity can be
expressed as the sum of two induced activities,
As = Ast + Ase
(2)
where Ast is the saturation activity due to thermal neutrons only and A se is the saturation activity due to
epithermal neutrons only. Since we are interested in measuring the thermal neutron flux, we would like
to obtain the activity due to the thermal neutrons only, Ast. This can be done by repeating the above
exposure for a foil encased in cadmium covers which will absorb essentially all of the thermal neutrons.
The activity for this foil obtained using equation (1) will be due exclusively to non-thermal neutrons,
As(Cd). This activity will, however, be slightly less then A se, the saturation activity induced in the bare
foil by non-thermal neutrons since some of the non-thermal neutrons will have been captured in the
cadmium covers. A correction for this loss can be made giving
Ase = FCd . As(Cd)
(3)
The value of FCd will depend on the thickness of the Cd covers and on the thickness of the foil . A graph
of the correction is appending to this write-up.
The net saturation activity due to thermal neutrons is then obtained using equations (2) and (3) to be
Ast = As – FCd . As(Cd)
(5)
Since the foil inserted in the neutron field is of finite thickness, its presence can serve to depress the
thermal neutron flux inside the foil thereby not making the thermal neutron flux uniform throughout the
foil. Hence, the saturation activity obtained using equation (5) should be increased somewhat to
represent the saturation activity that would be induced in the foil were the thermal neutron flux uniform
throughout the foil. The corrected saturation activity is then
Ast = Fth . Ast
(6)
The appropriate value of Fth can be obtained from the graph and equations attached hereto.
Now, it is easy to show that the saturation activity due to thermal neutrons can be written as
 v
'
Ast
 NT   o o n(v)v dv dV
V0 v
In the equation, the following definitions apply:

NT is the number density of a target nuclei in the foil. This number represents only those nuclei
whose activation is used for this measurement.
is the absorption cross section at the mean neutron velocity for the temperature of the
moderator.
vo is the mean neutron velocity at the temperature of the moderator.
n(v) is the thermal neutron number density as a function of neutron velocity. The product
n(v) . v =  (v) , the thermal neutron flux at velocity v in neutron/cm2 . sec.
Assuming the neutron flux is uniform over the volume of the foil, the integration over the volume of the
foil V can be carried out directly. Carrying out the integration over the neutron velocity over the range of
thermal neutron velocities then gives the total thermal neutron number density, nth.
This gives the saturation activity due to thermal neutrons as
A’st = NT V nth vo o
(7)
Equating equations (6) and (7) and substituting appropriately, we obtain
nth = Fth {As – FCd . As(Cd)} / (NT vo o V)
(8)
The thermal neutron flux can be obtained by multiplying nth by the mean neutron velocity for the
temperature of the moderator.
In this experiment, it is proposed to measure the induced activity of the foil by measuring the gamma
activity for a particular gamma energy using a 2”x2” NaI(Tl) detector and MCA. This method is chosen
since the total efficiency for the NaI(Tl) detector as a function of geometry and gamma energy can be
obtained from various references.ii Using this technique, the measured number of counts under the
photopeak for a particular photon energy C’ and background counts B’ under the same photopeak will
have to be corrected to account for the fact that not all disintegrations of the nuclide corrected of the
nuclide will necessarily result in a gamma ray of this particular energy. Hence, the net number of counts
to be used in equation (1) will be obtained from
(C – B) = (C’ – B’) / F
where Fis the fraction of the total disintegrations of the nuclide which will produce a gamma of the
energy collected under the photopeak. This value of F can be obtained from the decay schemes shown
graphically in Lederer, et. al.iii
It will be important to measure the temperature of the water moderator which will permit you to
calculate the proper values of the average neutron velocity to be used in finding the flux.
Your notebook should show all calculations clearly. Although a complete error analysis giving the
estimated error on the value of the flux obtained is somewhat involved, it is expected that your notebook
will show the appropriate error on all directly measured quantities. Special extra credit will be given to
students who attempt to propagate the errors on the measured quantities through to the error on the flux.
Help in completing this process can be obtained from the instructor.
i
Development9f the basis for equation (1) can be found in Wright and Foster, Chapter *, and Valente, Chapters 2
and 3.
NOTE: To correct for variations in the foil masses used in the different parts of the experiment, all activities should
be expressed in counts per time per unit mass.
ii
Heath, R.L., Scintillation Spectrometry: Gamma-Ray Spectrum Catalog, Vol. 1.
iii
Lederer, et. al. Is on reference in the library.