## REFERENCE DATABASE FOR NEUTRON ACTIVATION ANALYSIS

An IAEA Nuclear Data Section Co-ordinated Research Project 2005-2009

Project Officer: Mark A. Kellett

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## MATSSF Program - Details and Instructions

**Program MATSSF (Updated February 2016)**

The program helps the user to calculate the element and isotope
number densities and self-shielding factors, given the chemical
composition of the components, their weight-% fraction in the
mixture, the mass and dimensions of the sample.
For the most up-to-date input instructions please check the comments
in the source code.

**Installation instructions**

- Download the MATSSF program source.
- Download the MATSSF.DAT library.
- Download the MATSSF_XSR.TXT (36 MB) library (or (9.4 MB) in zipped form MATSSF_XSR.zip).
- Compile the Fortran source.
- Run ‘matssf’ and respond to command prompts.

**Instructions**

The program is designed to run interactively and the user is expected to respond to command prompts on the terminal and
enter the required information through the keyboard in order.

If the user prefers, the input instructions can be written to the file MATSSF_INP.TXT in the same order as they would be
entered interactively. The program searches for the existence of the file and if it exists, all input is read from this
file.

The program expects two libraries:

MATSSF.DAT atomic masses, abundances and self-shielding
factors, and

MATSSF_XSR.TXT activation cross sections in 640-group
ENDF format.

The default names can be changed in the configuration file MATSSF.CFG, which is updated after each MATSSF run.

**Material component definition**

Material components are defined by a pair of entries. The first
entry gives the chemical formula and the second the
corresponding weight-percent fraction.

- A character string read from input is parsed to identify
the element (or isotope) by its chemical symbol. Upper-
or lower-case characters are accepted. Isotopes are
distinguished from elements in that they contain their
respective mass number immediately after the chemical symbol,
with delimiter "-" or no delimiter at all. The element or
isotope symbol is followed by its molar number or fraction,
as seen from the examples below.

- The component weight-percent fraction in the mixture is read
from the next record. Blank response implies 100%. A negative
value implies the last entry and the weight fraction is
calculated internally to make 100% total.

Several pairs of records may be read to construct the full
mixture composition, until a blank is entered for a component
composition. The sum of all weight fractions is normalised
to 100%.

**Sample mass and geometry definition**

In order to calculate the self-shielding factors assuming the
equivalence theorem, which is well established in reactor
physics, the sample dimensions must be specified. Cylindrical
geometry is assumed, which is well suited for samples in the
form of wires of discs. Without any significant loss of
accuracy, equivalent diameters can be given for square-cut
foils such that foil area is conserved. The sample density
in units [g/cm] of the mixture is calculated from the mass
and the calculated volume. Input requests are as follows:

- mass of the sample [mg]
- diameter of the sample [mm]
- length (wires) or thickness (foils) [mm]

If any of the above are missing, a request to enter the density is issued. An attempt is made to reconstruct a single missing quantity, but if more than one is omitted, the calculated self-shielding factors correspond to infinite medium.

**Neutron source definitions**

The mean chord length depends on the assumptions about the
neutron source term. The built-in models allow the source to
be isotropic, or distributed uniformly on a finite cylinder
enclosing the sample (i.e. the irradiation channel). If the
sample is a wire oriented radially in the channel, the mean
chord length is independent of the channel dimensions. However,
if the sample is a wire (long cylinder) or a foil (short cylinder)
with cylinder axis coinciding with the channel axis, the height
and the diameter of the irradiation channel are needed to
calculate the mean chord length.

**Output**

The calculated quantities are printed on screen and on the
MATSSF_LST.TXT file. The labelling of the printed quantities
is self explanatory.
The input and normalised percent-weights are calculated
for each nuclide/element in the sample. Number densities in
units "x 1E24 atoms/cm^{3}" are given. If self-shielding
factor tables are available in the library for the nuclide,
the self-shielding factors and the corresponding Bondarenko
dilution cross sections are printed.

File units:

- 1 - MATSSF.DAT element and isotope library, defined and opened internally,
- 2 - MATSSF_LST.TXT output file defined and opened internally on each MATSSF run,
- 5 - keyboard input or default filename MATSSF_INP.TXT,
- 6 - terminal screen output.

Examples of valid entries to define the chemical composition of a component:

- " B 2 O 3" Boron oxide,
- "al 2 O 3 " Aluminium oxide,
- "SI O 2 " Silicon oxide,
- "B-10 .199 B11 .801" natural boron composition.

**Methods**

Thermal self-shielding factors (flux depression factors)
are calculated according to the method described by De Corte,
with improvements by M. Blaauw.
Resonance self-shielding factors are interpolated from tables
generated by NJOY in three-group structure. Self-shielding
factors for the second energy group with boundaries at 0.55 eV
and 2 MeV are included in the MATSSF.DAT library.

Self-shielding factors are tabulated in terms of the
Bondarenko dilution cross section, which is defined for a
resonance absorber as the macroscopic potential cross section
of the surrounding nuclei per absorber atom. The macroscopic
dilution cross section, Σ_{b}, is given by:

Σ_{b} = Sum(i) n(i)*σ_{p}(i) + Σ_{gb} (1)

where n(i) are the number densities of the surrounding nuclei
(i) and σ_{p}(i) are their potential scattering cross sections.

According to the equivalence theory the geometrical self-shielding is
equivalent to material self-shielding through
a suitably defined geometrical component contribution, Σ_{gb},
which is given by:

Σ_{gb} = a^{*}/l (2)

where (l) is the mean chord length and (a^{*}) is the Bell factor.
The nominal value 1.16 is used for the Bell factor for isotropic
sources and for wires lying along the irradiation channel axis.
For wires lying flat in the channel the Bell factor depends on
the scattering properties of the sample. Scattering causes
neutrons to be deflected in the direction of the longer dimension,
thus increasing the effective flux and reducing the self-shielding.
The expression for the Bell factor (a^{*}) is then:

a^{*} = 1.25 + 0.5(Σ_{s}/Σ_{t}) (3)

where Σ_{s} and Σ_{t} are the scattering and total cross sections of
the sample.

In its simplest form for an isotropic source, the mean chord length (l) is proportional to the volume-to-surface ratio defined by the diameter (d) and foil thickness or wire length (h), and is given by:

l = 4V/S = dh / (d/2+h) (4)

If the source is a cylindrical tube of height (H) and diameter (D), the mean chord length (l) can be derived analytically for a wire or a foil (i.e. a very short cylinder) lying along the axis of the source, and is given by:

^{2}] arctan(H/D)

l = | (5) |

^{2}] - 1)

If the wire is lying flat in the channel (perpendicular to the channel axis), then the mean chord length (l) is independent of channel dimensions and is given by:

^{2}r

^{2}d arctan(H/D)

l = | (6) |

^{2}H/D sqrt[1 + (H/D)

^{2}] )

where g is a non-elementary function, given by:

g = Int[0,π/2]
dp Int[0,x] sqrt[cos^{2}p.cos^{2}q + sin^{2}q] dq
(7)

and can be approximated by an 8-th order polynomial. See function GH2R for details.

The microscopic Bondarenko dilution cross section, σ_{b}, is given
by the relation:

σ_{b} = Σ_{b} / n(a) (8)

where n(a) is the number density of the absorber nuclei (a).

Resonance interference is taken into account approximately by solving the integral slowing-down equation with cross sections in 640-group structure.

Notes:

- The code is an extension of the MATCMP code by A. Trkov, Institute J. Stefan, Ljubljana, Slovenia (1992)
- For details on the origin of the data in the MATSSF.DAT library see comments in the file header.
- Full details on the methods for the calculation of the
self-shielding factors can be found in:

A. Trkov, G. Zerovnik, L. Snoj, M. Ravnik, "On the Self-Shielding Factors in Neutron Activation Analysis", Nuclear Instruments and Methods in Physics Research A**610**p.553–565 (2009).

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Last Updated: 03-Sep-2009