What Are the Fission Product Ranges in U-235?

[vanesch]

Hello,

I'm looking for the following data:
in pure U-235, what is the distribution of ranges of fission products (under thermal neutron irradiation). I know that the distances involved are rather small, but I'm looking for their range. This must have been established somewhere, by someone, some day, I have the impression, and before I try to puzzle this together myself using all possible fission channels, I'd like to know if this data is available somewhere...

Thanks,
Patrick.

 

[Astronuc]

It's about 6 microns, and probably 4-5 for the heavier isotopes and 6-10 for the lighter ones. I can give you references if you need - just give me a few hours to dig them up.

Grain size in UO₂ fuel is typcially 10-20 microns, and in MOX, the grains are generally slightly smaller - 6-10 microns on average.

 

[vanesch]

It's about 6 microns, and probably 4-5 for the heavier isotopes and 6-10 for the lighter ones. I can give you references if you need - just give me a few hours to dig them up.

Thanks. Ok, to be picky, I'd need a distribution, in fact.
I'll tell you what it is for: it is for a neutron detector with a very thin coating of U-235, but this coating takes on a special geometry (can't be more specific about it until it's published...). And I want to calculate the percentage of fission products that leave the surface as a function of the interaction distribution inside the coating - because it's those that get out that will be detected, and this internal distribution of interaction is of course function of the irradiation conditions (energy of neutrons and their direction).
Nevertheless, a "cutoff" to 6 microns will already give me a good estimate.

 

[Astronuc]

The fission product distribution for U²³⁵ is well known with a peak for nuclei of mass 92-100 and another peak for nuclei of masses 133-141.

Also, one can assume that the fission process is more or less isotropic, i.e. independent of direction, so if one fission product is ejected outward, the other travels inward, and there will be those products released more or less parallel with the surface.

 

[Morbius]

The fission product distribution for U²³⁵ is well known with a peak for nuclei of mass 92-100 and another peak for nuclei of masses 133-141.

The famous "Mae West" curve - the distribution of fission products as a
function of fission product mass can be seen at the bottom of:

http://t2.lanl.gov/tour/sch007.html

Dr. Gregory Greenman
Physicist

 

[vanesch]

The famous "Mae West" curve - the distribution of fission products as a
function of fission product mass can be seen at the bottom of:

http://t2.lanl.gov/tour/sch007.html

Yeah, THIS distribution is to be found everywhere of course. What I was looking for was the DISTRIBUTION OF RANGES of the mixture of fission products in U-235.
This distribution can be obtained as follows, but it is a lot of work, and I was thinking that it was already compiled somewhere:

1) take the curve you are talking about. Now, consider each fission product individually (with the weight given in the said distribution).
2) Find somewhere the ENERGY DISTRIBUTION of this fission product. 3) Calculate for each of these energies, of this fission product, the distribution of ranges, using a Monte Carlo program such as SRIM (Ziegler).
3) Give a weight to this distribution of ranges, corresponding to the weight of the energy choosen in the energy distribution. Go to the next energy, etc...
Sum over all these weighted range distributions: we now have the energy-weighted range distribution of one fission product.
4) Switch to the next fission product in the list and start all over...
5) Now, add together all these energy-weighted range distributions for each individual fission product, this time, weighted with their weight in the cited fission product distribution.We now have the final range distribution of the fission products of a representative ensemble of thermal neutron fission in U-235. *THAT*'s the curve I'm looking for...

 

[Nomy-the wanderer]

You mean something like that??

Edit: I scanned this from "Nuclear reactor fuel elements" for B.Frost.

 

[Astronuc]

We now have the final range distribution of the fission products of a representative ensemble of thermal neutron fission in U-235. *THAT*'s the curve I'm looking for...

The data for the fission yield curve to which Morbius provided the link should be available electronically, possibly from LANL or ORNL. The Frost data may also be suitable, but would have to be verified (i.e. it's old - 1969) and if OK converted to number of atoms of the element.

The data have been published, and I believe one of books on Radiation Health Protection such data, but it is also rather old.

I imagine the data would be available from IAEA or one of the OECD centers.

 

[Morbius]

Yeah, THIS distribution is to be found everywhere of course. What I was looking for was the DISTRIBUTION OF RANGES of the mixture of fission products in U-235.

vanesch,

Yes, I know. I was responding to Astronuc's comment [ quoted in my post ] that
the distribution of fission products by mass was a bimodal distribution.

Dr. Gregory Greenman
Physicist

 

[Astronuc]

I think the ranges/range distributions exist in electronic format, since I have used in the distant past linear energy transfer (LET) data to determine ranges of certain nuclides in certain materials.

I'll look around for some references, but perhaps Morbius has some at his finger tips.

 

[vanesch]

In any case thanks for the help already up to now!

A rough cutoff at 6 micrometer already helped me a lot.

 

[Astronuc]

You might find the range data in some of the following, particularly the last reference, but perhaps not all of the f.p.'s, but it's a start. Maybe the last reference has other references.

http://www.icru.org/pubs_cat.htm

ICRU Report 16, Linear Energy Transfer, deals with radiation quality. As dealt with in the report, quality refers to those features of the spatial distribution of energy transfers that influence the effectiveness of an irradiation in producing change, when other physical factors such as total energy dissipated, absorbed dose, absorbed dose rate and absorbed dose fractionation are kept constant. The report gives particular emphasis to the description of quality in terms of linear energy transfer (LET). Report 16 includes major sections on interaction of radiation with matter, definition and concepts of LET, calculation of distributions of absorbed dose in LET, applications of LET calculations, LET in radiation protection, limitations of the LET concept, and other methods of specifying radiation quality. The report also includes appendices covering formulae for mass collision stopping power or LET; measurement of, and theoretical and experimental values for, range, total average rate of energy loss per unit path length and LET; measurement of LET distributions; distributions of ions in clusters; the mean excitation energy; and application of LET in radiation biology and chemical dosimetry. [1970, 51 pages]

ICRU Report 55, Secondary Electron Spectra from Charged Particle Interactions, provides a comprehensive guide to quantitative information about emission of secondary electrons in collisions of fast electrons, protons, alpha particles, and heavier ions with free atoms and molecules and with condensed matter. Explanations of the various mechanisms of ionization are given. Experimental methods are described, and theoretical techniques are presented for determining total cross sections as well as cross sections differential in the ejection angle and energy of the secondary electrons. The semi-empirical and analytical models given enable the user to make rapid calculations of certain cross sections. Some applications of secondary electron spectra to radiological problems are also described. Data are available for impacts by electrons at energies from a few keV up to 10 keV, for incident protons from a few keV up to 5 MeV, and for heavier particles up to 1000 MeV. Methods are described for extrapolating cross section data to higher energies. The wide variety of targets reviewed include atoms (H, He, Ne, Ar, Kr, Xe, and Hg), molecules (H2 , N2, O2, CO2, H2O, CH4, C2H2, C3H8, C6H6, CH3NH2) and solids (C, Al, Pb, and Au). Some of the calculational methods can be used for all targets for which basic data, such as ionization potentials, are available. [1996, 114 pages]

ICRU Report 73, Stopping of Ions Heavier Than Helium
See Abstract as PDF-file [Journal of the ICRU Volume 5, No 1, 2005, 263 + V pages]
http://www.icru.org/ic_ab_73.pdf
http://www.icru.org/n_05_4.pdf