Re: Dangers of Pu / Air Activation c.s.

[Craig Harmon <charmon@skid.ps.uci.edu>]

On Thu, 31 Aug 1995, Dave Fuehne wrote:

> ok, now for an HP-related question:  are there any references
> that discuss cross sections of high-energy proton reactions?
> I'm doing some research at the Los Alamos Meson Physics Facility
> involving controlling activated air emissions.  I want to predict
> the generation of carbon-11 thru direct production (proton
> interactions) as well as indirect (neutron interactions). 
>   ( A little background:  LAMPF is an 800 MeV proton accelerator,
> operating at 1 milliampere of current.)
> 
>   The only values I can find are for energies "greater than 100 MeV"  
> and the like...   I believe the main reactions of interest are 
> the following:   N14(p,alpha)C11   and   O16(p,alpha+p+n)C11
> Neutron reactions are  N14(n,p+3n)C11  and  O16(n,alpha+2n)C11

The cross sections aren't going to be very easy to find for energies 
lower than that, though you might find some as low as 50 MeV, which I 
would assume to be the threshold.  
Try looking in the journal NUCLEAR PHYSICS A. Every two or three years they 
put out an issue with reaction cross sections for light nuclei.
If you have experimental cross sections for 100 Mev, use them.
Since you are only looking for the total yield, there is another option 
which will probably be more accurate than the error you will encounter 
estimating the stay proton and neutron flux. 

For protons: 
There is a series of arcticles published by Silberberg and Tsao, 
the most recent being "Spallation processes and nuclear interation 
products of cosmic rays" Physics Reports vol 191, Aug 1990 pgs 351-408 
and the references contained therein.
They have used a variation of Rudstam's formula and fit the parameters to 
experiment data for light nuclei.  The cross sections will be a good 
estimate for spallation of unstable nuclei which decay quickly, making 
measurements of the cross sections difficult.  

Also, for proton-induced reactions, if you can find cross sections for 
lower energy reactions for O16(p,4p2n)B11 say at 50 MeV or above, that 
should be good enough for the C11 reaction.  Since these are light 
MIRROR NUCLEI with the same spin parity values, and your energies are high 
enough, you can probably ignore the slight coulomb difference in evaporating 
the extra proton.  (Although there may be some dominant decay channel, so 
compare the 100 + MeV cross sections.)

For a journal search, try using the word "spallation" as the keyword as 
rightly or wrongly, that is the generic term given to these types of 
reactions.  

For neutrons:
Again, if you can find neutron cross sections use them, otherwise...

If you can't find the cross sections, you might want to try one more 
option.  There is a Monte Carlo detailed in "Cascade statistical model for 
nucleon-induced reactions on light nuclei in the energy range 50 MeV-1GeV"
in Physical Review C, vol 42 Oct 1990 pages 1598-1622.  This is not for 
physics wimps.  You need to be familiar with the optical potential, to 
calculate the inverse capture cross sections, and Monte Carlo methods to 
compute the results.  It also seems like overkill, as it has scattering 
angle information, which you don't need to model.

(Of course you could try going to the people working on the Los Alamos 
Spallation Radiation Effects Facility (LASREF).  The level of expertise 
there will certainly be higher than this mail list.)
 
Then you still have to generate pions and the havoc they will wreck.  You 
also would have to transport very high energy neutrons and pions.  Fluka 
might be able to handle this...   This is a high energy/nuclear physics 
problem, as there are all sorts of approximations and assumptions that need 
to be made.  It would probably be easier to find a way to experimentally 
measure this stuff.

If you are still determined to do this, a good intro book (excellent is 
more accurate) is _Introduction to Nuclear Reactions_ by G.R. Satchler.  
After reading that, you can read and understand any experimental journal 
article, and most theoretical articles.

Regards,

Craig
charmon@skid.ps.uci.edu