Subject: Re: Exploding Bullet in
From: dovesub@primenet.com (Carey Sublette)
Date: Jul 01 1996
Newsgroups: sci.military.moderated

From dovesub@primenet.com (Carey Sublette)

In article <Dto4oD.GJr@ranger.daytonoh.ncr.com>, Paul DeMone
<pdemone@tundra.com> wrote:
...
> 
>   The intent I think was to imply a micronuke (it was in the exploding
>   bullet thread) but it seems Cf would be nasty even without a boom.  I
>   consulted my handy CRC handbook (56th edition) and looked up Cf.  The
>   most likely candidate is Californium-252 and here is all the info:
> 
>      - half life of 2.65 yrs with 97% decay with 6 MeV alpha emission
>        and 3% spontaneous fission
>      - strong neutron emitter: 170 million per minute per microgram (ug).
>      - AEC sold it in 1975 for $100 per 0.1 ug.
> 
>   For the sake of argument lets arbitrarily say a micronuke requires 1 g
>   of Cf-252.  The interesting results from some simple math:
> 
>      o  cost of fissile raw material: $1 billion, although in this
>         quantity you would expect a volume discount :-) 
>      o  with a 2.65 yr half life your precious 1 g of Cf-252 would:
> 
>          - generate maybe 30-40 W of heat; it likely resembles a red
>            hot BB (although no one has ever made enough to bother to
>            reduce it to metallic form, according to CRC).  
...
> 
> 
>    BTW, detailed nuclear and metallurgical data for elements above 95 (Cf
>    is element 98) are still classified...


Due to its prodigious spontaneous fission rate, Cf-252 is useful as a 
compact, intense, fission-spectrum neutron source. This makes it the only 
industrially important, and thus only well known californium isotope. It 
not so hot as an explosive material however.

A general rule is that highly fissile isotopes have odd-numbered masses 
(and also have low spontaneous fission rates), while isotopes with even 
numbered masses are much less fissile, and have high spontaneous fission 
rates. Thus U-233 and U-235 are fissile, while U-238 is not; and U-238 has 
a spontaneous fission rate more than an order of magnitude higher than 
either of the two odd isotopes. Pu-239 and Pu-241 are highly fissile, with 
very low spontaneous fission rates, while Pu-238 and Pu-240 are much less 
fissile, with very high rates of spontaneous fission.

The same rule holds for other transuranics, including californium. Cf-246, 
Cf-252 and Cf-254 all have extremely high spontaeous fission rates; while 
Cf-249 has an emission rate 10 orders of magnitude lower. It is true that 
most cross section data on the transuranics is still classified in the U.S.,
 but some data is available nonetheless. I have some Japanese cross section 
curves for californium isotopes which, while a bit thin on data points, 
provide some idea of the fissile properties. Cf-252 does has have a pretty 
good combination of fission, scattering, and absorption cross sections - 
but Cf-251 is decidedly better. In addition Cf-251 has a comparatively low 
spontaneous fission rate, and a 800 year half-life (much better than 2.65 
years!).

The dimensions of a bare critical sphere can be calculated using the total 
neutron mean free path (average distance travelled before a collision), and 
the average number of secondary neutrons produced per collision (designated 
c):
  c = (cross_scatter + cross_fission*avg_n_per_fission)/cross_total;
where the total cross section, cross_total, is equal to:
  cross_total = cross_scatter + cross_fission + cross_absorb

The total neutron mean free path is given by:
     MFP = 1/(cross_total * N)
where N is the number of atoms per unit volume, determined by the density.

From neutron diffusion theory, the critical radius of a bare (unreflected) 
sphere in terms of mean free paths is determined by c:

c value          r_c
        (crit. radius in MFP)
1.0            infinite
1.02           12.027
1.05            7.277
1.10            4.873
1.20            3.172
1.40            1.985
1.60            1.476

The actual size can be calculated by multiplying the radius by the MFP 
value which is simply:
     MFP = 1/(cross_total * N)
where N is the number of atoms per unit volume, determined by the density.

Eyeballing the Cf-251 chart gives an estimate of:
cross_scatter:  4 barns
cross_fission:  2.5 barns 
cross_absorb:   negligible
Assuming 3.9 neutrons per fission (about equal to the neutron emissions of 
Cf-252 and Cf-254 from spontaneous fission) we get:
c = (4 + 2.5*3.9)/6.5 = 2.11

Unfortunately this is off the scale I have handy, but extrapolating the 
critical radius curve gives an estimate of 0.88 as the critical radius. 

I don't know the density of californium from actual measurement data, but 
it is unlikely to be dramatically different from other transuranics. 
Assuming an atom density of 5x10^22 atoms/cm^3 (similar to uranium, 
neptunium, and plutonium) we get MFP = 1/(6.5 x 10^-24)*(5 x 10^22) = 3.08 
cm. 

Result: a bare sphere critical radius of 2.7 cm, and a critical mass of 1.7 
kg. This is one-sixth that of plutonium-239, and if surrounded by a good 
reflector should get pushed down substantially below 1 kg - arguably in the 
"gram range". With a good implosion system, explosive yields from as little 
~200 g are conceivable. Of course, reflectors and implosion systems add 
weight - far more than the reduction in fissile mass.

Even leaving aside such factors as thermal output (this sucker should still 
be very hot, though maybe not quite red hot), and extravagant cost, we are 
basically looking at medium (maybe light) artillery not handgun 
projectiles.

Commercial californium production has always been from irradiating other 
transuranics in high flux reactors, not particle accelerators. A mixture
of isotopes is produced, so isotopic separation is also required. 

Carey Sublette