nucreonics DATA SHEET no. 8 
Fission-Neutron 
Reaction 
Cross Sections 
By W. INTHOFF 
Laboratory for Nuclear Chemistry* 
Chalmers University of Technology 
Géteborg, Sweden 
HvUGHES HAS SHOWN (1) how yields of 
(n,p) and (n,a) reactions induced by 
fission-spectrum neutrons can be calcu- 
lated with fair accuracy (about a factor 
2) for lighter elements. This nomo- 
gram facilitates such calculations. 
The first scale indicates the atomic 
number Z of the target element. The 
second scale gives the threshold energy 
Er as derived from 
Er = —Q(A+1)/A 
where A is the mass number of the tar- 
get nuclide and Q the reaction energy. 
A great number of Q values are tabu- 
lated (2, 3), otherwise they can be 
calculated from the atomic masses (4). 
Q values for (n,p) reactions may also be 
calculated from the total beta-disinte- 
gration energies Q(8-) (6) according 
to: 
Q(n,p) = 0.782 — Q(B-) 
The third scale gives the value of 
& X 10/A”, where ¢ is the mean value 
of the activation cross section for fission 
neutrons in millibarns. 
ExampP_es: For the reaction P#! 
(n,p) Si! the Q value is —0.97 MeV, 
hence Hr = 0.97 X 32/31 = 1.00 MeV. 
By drawing a straight line from Z = 15 
on the first scale through Ey = 1.00 on 
the second scale one gets@ XK 10/A¥ = 
8.4 on the third scale. As A = 31 the 
resulting cross-section is ¢ = 8.5 milli- 
* Operated by the Swedish Atomic En- 
ergy Commission. 
Neutron Physics 
Z (target) EY 10:6-A°3 
(Mev) (mb) 
x l2 0.01 
: 10 
10 
8 
iS 
20 6 ey 
25 4 
30 
35 2 
40 O 10 
45 
50 =2 
be}e) 
60 -4 
65 
70 -6 10 
75 
80 -8 20 
90 
= - 40 
35 10 4 
100 -12 60 
69+ 
t Scale should not be extrapolated beyond 
this point—theory no longer holds; e.g., 
B'°(n,a)Li’. 
barns. 
mb (1). 
For the reaction Cl*® (n,a) P*? one 
gets ¢ = 3.5 mb, in fair agreement with 
the experimental value of 3.0 mb. 
The calculations of Hughes are based 
on the assumption, that the energy- 
spectrum of the fast neutrons has the 
form 
The experimental value is 19 
N(BE) = e-¥ sinhy/2E 
This is valid for an unmoderated spec- 
trum of fission neutrons as available 
inside of uranium lumps in a reactor. 
In this case it is also possible to use the 
thermal-neutron flux as an approxima- 
tion for the fast-neutron flux. 
In the irradiation channels through 
the moderator of a reactor the flux of 
fast neutrons is somewhat smaller than 
the thermal flux, depending on the 
relative position of target and uranium 
rods. Moreover there are deviations 
of the actual spectrum from the fission 
spectrum given above. This was 
shown by the measurements of (n,a) 
(n, a) 
Z(target) Er lOG as 
(Mev) (mb) 
hs Ve 0.02 
5 10 
“ 8 
8 0.1 
9 6 
10 
4 
15 1.0 
oO 
20 “2 
-4 
25 10 
-6 
20 
=< 8 40 
=I10 60 
35 80 
-12 100 
7 146 + 
45 
50 
cross-sections of heavier elements by 
Saeland et al. (6). For (n,p) reactions 
these deviations are negligible. For 
(n,a) reactions, however, the results of 
Saeland et al. indicate that the above 
formula for the fission spectrum, and 
hence the nomogram presented here, 
can be used without corrections only 
for Z < 20. For heavier nuclei the 
nomogram gives values of ¢ that are 
too high. 
* * * 
The author is indebted to Dr. E. Saeland, 
JENER, Norway, for making JENER re- 
port No. 27 available before publication, and 
to the head of this laboratory, Dr. K. E. 
Zimen, for helpful discussions. 
BIBLIOGRAPHY 
1. D. J. Hughes, ‘‘ Pile Neutron Research,”’ ch. 4 
(Addison-Wesley, Cambridge, 1953) 
2. K. T. Bainbridge, ‘‘Experimental Nuclear 
Physics,” vol. 1, part V, E. Segré, ed. (Wiley 
and Sons, New York, 1953) 
3. J. Mattauch, A. Flammersfeld ‘“‘Landolt- 
Bornstein, Zahlenwerte und Funktionen’’ 6. 
Aufl. Berlin (Springer) 1952, Bd I, Teil 5. 
4. N. Metropolis, G. Reitwiesner. Table of 
atomic masses, AEC NP 1980 (1948) 
. R. W. King, Revs. Mod. Phys. 26, 327 (1954) 
. E. Saeland, et al. JENER No. 23 (1954) and 
No. 27 (1955) 
Qa 
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