As an example of the power of linear combination, consider the
problem of computing the helium production rate in graphite. The
C-12 evaluation in ENDF/B-IV includes an $(n,\alpha)$
reaction (called NA) and a continuum $(n,n^{\prime})3\alpha$
reaction (NCNAAA). An edit for helium production rate
(arbitrarily named N.HE4) can be obtained using the following
edit specifications:
... N.HE4 1 NA/ 1 NCNAAA 3./ ....The
NA reaction is multiplied by 1 (default) and added
into position 1, and the NCNAAA reaction is multiplied by
3 and added into position 1. Caution: A different representation
is used in ENDF/B-V and VI.
Sometimes it is useful to define special edits for particular materials. As an example, the ratios of U-235 capture to U-235 fission and U-238 fission to U-235 fission were measured at the center of the GODIVA critical assembly (Ref. 23). The following edit specifications added to Problem 4 will provide the responses needed to compute these reaction rate ratios:
... CHI F25 F28 C25 2 NFTOT 1. U235 3 NFTOT 1. U238 4 NG 1. U235 ....Note that the standard transport tables reserve
NED words
for each group, order, and material for edits that are not
required during the flux calculation but only at the end of the
problem when responses are computed. Also, the edits only appear
in the P0 table, so the words reserved in the higher tables
are wasted. Storage requirements can be reduced by defining a
special edit table with NTABL=NED, which is only read during the
response function edit calculation in the SN code. The
ONEDANT (Ref. 4) code uses this approach.
The input deck for Sample Problem 5 follows:
TEST 5 -- EDIT TABLE
0 5 0 1 2 1 0 0 0 0
30 1 13 0 0 1 1 1 13 37
AL-27
AL-27/
1 1 AL27/
ELAS NNG N2N N3N NG NA
NP ND NT NNP NNA
N.1H N.4HE
1 NELAS/
2 NINEL/
2 N75P -1/
2 N78P -1/
2 N80P -1/
2 N81P -1/
2 N82A -1/
2 N83P -1/
2 N84P -1/
2 N85P -1/
2 N86A -1/
3 N2N/
4 N3N/
5 NG/
6 NA/
7 NP/
8 ND/
9 NT/
10 N75P/
10 N78P/
10 N80P/
10 N81P/
10 N83P/
10 N84P/
10 N85P/
11 N82A/
11 N86A/
12 NP/
12 N75P/
12 N78P/
12 N80P/
12 N83P/
12 N84P/
12 N85P/
13 NA/
13 N82A/
13 N86A/
STOP
The Al-27 evaluation includes some discrete-inelastic levels
that decay by proton or alpha emission rather than by a cascade
of photons. The cross-sections for these reactions are
subtracted from the total inelastic cross section in position 2
to obtain an isolated $(n,n^{\prime})\gamma$ reaction. The parts
that were subtracted are added back into positions 10 and 11 to
obtain ($n,n^{\prime}p)$ and $(n,n^{\prime}\alpha)$,
respectively. They are also added to the $(n,p)$ and $(n,\alpha)$
reactions in positions 12 and 13 to obtain the gas production
cross sections for H-1 and He-4, respectively.
Note that the detailed aluminum edits are written into a
group-ordered binary interface file with the name GOXS
(see the format descriptions). If its name
is switched to SNXEDT,
the ONEDANT edit module can read the file directly.
An important mechanism of radiation damage in metals is the
displacement of atoms from their normal lattice positions caused
by the recoil particle of a nuclear reaction. The energy
available for producing displacements is given on the MATXS file
as the damage energy production cross section DAME in
eV-barns; it is less than the primary recoil energy because some
of the energy causes electronic excitations rather than
displacements. The primary recoil atom loses some of its energy
ejecting another atom, giving a pair of displacements; each of
these generates another pair, and so on, until all the energy is
used up. The number of displacements produced by this cascade is
equal to the damage energy divided by twice the energy required
to displace one atom from its normal site. Various values of the
displacement energy are used in practice; some
values (Ref. 24)
are given in the following table, which
can be used to determine the EDFACT needed to convert the
damage edit DAME into a ``Displacement
Per Atom'' (DPA) edit. The use of this factor is illustrated below.
-------------------------------------------------
Material Energy (eV) Material Energy (eV)
-------------------------------------------------
Be 31 Fe 40
C 31 Co 40
Na 25 Ni 40
Mg 25 Cu 40
Al 27 Zr 40
Si 25 Nb 40
K 40 Mo 60
Ca 40 Ag 60
Ti 40 Ta 90
V 40 W 90
Cr 40 Au 30
Mn 40 Pb 25
-------------------------------------------------
Except for the delayed neutron parameters CHID and
NUD, all the other data on the current MATXS files are
prompt data. However, many reactions such as
n + {^7{\rm Li}} \rightarrow{^8{\rm Li}} \rightarrow \beta\bar{~~}
+2\alpha~~~(850\;\hbox{ms}) \end{eqnarray*}
and
n +{^{27}{\rm Al}} \rightarrow {^{28}{\rm Al}} \rightarrow{ ^{28}{\rm Si}}
+ \beta\bar{~~} + \gamma~~~(2.24 \;\hbox{m})
have decays that take place in times that are short with respect to the
response desired. The steady-state heating due to capture in
Li-7 should really be the sum of the prompt HEAT from
the MATXS file and 9.31 MeV times the capture cross section. It
can easily be produced with the following TRANSX edit
specifications:
...
SSHEAT
1 HEAT/ PROMPT PART
1 NG 9.31E6/ DELAYED PART FROM 9.31 MEV CAPTURE GAMMA
...
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