Proposal for ENDF formats that describe emission of post-fission
-delayed photons

David Brown, Jason Pruet, Gerry Hedstrom, James Hall (N-Division, LLNL)
and Marie-anne Descalle (M-Division, LLNL)

## Purpose

Fission of heavy nuclides is accompanied by the birth of neutron rich
fragment nuclei born in highly excited states. Following emission of
prompt neutrons and -rays, these fragments are typically left with
atomic numbers that are 3-4 units smaller than stable nuclei with the
same mass number. As these nuclides undergo decay to reach stability, a
large number of -rays are emitted. Figure 1 illustrates some of the
processes leading to emission of delayed photons. A variety of
applications (most notably those concerned with the detection and
identification of clandestine fissile material) would benefit from a
clear description of the spectral and temporal evolution of these -rays.
This proposal describes formats for representing emission of delayed
photons and is based on the analysis presented in \[1\].

At the present time, no single evaluated data set exists that directly
provides for the temporal evolution of rays from the decay of the
fission products. However, evaluated data sets containing all of the
physical parameters required for such calculations have been prepared.
These include estimates of the independent and cumulative fission yields
of all fission products, branching ratios in the decay of ground and
isomeric states \[2\], lifetimes of these states, and the spectra of
rays emitted in their decay. Sizeable uncertainties and possibly
significant errors are likely present concerning the shortest-lived
fission products. However, the high-energy -ray spectra generated from
some of these data sets have been shown to be in reasonable agreement
with initial experiments designed specifically to test them under
conditions likely to be of interest to interrogation of sea-going cargo
containers \[1,3\].

For clarity we emphasize that the relationship between delayed neutron
emission and delayed photon emission is tenuous. Only a small fraction
of fission fragments -- typically those characterized by large decay Q
values -- undergo ^-^n emission. However, essentially all fission
fragment decays result in the emission of a few photons. Also, it would
be impractical to accurately specify and measure energies of delayed
neutrons. By contrast, most fission fragments have decay spectra known
to sub-keV accuracy that are readily resolved with inexpensive field
HpGe detectors.

## 2 Description

A basic quantity of interest to Monte Carlo modelers is the delayed -ray
source function . This function describes the production of photons
following spontaneous or induced fission. Specific details of are given
in section 3. Once has been determined, the spectrum for any fission
rate and counting history can be determined.

We propose two different representations of . This first is compact,
similar in spirit to common descriptions for the emission of -delayed
neutrons, and based on simple continuous functions. This is useful when
detailed spectral information is not needed. The second proposed
representation involves tabulating for discrete gamma-rays and
accommodates detailed spectral information.

So far, parameters describing the two representations have been
calculated for thermal, fission-spectrum, and 14 MeV neutron induced
fission of and . For illustration we show in table 1 fit parameters
describing the continuous approximation to photon emission following
fission-spectrum neutron induced fission of . In addition, the COG Monte
Carlo code at LLNL has been modified to sample photons represented in
the discrete approximation described below. Comparisons with experiment
have been done and are favorable. One drawback to the discrete approach
is the large size of the data files needed to represent photons with keV
resolution.

## Changes to ENDF/B Manual

**3.1 MF = 1 Changes:**

***Page 1.1, General Information:***

"File 1 may contain up to four \..." changed to "File 1 may contain up
to [five]{.underline} additional sections giving fission neutron [and
photon]{.underline} yields and energy release information."

***New Section:***

6.  **Delayed Photon Data (MT=460)**

This section describes the delayed photon source function resulting from
either particle induced or spontaneous fission. The delayed gamma source
function is defined as the number of gammas emitted per unit time after
the fission event, per unit energy for a fixed incident energy:

Here *E* is the energy of the fission-inducing projectile, is the energy
of the emitted photon, *t* is the time following fission at which the
photon is emitted, and is the number of photons emitted per fission per
second per eV. The source function may be given either in a discrete or
continuous representation.

In the discrete representation (LO=1), the source function is given as a
series of tables of photon multiplicities, *y~i~(E),* in File 12 with
LO=1, with their associated time dependences

The continuous representation (LO=2) is similar in spirit to the delayed
neutron data (MT=455). In this representation, one must give the photon
multiplicities in File 12 and the fraction of photons emitted at each
energy, *f~i~(E E),* in an MF=15 table, for each precursor family. The
time dependence of each precursor family is given as a list of time
constants:

Only the precursor family time constants are stored in MF=1.

**1.6.1 Formats**

**1.6.1.1 Discrete Representation (LO=1)**

The following quantities are defined:

**NG** The number of discrete photons.

**NR, NP, t~in~**~t~ Standard TAB1 parameters.

**E~i~** Energy of the i^th^ photon (eV).

**~i~(t)** Time dependence of the i^th^ photon's multiplicity (sec^-1^).

The structure of the time dependence data block is:

\[MAT, 1, 460/ ZA, AWR, LO=1, 0, NG, 0\] HEAD

\[MAT, 1, 460/ E~1~, 0.0, 1, 0, NR, NP/t~int~/T~1~(t)\] TAB1

\[MAT, 1, 460/ E~2~, 0.0, 2, 0, NR, NP/t~int~/T~2~(t)\] TAB1

...

\[MAT, 1, 460/ E~NG~, 0.0, NG, 0, NR, NP/t~int~/T~NG~(t)\] TAB1

\[MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

**1.6.1.2 Continuous Representation (LO=2)**

The following quantities are defined:

**NNF** The number of precursor families considered.

**~i~** Decay constant (sec^-1^) for the i^th^ precursor.

The structure of this data block is:

\[MAT, 1, 460/ ZA, AWR, LO=2, 0, 0, 0\] HEAD

\[MAT, 1, 460/ 0.0, 0.0, 0, 0, NNF, 0/~1~, ~2~, ... ~NNF~\] LIST

\[MAT, 1, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

**1.6.2. Procedures**

**1.6.2.1 Discrete Representation (LO=1)**

The photon multiplicity is given in File 12 with LO=1 in File 12 set.
Each discrete photon in File 12 must have an associated time dependence
table specified in File 1. It is recommended that the photon
multiplicities be given in the same order as the photons are listed in
File 1.

**1.6.2.2 Continuous Representation (LO=2)**

The probability of producing precursors for each family and the energy
distributions of photons produced by each precursor family are given in
Files 12 and 15. It is extremely important that the same precursor
families be given in Files 12 and 15 as in File 1 (MT=460) and the
ordering of families should be the same in all files. It is recommended
that all families be ordered by decreasing half-lives
(~1~\<~2~\<...\<~NNF~).

2.  **MF = 12 Changes:**

First paragraph:

"File 12 can be used to represent \..." change to "File 12 can be used
to represent the neutron energy dependence of photon production cross
sections [or delayed photon source functions]{.underline} by means of
either \..."

" Both methods rely upon \..." change to "Both methods rely upon
processing codes that use [either]{.underline} neutron cross sections
from File 2 and/or File 3 to generate absolute photon production cross
sections [or time constants from File 1 (MT=460) to generate delayed
photon source functions.]{.underline}"

**References**

> \[1\] Pruet, J., Hall, J., Descalle, M.-A. & Prussin, S.G. 2004, NIMB
> 222, 403
>
> \[2\] England, T.R. & Rider, B.F. 1994, LA-UR-94-3106, ENDF-349
>
> \[3\] Norman, E.B., Prussin, S.G., Larimer, R.-M., Shugart, H.,
> Browne, E., Smith, A., McDonald, R.J., Nitsche, H., Gupta, P. Frank,
> M., Gosnell, T., 2004, NIM A, 521, 608

Table 1: Fit parameters for continuous representation of for fission
spectrum neutrons on (*NNF*=27). Note, all f~i~ =1/(5.0e5 eV).

  ----------------------- ----------------------- -----------------------
  (eV)                                            (sec)

  2.50e+05                8.11e-02                4.81e-01

  2.50e+05                1.99e-01                8.40e-02

  2.50e+05                2.89e-01                1.38e-02

  7.50e+05                4.22e-02                5.56e-01

  7.50e+05                8.19e-02                8.80e-02

  7.50e+05                1.51e-01                1.18e-02

  1.25e+06                1.97e-02                4.90e-01

  1.25e+06                3.23e-02                9.99e-02

  1.25e+06                1.11e-01                1.19e-02

  1.75e+06                8.80e-03                7.30e-01

  1.75e+06                1.39e-02                1.37e-01

  1.75e+06                4.25e-02                1.33e-02

  2.25e+06                3.96e-03                1.04e+00

  2.25e+06                1.01e-02                9.22e-02

  2.25e+06                2.96e-02                1.42e-02

  2.75e+06                3.52e-03                7.14e-01

  2.75e+06                6.58e-03                1.07e-01

  2.75e+06                2.03e-02                1.50e-02

  3.25e+06                4.38e-03                3.77e-01

  3.25e+06                8.12e-03                1.36e-01

  3.25e+06                8.35e-03                1.38e-02

  3.75e+06                5.97e-04                3.32e-01

  3.75e+06                8.57e-03                1.26e-02

  3.75e+06                1.05e-03                9.98e-02

  4.25e+06                1.09e-03                7.14e-01

  4.25e+06                1.48e-03                1.19e-01

  4.25e+06                6.31e-03                1.04e-02
  ----------------------- ----------------------- -----------------------

![](media/image1.png){width="5.0in" height="4.083333333333333in"}

Figure 1: Illustration of some processes leading to the production of
post-fission -delayed photons. Here represents the photons emitted by
the highly excited fragment nucleus born just after fission.
Beta-delayed photons represented by the source function described in the
text are labeled .