**8. FILE 8, RADIOACTIVE DECAY AND FISSION PRODUCT YIELD DATA**

Information concerning the decay of the reaction products (any MT) is
given in this file. In addition, fission product yield data (MT=454 and
459) for fissionable materials (see Section 8.2) and spontaneous
radioactive decay data (MT=457) for the nucleus (see Section 8.3) are
included. See descriptions of File 9 and File 10 for information on
isomeric state production from the various reactions. Since a reaction
may result in more than one unstable end product, data for the most
important product should be entered, while others are allowed.

**8.1. Radioactive Nuclide Production**

For any isotope, sections may be given which specify that the end
product from the interaction of any incident particle or photon is
radioactive. Information is given for any MT by identifying the end
products in the reaction by their ZAP (ZA for the product), and noting
how these end products decay. A section will contain only minimal
information about the chain that follows each reaction. One or more
isomeric states of the target or the radioactive end product isotope
will be described.

The following quantities are defined:

+----------+-----------------------------------------------------------+
| **ZA**   | Designation of the original nuclide (ZA = 1000Z + A).     |
+----------+-----------------------------------------------------------+
| **ZAP**  | Designation of the nuclide produced in the reaction (ZAP  |
|          | = 1000Z + A).                                             |
+----------+-----------------------------------------------------------+
| **NS**   | Total number of states (LFS) of the radioactive reaction  |
|          | product for which decay data are given.                   |
+----------+-----------------------------------------------------------+
| **LMF**  | File number (3, 6, 9, or 10) in which the multiplicity or |
|          | cross section for this MT number will be found.           |
+----------+-----------------------------------------------------------+
| **LIS**  | State number (including ground and all levels) of the     |
|          | target (ZA).                                              |
+----------+-----------------------------------------------------------+
| **LISO** | Isomeric state number of the target.                      |
+----------+-----------------------------------------------------------+
| **LFS**  | Level number (including ground and all levels) of the     |
|          | state of ZAP formed by the neutron interaction (to be     |
|          | given in ascending order).                                |
+----------+-----------------------------------------------------------+
| **ELFS** | Excitation energy of the state of ZAP produced in the     |
|          | interaction (in eV above ground state).                   |
+----------+-----------------------------------------------------------+
| **NO**   | Flag denoting where the decay information is to be given  |
|          | for an important radioactive end product.                 |
|          |                                                           |
|          | NO = 0, complete decay chain given under this MT.         |
|          |                                                           |
|          | NO = 1, decay chain given in MT = 457 in MATP.            |
+----------+-----------------------------------------------------------+
| **ND**   | Number of branches into which the nuclide ZAP decays.     |
+----------+-----------------------------------------------------------+
| **HL**   | Half‑life of the nuclide ZAP in seconds.                  |
+----------+-----------------------------------------------------------+
| **ZAN**  | Z and mass identifier of the next nuclide produced along  |
|          | the chain.                                                |
+----------+-----------------------------------------------------------+
| **BR**   | Branching ratio for the production of that particular ZAN |
|          | and level.                                                |
+----------+-----------------------------------------------------------+
| **END**  | End‑point energy of the particle or quantum emitted (this |
|          | does not include the gamma energy, following beta decay,  |
|          | for example).                                             |
+----------+-----------------------------------------------------------+
| **CT**   | Chain terminator that gives minimal information about the |
|          | formation and decay of ZAN. The hundredths digit of CT    |
|          | designates the excited level in which ZAN is formed.      |
|          |                                                           |
|          | 1.0 CT \< 2.0 indicates that the chain terminates with    |
|          | ZAN, possibly after one or more gamma decays.             |
|          |                                                           |
|          | CT 2.0 indicates that ZAN is unstable and decays further  |
|          | to other nuclides. For example, consider the nuclide      |
|          | (ZAP) formed via a neutron reaction (MT number) in a      |
|          | final state (LFS number); ZAP then decays to a level in   |
|          | ZAN; the level number is part of the CT indicator and     |
|          | includes non-isomeric states in the count.                |
|          |                                                           |
|          | The following examples may help explain the use of CT:    |
|          |                                                           |
|          | CT = 1.00, ZAN was formed in the ground state which is    |
|          | stable.                                                   |
|          |                                                           |
|          | CT = 1.06, ZAN was formed in the sixth excited state; the |
|          | sixth state decayed to the ground state which is stable.  |
|          |                                                           |
|          | CT = 2.00, ZAN was formed in the ground state which is    |
|          | unstable. (No delayed gammas are associated with the      |
|          | formation and decay of this particular ZAN). The next     |
|          | decay in the chain is specified under the RTYP.           |
|          |                                                           |
|          | CT = 2.11, ZAN was formed in the 11th excited state but   |
|          | the chain does not terminate with that ZAN. The next      |
|          | decay in the chain is specified under the RTYP.           |
|          |                                                           |
|          | It is readily apparent from the above that CT = \"1.\"    |
|          | indicates that the chain terminates with that particular  |
|          | ZAN and CT = \"2.\" means that one or more decays are     |
|          | involved before stability is reached. Note, however, that |
|          | stability can be reached ***instantaneously*** upon       |
|          | occasion with the emission of one or more light           |
|          | particles.                                                |
+----------+-----------------------------------------------------------+
| **RTYP** | Mode of decay using the same definitions specified in     |
|          | MT=457 (see Section 8.3).                                 |
|          |                                                           |
|          | As an example, consider MT=102. Then RTYP = 1.44 would be |
|          | interpreted as follows:                                   |
|          |                                                           |
|          | The first two columns of the RTYP (1.) indicates β^-^     |
|          | decay of ZAP; the third and fourth columns (44) indicate  |
|          | that the nucleus ZAN (formed in the β^-^ decay) then      |
|          | immediately emits two α particles.                        |
|          |                                                           |
|          | This example is represented by the following reaction:    |
|          |                                                           |
|          | n + ^7^Li γ + ^8^Li (ground state)                        |
|          |                                                           |
|          | > β^-^ (MT=102)                                           |
|          | >                                                         |
|          | > [2.94 2^+^,0]{.underline}                               |
|          | >                                                         |
|          | > ^8^Be                                                   |
|          | >                                                         |
|          | > 2α                                                      |
|          |                                                           |
|          | For this example:                                         |
|          |                                                           |
|          | > ZA(^7^Li) = 3.007E+03 LIS(^7^Li) = 0 LISO(^7^Li) = 0    |
|          | >                                                         |
|          | > ZAP(^8^Li) = 3.008E+03 LFS(^8^Li) = 0                   |
|          | >                                                         |
|          | > ZAN(^8^Be) = 4.008E+03 CT(^8^Be) = 2.01                 |
|          |                                                           |
|          | Since Be has a half‑life of the order of compound‑nucleus |
|          | formation times, decay data for MT = 457 are not          |
|          | required, and the complete chain can easily be            |
|          | represented and read from the information given here.     |
+----------+-----------------------------------------------------------+

**8.1.1. Formats**

The structure of each section always starts with a HEAD record and ends
with a SEND record. Subsections contain data for a particular final
state of the reaction product (LFS).

The number of subsections NS is given on the HEAD record for the
section. The subsections are ordered by increasing value of LFS.

The structure of a section is:

> \[MAT, 8, MT/ ZA, AWR, LIS, LISO, NS, NO\] HEAD
>
> \<subsection for LFS~1~\>
>
> \<subsection for LFS~2~\>
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> \<subsection for LFS~NS~\>
>
> \[MAT, 8, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND
>
> For NO=0 the structure of the subsection is:
>
> \[MAT, 8, MT/ ZAP, ELFS, LMF, LFS, 6\*ND, 0/
>
> HL~1~, RTYP~1~, ZAN~1~, BR~1~, END~1~, CT~1~,
>
> HL~2~, RTYP~2~, ZAN~2~, BR~2~, END~2~, CT~2~,
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> HL~ND~,RTYP~ND~, ZAN~ND~, BR~ND~, END~ND~, CT~ND~\] LIST

If NO=1, then the reaction gives rise to a significant product which is
radioactive, and the evaluator wishes only to identify the radioactive
product. The evaluator must supply MF=8, MT=457 data elsewhere to
describe the decay of the product. It is understood that the cross
section for producing this radioactive product can be determined from
the data in File 3, 6, 9, or 10 depending upon the value of LMF.

For NO=1, the structure of the subsection is:

\[MAT, 8, MT/ ZAP, ELFS, LMF, LFS, 0, 0\] CONT

**8.1.2. Procedures**

1\. Data should be given for all ***unstable*** states of the reaction
product nucleus for which cross sections are given in File 3 or File 10
or multiplicities in File 6 or File 9. No information of this type is
allowed in evaluations for mixtures of elements, molecules, or elements
with more than one naturally occurring isotope.

2.  In order to provide more general usefulness as these files are being
    constructed, the following procedures are mandatory. For each
    reaction type (MT), File 6 yields, File 9 multiplicities, or File 10
    cross sections must be provided, except when LMF=3.

3\. If the ENDF/B file also contains a complete evaluation of the
neutron cross sections for the reaction product nucleus (ZAP, LIS), then
the radioactive decay data for the evaluation of (ZAP, LIS) found in
MF=8, MT=457 must be consistent with the decay data in this section.

4\. The method for calculating the nuclide production cross section is
determined by the choice of LMF: LMF = 3 implies that the production
cross section is taken directly from the

corresponding sections in File 3.

> LMF = 6 implies that the production cross section is the product of
> the cross section in File 3 and the yield in File 6.
>
> LMF = 9 implies that the production cross section is the product of
> the cross section in File 3 and the multiplicity in File 9.

LMF = 10 implies that the production cross section is given explicitly
in File 10 (in barns).

**8.2. Fission Product Yield Data (MT = 454 and MT = 459)**

MT numbers 454 and 459 specify the energy‑dependent fission product
yield data for each incident particle or photon. These MT numbers can
also be used to identify yields for spontaneous fission. A complete set
of fission product yield data is given for a particular incident neutron
energy. Data sets should be given at sufficient incident energies to
completely specify yield data for the energy range given for the fission
cross section (as determined from Files 2 or 3). These data are given by
specifying fission product identifiers and fission product yields.

MT=454 is used for independent yields (YI), and MT=459 is used for
cumulative yields (YC). The formats for MT=454 and MT=459 are identical.
Independent yields (YI) are direct yields per fission prior to delayed
neutron, beta, *etc.*, decay. The sum of all independent yields is 2.0
for any particular incident neutron energy. Cumulative yields (YC) are
specified for the same set of fission products. These account for all
decay branches, including delayed neutrons.

The fission products are specified by giving an excited state
designation (FPS) and a (charge, mass) identifier (ZAFP). Thus, fission
product nuclides are given, not mass chains. More than one (Z,A) may be
used to represent the yields for a particular mass chain.

The following quantities are defined

+----------+-----------------------------------------------------------+
| **NFP**  | Number of fission product nuclide states to be specified  |
|          | at each incident energy point (this is actually the       |
|          | number of sets of fission product identifiers ‑ fission   |
|          | product yields). (NFP2500).                               |
+----------+-----------------------------------------------------------+
| **ZAFP** | (Z,A) identifier for a particular fission product. (ZAFP  |
|          | = (1000Z + A).                                            |
+----------+-----------------------------------------------------------+
| **FPS**  | State designator (floating‑point number) for the fission  |
|          | product nuclide (FPS = 0.0 means the ground state, FPS =  |
|          | 1.0 means the first excited state, *etc*.)                |
+----------+-----------------------------------------------------------+
| **YI**   | (MT=454), independent yield for a particular fission      |
|          | product prior to particle decay.                          |
+----------+-----------------------------------------------------------+
| **DYI**  | (MT=454) 1σ uncertainty in YI.                            |
+----------+-----------------------------------------------------------+
| **YC**   | (MT=459) cumulative yield.                                |
+----------+-----------------------------------------------------------+
| **DYC**  | (MT=459) 1σ uncertainty in YC.                            |
+----------+-----------------------------------------------------------+
| **C~n~   | Array of yield data for the i^th^ energy point. This      |
| (E~i~)** | array contains NFP sets of four parameters in the order   |
|          | ZAFP, FPS, YI, and DYI in MT=454 and ZAFP, FPS, YC, and   |
|          | DYC in MT=459.                                            |
+----------+-----------------------------------------------------------+
| **NN**   | Number of items in the C~n~(E~i~) array, equal to 4\*NFP. |
+----------+-----------------------------------------------------------+
| **E~i~** | Incident neutron energy of the i^th^ point (eV).          |
+----------+-----------------------------------------------------------+
| **LE**   | Test to determine whether energy‑dependent fission        |
|          | product yields given:                                     |
|          |                                                           |
|          | LE = 0, implies no energy‑dependence (only one set of     |
|          | fission product yield data given);                        |
|          |                                                           |
|          | LE \> 0, indicates that (LE + 1) sets of fission product  |
|          | yield data are given at (LE + 1) incident neutron         |
|          | energies.                                                 |
+----------+-----------------------------------------------------------+
| **I~i~** | Interpolation scheme (see Appendix E) to be used between  |
|          | the E~i‑1~ and E~i~ energy points.                        |
+----------+-----------------------------------------------------------+

**8.2.1. Formats**

The structure of a section always starts with a HEAD record and ends
with a SEND record. Sets of fission product yield data are given for one
or more incident energies. The sets are ordered by increasing incident
energy. For a particular energy the data are presented by giving four
parameters (ZAFP, FPS, YI, and DYI in MT=454 and ZAFP, FPS, YC, and DYC
in MT 459) for each fission product state. The data are first ordered by
increasing values of ZAFP. If more than one yield is given for the same
(Z,A) the data are ordered by increasing value of the state designator
(FPS).

# The structure for a section is

\[MAT, 8, MT/ ZA, AWR, LE+1, 0, 0, 0\] HEAD

\[MAT, 8, MT/ E~1~, 0.0, LE, 0, NN, NFP/ C~n~(E~1~) \] LIST

\[MAT, 8, MT/ E~2~, 0.0, I, 0, NN, NFP/ C~n~(E~2~) \] LIST

\[MAT, 8, MT/ E~3~, 0.0, I, 0, NN, NFP/ C~n~(E~3~) \] LIST

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

\[MAT, 8, 0 / 0.0, 0.0, 0, 0, 0, 0\] SEND

where MT = 454 for independent yield data, and MT = 459 for cumulative
yield data. There are (LE + 1) LIST records.

**8.2.2. Procedures**

The data sets for fission product yields should be given over the same
energy range as that used in Files 2 and/or File 3 for the fission cross
section. The yields are given as a fractional value at each energy, and
normally the independent yields will sum to 2.0.

This format provides for the yields (YI or YC) to each excited state
(FPS) of the nuclide designated by ZAFP, and hence accommodates the many
metastable fission products having direct fission yields. Data may be
given for one or more fission product nuclide states to represent the
yield for a particular mass chain. If independent yield data are given
for more than one nuclide, the yield for the lowest Z (charge) nuclide
state for a particular mass chain should be the same as the cumulative
yield in MT=459, and all other independent yields for this same chain
should be direct yields.

The direct fission product yields are those prior to delayed neutron
emission; for this reason, the summation of independent yields over the
nuclides in each mass chain does ***not*** necessarily equal the
isobaric chain yield. The cumulative yield for each nuclide (ZAFP, FPS)
can be determined by use of the branching fractions in MT=457 or
directly from MT=459.

Yields for the same fission product nuclides should be given at each
energy point. This will facilitate interpolation of yield data between
incident energy points. Also, a linear‑linear interpolation scheme
should be used.

**8.3. Radioactive Decay Data (MT=457)**

The spontaneous radioactive decay data are given in Section 457. This
section is restricted to single nuclides in their ground state or an
isomeric state. (An isomeric state is a \"long-lived\" excited state of
the nucleus.) The main purpose of MT=457 is to describe the energy
spectra resulting from radioactive decay and give average parameters
useful for applications such as decay heat, waste disposal, depletion
and buildup studies, shielding, and fuel integrity. The information in
this section can be divided into three parts:

**a. General information about the material**

+----------+-----------------------------------------------------------+
| **ZA**   | Designation of the original (radioactive) nuclide         |
|          | (=1000Z+A).                                               |
+----------+-----------------------------------------------------------+
| **AWR**  | Ratio of the LIS state nuclide mass to that of neutron.   |
+----------+-----------------------------------------------------------+
| **LIS**  | State of the original nuclide (LIS=0, ground state,       |
|          | LIS=1, first excited state, *etc*.)                       |
+----------+-----------------------------------------------------------+
| **LISO** | Isomeric state number for the original nuclide (LISO=0,   |
|          | ground state; LISO=1, first isomeric state; *etc*.)       |
+----------+-----------------------------------------------------------+
| **NST**  | Nucleus stability flag (NST=0, radioactive; NST=1,        |
|          | stable)                                                   |
+----------+-----------------------------------------------------------+
| **       | Half‑life of the original nuclide (seconds).              |
| T~1/2~** |                                                           |
+----------+-----------------------------------------------------------+
| **NC**   | Total number of decay energies (eV) given (NC = 3 or 17). |
+----------+-----------------------------------------------------------+
| **E~     | Average decay energy (eV) of \"x\" radiation, *e.g.*, for |
| \"x\"~** | decay heat applications. The average energies must be     |
|          | given in an order specified in Section 8.3.2. Unknown     |
|          | average radiation energies are indicated by a value of    |
|          | --1.0.                                                    |
+----------+-----------------------------------------------------------+
| **SPI**  | Spin of the nuclide in its LIS state.                     |
|          |                                                           |
|          | (SPI = --77.777 = spin unknown)                           |
+----------+-----------------------------------------------------------+
| **PAR**  | Parity of the nuclide in its LIS state (±1.0).            |
+----------+-----------------------------------------------------------+

**b. Decay mode information ‑ for each mode of decay**

+----------+-----------------------------------------------------------+
| **NDK**  | Total number of decay modes given (cannot be zero).       |
+----------+-----------------------------------------------------------+
| ### RTYP | Mode of decay of the nuclide in its LIS state.            |
|          |                                                           |
|          | Decay modes defined:                                      |
|          |                                                           |
|          | ## RTYP Decay Mode                                        |
|          |                                                           |
|          | 0\. γ γ‑ray (not used in MT457)                           |
|          |                                                           |
|          | 1\. β^--^ Beta decay                                      |
|          |                                                           |
|          | 2\. e.c., (β^+^) Electron capture and/or positron         |
|          | emission                                                  |
|          |                                                           |
|          | > 3\. IT Isomeric transition (will in general be present  |
|          | > only when the state being considered is an isomeric     |
|          | > state)                                                  |
|          |                                                           |
|          | 4\. α Alpha decay                                         |
|          |                                                           |
|          | 5\. n Neutron emission (***not*** *delayed neutron        |
|          | decay*, below)                                            |
|          |                                                           |
|          | 6\. SF Spontaneous fission                                |
|          |                                                           |
|          | 7\. p Proton emission                                     |
|          |                                                           |
|          | 10\. ‑ Unknown origin                                     |
|          |                                                           |
|          | Multiple particle decay is also allowed using any         |
|          | combination of the above RTYP variables as illustrated in |
|          | the following examples:                                   |
|          |                                                           |
|          | **RTYP Decay Mode**                                       |
|          |                                                           |
|          | > 1.5 β^--^,n Beta decay followed by neutron emission     |
|          | > (*delayed neutron decay*)                               |
|          | >                                                         |
|          | > 1.4 β^--^,α Beta decay followed by alpha emission       |
|          | > (^16^N decay)                                           |
|          | >                                                         |
|          | > 2.4 β^+^,α Positron decay followed by alpha emission.   |
+----------+-----------------------------------------------------------+

+----------+-----------------------------------------------------------+
| **RFS**  | Isomeric state flag for daughter nuclide.                 |
|          |                                                           |
|          | RFS=0.0, ground state;                                    |
|          |                                                           |
|          | RFS=1.0, first isomeric state, *etc*.                     |
+----------+-----------------------------------------------------------+
| **Q**    | Total decay energy (eV) available in the corresponding    |
|          | decay process. This is not necessarily the same as the    |
|          | maximum energy of the emitted radiation. In the case of   |
|          | an isomeric transition Q will be the energy of the        |
|          | isomeric state. For both β^+^ and β^--^, Q equals the     |
|          | energy corresponding to the mass difference between the   |
|          | initial and final atoms).                                 |
+----------+-----------------------------------------------------------+
| **BR**   | Fraction of the decay of the nuclide in its LIS state     |
|          | which proceeds by the corresponding decay mode, *e.g*.,   |
|          | if only β^--^ occurs and no isomeric states in the        |
|          | daughter nucleus are excited then BR = 1.0 for β^--^      |
|          | decay.                                                    |
+----------+-----------------------------------------------------------+

**c. Resulting radiation spectra**

+----------+-----------------------------------------------------------+
| ### NSP  | Total number of radiation types (STYP) for which spectral |
|          | information is given (NSP may be zero).                   |
+----------+-----------------------------------------------------------+
| **STYP** | Decay radiation type                                      |
|          |                                                           |
|          | Decay radiations defined:                                 |
|          |                                                           |
|          | **STYP Radiation type**                                   |
|          |                                                           |
|          | > 0\. γ Gamma rays                                        |
|          | >                                                         |
|          | > l\. β^--^ Beta rays                                     |
|          | >                                                         |
|          | > 2\. e.c., (β^+^) Electron capture and/or positron       |
|          | > emission                                                |
|          | >                                                         |
|          | > 4\. α Alpha particles                                   |
|          | >                                                         |
|          | > 5\. n Neutrons                                          |
|          | >                                                         |
|          | > 6\. SF Spontaneous fission fragments                    |
|          | >                                                         |
|          | > 7\. p Protons                                           |
|          | >                                                         |
|          | > 8\. e^--^ \"Discrete electrons\"                        |
|          | >                                                         |
|          | > 9\. x X‑rays and annihilation radiation (photons not    |
|          | > arising as transitions between nuclear states)          |
+----------+-----------------------------------------------------------+
| **ER**   | discrete energy (eV) of radiation                         |
|          | produced(E~γ~,E~β‑~,E~e.c.~,*etc*.)                       |
+----------+-----------------------------------------------------------+
| **RI**   | intensity of discrete radiation produced (relative        |
|          | units).                                                   |
+----------+-----------------------------------------------------------+
| **RP**   | spectrum of the continuum component of the radiation in   |
|          | units of probability/eV such that RP(E)dE = 1.            |
+----------+-----------------------------------------------------------+
| **TYPE** | Type of transition for beta and electron capture.         |
|          |                                                           |
|          | Types Defined:                                            |
|          |                                                           |
|          | ### TYPE Spectrum Definition                              |
|          |                                                           |
|          | > 0.0 not required for STYP                               |
|          | >                                                         |
|          | > 1.0 allowed, non-unique                                 |
|          | >                                                         |
|          | > 2.0 First‑forbidden unique                              |
|          | >                                                         |
|          | > 3.0 Second‑forbidden unique                             |
+----------+-----------------------------------------------------------+
| **RICC** | Total internal conversion coefficient (STYP=0.0 only)     |
+----------+-----------------------------------------------------------+
| **RICK** | K‑shell internal conversion coefficient (STYP=0.0 only)   |
+----------+-----------------------------------------------------------+
| **RICL** | L‑shell internal conversion coefficient (STYP=0.0 only)   |
+----------+-----------------------------------------------------------+
| **RIS**  | Internal pair formation coefficient (STYP=0.0)            |
|          |                                                           |
|          | > STYP=2.0, positron intensity,                           |
|          | >                                                         |
|          | > STYP=0.0 otherwise.                                     |
+----------+-----------------------------------------------------------+
| **LCON** | [^1]Continuum spectrum flag                               |
|          |                                                           |
|          | # LCON = 0, no continuous spectrum given                  |
|          |                                                           |
|          | ##### LCON = 1, only continuous spectrum given            |
|          |                                                           |
|          | # LCON = 2, both discrete and continuum spectra.          |
+----------+-----------------------------------------------------------+
| **NT**   | Number of entries given for each discrete energy (ER).    |
+----------+-----------------------------------------------------------+
| **FC**   | ^1^Continuum spectrum normalization factor (absolute      |
|          | intensity/relative intensity).                            |
+----------+-----------------------------------------------------------+
| **FD**   | ^1^Discrete spectrum normalization factor (absolute       |
|          | intensity/relative intensity).                            |
+----------+-----------------------------------------------------------+
| **NER**  | Total number of tabulated discrete energies for a given   |
|          | spectral type (STYP).                                     |
+----------+-----------------------------------------------------------+
| **       | [^2]Average decay energy of radiation produced.           |
| ER~AV~** |                                                           |
+----------+-----------------------------------------------------------+
| **NR**   | Number of interpolation ranges for the continuum          |
|          | spectrum.                                                 |
+----------+-----------------------------------------------------------+
| **NP**   | Number of points at which the distribution will be given. |
+----------+-----------------------------------------------------------+
| **       | Interpolation scheme for the continuum spectrum.          |
| E~int~** |                                                           |
+----------+-----------------------------------------------------------+
| **NK**   | Number of partial energy distributions when LCON = 5 is   |
|          | used.                                                     |
+----------+-----------------------------------------------------------+
| **Δ**    | Uncertainty in any quantity.                              |
+----------+-----------------------------------------------------------+
| **LCOV** | Flag indicating whether covariance data are given for     |
|          | continuum spectrum data. (LCON = 1 or 2).                 |
|          |                                                           |
|          | #### LCOV=0, no covariance data given                     |
|          |                                                           |
|          | LCOV=1, covariance data given                             |
+----------+-----------------------------------------------------------+
| **LB**   | Flag indicating the meaning of the numbers given in the   |
|          | array{E~k~,F~k~}. (Only LB=2 presently allowed, See       |
|          | chapter 33).                                              |
+----------+-----------------------------------------------------------+
| **NPP**  | Number of pairs of numbers in the {E~k~,F~k~} array.      |
+----------+-----------------------------------------------------------+

{E~k~,F~k~} is an array of pairs of numbers, referred to as an E~k~
table. In each E~k~ table the first member of a pair is an energy, E~k~,
the second member of the pair, F~k~, is a number associated with the
energy interval between the two entries E~k~ and E~k+1~.

The E~k~ table must cover the complete range of secondary particle
energies. Some of the F~k~\'s

may be zero, as must be the case below threshold for a threshold
reaction, and the last value of F in an E table must be zero or blank
since it is not defined.

The meaning of the F~k~ values in the E~k~ table for the allowed LB=2 is
as follows:

LB=2 Fractional components fully correlated over all E~k~ intervals

$\text{COV}X_{i}X_{j}\underset{\text{kk}\prime}{\Sigma}S_{i}^{k}S_{j}^{k\prime}F_{k}F_{k\prime}X_{i}X_{j}$where
S~i~^k^ = 1 when the energy E~i~ is in the interval E~k~ to E~k+1~ of
the E~k~ table

= 0 otherwise

Here X~i~ is the normalized spectral intensity at decay particle emitted
kinetic energy range E~i~ obtained from the {E,RP} TAB1 record
indicated.

**8.3.1. Formats**

The structure of this section always starts with a HEAD record and ends
with a SEND record.

For a radioactive nucleus (NST=0), this section is divided into
subsections as follows:

\[MAT, 8,457/ ZA, AWR, LIS, LISO, NST, NSP\] HEAD (NST=0)

\[MAT, 8,457/ T~1/2~, ΔT~1/2~, 0, 0, 2\*NC, 0/ (E~\"x\"~,Δ\_~\"x\"~)[^3]
/ LIST

\[MAT, 8,457/ SPI, PAR, 0, 0, 6\*NDK, NDK/

> RTYP~1~, RFS~1~, Q~1~, ΔQ~1~, BR~1~, ΔBR~1~,
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> RTYP~NDK~, RFS~NDK~, Q~NDK~, ΔQ~NDK~, BR~NDK~,ΔBR~NDK~\] LIST
>
> \<Subsection for Spectrum~1~\>
>
> \<Subsection for Spectrum~2~\>
>
> **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--**
>
> \<Subsection for Spectrum~NSP~\>

\[MAT, 8, 0/ 0.0, 0.0, 0, 0, 0, 0\] SEND

The structure of a subsection is:

\[MAT, 8,457/ 0.0, STYP, LCON, 0, 6, NER/

> FD, ΔFD, ER~AV~, ΔER~AV~, FC, ΔFC\] LIST

\[MAT, 8,457/ ER~1~, ΔER~1~, 0, 0, NT, 0/

> RTYP~1~, TYPE~1~, RI~1~, ΔRI~1~, RIS~1~, ΔRIS~1~,
>
> RICC~1~,ΔRICC~1~, RICK~1~,ΔRICK~1~, RICL~1~,ΔRICL~1~\] LIST
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> ER~NER~, ΔER~NER~, 0, 0, NT, 0/
>
> RTYP~NER~,TYPE~NER~, RI~NER~, RI~NER~, \-\-\-\-\-\-\-\-\-\-\--\] LIST
>
> (omit these LIST records if LCON=1)

\[MAT, 8,457/ RTYP, 0.0, 0, LCOV, NR, NP/ E~int~ / RP(E) \] TAB1

> (omit if LCON=0)

\[MAT, 8,457/ 0.0, 0.0, 0, LB, 2\*NPP, NPP/ (E~k~,F~k~) \] LIST

> (omit if LCOV=0 or LCON=0)

For a stable nucleus (NST=1), this section is divided into subsections
as follows:

\[MAT, 8,457/ ZA, AWR, LIS, LISO, NST, 0\] HEAD (NST=1)

\[MAT, 8,457/ 0.0, 0.0, 0, 0, 6, 0/

0.0, 0.0, 0.0, 0.0, 0.0, 0.0\] LIST

\[MAT, 8,457/ SPI, PAR, 0, 0, 6, 0\]

0.0, 0.0, 0.0, 0.0, 0.0, 0.0\] LIST

**8.3.2. Procedures**

1\. The initial state of the parent nucleus is designated by LISO, which
equals 0 for the ground state and equals n for the n^th^ isomeric state.
Only isomeric states are included in the count of LISO. (In other files
isomeric and non‑isomeric states may be included in the count of
levels.)

2\. The average decay energy \_~\"x\"~ for decay heat application is
given for three general radiation types, E~LP~ (for light particles),
E~EM~ (for electromagnetic radiation), and E~HP~ (for heavy particles),
followed by the individual components. The sum of these three general
quantities is the total average (neutrino energies excluded) energy
available per decay to the decay heat problem. The three quantities are
more precisely defined as

> $${\overline{E}}_{\text{LP}} = {\overline{E}}_{\beta^{-}} + {\overline{E}}_{\beta^{+}} + {\overline{E}}_{e^{-}} + \ldots$$
>
> $${\overline{E}}_{\text{EM}} = {\overline{E}}_{\gamma} + {\overline{E}}_{x - \text{ray}} + {\overline{E}}_{\text{ann}\text{.}\text{rad}\text{.}} + \ldots$$
>
> $${\overline{E}}_{\text{HP}} = {\overline{E}}_{\alpha} + {\overline{E}}_{\text{SF}} + {\overline{E}}_{p} + {\overline{E}}_{n} + \ldots$$
>
> where ${\overline{E}}_{\text{LP}}$ means the average energy of
> ***all*** \"electron‑related\" radiation such as β^-^, β^+^
> conversion‑electrons, Auger, *etc*. The
> quantity${\overline{E}}_{\text{EM}}$, means the average energy of all
> \"electromagnetic\" radiations such as gamma rays, x‑rays, and
> annihilation radiation. The quantity${\overline{E}}_{\text{HP}}$ is
> the average energy of ***all*** heavy charged particles and neutrons,
> and also includes the recoil energy; but the alpha energy alone can be
> separated out by the usual M~R~/(M~R~+M~α~) factor, where M~R~ and
> M~α~ are the recoil nucleus and alpha masses, respectively.
>
> The average decay energies ${\overline{E}}_{\text{x}}$ must be given
> in the following order:

  ----------------------------------------------------------- --------------------------------------------------------
  $${\overline{E}}_{\text{LP}}$$                              Average energy of all light particles.

  $${\overline{E}}_{\text{EM}}$$                              Average energy of all electromagnetic radiation.

  $${\overline{E}}_{\text{HP}}$$                              Average energy of all heavy particles.

  $${\overline{E}}_{\beta^{-}}$$                              Average β^-^ energy.

  $${\overline{E}}_{\beta^{+}}$$                              Average β^+^ energy.

  $${\overline{E}}_{\text{Ae}^{-}}$$                          Average Auger-electron energy.

  $${\overline{E}}_{\text{ce}^{-}}$$                          Average conversion-electron energy.

  $${\overline{E}}_{\gamma}$$                                 Average gamma-ray energy.

  $${\overline{E}}_{x - \text{ray}}$$                         Average x-ray energy.

  $${\overline{E}}_{\text{InB}}$$                             Average internal Bremsstrahlung energy.

  $${\overline{E}}_{\text{ann}\text{.}\text{rad}\text{.}}$$   Average annihilation energy.

  $${\overline{E}}_{\alpha}$$                                 Average α energy.

  $${\overline{E}}_{\text{recoil}}$$                          Average recoil energy.

  $${\overline{E}}_{\text{SF}}$$                              Average SF energy.

  $${\overline{E}}_{n}$$                                      Average prompt and/or delayed neutron energy.

  $${\overline{E}}_{p}$$                                      Average proton energy.

  $${\overline{E}}_{\nu}$$                                    Average neutrino or antineutrino energy.
  ----------------------------------------------------------- --------------------------------------------------------

3\. The symbol RTYP indicates the mode of decay as determined by the
initial event. A nucleus undergoing beta decay to an excited state of
the daughter nucleus, which subsequently decays by gamma emission, is in
the beta decay mode. RTYP = 0.0 is not allowed in MT = 457 (although
used under 8.l).

An isomeric state of the daughter nuclide resulting from the decay of
parent nuclides is designated by RFS following the procedures used for
LISO. Q represents the total energy available in the decay process and
is equal to the energy difference available between the initial and
final states (both of which may be isomeric). The branching ratio BR for
each decay mode is given as a fraction and the sum over all decay modes
must equal unity.

Multiple particle emission is also allowed by using any combination of
the RTYP variables. This will account for particle emission from nuclear
states excited in the decay of the parent (\"delayed‑particle\"
emission) whose half‑lives are too short to warrant separate entry in
the file. It will also allow users and processing codes to identify the
various intermediate states, without having to examine all the spectrum
listings to determine radiation types. The multiple‑particle RTYP should
be constructed in the order in which the particles are emitted. (*e.g.*,
RTYP = 1.5 indicates decay followed by neutron emission).

4\. The source‑of‑radiation should be specified for each spectral line
or continuous spectra. The source of radiation is a floating-point
integer corresponding to the RTYP definitions. If the
source‑of‑radiation is not known RTYP = 10. should be used.

5\. The energy spectra should be specified if they are known and
identified by STYP. Gamma spectra are described using STYP = 0.0.
Relative intensities and errors in the relative intensity should be
specified. Absolute normalization is made through multiplication by FC
and FD. If absolute discrete spectra are given FD must equal unity. The
radiation intensity should total the contributions from all decays
leading to radiation within a particular decay type, STYP, having energy
E~r~±ΔE~r~.

> a\. For gamma ray emission (STYP = 0.0), no other information is
> required if X-ray, Auger electron, conversion electron, and pair
> formation intensities have not been calculated for these transitions.
> In this case NT = 6.
>
> The amount of additional information depends upon the detail in which
> quantities were obtained for inclusion in STYP = 8. or 9. spectra, and
> the number of decay modes. (This detail will also be reflected in the
> uncertainties assigned in STYP = 8. or 9. spectra.) If only the total
> conversion electron emission is calculated, RICC and ΔRICC should be
> included and NT is specified as 8. If contributors from the individual
> K, L, and M shells are calculated, the K and L shell conversion
> coefficients should be included and NT = 12. In the rare case
> (*i.e.*,$_{7}^{\text{16}}N$), where internal pair formation is needed,
> the internal pair formation coefficient should be included as the
> quantities RIS and ΔRIS.
>
> b\. For electron capture (STYP = 2.), the quantity RIS is 0.0 provided
> E~e.c.~1.022 MeV. If positron emission is energetically possible, RIS
> and ΔRIS must be specified (as I~β+~and Δi~β+~).
>
> c\. The spectra should be ordered in increasing values of STYP, and
> discrete spectral data should be specified before continuous spectra.
>
> d\. For STYP = 5. (spontaneous fission neutrons), LCON = 0, NER = 0,
> and EAV and ΔEAV should be given.
>
> e\. For STYP = 6. (spontaneous fission fragments) LCON = 0, NER = 0,
> and \_ ~SF~ and Δ \_ ~SF~ should be given.

6\. The specification of data uncertainties is an important quantity
which is difficult to represent in a simple way. Although a one sigma
variance is desired, a number should be entered that at least indicates
qualitatively how well the parameter is known.

For STYP = 8. and 9., ΔE will reflect the detail in which these values
were derived. For example, if only the total conversion electron
emission has been calculated, ΔE would be the spread between
K‑conversion and M‑conversion electron energies. If a very detailed
calculation has been made, ΔE would reflect the uncertainties in the
electron binding energy and the transition energy.

7\. The spontaneous fission spectrum is specified using MF = 5 in
sub-library 4 (no incoming projectile).

8.  Every effort should be made to determine the spin and parity of the
    original nucleus, either by experimental evidence or by strong
    theoretical arguments. If the spin cannot be determined, it should
    be reported as ‑77.777; if the parity cannot be determined it should
    be reported as zero.

9\. Because the continuum spectrum is normalized, the absolute
covariance matrix of a multi-component normalized spectrum processed
from this file must have zero for the sum of each row and column.
(Processing codes should perform this check).

> ![](media/image1.wmf)Since the covariance form for radioactive product
> spectra is confined to LB = 2, meeting this test is equivalent to the
> following condition on the F~k~ of the E~k~ covariance table:
>
> and y~k~ is the energy spectrum on the uncertainty evaluation grid.
> Σy~k~ = 1. If the initial F~k~ do not meet this condition, the
> corrected values F~k~ are given by:
>
> ![](media/image2.wmf)Note that unlike the case for File 33, some of
> the F~k~ will be negative. Also, the processed multigroup correlation
> matrix will show some off‑diagonal components that are ‑1 as well as
> others that are +1.
>
> When a processing code constructs the absolute covariance V~mn~ on the
> user\'s energy grid E~m~, the simplest relations to use are

![](media/image3.wmf)where, ![](media/image4.wmf)

> and the integral is easy because F(E) is piece-wise continuous on the
> E~k~ grid. By this construction we are assured that the null sum
> condition will be retained for the covariance matrix of the processed
> multigroup spectrum.

[^1]: Spontaneous \_v for RTYP = 6. and STYP = 5., LCON = 1 and FC
    =\_v~p~ and FD = \_v~d~.

[^2]: For STYP = 2, this is the average positron energy, for STYP = 4,
    this includes energy of recoil nucleus.

[^3]: Data must be given in order specified in Section 8.3.2.