**28. FILE 28. ATOMIC RELAXATION DATA**

**28.1. General Comments on Atomic Relaxation**

An atom can be ionized due to a variety of interactions. For example,
due to photon or electron interactions the probability of ionizing a
particular subshell of the atomic structure (K, L1, L2, *etc*.) is
determined by using the subshell cross sections (MT=534-599). For
example, if an incident photon of energy E ionizes the K subshell with
binding energy EK, the atom will emit an electron with energy E-EK, and
the atomic structure will be left ionized, with a \"hole\" in the K
subshell. One way the atom can proceed to fill this hole is to bring
down an electron from a higher energy level, for example L1, with the
simultaneous emission of an X-ray of energy EK-EL1. This is a radiative
transition. An alternative path is to bring down an electron from a
higher level with the simultaneous emission of an electron from that
level or a higher one. As an example, you might see an electron of
energy EK-EL1-EM1, which fills the vacancy in the K shell and leaves new
holes in the L1 and M1 shells. These are called non-radiative
transitions. The process will then continue by filling the new holes
from higher levels, *etc*., until all the ionization energy has been
accounted for by the emission of X-rays and electrons.

The electrons produced by this atomic relaxation can be used as a source
for a subsequent electron transport calculation, or their energy can
just be added to the local heating. The X-rays can be transported
elsewhere to cause additional photo-atomic reactions. In general, the
use of File 28 is indicated when high-Z materials are present and photon
energies of less than 1 MeV are of interest.

This file is provided to give the information necessary to compute the
emission of X-rays and electrons associated with atomic relaxation cross
section. It is based on EADL, the Evaluated Atomic Data Library
developed by D. E. (Red) Cullen at the Lawrence Livermore National
Laboratory (LLNL).

**28.2. General Description**

This file gives the subshell energies, emission energies, transition
probabilities, and other quantities needed to compute the X-ray and
electron spectra from ionized atoms. It always uses MT=533. It works
together with the photoelectric subshell cross sections from MF=23,
MT=534-599.

**28.3. Formats**

The following quantities are defined

+----------+-----------------------------------------------------------+
| ZA, AWR  | Standard material charge and mass parameters              |
+----------+-----------------------------------------------------------+
| NSS      | Number of subshells                                       |
+----------+-----------------------------------------------------------+
| SUBI     | Subshell designator (see the table below)                 |
+----------+-----------------------------------------------------------+
| SUBJ     | Secondary subshell designator                             |
+----------+-----------------------------------------------------------+
| SUBK     | Tertiary subshell designator                              |
|          |                                                           |
|          | (if SUBK is zero for a particular transition, it is a     |
|          | radiative transition; otherwise, it is a non-radiative    |
|          | transition.)                                              |
+----------+-----------------------------------------------------------+
| EBI      | Binding energy for subshell (eV)                          |
+----------+-----------------------------------------------------------+
| ELN      | Number of electrons in subshell when neutral (given as a  |
|          | floating-point value)                                     |
+----------+-----------------------------------------------------------+
| NTR      | Number of transitions                                     |
+----------+-----------------------------------------------------------+
| FTR      | Fractional probability of transition                      |
+----------+-----------------------------------------------------------+
| ETR      | Energy of transition (eV)                                 |
+----------+-----------------------------------------------------------+

Table of Subshell Designators

  --------------------- ------------------------------ -------------------
  Designator            Subshell                       MT

  1\.                   K (1s1/2)                      534

  2\.                   L1 (2s1/2)                     535

  3\.                   L2 (2p1/2)                     536

  4\.                   L3 (2p3/2)                     537

  5\.                   M1 (3s1/2)                     538

  6\.                   M2 (3p1/2)                     539

  *etc*.                                               
  --------------------- ------------------------------ -------------------

The structure of a section of File 28 is as follows:

> \[MAT,28,533/ ZA, AWR, 0, 0, NSS, 0\]HEAD
>
> \[MAT,28,533/SUBI~1~, 0.0, 0, 0, NW, NTR/ NW=6\*(1+NTR)
>
> EBI~1~ , ELN~1~, 0.0, 0.0, 0.0, 0.0,
>
> SUBJ~1~, SUBK~1~, ETR~1~, FTR~1~, 0.0, 0.0,
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> SUBJ~NTR~,SUBK~NTR~,ETR~NTR~,FTR~NTR~, 0.0, 0.0\]LIST
>
> \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--
>
> \[repeat LIST for the rest of the NSS subshells\]
>
> \[MAT,28,533/ 0.0, 0.0, 0, 0, 0, 0\] SEND

**28.4 Procedures**

Sections with MF=28,MT=533 are used together with either photo-atomic or
electro-atomic data evaluations. The value of NSS must be consistent
with the number of subshell ionization cross sections given in File 23
(MT=534,535, \...). Note that the subshell cross section MT value equals
the subshell designator number SUBI plus 533. Subshell LIST records are
given in order of increasing SUBI. Similarly, transitions are given in
order of increasing SUBJ first, and increasing SUBK second. This means
that radiative transitions appear before non-radiative ones for each
subshell.

It is possible to have NTR=0 if there are no allowed transitions from
higher subshells to a particular subshell.

[Example 1: Atomic Relaxation Data]{.underline}

1 0 0 0

6.000000+3 11.9078164 -1 0 0 0 600 1451 1

0.000000+0 0.000000+0 0 0 0 6 600 1451 2

0.000000+0 0.000000+0 0 0 6 6 600 1451 3

0.000000+0 0.000000+0 0 0 6 2 600 1451 4

6-C - 0 LLNL EVAL-DEC90 CULLEN 600 1451 5

DIST- 600 1451 6

\-\-\--ENDF/B-VI MATERIAL 600 600 1451 7

\-\-\-\--ATOMIC RELAXATION DATA 600 1451 8

\-\-\-\-\--ENDF-6 FORMAT 600 1451 9

converted from EADL 600 1451 10

1 451 12 0 600 1451 11

28 533 17 0 600 1451 12

600 1 0 13

600 0 0 14

6.000000+3 11.9078164 0 0 4 0 60028533 15

1.000000+0 0.000000+0 0 0 54 8 60028533 16

2.910100+2 2.000000+0 0.000000+0 0.000000+0 0.000000+0 0.000000+0
60028533 17

5.000000+0 0.000000+0 2.820200+2 5.614880-4 0.000000+0 0.000000+0
60028533 18

6.000000+0 0.000000+0 2.820300+2 1.120600-3 0.000000+0 0.000000+0
60028533 19

3.000000+0 3.000000+0 2.558900+2 4.136090-1 0.000000+0 0.000000+0
60028533 20

3.000000+0 5.000000+0 2.644600+2 1.361900-1 0.000000+0 0.000000+0
60028533 21

3.000000+0 6.000000+0 2.644700+2 2.710990-1 0.000000+0 0.000000+0
60028533 22

5.000000+0 5.000000+0 2.730300+2 4.207480-3 0.000000+0 0.000000+0
60028533 23

5.000000+0 6.000000+0 2.730400+2 1.100120-1 0.000000+0 0.000000+0
60028533 24

6.000000+0 6.000000+0 2.730500+2 6.320080-2 0.000000+0 0.000000+0
60028533 25

3.000000+0 0.000000+0 0 0 6 0 60028533 26

1.756000+1 2.000000+0 0.000000+0 0.000000+0 0.000000+0 0.000000+0
60028533 27

5.000000+0 0.000000+0 0 0 6 0 60028533 28

8.990000+0 6.700000-1 0.000000+0 0.000000+0 0.000000+0 0.000000+0
60028533 29

6.000000+0 0.000000+0 0 0 6 0 60028533 30

8.980000+0 1.330000+0 0.000000+0 0.000000+0 0.000000+0 0.000000+0
60028533 31

60028 0 32

600 0 0 33

0 0 0 34

-1 0 0 35

[Example 2: Electron Interaction Data]{.underline}

electron interaction data converted from EEDL 1 0 0 0

6.000000+3 11.9078164 -1 0 0 0 600 1451 1

0.000000+0 0.000000+0 0 0 0 6 600 1451 2

5.438673-4 1.00000+11 0 0 113 6 600 1451 3

0.000000+0 0.000000+0 0 0 6 14 600 1451 4

6-C - 0 LLNL EVAL-DEC89 CULLEN 600 1451 5

DIST- 600 1451 6

\-\-\--ENDF/B-VI MATERIAL 600 600 1451 7

\-\-\-\--ELECTRO-ATOMIC DATA 600 1451 8

\-\-\-\-\--ENDF-6 FORMAT 600 1451 9

converted from EEDL 600 1451 10

1 451 24 0 600 1451 11

23 526 37 0 600 1451 12

23 527 31 0 600 1451 13

23 528 64 0 600 1451 14

23 534 12 0 600 1451 15

23 536 14 0 600 1451 16

23 538 15 0 600 1451 17

23 539 15 0 600 1451 18

26 526 353 0 600 1451 19

26 527 197 0 600 1451 20

26 534 120 0 600 1451 21

26 536 151 0 600 1451 22

26 538 155 0 600 1451 23

26 539 155 0 600 1451 24

600 1 0 25

600 0 0 26

6.000000+3 11.9078164 0 0 0 0 60023526 27

0.000000+0 0.000000+0 0 0 1 101 60023526 28

101 2 60023526 29

1.000000+1 3.063510+9 1.258930+1 2.498030+9 1.584890+1 2.036940+9
60023526 30

1.995260+1 1.660950+9 2.511890+1 1.354370+9 3.162280+1 1.104370+9
60023526 31

3.981070+1 9.008210+8 5.011870+1 7.347880+8 6.309570+1 5.993570+8
60023526 32

7.943280+1 4.889770+8 1.000000+2 3.991460+8 1.258930+2 3.258180+8
60023526 33

1.584890+2 2.659610+8 1.995260+2 2.171000+8 2.511890+2 1.772160+8
60023526 34

3.162280+2 1.447630+8 3.981070+2 1.183030+8 5.011870+2 9.667950+7
60023526 35

6.309570+2 7.900840+7 7.943280+2 6.458900+7 1.000000+3 5.282720+7

...

6.000000+3 11.9078164 0 0 1 0 60026526 223

1.100000+1 5.438673-4 0 2 1 2 60026526 224

2 2 60026526 225

1.000000+1 1.000000+0 1.00000+11 1.000000+0 60026526 226

0.000000+0 0.000000+0 0 0 1 16 60026526 227

16 2 60026526 228

0.000000+0 1.000000+1 12 0 4 2 60026526 229

-1.000000+0 5.000000-1 9.999990-1 5.000000-1 60026526 230

0.000000+0 1.000000+3 12 0 54 27 60026526 231

-1.000000+0 7.349540-3-6.350000-1 1.014680-2-3.300000-1 1.408430-2
60026526 232

-7.500000-2 1.996880-2 1.350000-1 2.832790-2 3.000000-1 3.982680-2
60026526 233

4.300000-1 5.580130-2 5.350000-1 7.828660-2 6.225000-1 1.108190-1
60026526 234

6.925000-1 1.559570-1 7.500000-1 2.204030-1 7.950000-1 3.078220-1
60026526 235

8.325000-1 4.339260-1 8.625000-1 6.085020-1 8.875000-1 8.591520-1
60026526 236

9.080000-1 1.212620+0 9.250000-1 1.713720+0 9.390000-1 2.413930+0
60026526 237

9.510000-1 3.432260+0 9.610000-1 4.874960+0 9.690000-1 6.802370+0
60026526 238

9.760000-1 9.598280+0 9.820000-1 1.360430+1 9.870000-1 1.914880+1
60026526 239

9.915001-1 2.744700+1 9.956001-1 4.014720+1 9.999990-1 6.259920+1
60026526 240

0.000000+0 2.000000+3 12 0 64 32 60026526 241

-1.000000+0 3.008670-3-9.000000-1 3.301630-3-5.350000-1 4.906250-3

...

6.000000+3 11.9078164 0 0 1 0 60026534 775

1.100000+1 5.438673-4 0 1 1 2 60026534 776

2 2 60026534 777

2.910100+2 1.000000+0 1.00000+11 1.000000+0 60026534 778

0.000000+0 0.000000+0 1 2 1 7 60026534 779

7 2 60026534 780

0.000000+0 2.910100+2 0 0 4 2 60026534 781

1.000000-2 1.111110+1 1.000000-1 1.111110+1 60026534 782

0.000000+0 2.973140+2 0 0 4 2 60026534 783

3.152220-2 3.265060-1 3.152220+0 3.143760-1 60026534 784

0.000000+0 1.995260+3 0 0 28 14 60026534 785

1.000000-1 7.771360-3 6.309570+0 7.133700-3 1.412540+1 6.229690-3
60026534 786

3.162280+1 5.440240-3 6.309570+1 4.054250-3 8.912520+1 3.138130-3
60026534 787

1.258930+2 2.429030-3 1.778280+2 1.605960-3 2.511890+2 1.061790-3
60026534 788

3.162280+2 7.491710-4 3.758380+2 5.767510-4 4.869680+2 3.895820-4
60026534 789

6.309570+2 2.631530-4 8.521260+2 2.098710-4 60026534 790

0.000000+0 3.981070+4 0 0 70 35 60026534 791

1.000000-1 7.237010-3 6.309570+0 6.655140-3 1.412540+1 5.837310-3
60026534 792

3.162280+1 5.119990-3 6.309570+1 3.846900-3 8.912520+1 2.990940-3
60026534 793

1.258930+2 2.325440-3 1.496240+2 1.886340-3 1.938660+2 1.378130-3

...

2.06836+10 4.46563-21 2.51189+10 3.13693-21 3.16228+10 2.30613-21
60026539 1357

3.98107+10 1.69536-21 5.00000+10 1.51523-21 60026539 1358

60026 0 1359

600 0 0 1360

0 0 0 1361

-1 0 0 1362