22
Requirements for TSL data in new format David Brown NNDC, BNL

Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

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Page 1: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Requirements for TSL data in new format

David Brown NNDC, BNL

Page 2: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

SG38: “Beyond the ENDF Format”

! WPEC-SG38 approved in May 2012 ! Develop new format to replace ENDF ! Requirements essentially developed

(that’s why I’m here) ! Designing specifications ! Have working prototype of format (GND) and

processing/translation code (Fudge)

2

Page 3: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Special issues! In US (CSEWG), TSL data has lower profile, compared to

say neutron sub library ! Want to revise overly complicated format

• Hierarchy of approximations unclear to uninitiated • Precision/dynamic range of Sαβ • Covariance data

! Take advantage of improved methodology • LEAPR ! Split self & distinct ! dσ(E,T)/dE’dΩ directly vs. Sαβ(α,β,T)

! How to group together evaluations • TSL matching onto higher energies • How to resolve issues of stoichiometry and normalization • TSL is not just vs. T, but P and other parameters

(EOS-related or not)3

Page 4: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

ENDF library has gradually evolved to current state

4

Num

ber o

f TSL

eva

luat

ions

0

10

20

30EN

DF-

269

I (19

68)

II (1

970)

III (1

973)

IV (1

975)

V (1

979)

V.2

(198

5)VI

(199

0)VI

.1 (1

991)

VI.2

(199

3)VI

.3 (1

995)

VI.4

(199

6)VI

.5 (1

998)

VI.6

(199

9)VI

.7 (2

000)

VI.8

(200

1)VI

I.0 (2

006)

VII.1

(201

1)in

pre

para

tion

New evals. Mod evals. Unchanged evals.

Page 5: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

ENDF library has gradually evolved to current state

5

eval

uatio

ns

0

10

20

30EN

DF-

269

I (19

68)

II (1

970)

III (1

973)

IV (1

975)

V (1

979)

V.2

(198

5)VI

(199

0)VI

.1 (1

991)

VI.2

(199

3)VI

.3 (1

995)

VI.4

(199

6)VI

.5 (1

998)

VI.6

(199

9)VI

.7 (2

000)

VI.8

(200

1)VI

I.0 (2

006)

VII.1

(201

1)in

pre

para

tion

New evals. Mod evals. Unchanged evals.

Koppel, Houston, et al. (General Atomics)

MacFarlane, et al. (LANL)

Holmes, al-Qasir, Hehr, Hawari (NCSU)

Page 6: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

ENDF library has gradually evolved to current state

6

eval

uatio

ns

0

10

20

30EN

DF-

269

I (19

68)

II (1

970)

III (1

973)

IV (1

975)

V (1

979)

V.2

(198

5)VI

(199

0)VI

.1 (1

991)

VI.2

(199

3)VI

.3 (1

995)

VI.4

(199

6)VI

.5 (1

998)

VI.6

(199

9)VI

.7 (2

000)

VI.8

(200

1)VI

I.0 (2

006)

VII.1

(201

1)in

pre

para

tion

New evals. Mod evals. Unchanged evals.

Koppel, Houston, et al. (General Atomics)

MacFarlane, et al. (LANL)

Holmes, al-Qasir, Hehr, Hawari (NCSU)

Very few evaluators (GA, LANL, NCSU) + Few processing codes (AMPX, NJOY) - Retirements of key personal (LANL, ORNL) + Many important applications and users ================================== Potential for lots of angry users

Page 7: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

These are the requirements that we’ve gathered from you, the nuclear data community

7

DRAFT

Requirements for a next generation nuclear data format

OECD/NEA/WPEC SubGroup 38⇤

(Dated: April 1, 2015)

This document attempts to compile the requirements for the top-levels of a hierarchicalarrangement of nuclear data such as is found in the ENDF format. This set of require-ments will be used to guide the development of a new set of formats to replace the legacyENDF format.

CONTENTS

I. Introduction 2A. Scope of data to support 3B. How to use these requirements 4C. Main requirements 4D. Hierarchal structures 5E. Complications 6

1. Is it a material property or a reaction property? 62. Di↵erent optimal representation in di↵erent

physical regions 73. Ensuring consistency 74. Legacy data 75. Special cases 8

II. Common motifs 8A. Documentation 8B. What data are derived from what other data? 11C. Product list elements 13D. <product> elements 13E. <distributions> and <distribution> elements 16F. Multiplicities 17

III. Particle and/or material properties database 18

IV. One evaluation 20A. Reaction designation 23B. The collection of reactions: <reactions> 24C. The <reaction> element 24D. Di↵erential cross sections: d�(E)/d⌦ and

d�(E)/d⌦dE 26E. Integral cross sections: �(E) 27F. Defining data styles 27G. Derived reactions 27H. Resonances 29

1. Designating channels 322. Resolved Resonances 343. Unresolved Resonances 364. Correcting cross sections and distributions with

background data 36

V. Grouping together evaluations 37A. Defining a collection of evaluations 37B. “E↵ective” or “Meta” evaluations 37

VI. Covariance data 41A. Covariance Definitions 41B. Covariance of continuous functions 43C. Covariance of multi-dimensional functions 44D. Covariance and correlation matrices 44E. Weighted sums of covariance 45F. The “Sandwich Formula” 46G. Monte Carlo Sampling 47

⇤Edited by D.A. Brown ([email protected])

H. Examples of covariance data usage in this hierarchy 48

VII. Required low-level containers 49A. The lowest-level 51B. General data containers 52C. Text 53D. Hyperlinks 53

VIII. Special reaction case: Atomic Scattering Data 54A. Incoherent Photon Scattering 55B. Coherent Photon Scattering 55

IX. Special reaction case: Particle production or Spallationreactions 56

X. Special reaction case: Radiative capture 56

XI. Special reaction case: Fission 57A. Introduction 57B. Existing ENDF format 58C. Fission format requirements 58

XII. Special component case: Fission Product Yields 59A. Introduction 59B. Existing ENDF format 59C. Detailed FPY format requirements for GND 60D. Discussion of possible implementations 61

XIII. Special reaction case: Large Angle Coulomb Scattering(LACS) 62

XIV. Special reaction case: Thermal Scattering Law 64A. Theoretical Background 64B. Gaussian approximation of the self part of the

scattering kernel 661. Coherent Elastic Scattering 672. Incoherent Elastic Scattering 683. Incoherent Inelastic Scattering in the Short

Collision Time Approximation 68

XV. Additional derived data elements for applications 68A. General Transport Data 69

1. Product average kinetic energy and forwardmomentum 69

2. µ̄lab(E) 693. CDF’s from PDF’s 694. Probability tables in the URR 69

B. Grouped Transport Data 701. Inverse speed 712. Multiplicity 713. Q-value 714. Projectile kinetic energy and momentum 71

C. Production data 71D. Damage cross sections 72

XVI. Prototyping Functions 72

Acknowledgments 73

Page 8: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

This is (or will be anyway) your format

8

DRAFT

Requirements for a next generation nuclear data format

OECD/NEA/WPEC SubGroup 38⇤

(Dated: April 1, 2015)

This document attempts to compile the requirements for the top-levels of a hierarchicalarrangement of nuclear data such as is found in the ENDF format. This set of require-ments will be used to guide the development of a new set of formats to replace the legacyENDF format.

CONTENTS

I. Introduction 2A. Scope of data to support 3B. How to use these requirements 4C. Main requirements 4D. Hierarchal structures 5E. Complications 6

1. Is it a material property or a reaction property? 62. Di↵erent optimal representation in di↵erent

physical regions 73. Ensuring consistency 74. Legacy data 75. Special cases 8

II. Common motifs 8A. Documentation 8B. What data are derived from what other data? 11C. Product list elements 13D. <product> elements 13E. <distributions> and <distribution> elements 16F. Multiplicities 17

III. Particle and/or material properties database 18

IV. One evaluation 20A. Reaction designation 23B. The collection of reactions: <reactions> 24C. The <reaction> element 24D. Di↵erential cross sections: d�(E)/d⌦ and

d�(E)/d⌦dE 26E. Integral cross sections: �(E) 27F. Defining data styles 27G. Derived reactions 27H. Resonances 29

1. Designating channels 322. Resolved Resonances 343. Unresolved Resonances 364. Correcting cross sections and distributions with

background data 36

V. Grouping together evaluations 37A. Defining a collection of evaluations 37B. “E↵ective” or “Meta” evaluations 37

VI. Covariance data 41A. Covariance Definitions 41B. Covariance of continuous functions 43C. Covariance of multi-dimensional functions 44D. Covariance and correlation matrices 44E. Weighted sums of covariance 45F. The “Sandwich Formula” 46G. Monte Carlo Sampling 47

⇤Edited by D.A. Brown ([email protected])

H. Examples of covariance data usage in this hierarchy 48

VII. Required low-level containers 49A. The lowest-level 51B. General data containers 52C. Text 53D. Hyperlinks 53

VIII. Special reaction case: Atomic Scattering Data 54A. Incoherent Photon Scattering 55B. Coherent Photon Scattering 55

IX. Special reaction case: Particle production or Spallationreactions 56

X. Special reaction case: Radiative capture 56

XI. Special reaction case: Fission 57A. Introduction 57B. Existing ENDF format 58C. Fission format requirements 58

XII. Special component case: Fission Product Yields 59A. Introduction 59B. Existing ENDF format 59C. Detailed FPY format requirements for GND 60D. Discussion of possible implementations 61

XIII. Special reaction case: Large Angle Coulomb Scattering(LACS) 62

XIV. Special reaction case: Thermal Scattering Law 64A. Theoretical Background 64B. Gaussian approximation of the self part of the

scattering kernel 661. Coherent Elastic Scattering 672. Incoherent Elastic Scattering 683. Incoherent Inelastic Scattering in the Short

Collision Time Approximation 68

XV. Additional derived data elements for applications 68A. General Transport Data 69

1. Product average kinetic energy and forwardmomentum 69

2. µ̄lab(E) 693. CDF’s from PDF’s 694. Probability tables in the URR 69

B. Grouped Transport Data 701. Inverse speed 712. Multiplicity 713. Q-value 714. Projectile kinetic energy and momentum 71

C. Production data 71D. Damage cross sections 72

XVI. Prototyping Functions 72

Acknowledgments 73

• We’ve been listening to you and others, but…

• Did we get it right? • What are we still missing? • What is wrong?

Page 9: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Main goals/requirements1. The hierarchy should reflect our understanding of nuclear

reactions and decays, clearly and uniquely specifying all such data.

2. It should support storing multiple representations of these quantities simultaneously, for example evaluated and derived data.

3. It should support both inclusive and exclusive reaction data, that is discrete reaction channels as well as sums over multiple channels.

4. It should use general-purpose data containers suitable for reuse across several application spaces.

5. It should eliminate redundancy where possible. 6. As a corollary to requirements 1 and 2, multiple representations of

the same data should be stored as closely together in the hierarchy as feasible.

9

Page 10: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Special issues! In US (CSEWG), TSL data has lower profile, compared to

say neutron sub library ! Want to revise overly complicated format

• Hierarchy of approximations unclear to uninitiated • Precision/dynamic range of Sαβ • Covariance data

! Take advantage of improved methodology • LEAPR ! Split self & distinct ! dσ(E,T)/dE’dΩ directly vs. Sαβ(α,β,T)

! How to group together evaluations • TSL matching onto higher energies • How to resolve issues of stoichiometry and normalization • TSL is not just vs. T, but P and other parameters

(EOS-related or not)10

Page 11: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Main approximations in TSL treatments

! First Born approximation ! Lots of scatterers !Orientation average !Gaussian approximation

• coherent elastic • incoherent

- elastic - inelastic

- short collision time approximation

11

Always have to do these in practice

ENDF always assumes these, but it could be done better

Page 12: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Supporting ENDF’s Thermal Scattering Law would be easy…

! 3 cases supported by ENDF: • coherent elastic (off ordered substances) • incoherent elastic (hydrogenous solids) • incoherent inelastic (famous Sαβ data)

! All cases are parameterized forms of dσ/dΩdE’, so use • <dcrossSection_dOmega> (elastic) or<dcrossSection_dOmega_dE> (inelastic)

• Parameterizations for elastic cases given in ENDF manual • Parameterization for inelastic case implied in ENDF manual

12

Page 13: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

In general case, can break scattering kernel up to some extent, but not enough to help

13

DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37

DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37

DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37

DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37

DRAFT

A Theoretical Background XI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

di↵erent nuclei,

hbj

bj

0i = hbj

i hbj

0i = hbi2 if j0 6= jhb

j

bj

i =⌦

b2↵

for j = j0(38)

Using this, we can define the coherent scattering crosssection as �

coh

= 4⇡ hbi2 and the incoherent as �inc

=4⇡(

b2↵

� hbi2). Now, define an intermediate function

I(~, t) =1

N

X

j,j

0

D

e�~·~Rj

0 (0)e�~·~Rj

(t)

E

(39)

The intermediate function can be computed from con-densed matter theory assuming that the dynamics (de-scribed in terms of vibrational eigenmodes or phonon-type spectra) and structure (e.g., a certain order or cor-relations in the positions of scatterers in space) of themedium of interest are well understood.

In terms of the intermediate function, the scatteringkernel is

S(~,!) =1

2⇡~

Z 1

�1dte�!tI(~, t) (40)

Now both S(~,!) and I(~, t) may include all j, j0 in thesum in Eq. (37) or they may be broken out into j = j0

(self) and j 6= j0 (distinct) contributions. This is usefulbecause the incoherent cross section only contains the selfcorrelation between an atom at time t = 0. We have

d2�(E)

d⌦dE0 =k0

k[�

coh

S(~,!) + �inc

Ss

(~,!)] (41)

where

S(~,!) = Ss

(~,!) + Sd

(~,!) (42)

discussion point Reaction annotations could beused to split the scattering kernel into “self” and “dis-tinct” parts. This is useful for a model-based evaluationwhere both components can be computed separately.

In practice, one assumes that we may average over ori-entation of the scatterers such that we can replace thedirectional dependence of ~ with a directionless depen-dence. Also, one uses the scattering kernel rewritten interms of the dimensionless variables ↵ and � so

S(↵,�) = kB

T

~ S(,!) (43)

where ↵ = ~22/2MkB

T = (E0 + E � 2pEE0µ)/Ak

B

Tand � = ~!/k

B

T = (E0 � E)/kB

T .discussion point Whether we use ↵ and � or

and !, we have reduced the parametric dependence ofthe scattering kernel to three. These are , ! and animplicit material temperature dependence. This makesstoring the scattering kernel directly in ENDF feasible.resolution We should stick to storing the kernel interms of ↵ and � for backwards compatability

discussion point New experiments fromNCSU/RPI/ORNL collaboration will directly mea-sure the d�(E)/dE0d⌦. This is equivalent to measuring

the full scattering kernel. Storing the covariance onthe full scattering kernel may be unfeasible. Storingthe covariance on data using the approximations anddistinctions below may be feasible.

The scattering kernel can be divided and simplified fur-ther by taking advantage of the elastic limit (! ! 0) orby making several approximations

• In the Gaussian approximation the “self” part ofthe scattering kernel may be written in terms of thematerial’s phonon frequency ⇢(!) and computed us-ing the LEAPR approach

• The short collision time approximation

scattering kernel requirements

R:1 Allow TSL data to be broken out into separate re-actions as specified by the evaluator. Each reactionis treated independently for the purposes of neutrontransport.

R:2 Allow reactions to be annotated by combina-tions of self, distinct, coherent, incoherent,tsl elastic and tsl inelastic labels. Becauseof this flexibility, care will need to be taken by eval-uators to ensure that double counting does not oc-cur.

R:3 All reaction data contained in<dcrossSection dOmega dE> or<dcrossSection dOmega> elements, depending onthe evaluators needs.

R:4 All reaction data must be broken out by the classscatterer (e.g. HinH2O), even if only one class ofscatterer is needed to describe the reaction. Thestoichiometric fraction of each class of scatterermust be given.

R:5 The scattering kernel S(↵,�, T ) can be given asan interpolation table or using one of the approxi-mations or distinctions given below in subsectionsXIB 1-XIB 3

R:6 Coherent or incoherent cross sections are associatedwith their respective scattering kernels.

discussion point Annotations might also be usedto denote “tsl elastic” and “tsl inelastic” data as TSLdata does not have the same two-body kinematics ofhigher energy data. When ! ! 0, E = E0 in the labframe and the center of mass frame is meaningless.

B. Gaussian approximation of the self part of thescattering kernel

By making the so-called Gaussian approximation to thescattering kernel [34, 35] the self part of the scattering

37

Write

Just store these? Note S(κ,ω) is rewritten Sαβ so this is still huge

Page 14: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

In the incoherent Gaussian approximation, the scattering kernel is computed by LEAPR as follows

14

DRAFT

B Gaussian approximation of the self part of the scattering kernelXI SPECIAL REACTION CASE: THERMAL SCATTERING LAW

kernel can be written in terms of the material phononspectrum ⇢(!):

Ss

(↵,�) =1

2⇡

Z 1

�1dt ei�te��(t) (44)

where

�(t) = ↵

Z 1

�1d!⇢(!)

1� e�i!t

� e�!/2

2! sinh(!/2)

(45)

This Fourier transform is coded in R.E. MacFarlane’sLEAPR module of NJOY [16] and can be used to gener-ate the inelastic scattering kernel.

We note that if the full scattering kernel is well approx-imated by only the self term and in this Gaussian approx-imation, the entire scattering kernel can be specified withon phonon spectrum. This spectrum may have a discreteportion and/or a continuous portion. Nevertheless, thiso↵ers us a compact way to encapsulate the scattering ker-nel and it provides us with a two-dimensional object thatwe can specify covariance on.

Gaussian self-part scattering kernel requirements

R:1 An encapsulating element that specifies that thisdata is the self part of the scattering kernel only.

R:2 The phonon spectrum ⇢(!) as a discrete and/orcontinuous distribution.

R:3 Optionally, a <link> to the covariance on thephonon spectrum.

Following [36], we can expand the time-dependent partof the scattering kernel to arrive at the phonon expansion:

e��(t) = �↵�s

1X

n=0

1

n!

Z 1

�1d!P

s

(!)e�!/2e�i!t

n

(46)

where Ps

(!) = ⇢(!)/2! sinh (!/2kB

T ) and the Debye-Waller coe�cient is

�s

=

Z 1

�1d!P

s

(!)e�!/2 (47)

The nth term in this expansion is identified with the num-ber of phonons involved in the collision [36]. This expan-sion allows us to arrive at two approximations given inthe ENDF format manual that must be grandfatheredinto the new format: elastic coherent, elastic incoherentand the short collision time approximations. In the caseof the elastic (in)coherent data, we set E = E0 whichthen forces � ! 0 and simplifies the phonon expansionto the first term, the zero phonon limit. Alternatively, inthe limit of large n, we arrive at the short collision timeapproximation (call this because the large number of col-lisions implies a short time for each individual collision).

0.1

1.0

10.0

100.0

10-5 10-4 10-3 10-2 10-1 100 101

Cro

ss S

ectio

n [

b ]

Energy [ eV ]

inelastic scatt. contribution

C-nat, scatt. ENDF/B-VII.0, free gas model (299.15 K)C-nat in Graphite, therm. scatt. ENDF/B-VII.0, (299.15 K)

FIG. 26. Elastic scattering cross-sections of carbon at roomtemperature (free gas model) vs. thermal scattering cross-sections of carbon in graphite at room temperature.

1. Coherent Elastic Scattering

For crystals (polycrystalline materials), the informa-tion about the crystal structure is expressed in termsof the so-called Bragg edges (a discrete set of energiesE

j

⇠ 1 meV - 1 eV) and a set of crystallographic struc-ture factors s

j

associated with Ej

and a neutron scattererin a crystal unit cell. In addition, one has to estimate thetemperature dependent Debye-Waller coe�cient W 0 (inthe units of eV�1). Then it is possible to generate thedata structure that can be used to generate the contribu-tion of coherent elastic neutron scattering into the ther-mal neutron scattering kernel, scattering cross sections,etc., for a given scatterer in the polycrystal.

Figure 26 compares the di↵erent elastic scattering pre-scriptions for two di↵erent forms of carbon. Here one canclearly see the Bragg edges in the elastic cross section.

In the early 1990’s, parameterized coherent and inco-herent elastic scattering were added to ENDF format.Neutrons can only elastically scatter coherently o↵ of reg-ular substances such as crystals. The di↵erential crosssection for such scattering can be written [13]

d2�

dE0 d⌦(E, T ) =

1

2⇡E

E

i

<E

X

i=1

si

(T ) �(µ�µi

) �(E�E0)

(48)

where:

µi

= 1� 2Ei

E(49)

The quantity actually given in the file is S(E, T ) whichthe ENDF manual states is conveniently represented asa stairstep function with breaks at the Bragg edges E

i

using histogram interpolation. Here, we must store thestructure factor s(E, T ) tables in ENDFs MF=7 (notethese factors are given as a histogram in ENDF, hencethe notation above).

38

Phonon spectrum is sole input, rest is math, including the structure factor in ω➞0 limit

In this approximation, only store ρ(ω) & its covariance

Page 15: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

However, we were asked to support much more in the new format

! Requested to support covariance data in TSL ! Requested to store stuff to generate Sαβ using

photon spectrum ρ(ω) of material and structure factor S(q) in NJOY’s LEAPR module • Both ρ(ω) and S(q) are 2d tables that can have covariance • Would need to “encode” LEAPR somehow • Could put covariance on these very easily but uncertainty

propagation through LEAPR tough

• New measurements and theory produce Sαβ directly, without ENDF’s approximations • Can we store this? It is a 4d data set (S x α x β x T)! • What about covariance?

15

Page 16: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Special issues! In US (CSEWG), TSL data has lower profile, compared to

say neutron sub library ! Want to revise overly complicated format

• Hierarchy of approximations unclear to uninitiated • Precision/dynamic range of Sαβ • Covariance data

! Take advantage of improved methodology • LEAPR ! Split self & distinct ! dσ(E,T)/dE’dΩ directly vs. Sαβ(α,β,T)

! How to group together evaluations • TSL matching onto higher energies • How to resolve issues of stoichiometry and normalization • TSL is not just vs. T, but P and other parameters

(EOS-related or not)16

Page 17: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

17

Lawrence Livermore National Laboratory 3

!  For benzene (C6H6): – T.ENDFB7R0 transitions smoothly across the thermal boundary – T.ENDFB7R0.LANL is off by a factor of 6 – T.ENDFB7R1.LANL is off by a factor of 12

From Dave Heinrichs

Page 18: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Think about water from a neutron’s perspective

18

Dissociated H & O

Water vapor

Liquid water

Water ice

(use TSL)

(use TSL)

(use TSL)

2 x elemental H

1 x elemental O

1H (99.985%) 2H (0.005%)

18O (0.2%)17O (0.038%)

16O (99.762%)

T (°

K)

373.3

273.16

E (eV)10-5 5

Page 19: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Gluing together evaluations: <metaEvaluation>

! An xsdir-like facility is used by many institutions to glue together evaluations • In LANL's MCNP code system, the xsdir file allows one to connect the

thermal neutron scattering data with the neutron nuclear reaction data and even various high energy models such as CEM.

• The LLNL transport codes AMTRAN and Mercury both allow one to define target macros to describe the material in a zone.

• AECL, there is another, similar, facility to connect thermal neutron scattering data at different temperatures and even different phases of the target material.

! There are other uses for connecting evaluations: • Defining elemental evaluations • Grouping data on same target, but heated to different temperatures • Defining generic fission fragments w/ weighted average of fission fragment

evals. • Putting together the parts of a TSL evaluation at fixed temperature, but

including all the scatterers. 19

Page 20: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Defining a <metaEvaluation>

! <axis> elements define grid on which we will use evaluations. Could be: • incident neutron energy • material temperature

! <referredEvaluation>s link region to the actual evaluation • define stoichiometry • define location in grid

defined by axis

20

++

= 1 = 1 or 0

= Any num.

DRAFT

40

FIG. 23 Sample <metaEvaluation> specification, in this case for water. This files requires another <metaEvaluation> to specifythe composition of dissociated water into the elements hydrogen and oxygen. These then require other <metaEvaluation>s tospecify the elemental composition of H0 and O0 in terms of their isotopics.

FIG. 24 The <metaTargElement> element.

Resolution:

Yes but at the cost of creating an unnecessarycoupling between a <metaEvaluation> and thematerial database or there will be mistakes.Additionally, testing that the sum of fractionalcompositions sum to the correct value will bedi�cult.

Discussion point:

Should the the <referredEvaluation> also containa nativeData attribute to handle Doppler broad-ened data better?

Resolution:

No, this should be done at the <evaluation>level so the nativeData information is associ-ated with the evaluation file itself and not some-where else.

Discussion point:

Is there a need for a separate <metaTarget> con-cept to handle arbitrary projectiles so we needn’tmaintain 7-8 di↵erent (but nearly identical) elementspecifications?

Resolution:

Good point. Maybe allowing any or * as aprojectile would serve this purpose. Alter-natively, we could make the projectile at-tribute optional and if it is not present than the<metaEvaluation> is valid for all projectiles.Either way the links to the actual evaluation be-come meaningless. This requires some thought.Perhaps the resolution is to pre-make the el-emental <metaEvaluation>s for the standardtargets with fake URLs. Then users can swap-n-replace them with the correct URLs for theirown needs. However, if one of the <axis> ele-ments covered incident energy, there is a ques-tion of how to handle Q values and di↵erentchannels opening up.

Discussion point:

It was felt at the WPEC SG38 meeting in May2014 that implementing metaEvalautions amountsto “scope creep”, meaning that this capability wasnot included in the original requirements. That said,it was generally agreed that this was a useful idea

Page 21: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Notes on metaEvaluation concept! referredEvaluation points to a evaluation or

another metaEvaluation ! stoichiometricFraction tag lets you specify, say,

chemical or isotopic make-up if multiple referredEvaluations are allowed

! stoichiometricFraction better add up to 1! ! outside of parameter ranges in axis tags, the metaEvaluation does not exist

! metaEvaluation only valid for listed projectile! need to make sure every region in axes covered by a referredEvaluation

! metaEvaluations are often reusable across different libraries 21

Page 22: Requirements for TSL data in new format€¦ · • TSL is not just vs. T, ... Special reaction case: Thermal Scattering Law 64 A. Theoretical Background 64 B. Gaussian approximation

Hopefully we’ve captured your input see https://www.oecd-nea.org/science/wpec/sg38/top_level_hierarchy.pdf

22

DRAFT

Requirements for a next generation nuclear data format

OECD/NEA/WPEC SubGroup 38⇤

(Dated: April 1, 2015)

This document attempts to compile the requirements for the top-levels of a hierarchicalarrangement of nuclear data such as is found in the ENDF format. This set of require-ments will be used to guide the development of a new set of formats to replace the legacyENDF format.

CONTENTS

I. Introduction 2A. Scope of data to support 3B. How to use these requirements 4C. Main requirements 4D. Hierarchal structures 5E. Complications 6

1. Is it a material property or a reaction property? 62. Di↵erent optimal representation in di↵erent

physical regions 73. Ensuring consistency 74. Legacy data 75. Special cases 8

II. Common motifs 8A. Documentation 8B. What data are derived from what other data? 11C. Product list elements 13D. <product> elements 13E. <distributions> and <distribution> elements 16F. Multiplicities 17

III. Particle and/or material properties database 18

IV. One evaluation 20A. Reaction designation 23B. The collection of reactions: <reactions> 24C. The <reaction> element 24D. Di↵erential cross sections: d�(E)/d⌦ and

d�(E)/d⌦dE 26E. Integral cross sections: �(E) 27F. Defining data styles 27G. Derived reactions 27H. Resonances 29

1. Designating channels 322. Resolved Resonances 343. Unresolved Resonances 364. Correcting cross sections and distributions with

background data 36

V. Grouping together evaluations 37A. Defining a collection of evaluations 37B. “E↵ective” or “Meta” evaluations 37

VI. Covariance data 41A. Covariance Definitions 41B. Covariance of continuous functions 43C. Covariance of multi-dimensional functions 44D. Covariance and correlation matrices 44E. Weighted sums of covariance 45F. The “Sandwich Formula” 46G. Monte Carlo Sampling 47

⇤Edited by D.A. Brown ([email protected])

H. Examples of covariance data usage in this hierarchy 48

VII. Required low-level containers 49A. The lowest-level 51B. General data containers 52C. Text 53D. Hyperlinks 53

VIII. Special reaction case: Atomic Scattering Data 54A. Incoherent Photon Scattering 55B. Coherent Photon Scattering 55

IX. Special reaction case: Particle production or Spallationreactions 56

X. Special reaction case: Radiative capture 56

XI. Special reaction case: Fission 57A. Introduction 57B. Existing ENDF format 58C. Fission format requirements 58

XII. Special component case: Fission Product Yields 59A. Introduction 59B. Existing ENDF format 59C. Detailed FPY format requirements for GND 60D. Discussion of possible implementations 61

XIII. Special reaction case: Large Angle Coulomb Scattering(LACS) 62

XIV. Special reaction case: Thermal Scattering Law 64A. Theoretical Background 64B. Gaussian approximation of the self part of the

scattering kernel 661. Coherent Elastic Scattering 672. Incoherent Elastic Scattering 683. Incoherent Inelastic Scattering in the Short

Collision Time Approximation 68

XV. Additional derived data elements for applications 68A. General Transport Data 69

1. Product average kinetic energy and forwardmomentum 69

2. µ̄lab(E) 693. CDF’s from PDF’s 694. Probability tables in the URR 69

B. Grouped Transport Data 701. Inverse speed 712. Multiplicity 713. Q-value 714. Projectile kinetic energy and momentum 71

C. Production data 71D. Damage cross sections 72

XVI. Prototyping Functions 72

Acknowledgments 73