Nuclear Data Section
International Atomic Energy Agency
P.O.Box 100, A-1400 Vienna, Austria

Memo CP-D/409

Date:
To:
From:

24 August 2004
Distribution
O. Schwerer

Subject:

Angular distribution data
Re: Memo CP-C/350, CP-C/346, CP-C/348, CP-E/049

1)
I agree with the proposed new coding rules for angular distributions, provided that
correction of existing entries is taken care of. In particular I appreciate the removal of the code
DA/CRL and the new clear definition of angular correlations, now to be coded as DA/DA.
2)
I have only the following small changes to propose to the draft LEXFOR entry ofCP-C/350 and I append a revised version of it, with the following modifications:-An additional sentence in the introduction about the nomenclature (differential crosssections vs. angular distributions)-

Editorial / typographical corrections for the definitions of ,DA,,RS and ,LP,DP-I think double-, triple- and quadruple-differential cross sections should consistently bewritten as d2σ/…., d3σ/…, and d4σ/….

3)
The proposed and agreed new CINDA quantity COR for correlation is now nolonger meaningful and appropriate changes in all affected dictionaries (not only dictionary36/236) will be needed.
4)
The existing LEXFOR entry "Correlations" should now consist only of a crossreference to the new page on "Differential Data" and some remark or cross-reference to thereamining other correlations (EMC and MCO).

Distribution:
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vml@bnl.gov
nordborg@nea.fr

manokhin@ippe.obninsk.ru
maev@ippe.obninsk.ru
may@obninsk.ru

Mmarina@ippe.obninsk.rug
blokhin@ippe.obninsk.ru
feliks@polyn.kiae.su
chukreev@polyn.kiae.su
S.Dunaeva@iaea.org
taova@expd.vniief.ru
varlamov@depni.sinp.msu.ru
chiba@earth.sgu.ac.jp
kato@nucl.sci.hokudai.ac.jp
ohnishi@nucl.sci.hokudai.ac.jp
oba@nrdf.meme.hokudai.ac.jp
yxzhuang@iris.ciae.ac.cn
gezg@iris.ciae.ac.cn
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tarkanyi@atomki.hu

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vlasov@kinr.kiev.ua
kaltchenko@kinr.kiev.ua
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jhchang@kaeri.re.kr
ohtsuka@nucl.sci.hokudai.ac.jp
m.wirtz@iaea.org
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v.pronyaev@iaea.org
schwerer@iaeand.iaea.org
v.zerkin@iaea.org
henriksson@nea.fr
exfor@nea.fr

Differential Data
(See also Fitting Coefficients, Angle, Polarization).
Definitions
Reaction plane: The plane defined by the incident beam direction and the outgoing particle
direction. For the following discussions plane A is defined by the incident beam direction andthe outgoing particle a direction
Differential data refers, in general, to:•••the particle given in the REACTION string SF3,
for production or fission, the product given in SF4 or in the data table
the particle defined in the REACTION string SF7.
A particle must be specified in SF7 (particle considered) if:•
there is more than one particle given in SF3,•
the data refers to a different particle or nuclide than those specified above,•or the data refers to more than one outgoing particle.
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Nomenclature
In the literature, usually data given in units of cross sections (millibarns/sterad, barns/MeVetc.) are called differential (double-differential, triple-differential, quadruple-differential)
cross sections, while data given in dimensionless units are called angular, energy, orangle/energy distributions. However, these names are often used interchangeably. In thischapter we call them all "distributions" because the independent variables can be more easily
added to the name (as in angle/energy distributions).

Angular Distributions
1. Angular distribution: probability for a particle to be emitted into an area of solid angle dΩlying at a mean angle of θ to the incident beam direction in the reaction plane; given as σ(θ) =dσ/dΩ. The data are given in units of cross section per unit solid angle (e.g., mb/sr).

beam

θ

REACTION coding:DA in SF6.
Unit type: DA (e.g., B/SR)
2. Relative angular distributionsa.) The shape of the angular distribution W(θ); the data are dimensionless, and are mostoften normalized to W(90°) = 1.
REACTION coding: DA in SF6; modifier REL in SF8.
Units: ARB-UNITS.

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b. Ratio to 90°
REACTION coding: DA in SF6; modifier RSD in SF8.
Units: NO-DIMc. Ratio to 0°
REACTION coding: DA in SF6; modifier RS0 in SF8.
Units: NO-DIM

d. Ratio to average value from 0° - 180°:dσ/dΩ / σ/4π
REACTION coding: DA in SF6; modifier RS in SF8.
Units: NO-DIM
e. Ratio to the value at another angle:dσdσ(θ 1 )(θ 2 )dΩdΩCode as a ratio using the separator //, see Ratios.
f. Ratios to the integrated cross section:
Code as a ratio with the separator /, see Ratios.
g. Ratio to Rutherford or Mott scattering
REACTION coding: DA in SF6; modifier RTH (Rutherford) or MOT (Mott) in SF8.
Units: NO-DIM
3. Angular distribution for a correlated pair
Probability that a particle a and a particle b will be emitted at a mean angle θ m to the incident
beam, dσ/dΩ for θ m :θm

REACTION coding:
DA in SF6; particles in SF7 as a+b (e.g., P+A).
Unit type: DA (e.g., B/SR)
The angle is given under the heading ANG-MN
3. Angular correlation: probability that, if a particle a in emitted at a mean angle of θ a to theincident beam direction in the reaction plane, particle b will be emitted at a mean angle of θ b
to the incident beam direction in the same plane (coplanar); given as d2σ/dΩ a dΩ b . The data
are given in units of cross section per unit solid angle squared (e.g., mb/sr2).

θaθb

REACTION coding:
DA/DA in SF6; particles in SF7 as a/b (e.g., P/D).
Unit type: DA2 (e.g., MB/SR2)
The angles θ a and θ b are coded under the headings ANG1 and ANG2, in the same order as theparticles appear in SF7. If the particles are measured on opposite sides of the beam direction,
the angles will be given as, for example, 30. and –30.

Alternately, the angle of particle b, θ b , may be given with the angle between the two emitted
particles θ rel .
θrelθaREACTION coding:
DA/DA in SF6; particles in SF7 (e.g., P/P+A).
Unit type: DA2 (e.g., MB/SR2)
The angles are given as ANG1 and ANG-RL.
The angular correlation is often given as an angular correlation function W(θ a ,θ b ); the data
are dimensionless.
REACTION coding:
Units: ARB-UNITS.

DA/DA in SF6; particles in SF7, REL in SF8.

4. Non-coplanar angular correlations: The more general situation is for particle a andparticle b not in the same reaction plane. Then θ a is the angle of particle a relative to thebeam direction in plane A, θ b is the angle of particle b relative to the beam direction in planeB, and a third angle φ is defined as the angle between the A and B reaction planes (azimuthalangle).
φREACTION coding: DA/DA in SF6; particles in SF7 as a/b (e.g., N/P) ; NCP in SF8.
Unit type: DA2 (e.g., MB/SR2).
The angles θ a and θ b are coded under the headings ANG1 and ANG2, in the same order as theparticles appear in SF7. The azimuthal angle is coded under the heading ANG-AZ-RL.
The angular correlation function is then given as W(θ a ,θ b ,φ).
REACTION coding:
Units: NO-DIM

DA/DA in SF6; particles in SF7; NCP/REL in SF8.

Secondary Energy Distributions
1. Energy distribution: probability for a particle to be emitted with a given energy E΄ or in agiven energy range E min to E max ; given as σ(E΄) = dσ/dE. The data are given in units of crosssection per unit of secondary energy (e.g., mb/MeV).
REACTION coding: DE in SF6.
Unit type: DE (e.g., B/MEV)2. Energy distribution for a correlated pair: Probability that a particle a and a particle b will
be emitted at a mean energy E m or in a given energy range, dσ/dE, usually given for thecenter-of-mass energy of the emitted particles:
REACTION coding: DE in SF6; particles in SF7 as a+b (e.g., P+A).
Unit type: DE (e.g., B/MEV)The angle is given under the data heading E-MN-CM
3. Linear momentum distribution: probability for a particle to be emitted with a given
momentum p΄; given as σ(p΄) = dσ/dp. The data are given in units of cross section per unit ofsecondary linear momentum (e.g., mb/MeV/c).
REACTION coding: DP in SF6.
Unit type: DA DP (e.g., MB/MEV/C)
Example:(……(N,X)……,LP,DP) longitudinal momentum distribution of emitted particles.
The linear momentum is given under the data heading MOM-SEC.
4. Linear momentum for a correlated pair: Probability that a particle a and a particle b will
be emitted at a mean linear momentum p m .
REACTION coding:
DP in SF6; particles in SF7 as a+b (e.g., P+A).
Unit type: DA (e.g., MB/MEV/C)
The linear momentum is given under the heading MOM-SEC-MN.
Angle/Energy Distributions
1. Angle/energy distribution: probability for a particle to be emitted at a given energy E΄ andinto an area of solid angle Ω lying at a mean angle of θ to the incident beam direction in thereaction plane; given as σ(θ) = d2σ/dΩ/dE. The data are given in units of cross section perunit solid angle per unit of energy (e.g., mb/sr/MeV).
REACTION coding:
DA/DE in SF6.
Unit type: DAE (e.g., B/SR/MEV)The energy is given under the data heading E or E-MIN and E-MAX.
2. Angle/energy correlations:a.) probability that, if a particle a in emitted at a mean angle of θ a to the incident beam
direction in the reaction plane and an energy E΄, particle b will be emitted at a mean angle ofθ b to the incident beam direction in the same plane (coplanar); given as d23σ/dΩ a dΩ b dE a .
The data are given in units of cross section per unit solid angle squared per unit energy (e.g.,mb/sr2/MeV).
REACTION coding: DA/DA/DE in SF6, . particles in SF7 as a/b/a (e.g., P/A/P)
Unit type: D3A (e.g., MB/SR2/MEV)The angles θ a and θ b are coded under the headings ANG1 and ANG2 in the same order as theparticles appear in SF7; the energy is coded under the heading E1 or E2 to correlate the energy
with the angle of the same particle.

書式変更b.) probability that, if a particle a in emitted at a mean angle of θ a to the incident beam
direction in the reaction plane and an energy E a , particle b will be emitted at an energy E b ;given as d23σ/dΩ a dE a /dE b . The data are given in units of cross section per unit solid angle perunit energy squared (e.g., mb/sr/MeV2).
REACTION coding: DA/DE/DE in SF6, . particles in SF7 as a/b/a (e.g., P/A/P)
Unit type: D3 (e.g., MB/SR/MEV2)The energies are coded under the data heading E1 and E2 in the same order as the particles
appear in SF7; the angle θ a is coded under ANG1 or ANG2 to correlate with the energy of thesame particle.
c.) probability that, if a particle a in emitted at a mean angle of θ a to the incident beam
direction in the reaction plane and an energy E a , particle b will be emitted at a mean angle ofθ b to the incident beam direction in the reaction plane and an energy E b ; given as
d24σ/dΩ a dΩ b /dE a /dE b . The data are given in units of cross section per unit solid angle perunit energy squared (e.g., mb/sr2/MeV2).
REACTION coding: DA2/DE2 in SF6, . particles in SF7 as a/b (e.g., P/A)
Unit type: D4A (e.g., MB/SR2MEV2)
The angles θ a and θ b are coded under the headings ANG1 and ANG2 in the same order as theparticles appear in SF7; the energies are, similarly, coded under the headings E1 and E2.
d.) Angle/linear momentum distribution: probability for a particle to be emitted with agiven momentum p΄ and angle θ; given as σ(θ,p΄) = dσ/dΩdp. The data are given in units ofcross section per unit of solid angle per unit of secondary linear momentum (e.g., mb/MeV/c).
REACTION coding: DA/DP in SF6.
Unit type: DAP (e.g., MUB/SRMEVC)
The linear momentum is given under the data heading MOM-SEC.

Treiman-Yang Angular Distribution
Definition: The angular distribution measured as a function of the angle between tworeaction planes for three-particle final states in the anti-laboratory system (i.e., X is at rest).
That is, for the reaction between particles X and Y producing particles a, b, c (see diagrambelow), the angle between the planes (X,a,b) and (Y,c). Data are given in the center-of-masssystem.
aX0bc
Y

For photonuclear reactions in the center-of-mass system, it is the angle between the (X,a) and(Y,b) or (Y,c) planes, where X is the incident gamma, Y is the target nucleus.
(X,a)
aXc(Y,c)Y

See Shapiro 1 for more information.
The reaction planes are defined as:• Plane 1: defined by target (SF1) and residual nucleus (SF4)• Plane 2: defined by incident projectile (SF2) and particle designator (SF7)
REACTION coding: parameter code TYA in SF6, outgoing particle in SF7.
Example:REACTION(2-HE-4(G,N+P)1-H-2,,DA/TYA,P) distribution
overTreman-Yang angle between(4He,2H) and (γ,p) planes

The data headings ANG-CM and DATA-CM should be used in the data table.
Reference SystemAn indication that the differential cross section, the angle, or the energy is given in center-ofmass system is given in the data headings; see Center-of-Mass System.

1I. S. Shapiro et al., Nucl.Phys. 61, 353 (1965)