NATIONAL NUCLEAR DATA CENTER
Bldg. 197DBrookhaven National Laboratory
P. O. Box 5000
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Memo CP-C/350
DATE:
TO:
FROM:
SUBJECT:

August 20, 2004
Distribution
V. McLane
Angular distribution data
Re: Memo CP-C/346, CP-C/348, CP-E/049.

This memo is meant to consolidate the proposals of the above three memos.
Regarding the points made in Memo CP-E/049:
1. I agree that it’s best to be consistent, and propose the addition of ANG-AZ-RL toDictionary 24. The heading ANG-AZ will be reserved for possible future use.
2. I agree that ARB-UNITS should be used, and have updated to LEXFOR entry.
3. I agree; I have discussed this same point in Memo CP-C/348. I believe the code CRL isnot necessary; the data are fully defined by the use of SF7.
To clarify some points brought up in comments by Naohiko Otsuka on the corrected entries
that I sent, I am now suggesting (as stated, but not emphasized, in the new LEXFOR entry)
that, for all reactions for which the quantity measured is a function of more than one outgoingparticle, the particles must be specified in SF7. This is an extension of the rule currently inplace for triple-differential data.
I have also looked at the other differential data and updated the LEXFOR entry accordingly.
Add to Dictionary 24 (Data headings)
Azimuthal angle between two reaction planes.
Mean secondary linear momentum of correlated particle pair.

ANG-AZ-RL
MOM-SEC-MN

Distribution:
M. Chiba, Sapporo
F. E. Chukreev, CAJaD
S. Dunaeva, NDS
S. Taova, SarovO. Gritzay, KINR
K. Kato, JCPDG
M. Kellett, NEADB
V. N. Manokhin, CJD
S. Maev, CJD

M. Mikhaylyukova, CJD
N. Otsuka, JCPDG
O. Schwerer, NDS
S. Takács, ATOMKI
F. T. Tárkányi, ATOMKI
V. Varlamov, CDFE
CNDC
NNDC Distribution

Attached is a complete updated LEXFOR entry for Differential data.

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
and the 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.

Angular Distributions
1. Angular distribution: probability for a particle to be emitted into an area of solid angle dΩ
lying 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.
b. Ratio to 90°
REACTION coding: DA in SF6; modifier RSD in SF8.
Units: NO-DIM
c. Ratio to 0°
REACTION coding: DA in SF6; modifier RS0 in SF8.
Units: NO-DIM

d. Ratio to average value from 0° - 180°: 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 θm to the incident
beam, dσ/dΩ for θm:

θm

DA in SF6; particles in SF7 as a+b (e.g., P+A).
REACTION coding:
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 θa to theincident beam direction in the reaction plane, particle b will be emitted at a mean angle of θbto the incident beam direction in the same plane (coplanar); given as d2σ/dΩadΩb. 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 θa and θb 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, θb, may be given with the angle between the two emitted
particles θrel.
θ re lθaREACTION 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(θa,θb); 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 θa is the angle of particle a relative to thebeam direction in plane A, θb 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 θa and θb 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(θa,θb,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 Emin to Emax; 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 Em 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 (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 pm.
DP in SF6; particles in SF7 as a+b (e.g., P+A).
REACTION coding:
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) = dσ/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 θa to the incident beam
direction in the reaction plane and an energy E΄, particle b will be emitted at a mean angle ofθb to the incident beam direction in the same plane (coplanar); given as d2σ/dΩadΩbdEa. 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 θa and θb 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.

b.) probability that, if a particle a in emitted at a mean angle of θa to the incident beam
direction in the reaction plane and an energy Ea, particle b will be emitted at an energy Eb;
given as d2σ/dΩadEa/dEb. 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 θa 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 θa to the incident beam
direction in the reaction plane and an energy Ea, particle b will be emitted at a mean angle ofθb to the incident beam direction in the reaction plane and an energy Eb; given as
d2σ/dΩadΩb/dEa/dEb. The data are given in units of cross section per unit solid angle per unit
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 θa and θb 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 Shapiro1 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 over Treman-Yang

angle between (4He,2H) and (γ,p)
planesThe 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)