Japan Charged-Particle Nuclear Reaction Data Group
Division of Physics, Graduate School of Science
Hokkaido University
060-0810 Sapporo, JAPANE-mail: nrdf@jcprg.org
Internet: http://www.jcprg.org/Telephone +81(JPN)-11-706-2684
Facsimile +81(JPN)-11-706-4850

Memo CP-E/052
Date:
To:
From:
Subject:

August 27, 2004
Distribution
OTSUKA Naohiko
Effective mass correlation“,EMC” (effective mass correlation) is a correlation quantity defined in EXFOR. In EXFOR, wehave some codes for “effective mass squared” e.g. information identifier EMS-SEC, data heading
EMS, EMS1, EMS1-MAX,…, quantity code “,EMC”. Only one subentry M0035.028 uses thesecodes. I study the possibility of translating “,EMC” into “differential with effective masssquared” as done for “energy distribution for a correlated pair” in CP-C/350. Hereafter, I put light
velocity c assuming effective mass M has the dimension of energy (e.g. MeV) in EXFOR, as
done in M0035.028.
So far I did not know the definition of “effective mass squared” in EXFOR. Therefore I start withthe clarification of the definition by checking the reference of M0035 (Yu. M. Arkatov,UFZ,25,933,1980), which studies p-n correlation in 4He (γ, p+n+d). “Effective mass squared”
M pn 2 is given in Eq.(3) of this article:
M pn 2 = s γ4He + ( m d c2)2 – 2 E d √s γ4He
(in c.m.s. of beam and target pair), where m d is the mass of deuteron, s γ4He is “c.m.s. energy squared” for this reaction system:s γ4He = ( E γ + E 4He )2 – ( c p γ + c p 4He )2 = ( E p + E n + E d )2 – ( c p p + c p n + c p d )2
From these equations, we obtain the definition of “effective mass squared” in this article,
M pn 2 = s pn = [ ( E p + E n )2 – ( c p p + c p n )2 ], this is center-of-mass energy squared for proton-neutron pair.
Therefore I conclude that “effective mass squared” in EXFOR means center-of-mass energy
squared in relativistic kinematics (= invariant mass squared) [ ( ∑E i )2 – (∑ c p i )2 ] for morethan 2 particles. This quantity is Lorentz invariant. An example of LEXFOR entry is as follows:
Effective (invariant) mass squared distribution for a correlated pair : Probability that a particle aand a particle b will be emitted at effective (invariant) mass squareds = [( E a + E b )2 – ( c p a + c p b )2], dσ / ds :REACTION coding : DS in SF6; particles in SF7 as a+b (e.g., P+A).
Unit type: DE2 (e.g. B/MEV2)

The effective (invariant) mass squared is given under the data heading EMS.
I put “(invariant)” after “effective”, because “effective mass” has various meanings inphysics, for example mass of nucleon or other hadrons in nuclear matter is called as “effectivemass” in nuclear physics, while the definition of “invariant mass” is probably unique.
Using “,DS,A+B”, M0035.028 can be coded by “,DS,N+P,,REL” with ARB-UNITS.
Relations of invariant mass squared to other variables found in EXFOR are as follows:1) √s is the sum of energy (including mass energy mc2) for particles in their center-of-masssystem. This is a relativistic extension of “energy of relative motion” E rel (=center-ofmass energy in non-relativistic kinematics) given in Eq.(1) of CP-E/051, and a relativistic
extension of EN-CM for incoming channel.
2) The set of s, t (4-momentum transfer squared, given under –t in EXFOR) and u is called
Lorentz-invariant Mandelstam variables. For reaction 1+2→3+4,s = ( E 1 + E 2 )2 – ( p 1 + p 2 )2 = ( E 3 + E 4 )2 – ( p 3 + p 4 )2t = ( E 1 – E 3 )2 – ( p 1 – p 3 )2 = ( E 2 – E 4 )2 – ( p 2 – p 4 )2u = ( E 1 – E 4 )2 – ( p 1 – p 4 )2 = ( E 2 – E 3 )2 – ( p 2 – p 3 )2s + t + u = m12 + m22 + m32 + m42
using natural unit ( c = 1 ).

Distribution:
S. Babykina, CAJaD
S. Dunaeva, NDS
A. Kaltchenko, KINR
M. Lammer, NDS
M.Mikhaylyukova, CJD
S. Takacs, ATOMKI
V. Varlamov, CDFE

J.H. Chang, KAERI
Z.G. Ge, CNDC
K. Katō, JCPRG
S. Maev, CJD
C. Nordborg, NEA-DB
S. Taova, VNIIEF
M. Vlasov, KINR

M. Chiba, JCPRG
O. Gritzay, KINR
M. Kellet, NEA-DB
V.N. Manokhin, CJD
P. Oblozinsky, NNDC
T. Tárkányi, ATOMKI
M. Wirtz, NDS

F.E. Chukreev, CAJaD
A. Hasegawa, JAERI
M. Lammer, NDS
V. McLane, NNDC
O. Schwerer, NDS
V. Pronyaev, NDS
H.W. Yu, CNDC

V. Zerkin, NDS

Y.X. Zhuang, CNDC

EXFOR, NEA-DB

JCPRG Distribution