Post on 20-Dec-2015
EPAX : an Empirical PArametrization of fragmentation CROSS sections
Klaus Sümmerer, GSI Darmstadt (Germany)
2. The EPAX formula
Ingredients: Parameters and their mass dependence
3. Attempts to derive a new set of parameters
Measured data vs. EPAX predictions
work in progress!
1. Introduction:
High-energy proton-induced reactions
History of empirical parametrizations
Two-step models of high-energy reactions
High-energy proton-induced nuclear reactions
Some early high-energy proton accelerators:Facility Energy From yearBevatron (Berkeley) 6 GeV 1954......AGS (Brookhaven) 11 GeV 1960......Fermilab (Chicago) >300 GeV 1967......
They were also used to bombard various stable target materials.
These targets were analyzed with radiochemical methods,
i.e.: -spectroscopy with or without chemical separations,
Production cross sections and (some) kinematics for suitable radioactive
isotopesImportant findings:
• Reaction products are practically at rest in the target.
• Above 3-10 GeV, the cross sections do not change any more.
• At high energies, the mass yields show an exponential slope.
• The Z-distributions for each fragment mass exhibit a "bell" shape.
High-energy proton-induced nuclear reactions: Isobaric cross sections
Mass yields: exponential slope
Energy-independence of cross sections
Bell-shaped Z-distributions for constant A
p+Au
High-energy nuclear reactions: Models
At GeV energies, a nucleon can be regarded as a classical particle• Nucleon-nucleon collisions can be treated classically using
measured free nucleon-nucleon cross sections (intra-nuclear
cascade).
• In these collisions, very little transverse momentum is
exchanged.
• After the cascade, the residual nucleus is highly excited.
• Heavy-ion projectiles can be treated as a bag of individual nucleons.Physical models: Two-step approach
Step 1:•Intranuclear-cascade models or•Abrasion models
Step 2: evaporation calculation
not very accurate in the1970's and 1980's
Empirical parametrizations looked more promisingat that time
High-energy nuclear reactions: Two-step models
after intra-nuclear cascade after evaporation
400 A MeV 20Ne + 197Au
slope:~ Zp/Np
Zprob(A) line
β-stability line
Early attempts for empirical parametrizations
Proton-induced reactions:
• Silberberg-Tsao parametrization
Mainly used for cosmic-ray purposes: Collisions of light (<Fe) nuclei with
H 2
Not useful for heavier targets or projectiles.
• Rudstam parametrization (from 1966)
• Rudstam parametrization was
later
extended and modified
Proton- vs. heavy-ion induced reactions
Proton- and heavy-ion inducedreactions give very similarisotope distributions:Important observations:The "bell" slopes are asymmetric!The peaks of the distributions seem to follow a universal "corridor" located on the p-rich side of the valley of β-stabilityThe widths depend mainly n fragment mass.The fragments reflect the proton/neutron-excess of the projectile
28 GeV p+238U
8 GeV 48Ca+Be
Na
Target fragmentation: GeV p + Ap A Projectile fragmentation: GeV/nucleon Ap + p Aare equivalent!
History of EPAX Versions
EPAX Version 1: Phys. Rev. C 42, 1990
based on p+A cross sections; Bevalac heavy-ion data for 40 Ar+C,
48 Ca+Be
First parametrization of "memory effect"
EPAX Version 2: Phys. Rev. C 61, 2000
only high-energy heavy-ion data (E/A > 200
MeV)
Bevalac: 40 Ar+C, 48 Ca,
GSI/FRS: 58 Ni,86 Kr+Be, 129 Xe+Al, 208 Pb+Cu
Main problem of EPAX Version 1:
strong overprediction of p-removal cross
sections
Ingredients of EPAX
ZprobEPAX uses a modified "Rudstam
formula":
Y = Y A • n • exp(R|Z prob-Z|Un,p )
Y A = S • P • exp(P(A p-A)) R UpUn
exp.slope
n-rich p-rich
Zprob(A) and R(A) are fragment-mass
dependent
Un=1.65 and Up=2.1 ("Gauss") can be fixed
For very small cross-sections of very p-
rich fragments, the "Gauss" curve turns
into an exponential
500 A MeV 58Ni + Be A=50
Z
(b
arn)
Mass yield YA:
exponential slope
slope parameter depends on Ap
Heavy-ion-induced fragmentation cross-section datasets
System Energy (A MeV) Laboratory Remarks
40Ar + C 200 LBL pioneering work48Ca + Be 212 LBL -"-58Ni + Be 500 GSI p-rich, very small xsects86Kr + Be 500 GSI large fluctuations129Xe + Al 700 GSI
208Pb + Cu 750 GSI36Ar + Be 1050 GSI p-rich only
112Sn + Be 1000 GSI p-rich only124Xe + Pb 1000 GSI Pb target!136Xe + Pb 1000 GSI Pb target!
40,48Ca + Be 140 MSU new dataset58,64Ni + Be 140 MSU -"-136Xe + Be 1000 GSI n-rich, p-removal86Kr + Be 64 MSU/RIKEN very low energy!
new
EPA
X 1
EPA
X 2
Attempts to improve EPAX
2006: GSI
First attempt to modify EPAX parameters compared to Version 2Slightly better fits, but no drastic improvementProblems occur with 124Xe+Pb
2009: Santiago de Compostela
Second attempt to modify EPAX parametersInclude new datasets from MSU at 140 A MeV
the following examples date from this attempt
Most probable fragments – Zprob(A)
line of ß-stability
136Xe
124Xe
ch
arg
e n
um
be
r Z
loci of largest cross sections, Zprob(A)
evaporation-residue corridor
Zprob(A) can be expressed relative tothe line of -stability:
Z prob(A) = Z ß(A)+ Δ(A) + corr(A,Ap)
depends on n(p)-excess of
projectile
"memory effect":fragments "remember" then(p)-excess of the projectile
Centroid Zprob(A)
line of beta stability
residue corridor
Z-
units
rela
tive
diffe
renc
e to
co
rrid
or
n-rich projectile (136Xe)
n-deficient projectile (124Xe) ??
ß-stable projectiles (129Xe, 208Pb)
Δ
corr Z prob(A) = Z ß(A)+ Δ(A) +
corr(A,Ap)
For A=Ap, Zprob =Zp !
Width parameter R(A)
witd
h pa
ram
eter
R
n-deficient projectile (124Xe) ??
ß-stable projectiles (40Ar,129Xe,208Pb)
n-rich projectiles (86Kr, 136Xe)
Y ~ exp(R|Z p-Z|
Un,p )
For A=Ap, the width must shrink!
A
1 A GeV 36Ar+Be
neutron-deficientfragments only!
new version 3.02
old version 2.1
data:M.Caamano et al.NP A733, 187 (2004)
electromagneticdissociation
1 A GeV 136Xe+Pb
bad fit!
bad fit!
data:D. Henzlova et al.Phys. Rev. C 78, 044616 (2008)
Zσ
(b)
1 A GeV 112Sn+Be
neutron-deficientfragments only!
new version 3.02
old version 2.1
data:A. Stolz et al.PR C 65, 064603 (2002)
50Sn
49In
48Cd
47Ag
46Pd
45Rh
44Ru
43Tc
Proton-removal channels?
good!
bad!
1 A GeV 136Xe+Be
data:J.Benlliure et al.Phys. Rev. C 78, 054605 (2008)
Status and outlook New EPAX fits to old and new data sets give satisfactory results
Parameter dependences of Y A(A) and R(A) yield slightly better
quality than EPAX Version 2
Z prob(A)-dependence for 124 Xe+Pb is difficult to describe with the
current parameterization
Problem with p-removal cross sections less severe, shifted to larger
Z
There is still much room for improvement....therefore:
work in progress at
Mass Yield YA(Ap)
slope parameter P ofmass yield depends on size of projectile:
exponential slope for0.50 < A/Ap < 0.90
new: S ~ S0 . (Ap2/3 + At
2/3) Y(A,Ap) = S P exp(-P(Ap-A))