INC Model for High -Energy Hadron -Nucleus Reactions · 2009. 5. 20. · Einc > ≈≈≈≈ 50 MeV...
Transcript of INC Model for High -Energy Hadron -Nucleus Reactions · 2009. 5. 20. · Einc > ≈≈≈≈ 50 MeV...
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INC Model INC Model
for Highfor High--EnergyEnergy
HadronHadron--Nucleus ReactionsNucleus Reactions
Y.Yariv
SOREQ NRC, Yavne 81800, Israel
International Topical Meeting on Nuclear Research,
Application and Utilization of Accelerators
IAEA, Vienna, Austria
4-8 May, 2009
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OutlineOutline Introduction
Why INC?
What is INC?
Basic Assumptions Requirements
Expected limitations
INC implementations
Continuous target density models
• Space–Like Monte Carlo
• Time-Like Monte Carlo
Nucleon Dynamics
Examples
Y.Yariv, INC Model 2
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Why INC?Why INC?
Transport codes for projectile in energy range up to few GeV important for many applications (e.g. RIB, Spallation Sources)
Existing cross-section libraries limited to 150MeV or, for some isotopes to 20 MeV (for radioactive “residua” – 20 MeV)
Need for fast “event generator” code
to fill the 20 MeV – 3 GeV gap
Y.Yariv, INC Model 3
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What is INC?What is INC?
intranuclear cascade model
intranuclear cascade model
On this page: Select Article
Science and Technology Dictionary
Library > Science > Science and Technology Dictionary
intranuclear cascade model
(¦in·trə′nü·klē·ər kas′kād ′mäd·əl)
(nuclear physics) A model of nuclear collisions that
assumes a series of independent nucleon-nucleon
collisions between particles that act like billiard balls.
Y.Yariv, INC Model 4
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INC Models (seriously)INC Models (seriously)R.Serber, Phys. Rev. 72, 1114 (1947)R.Serber, Phys. Rev. 72, 1114 (1947)
Particle on Nucleus reaction treated as series of two-body scatterings
“Realistic” target density and momentum distributions (Fermi sea)
Approximated Pauli principle
“Fast Phase” followed by “slow” target de-excitation
No “fitting parameters”
Y.Yariv, INC Model 5
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AssumptionsAssumptions Requirements Requirements (1)(1)
Many-body scattering in terms of on shell single particle cross sections
“Deep Inelastic” collisions, “Energetic” collisions
Interacting particles followed on classical trajectories
de Broglie wave-length shorter than inter-nucleon distance DDDD<<d
Asymptotic value of scattered wave before next collision
de Broglie wave-length shorter than m.f.p.
DDDD<ΛΛΛΛ
Y.Yariv, INC Model 6
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AssumptionsAssumptions Requirements Requirements (2)(2)
Interference terms between collisions cancel out
m.f.p. shorter than target radius
ΛΛΛΛ<R
Independent scattering from different nucleons in the target
m.f.p. (ΛΛΛΛ) larger than inter-nucleon distance (d); Time between interactions (ΛΛΛΛ /ββββc) shorter than interaction time (10-23sec.)
ΛΛΛΛ>d
ΛΛΛΛ /ββββc > ≈ 10-23sec. ΛΛΛΛ /3ββββ > ≈ 1
Y.Yariv, INC Model 7
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Central collision p+208PbCentral collision p+208Pb
Y.Yariv, INC Model 8
MeVE
fm
Rd
.2000.1
10//
13/
>≈⇒>
Λ≡
>≈Λ
<Λ<<<
ξ
ξ
β
D
D
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Expected limitationsExpected limitations
Einc> ≈≈≈≈ 50 MeV for:
Total nucleon yields
Peripheral collisions, e.g. “quasi-elastic”,(p,2p)
Einc > ≈≈≈≈ 200 MeV for:
“Violent reactions” (high multiplicity, high
excitation energy)
Significant discrepancies expected for outgoing particles for Einc lower than few tens MeV
Y.Yariv, INC Model 9
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Continuous Target Density Continuous Target Density
ModelsModels
The target nucleus is represented by continuous density distribution in a potential well (e.g. Woods Saxon) and degenerate “local density” Fermi gas momentum distribution
Probability per unit path length of a particle to interact with the nucleons of the nucleus
Probability of a particle to interact at a distance between a and a+da is:
Y.Yariv, INC Model 10
2
2
21212
1
2
2
21212
1
11p
pv
vpd
pv
vQ
rr
rr ∆
∂
∂≈
∂
∂= ∑∫
ρσ
ρσ
QdaeadPQa−=)(int
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HadronHadron--Hadron InteractionsHadron Interactions
On-mass-shell, free cross sections
Elastic
Inelastic (1π production & absorption)
Y.Yariv, INC Model 11
N
NNN
+⇔∆
+∆⇔+
π33
33
NNNN +⇒+
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SpaceSpace--Like Basis MCLike Basis MC
The first collision site is determined and the collision partner chosen
The types and momenta of the particles after the collision are chosen according to isospin and branching ratio considerations. Only “Pauli allowed”interactions are permitted.
After the collision the particle is followed, and its possible next collision site and partner chosen. The process is repeated until the particle leaves the nucleus or falls below “energy cutoff”
The interaction partners are treated the same way –one after another
Y.Yariv, INC Model 12
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TimeTime--Like Basis MC (1)Like Basis MC (1)
Cascade evolution divided into small “time intervals”. The probability of interaction of the
projectile in a time interval δτδτδτδτ is P(δτδτδτδτ)≈ρσδτ≈ρσδτ≈ρσδτ≈ρσδτ.
If collision occurs, the types and momenta of the particles after the collision (“participants”) are chosen according to isospin and branching ratio considerations. If there is no collision, next time interval is considered
Y.Yariv, INC Model 13
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TimeTime--Like Basis MC (2)Like Basis MC (2)
After each interaction the target Fermi Sea is “depleted”
In each “time interval” all the “participants”are followed. With each interaction the number of particles to be followed in the next time interval increases
Event ends when all participants escape or are absorbed
Y.Yariv, INC Model 14
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Nucleon DynamicsNucleon Dynamics
(INCL)(INCL)
The target nucleus is represented by discrete nucleons following nuclear density distributions in a potential well and “local density” degenerate Fermi gas momentum distribution
The participants are moving on straight trajectories interacting when their “minimal distance of approach” is less than √(σσσσ(s)/ππππ)
Interactions with Erel<≈≈≈≈100 MeV are not allowed (range restriction of ≈≈≈≈1.3 fm).
Only “Pauli allowed” interactions are permitted
Event ends when properties of reaction “stabilize”
Y.Yariv, INC Model 15
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Y.Yariv, INC Model 16
N
N
N
N
NNN
N
p pD
D
D
N
N
N
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OutputOutput
Total reaction cross-section
Outgoing particle statistics →“Fast” particle spectra
Residual target momenta andexcitation energy from In-Out balance or Particle-Hole considerations
Y.Yariv, INC Model 17
))(
1(**.Pr
.2
oj
K
Coul
tot
Transptot
RE
RV
N
NNR −
−= πσ
R
’
R
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Y.Yariv, INC Model 18
ISABEL איזבל
אשד תוך גרעיניEshed Toch Gar’ini → ETGAR אתגר Etgar = Challenge
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HistoryHistory
R.Serber, Phys. Rev. 72, 1114 (1947)
M.L.Goldberger, Phys. Rev. 74, 1269 (1948)
N.Metropolis et al., Phys. Rev. 110, 185 (1958); Phys. Rev. 110, 204 (1958)
VEGAS: K.Chen et al., Phys. Rev. 166, 949 (1968)
ISOBAR: G.D.Harp et al., Phys. Rev. C8, 581 (1973); C10 2387 (1974)
ISABEL: Y.Yariv and Z.Fraenkel, Phys. Rev. C20, 2227 (1979); Phys. Rev. C24, 488 (1981)
ETGAR…
Y.Yariv, INC Model 19
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HadronHadron--Hadron Cross Sections (1)Hadron Cross Sections (1)
N+N
σtot, σinel , σel G.D.Harp, Phys. Rev. C10, 2387 (1974)Arndt phase shift analysis
dσel /dωP.C.Clements, L.Winsberg, UCRL 9043 (1960), unpublished
Y.Yariv, INC Model 20
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HadronHadron--Hadron Cross Sections (2)Hadron Cross Sections (2)
N+N → N+∆Type of outgoing N, ∆ determined by Isotopic Spin considerationZ.Fraenkel, Phys. Rev. 130, 2407 (1963)
Mass of ∆ is chosen from distribution:
F = two body phase factor for the produced N+∆S.Lindenbaum and R. Sternheimer, Phys. Rev. 105, 1874 (1957); 109, 1723 (1958); 123, 333 (1961)
P(coscm)=.25+.75*(coscm)2
Y.Yariv, INC Model 21
MeVmmmmm
EmFEconstEmP
NN
NN
cm
NN
cm
p
tot
NN
cm
500
),(*)(*.),(
++<<+
=
∆
+∆
+++∆
+
ππ
πσ
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HadronHadron--Hadron Cross Sections (3)Hadron Cross Sections (3)
∆+N → N+N (π capture)
Type of outgoing N, ∆ determined by Isotopic Spin consideration
σ, dσ/dω calculated from inverse process (∆ production) using the principle of “detailed balance”
∆ production calculated using theoretical model (OPE)
Y.Yariv, INC Model
l
22
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HadronHadron--Hadron Cross Sections (4)Hadron Cross Sections (4)
∆+N → ∆’+N’ (“exchange”)
Naively two step process:
Decay of initial Isobar, ∆→π+N’
Interaction of decay π with another Nucleon, π+N→∆’
G.D.Harp et al., Phys. Rev. C6, 581 (1973),
Z.Fraenkel, Nuovo Cimento 30, 512 (1963)
Z.Fraenkel, Phys.Rev. 130, 2407 (1963)
Y.Yariv, INC Model
l
23
N’
p
D’
ND
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HadronHadron--Hadron Cross Sections (5)Hadron Cross Sections (5)
π+N → ∆→ π’+N’(elastic & charge exchange)
Experimental dσ/dω + isospin considerationsG.Giacomelli et al., CERN/HERA 69-1 (1969)
For ∆ decaying without interaction proper π+N differential cross section
Isotropic ∆ decay after scattering or exchange
Y.Yariv, INC Model 24
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HadronHadron--Hadron Cross Sections (6)Hadron Cross Sections (6)
∆ → π+N
Energy dependant ∆ width
J.N. Ginocchio, Phys. Rev. C17, 195
(1978)
Y.Yariv, INC Model 25
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Density depletionDensity depletion
After each interaction Fermi sea density, ρi, is depleted
Fast rearrangement: ρiof the “partner
type” Fermi sea is uniformly reduced for
the whole nucleus
Slow rearangement: “partner type” hole
of radius r is punched in the position of
the interaction. No interactions are
allowed in the hole with particles of
“partner type” .Y.Yariv, INC Model 26
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Pauli BlockingPauli Blocking
Options:
Full Pauli Blocking: Interaction resulting
in nucleon falling below Fermi sea is
forbidden
“Depleted” Pauli Blocking: Reaction
resulting in nucleon falling below Fermi
sea is allowed with probability of the
relative depletion of the Fermi sea
Y.Yariv, INC Model 27
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p(p(208208Pb,nX) at 1.2 GeVPb,nX) at 1.2 GeV
Y.Yariv, INC Model 28
1.2 GeV p + Pb, Isabel or INCL44 and ABLA-v3p
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
1
10
102
103
1 10 102
103
2007/04/20 11.36
neutron energy (MeV)
d2 σ/dΩ
dEn (
mb/
sr.M
eV),
norm
e=1
for 0
0
Isabel-ABLA
INCL44-ABLA
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n(n(208208Pb,pX) at 96 MeV, n(Pb,pX) at 96 MeV, n(209209Bi,pX) at 63 MeVBi,pX) at 63 MeV
Y.Yariv, INC Model 29
10-1
1
10
0 10 20 30 40 50 60 70 80 90 100
96 MeV
Data: V. Blideanu et al.
dσ/d
E [m
b/M
eV]
Isabel-ABLA
INCL4.4-ABLA
10-1
1
10
0 10 20 30 40 50 60 70
63 MeV Data: E. Raeymackers et al.
Isabel-ABLA
INCL4.4-ABLA
dσ/d
E [m
b/M
eV]
E [MeV]
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n(n(209209Bi,pX) at 41 MeVBi,pX) at 41 MeV
Y.Yariv, INC Model 30
10-1
1
10
0 5 10 15 20 25 30 35 40 45 50
Data: E. Raeymackers et al.
Isabel-ABLA
INCL4.4-ABLA
dσ/d
E [m
b/M
eV]
10-2
10-1
1
10
0 10 20 30 40 50
θp= 20
0
10-3
10-2
10-1
1
0 10 20 30 40 50
θp= 100
0
d2 σ/dΩ
dE [
mb/
sr.M
eV]
E [MeV]
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Thank You!
Questions, Remarks?
Y.Yariv, INC Model 31