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Coupling of UrQMD Model with Statistical Multi- Fragmentation ModelA.Galoyan, V.UzhinskyVBLHEP and LIT JINR

Aim - understanding/description of nuclear fragmentation at high energies

Needs: 1. Centrality control; 2. Radiation load; 3. Cosmic ray studies

Contents

- Theoretical models:
- AA, QMD, Glauber+RTIM
- UrQMD and SMM
- Calculation results
- Conclusion

J. Hufner, K. Schafer, B. Schurmann Phys.Rev.C12:1888-1898,1975

Abrasion-ablation in reactions between relativistic heavy ions.

L.F. Oliveira, R. Donangelo, J. O. Rasmussen Phys.Rev.C19:826-33,1979.

Abrasion-ablation calculations of large fragment yields from relativistic heavy ion reactions.

J.J. Gaimard, K.H. Schmidt Nucl.Phys.A531:709-746,1991.

A Reexamination of the abrasion - ablation model for the description of the nuclear fragmentation reaction.

Models: Abrasion-ablation

The expression for the cross section for abrasion of n nucleons:

The excitation energy:

A. Pshenichnov, J. P. Bondorf, I. N. Mishustin, A. Ventura, S. Masetti

Phys. Rev. C64, 024903, 2001 Mutual heavy ion dissociation in peripheral collisions at ultrarelativistic energies

Models: Abrasion-ablation – RELDIS code

The model is a combination of the electromagnetic dissociation,

the abrasion-ablation model,

the Statictical Multi-Fragmentation

model

C. Scheidenberger et al. Phys. Rev. C70, 014902, 2004

Charge-changing interactions of ultrarelativistic Pb nuclei

Models: Abrasion-ablation – RELDIS code

Models: Quantum Molecular Dynamics Model

J.Aichelin, Phys. Rep. 202 (1991) 233;

D.H.Boal and J.N.Glosli, Phys. Rev. C38 (1988) 1870; 2621

K.Niita, S.Chiba et al., Phys. Rev. C52 (1995) 2620;

Ch.Hartnack, Rajeev K. Puri, J.Aichelin, J.Konopka, S.A.Bass,

H.Stoker and W.Greiner, Eur. Phys. J. A1 (1998) 151.

In the QMD model each nucleon (or quasi-particle) is assumed to be aconstant width minimal wave packet (coherent state).

V(ri-rj) ?

Models: Quantum Molecular Dynamics Model

The N-body ''wavefunction'', ψN, describing the entirenucleus is taken to be a direct product of single particle statesψi. Here r0iandp0i are the mean position andmomentum of the nucleoni and the width of the wave packet is characterized byparameterL.

Models: Quantum Molecular Dynamics Model

Models: Quantum Molecular Dynamics Model

Models: Quantum Molecular Dynamics Model

The total energyarising

from the "Pauli interaction“:

where the Kronecker deltas ensure that the potential acts between quasi-particles only.

The Coulomb potential for Gaussian charge distribution can be expressed interms of the erf functions:

Models: Quantum Molecular Dynamics Model

Stohastic interactions

Clusterization

Rij< Rc~ 2-4 fm

- ANALYSIS OF THE (N, X N-PRIME) REACTIONS BY QUANTUM MOLECULAR DYNAMICS PLUS STATISTICAL DECAY MODEL.K. Niita, S. Chiba, Toshiki Maruyama, Tomoyuki Maruyama, H. Takada, T. Fukahori, Y. Nakahara, A. Iwamoto (JAERI, Tokai),.
- Phys.Rev.C52:2620-2635,1995

Neutron energy spectra for the reaction p(1500 MeV)+Pb. The solid histograms are the results of QMD+SDM, and points are experimental data.

Models: Glauber + RTIM+SMM = New FRITIOF

K. Abdel-Waged, V. Uzhinsky Yad.Fiz.60:925-937,1997.

Model of nuclear disintegration in high-energy nucleus nucleus

interactions

Glauber approximation underestimates nuclear destrustion!

We have considered enhansed

Diagram contributions

Models: Glauber + RTIM+SMM = New FRITIOF

K. Abdel-Waged, V. Uzhinsky Phys.Atom.Nucl.60:828-840,1997,

Yad.Fiz.60:925-937,1997.

Model of nuclear disintegration in high-energy nucleus nucleus interactions

Si+Al, Cu, Pb, 14.8 GeV/c/nucleon

RTIM

CEM (DCM)

Models: Glauber + RTIM+SMM = New FRITIOF

K. Abdel-Waged, V. Uzhinsky Phys.Atom.Nucl.60:828-840,1997,

Yad.Fiz.60:925-937,1997.

Model of nuclear disintegration in high-energy nucleus nucleus interactions

O+A, 60 GeV/N

Models: Glauber + RTIM+SMM = New FRITIOF

K. Abdel-Waged, V. Uzhinsky Phys.Atom.Nucl.60:828-840,1997,

Yad.Fiz.60:925-937,1997.

M.I.Adamovich et al. (EMU-01 collab.) Zeit. Fur Phys. A359,277, 1997

Multifragmentation of gold nuclei in the interactions with photoemulsion

nuclei at 10.7-GeV/nucleon.

UrQMD Model

Initialization

UrQMD Model

In configuration space the centroids of the Gaussians are randomly

distributed within a sphere with R=r0(0.5*[A+(A1/3-1)3])1/3 (fm)

The initial momenta of the nucleons are randomly chosen between 0

and local Thomas-Fermi momentum

The initialized nuclei are not in their ground state, and can evaporate

single nucleons after 20-30 fm/c. Pauli potential is not included. It can

be included optionally.

Potentials

Skyrme-type, Yukawa, Coulomb and Pauli ones

Collisions

Cross sections

are very good!

Pauli blocking

included

Clusterization

does not considered

Evaporation

does not considered

UrQMD Model

Patches to UrQMD Model Code

A. Galoyan, J. Ritman, V. Uzhinsky

e-Print: nucl-th/0605021

Patches to UrQMD Model Code.

Changes in the file URQMD.F

c optional decay of all unstable particles before final output

c DANGER: pauli-blocked decays are not performed !!!

if(CTOption(18).eq.0) then

c no do-loop is used because npart changes in loop-structure

i=0

nct=0

actcol=0

c disable Pauli-Blocker for final decays

old_CTOption10=CTOption(10) ! Aida

CTOption(10)=1

c decay loop structure starts here

40 continue

i=i+1

c is particle unstable

if(dectime(i).lt.1.d30) then

41 continue

isstable = .false.

do 44 stidx=1,nstable

if (ityp(i).eq.stabvec(stidx)) then

c write (6,*) 'no decay of particle ',ityp(i)

isstable = .true.

endif

44 enddo

if (.not.isstable) then

c perform decay

call scatter(i,0,0.d0,fmass(i),xdummy)

c backtracing if decay-product is unstable itself

if(dectime(i).lt.1.d30) goto 41

endif

endif

c check next particle

if(i.lt.npart) goto 40

endif ! final decay

CTOption(10)=old_CTOption10 ! Return to the old value !

c final output

Changes in the file STRING.F

! call getmas(m0,w0,mindel,isoit(mindel),mmin,mmax,-1.,amass) !Aida

call getmas(m0,w0,mindel,isoit(mindel),mmin,mmax,-1.d0,amass)!Aida

! ^^

UrQMD Model

Patches to UrQMD Model Code

Changes in the file PROPPOT.F

REAL*8 ERF (in Proppot.f)

REAL*4 ERF (Erf.f)

Original line : Cb = Cb0/rjk(j,k)*erf(sgw*rjk(j,k))

was replaced by: Cb = Cb0/rjk(j,k)*erf(sngl(sgw*rjk(j,k))) ! Aida

! ^^^^^ ^

Original lines :

dCb = Cb0*(er0*exp(-(gw*rjk(j,k)*rjk(j,k)))*sgw*rjk(j,k)-

+ erf(sgw*rjk(j,k)))/rjk(j,k)/rjk(j,k)

were replaced by:

dCb = Cb0*(er0*exp(-(gw*rjk(j,k)*rjk(j,k)))*sgw*rjk(j,k)-

+ erf(sngl(sgw*rjk(j,k))))/rjk(j,k)/rjk(j,k) ! Aida

^^^^^ ^

Changes in the file INIT.F

Parameter (nnucl=1) ! 10) ! Aida

For debugging purposes

UrQMD Model

Patches to UrQMD Model Code

Changes in the file ANNDEC.F

In file "tabinit.f", in "subroutine mkwtab", it is checked that the

probability of decay channel of a resonance is not zero ("bran.gt.1d-9").

If it is zero, the spline coefficients are not determined. At the same time,

in the file anndec.f, in subroutine anndex, it is not checked that the

probability is zero. Due to this the code go out of the allowed region. To

improve the situation we have added many lines in the subroutine anndex.

C one ingoing particle --> two,three,four outgoing particles

C

c... decays

do 3 i=0,maxbr

if((minbar.le.iabs(i1)).and.(iabs(i1).le.maxbar)) then ! Uzhi

call b3type (i1,i,bran_uz,i1_uz,i2_uz,i3_uz,i4_uz) ! Uzhi

if(bran_uz.le.1.d-9) then ! Uzhi see mkwtab

prob(i)=0.d0 ! Uzhi

else ! Uzhi

if(isoit(btype(1,i))+isoit(btype(2,i))+isoit(btype(3,i))+ ! Uzhi

& isoit(btype(4,i)).lt.iabs(iz1).or. ! Uzhi

& m1.lt.mminit(btype(1,i))+mminit(btype(2,i)) ! Uzhi

& +mminit(btype(3,i))+mminit(btype(4,i)) )then ! Uzhi

prob(i)=0.d0 ! Uzhi

UrQMD Model

Patches to UrQMD Model Code

Changes in the file ANNDEC.F

else ! Uzhi

prob(i)=fbrancx(i,iabs(i1),iz1,m1,branch(i,iabs(i1)), ! Uzhi

& btype(1,i),btype(2,i),btype(3,i),btype(4,i)) ! Uzhi

endif ! Uzhi

endif ! Uzhi

else ! For mesons ! Uzhi

if(isoit(btype(1,i))+isoit(btype(2,i))+isoit(btype(3,i))+

& isoit(btype(4,i)).lt.iabs(iz1).or.

& m1.lt.mminit(btype(1,i))+mminit(btype(2,i))

& +mminit(btype(3,i))+mminit(btype(4,i)) )then

prob(i)=0.d0

else

prob(i)=fbrancx(i,iabs(i1),iz1,m1,branch(i,iabs(i1)),

& btype(1,i),btype(2,i),btype(3,i),btype(4,i))

endif

endif ! Uzhi

3 continue

Due to all of these changes the code works quite fast and stable!

Simulation of 10000 events of Au+Au interactions at 25 GeV/c/nucleon

took only 10 hours in cascade mode.

UrQMD Model: Input-Output Changes

Input.f

CTOption(5) = 0 -> 1 (random b from bmin to bmax bdb weighted)

CTOption(21) = 0 -> 1 (Lund Fragmentation Function)

CTOption(27) = 0 -> 1 (target lab frame)

Tottime = 100 fm/c (total time to calculate for event)

Outtime = 100 fm/c (time interval for output)

Random number generator is changed

Fortran operators - open file, read, write are closed

Output.f ( output to file13, 14, 15, 16, 17, 20 is closed)

i_f=i_f+1 !aida id_f(i_f)=id !aida charge_f(i_f)=charge(i) !aida px_f(i_f) = px(i)+ffermpx(i) !aida py_f(i_f) = py(i)+ffermpy(i) !aida

pz_f(i_f) = pz(i)+ffermpz(i) !aida p0_f(i_f) = p0(i) !aida fmass_f(i_f)= fmass(i) !aida

Current random number - ranseed

Output to file 19:

ROOT TTree : “data”

Statistical Multi-Fragmentation Model - SMM

J.P. Bondorf, A.S. Botvina, A.S. Ilinov, I.N. Mishustin, K. Sneppen

Phys.Rept.257:133-221,1995.Statistical multifragmentation of nuclei.

Statistical Multi-Fragmentation Model - SMM

Old SMM

New SMM by A.S. Botvina

Statistical Multi-Fragmentation Model - SMM

Program implementation

Root TTree

Baryons

Mesons

Fragments,

baryons

Potential

calculations

Eos = 1

UrQMD

Excitation

energy

SMM

Fragments?

Calculations: p+A

Calculations: p+A

Calculations: p+A

Exp. Data - PS208 Collab.,LEAR

SMM or Evaporation

With and without SMM

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N, JINR, Prop. chamber

Charged particles multiplicities.

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Pion multiplicities as functions of Q – involved protons

π--mesonsπ+ -mesons

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Proton multiplicities versus Q

Proton-participantEvaporated protons

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Multiplicities of spectator protons

Multiplicities of multi-charged fragments

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Average pion momenta as functions of Q

π- -mesons

π+ -mesons

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Average pion momenta as functions of Q

π- -mesons

π+ -mesons

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Average participant proton momenta versus Q

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

π– meson rapidity distributions in CC-interactions

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Rapidity distributions of participant protons in CC interactions

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: p, d, He-4, C-12 + C, 4.2 GeV/c/N,

Laboratory momentum distributions of participant protons in CC-interactions

Points – Exp. Data. Red – UrQMD+SMM, green – Fritiof+SMM, blue – Cascade.

Calculations: Au+Au

Calculations: Au+Au

ZDC must be tuned!

Too strong destruction!!!

- Clusterization and evaporation/fragmentation are implemented into the UrQMD program versions 1.3 and 2.3.
- It is checked that results have a weak dependence on evaporation/fragmentation model.
- Neutron energy spectra for pA interactions are calculated. Good results are obtained.
- The model underestimates yield of neutrons with energy less than 10 MeV.
- Good results are obtained for AC-interactions.
- Some calculations are done for Au+Au interactions.
- Tuning and checking of the combination is needed!

Conclusion

- New version of Statistical Multi-fragmentaion Model has been coupled with UrQMD model to further use in CBM and PANDA software. Additional testing of the UrQMD + SMM is needed.
- Some drawbacks were located in UrQMD 1.3 and 2.3.

Problems:

- Calculations using UrQMD+SMM model require too many computer time.

Operation of Cascade, New Fritiof and UrQMD 1.3 codes can

be checked at WEB-portal – HEPWEB.JINR.RU (LIT JINR)