Coupling of UrQMD Model with Statistical Multi- Fragmentation Model

A.Galoyan, V.Uzhinsky

VBLHEP and LIT JINR

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

Contents

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

Aim - understanding/description of nuclear fragmentation at high energies

Models: Abrasion-ablation

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

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.

The excitation energy:

Models: Abrasion-ablation – RELDIS code

The model is a combination of the electromagnetic dissociation, the abrasion-ablation model, the Statictical Multi-Fragmentation model

A. Pshenichnov, J. P. Bondorf, I. N. Mishustin, A. Ventura, S. MasettiPhys. Rev. C64, 024903, 2001 Mutual heavy ion dissociation in

peripheral collisions at ultrarelativistic energies

Models: Abrasion-ablation – RELDIS code C. Scheidenberger et al. Phys. Rev. C70, 014902, 2004Charge-changing interactions of ultrarelativistic Pb nuclei

V(ri-rj) ?

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

J.Aichelin, Phys. Rep. 202 (1991) 233;D.H.Boal and J.N.Glosli, Phys. Rev. C38 (1988) 1870; 2621K.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.

Models: Quantum Molecular Dynamics Model

The N-body ''wave function'', ψN , describing the entire nucleus is taken to be a direct product of single particle states ψi. Here r0i and p0i are the mean position and momentum of

the nucleon i and the width of the wave packet is characterized by parameter L.

Models: Quantum Molecular Dynamics Model

Models: Quantum Molecular Dynamics Model

Models: Quantum Molecular Dynamics Model

The total energy arising 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 in terms of the erf functions:

Models: Quantum Molecular Dynamics Model

Stohastic interactions

Clusterization

Rij< Rc~ 2-4 fm

Models: Quantum Molecular Dynamics Model

• 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 enhansedDiagram 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

RTIM CEM (DCM)

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

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, 1997Multifragmentation of gold nuclei in the interactions with photoemulsion nuclei at 10.7-GeV/nucleon.

UrQMD Model

InitializationIn 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 0and local Thomas-Fermi momentum

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

does not consideredEvaporation

UrQMD Model

Patches to UrQMD Model Code

Changes in the file URQMD.Fc optional decay of all unstable particles before final outputc DANGER: pauli-blocked decays are not performed !!! if(CTOption(18).eq.0) thenc no do-loop is used because npart changes in loop-structure i=0 nct=0 actcol=0c disable Pauli-Blocker for final decays old_CTOption10=CTOption(10) ! Aida CTOption(10)=1c 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)) thenc write (6,*) 'no decay of particle ',ityp(i) isstable = .true. endif 44 enddo if (.not.isstable) thenc 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 endifc check next particle if(i.lt.npart) goto 40 endif ! final decay

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

c final outputChanges 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 A. Galoyan, J. Ritman, V. Uzhinskye-Print: nucl-th/0605021Patches 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 theprobability 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 particlesCc... 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

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 ! Uzhi3 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/nucleontook only 10 hours in cascade mode.

UrQMD Model Changes in the file ANNDEC.F

Patches to UrQMD Model Code

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 to file 19:

Input.f

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) !aidaCurrent random number - ranseed

ROOT TTree : “data”

UrQMD Model: Input-Output Changes

Statistical Multi-Fragmentation Model - SMM J.P. Bondorf, A.S. Botvina, A.S. Ilinov, I.N. Mishustin, K. SneppenPhys. Rept. 257: 133-221, 1995. Statistical multifragmentation of nuclei.

New SMM by A.S. Botvina

Statistical Multi-Fragmentation Model - SMM Old SMM

Program implementation

Statistical Multi-Fragmentation Model - SMM

UrQMD

Mesons

Potentialcalculations

Excitationenergy

SMM

Baryons

Fragments,baryons

Root TTree

Fragments?

Eos = 1

Calculations: p+A

Calculations: p+A

Calculations: p+A

Calculations: p+AExp. Data - PS208 Collab.,LEAR

With and without SMM SMM or Evaporation

Isotope production in p+16O

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, JINR, Prop. chamber

Pion multiplicities as functions of Q – involved protons π--mesons π+ -mesons

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

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

Proton multiplicities versus QProton-participant Evaporated protons

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

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

Multiplicities of spectator protons

Multiplicities of multi-charged fragments

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

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

Average pion momenta as functions of Q π- -mesons π+ -mesons

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

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

Average pion momenta as functions of Qπ- -mesons π+ -mesons

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

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

Average participant proton momenta versus Q

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

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

π– meson rapidity distributions in CC-interactions

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

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

Rapidity distributions of participant protons in CC interactions

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

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

Laboratory momentum distributions of participant protons in CC-interactions

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

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

Calculations: Au+Au

Calculations: Au+Au

ZDC must be tuned!

Problems

Too strong destruction!!!

Conclusion1. Clusterization and evaporation/fragmentation are

implemented into the UrQMD program versions 1.3 and 2.3.

2. It is checked that results have a weak dependence on evaporation/fragmentation model.

3. Neutron energy spectra for pA interactions are calculated. Good results are obtained.

4. The model underestimates yield of neutrons with energy less than 10 MeV.

5. Good results are obtained for AC-interactions.

6. Some calculations are done for Au+Au interactions.

7. Tuning and checking of the combination is needed!

• 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.

Conclusion

Operation of Cascade, New Fritiof and UrQMD 1.3 codes can be checked at WEB-portal – HEPWEB.JINR.RU (LIT JINR)