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)