1. The National Superconducting Cyclotron Laboratory
Working group on Fragments/Theory: Comparison of statistical models for fragment production
Betty Tsang
WCI 2005
Texas A & M
Feb 12-16, 2004
The National Superconducting
Cyclotron Laboratory
@Michigan State University

2. Resource Letters in Frontiers in Physics, AJP, 72(2004)
“Going up in Ex … one comes to a domain where the nuclei produced in the reaction have time to equilibrate and are best described with statistical concepts.”
Resource Letters in Frontiers in Physics, AJP, 72(2004)
The successful use of statistical models to describe nuclear reactions and provide insights to the physics of Multifragmentation is an achievement in our field.

3. Limited Goals
To compare different statistical models for multifragmentation.
3 Bench-mark systems; E*/A=5 MeV, r/ro=1/3
A=186, Z=75, N/Z=1.48
A=168, Z=75, N/Z=1.24
A=168, Z=84, N/Z=1.0
To test out different after-burners
2 Bench-mark systems; E*/A=2 MeV

4. Disclaimer
The results presented here have not been discussed in detail with the relevant persons.
(authors, users)

5. Program codes I. Fragment production codes and corresponding users
1) Statistical Multifragmentation Models :
        a.   Bougault: SMM95 by Botvina et al
        b.   Souza : ISMM – microcanonical by Souza & Donangelo
c. Tsang : ISMM – canonical by Das Gupta 
   2)    Friedman : EES by Friedman
    3)   Raduta / Alexandru & Adriana : MMM by Raduta’s
4) Lefevre : MMMC by Gross
    5)    Regnard : (LG-Caen) LGM by Gulminelli
6) Trautmann : QSM by Stoecker
7) Colonna: BNV in a box by Colonna
II. After-Burner:
1) Charity: Gemini by Charity
2) Wada : Texas A&M Gemini+ by Wada
3) Durand : Simon by Durand
4) Tsang : MSU decay by Tan

6. Observable used in comparisons
<NIMF>
A & Z distributions
Isotope Distributions : Centroid & widths
N/Z distributions
Isoscaling
Isotope thermometers (Albergo temperatures)
To test the after-burners …
Effect from primary to secondary decays

8. Final
Primary

9. Final
Primary

10. <NIMF>
Common Features: sequential decays reduce the multiplicities -- Except SMM95
Similar values of <N_IMF>
Low values: LP-Caen
High values : QSM – no heavy fragments
Indication of larger multiplicity with neutron-poor emitting systems ?

14. A & Z Distributions
Similar general trends but differ in details

15. Isotope distributions
Effects of sequential decay on isoscaling
Primary (wider)
Final (narrower )

19. Isoscaling in statistical models
Primary distributions show good isoscaling
A2=186, Z2=75; A1=168, Z1=75
WCI statistical model working group (2004)

21. Effects of sequential decay on isoscaling

22. Effects of Sequential decays on alpha

23. BNV in a box
The isoscaling occurs over four orders of magnitude while the range is 2 order of magnitude for other statistical model. a(BNV) is about factor of 10 larger.

24. Temperature determined from Isotope yield ratio (Albergo temperatures)
Not used as temperatures but test for sequential decays from the fluctuations.
Fragment yield ratios e.g. (3He/4He)/(6Li/7Li) -7 -5 -3
3He
4He
(3He/4He)/(9Be/10Be)
(3He/4He)/(12C/13C)
(11C/12C)/(6Li/7Li)
(11C/12C)/(9Be/10Be)
6Li
Binding Energy
7Li
g.s. assumed

26. Program codes I. Fragment production codes and corresponding users
1) Statistical Multifragmentation Models :
        a.   Bougault: SMM95 by Botvina
        b.   Souza : ISMM – microcanonical by Souza
c. Tsang : ISMM – canonical by Das Gupta 
   2)    Friedman : EES by Friedman
    3)   Raduta / Alexandru & Adriana : MMM by Raduta’s
4) Lefevre : MMMC by Gross
    5)    Regnard : (LG-Caen) LGM by Gulminelli
6) Trautmann : QSM by Stoecker
7) BNV in a box by Colona*
II. After-Burner:
1) Charity: Gemini by Charity
2) Wada : Texas A&M Gemini+ by Wada
3) Durand : Simon by Durand
4) Tsang : MSU decay by Tan

32. Summary
Most “SMM” models are good for predicting gross features but details required “fitting” to data.
Some models may not be good to reproduce experimental data but may be used to provide physics insights.
Files and figures are available in the WCI strategy web site.
Need the insights and inputs from the code owner and users to sort out the differences