Mid-rapidity Emission in Reactions of Sn Isotopes at 26A MeV
Use of a Nucleation Based Ternary Fission Model to Reproduce Neck Emission in Heavy-Ion Reactions Jerome Gauthier Cyclotron Institute, Texas A&M University SOTANCP4 May 2018 Ternary fission: about 0.3% of heavy nucleus fissions produce a third fragment coming from the low density neck region. Pu 241 Fission Fragment Ternary Fission Most of those fragments are particles.
A high yield of tritons relative to protons is observed and the heavy fragment yields are decreasing with Z. The use of a nuclear statistical equilibrium (NSE) model based on the chemical potential for low density and temperature is in pretty good agreement with experimental observations for A15. To reproduce the heavier fragment yields, one has to take into account the reaction time and the critical cluster size (nucleation). S. Wuenschel et al., Physical Review C 90, 011601 (2014) This behavior should not be restricted to fission necks and is more likely to be a general nuclear matter property. It thus needs to be
studied at higher temperature. Mid-peripheral collisions with a heavy system like 124Sn+124Sn are similar to the fission process but at higher temperature and density. We want to see if NSE with nucleation (NESC) calculation can reproduce the mid-rapidity (ternary fission like) isotopic yields. We use 124Sn+124Sn and 124Sn+112Sn at 26A MeV from the December 2007 NIMROD experiment. Nimrod Detection Array Neutron Ball 156 CsI(Tl) distributed on 11 rings from 3 to 100o. 100 Si (300m)-CsI(Tl) telescopes from ring 2 to 9. 30 Si(150m)-Si(500)-CsI(Tl) super telescopes from ring 2 to 9.
4 neutron detector array (Neutron Ball). Peripheral and mid-peripheral event selection: Zmax > 20 Multiplicity > 1 Relative angle selection The relative angle between the biggest fragment (Zmax) and the fragment of interest velocity vectors is calculated in order to select the mid-rapidity emission. Laboratory frame CM frame Relative Angle Window Selection Vcm
Vproj Charge versus parallel velocity for several relative angle windows centered at 90o in the center of mass. Relative Angle Window Selection To select the ternarylike-fragments the relative angle (in the center of mass) should be close to 90o. But the statistic goes down very quickly when shrinking that window. To maximize the statistic, we select the interval for which stops to drop. The 50130o selection seems
to be a good compromise. Isotopic Yield Evaluation Each isotope count of a particular Z is multiplied by a correction factor to take into account: missing detectors imperfect isotopic identification energy thresholds Fit free parameter values for Z<15 minimization: NSEC Fitting (colored lines)
T = 2.76 MeV Time = 6000 fm/c = 18.67x10 fm -4 Li Be B C N O F -3 Na
Ne Mg Al Si Z/A=0.47 Ac = 15.8 M2 (for Z<15)=1.11 T = 2.72 MeV Li Be B Time = 7300 fm/c
= 16.38x10-4 fm-3 Z/A=0.44 Ac = 16.1 M2 (for Z<15)=1.07 C N O F Ne Na Mg Al
Si NSEC Fitting (Z only) Fit free parameter values for Z only minimization: T = 2.33 MeV Time = 9 600 fm/c = 14.2x10-4 fm-3 Z/A=0.42 Ac = 16.0 M2 =0.29 T = 2.35 MeV Time = 9 600 fm/c = 14.2x10-4 fm-3 Z/A=0.42 Ac = 16.0 M2 =0.28
NSEC Fit Parameters System Selection Temperature Sn+124Sn Isotope Isotope A 2.76 2.72 1.4 1.4
18.67 16.38 4 4 Ac Proton ratio 6000 15.8 0.47 7300 16.1 0.44
Fit Metric 1.11 1.07 1.18 0.561 (MeV) Density (10-4 fm-3) Time (fm/c) Using Albergo light particle yield ratio temperature measurement*:
*S. Albergo et al., Il Nuovo Cimento, vol. 89 A, N. 1 (1985). Sn+112Sn Isotope 124 124 241 Pu Equilibrium constant na nb n... c K c a n b n ... n
We calculate several K using the Sn+Sn system (KSn) and 241 Pu fission (KPu). We know KSn, KPu, TSn, TPu, and assuming ground states for Pu (first approximation) we know GGoPu, so we can extract GGoSn. GGoSn is 33% higher than GGoPu (in average). Work still in progress Summary We are able to apply the NSEC model to heavy-ion collisions with reasonable results. Most of the fit parameters are in a realistic range.
Equilibrium constant ratio calculation results are promising. Collaborators to this work J. Gauthier, M. Barbui, X. Cao, K. Hagel, R. Wada, S. Wuenschel and J. B. Natowitz. Special thanks to Alan McIntosh and Sherry Yennello for useful discussions and advices. Thank you for being listening! C. Eccles et al., Physical Review C 96, 054611 (2017).
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