Implementation of Angular Momentum Formalism in Low-Energy Fusion Reactions

This update focuses on integrating the angular momentum formalism into low-energy fusion reactions using the LISE++ platform. It explores fission barriers, potential energy pockets, compound formation, and de-excitation processes in fusion reactions. The documentation delves into fusion residue transmission, fusion-fission mechanisms, and the role of angular momenta in reaction channels. Examples using various projectiles and targets are provided, highlighting the importance of fission barrier modifications for understanding fusion-fission or residue outcomes. The significance of barrier factors in describing experimental data and sophisticated calculations is also discussed, emphasizing the crucial role of fission barriers in the competition between particle evaporation and fission during the de-excitation process.

• Fusion Reactions
• Angular Momentum
• Fission Barriers
• LISE++
• Reaction Mechanisms

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1. Update of Fusion reaction mechanism in LISE++ 1. Fission barrier dialog modification v.9.10.60 from 04/09/15 Purpose: implementation of angular momentum formalism into low-energy reactions 2. Fusion dialogs Potential energy Potential pocket, L critical , DIC Fission barrier vanishing, L Bfis=0 , Fast Fission (FA) Compound Formation, Quasi-Fission Barrier penetration, Quasi-Elastic (QE) Compound de-excitation : Fusion Fission or Residue? 3. LISE++ definitions and features of fusion mechanism LISE++ documentation: Fusion residue transmission v.5.15 Fusion-Fission v.7.8 Angular momenta vs reaction channels 4. Examples: 238U (20 MeV/u) + Be, C 58Ni + 60Ni 36S (12 MeV/u) + 12C, 238U 40Ar + 208Pb 1

2. Fission barrier dialog modification 1. Fission barrier and Yrast line plots as function of L 2. New Fission barriers from P.Moller et al., PRC91(2015)024310 3. BarFac parameter for the SHE region 4. Sierk s fission barrier validity 2 O.Tarasov, 10-Apr-2015, East Lansing

3. Fission barrier dialog modification 1. Fission barrier and Yrast line plots as function of L 2. New Fission barriers from P.Moller et al., PRC91(2015)024310 3. BarFac parameter for the SHE region 4. Sierk s fission barrier validity It looks like a high Barrier value with AME2012 use. But LISE++ allows to load an user mass excess table 3 O.Tarasov, 10-Apr-2015, East Lansing

4. Fission barrier dialog modification 1. Fission barrier and Yrast line plots as function of L 2. New Fission barriers from P.Moller et al., PRC91(2015)024310 3. BarFac parameter for the SHE region 4. Sierk s fission barrier validity Barrier factor to describe experimental data or sophisticated calculations Fission barrier value plays crucial role between particle evaporation and fission competition in de-excitation process 4 O.Tarasov, 10-Apr-2015, East Lansing

5. Fission barrier dialog modification 0. Sierk s fission barrier is operating up to Z 110 @ L=0 or Z 102 @ L>0 1. Fission barrier and Yrast line plots as function of L 2. New Fission barriers from P.Moller et al., PRC91(2015)024310 1. So, if Sierck s fission barrier has been selected , and nucleus atomic number is higher 110 at L=0, than Cohen s barrier will be used. 3. BarFac parameter for the SHE region 4. Sierk s fission barrier validity 2. If if Sierck s fission barrier has been selected , and nucleus atomic number is higher 102 at L>0, then vanishing factor for Z=102 (with the same N/Z ratio) will be used, where the Vanishing factor (L) is the ratio of Barrier(A,Z,L) / Barrier(A,Z,0) Vanishing barrier factor for data from FILEs is based on selection from Sierk or Cohen models in the Fusion dialog 5 O.Tarasov, 10-Apr-2015, East Lansing

6. Fusion-Residue and Fusion-Fission dialogs in LISE++ Do not hesitate to use Low-Energy reaction computing centers as NRV for more sophisticated solutions with Channel Coupling, Langevin equations and so on 6 O.Tarasov, 10-Apr-2015, East Lansing

7. Coming back to the Eighties for definitions 7 O.Tarasov, 10-Apr-2015, East Lansing

8. Potential Energy Default NRV parameters 8 O.Tarasov, 10-Apr-2015, East Lansing

9. Critical momentum Critical momentum : L-value corresponds to potential energy when the pocket is washed out. No fusion Deep Inelastic Collision region Lcritical L < Ldirect Lcritical The potential pocket does not exists, and the EnergyCM is above the barrier 9 O.Tarasov, 10-Apr-2015, East Lansing

10. Deep Inelastic Collision region Deep Inelastic Collision region Lcritical L < Ldirect The potential pocket does not exists, and the EnergyCM is above the barrier 10 O.Tarasov, 10-Apr-2015, East Lansing

11. Fission Barrier Vanishing as f(L) Fast Fission (FA) Fast Fission region LBfis=0 L < Lcritical The potential pocket still exists, but no compound formation 11 O.Tarasov, 10-Apr-2015, East Lansing

12. Compound formation, Quasi-Fission : 48Ca + 208Pb 12 O.Tarasov, 10-Apr-2015, East Lansing

13. Compound formation, Quasi-Fission : 58Fe + 208Pb 13 O.Tarasov, 10-Apr-2015, East Lansing

14. Barrier penetration, Quasi-Elastic (QE) : 238U(5.4 MeV/u) + C Tl(E) denotes the transmission coefficient of the l-th partial wave through the barrier in the total potential 14 O.Tarasov, 10-Apr-2015, East Lansing

15. Barrier penetration, Quasi-Elastic (QE) : 238U(20.0 MeV/u) + C Tl(E) denotes the transmission coefficient of the l-th partial wave through the barrier in the total potential 15 O.Tarasov, 10-Apr-2015, East Lansing

16. Fusion Fission or Residue? 1st step compound de-excitation plot fission 16 O.Tarasov, 10-Apr-2015, East Lansing

17. LISE++ reaction interpretation from R & L 17 O.Tarasov, 10-Apr-2015, East Lansing

18. What cross sections will be used in LISE++ to get rates? LISE++ still uses the Bass formalism to calculate fragment rates !!!! You have to use this calculated factor later to take into account the analysis of partial cross sections 18 O.Tarasov, 10-Apr-2015, East Lansing

19. Fusion dialog warning message for barrier settings Go to the Fission barrier dialog to modify settings for this SHN region You will get this message if The compound Z > 95 In-built fission model (Barfit, FisRot, or LDM) was selected BarFac parameter < 1.2 19 O.Tarasov, 10-Apr-2015, East Lansing

20. 238U (20.6 MeV/u) with Be vs. C targets Carbon target.. 50% split Why? This is due to difference of moments of inertia between C+U and Be+U just above where fission barrier go to zero 20 O.Tarasov, 10-Apr-2015, East Lansing

21. Fission channels for 238U (20 MeV/u) + Be,C reactions Partially go to fission Fissile Z~92 Low Excitation Energy Compound fission ~100% Fissile Z = 96 High Excitation Energy Sequential fission after DIC Fissile Z < 92 High Excitation Energy 21 O.Tarasov, 10-Apr-2015, East Lansing

22. Experimental study of barrier distributions for 58Ni+60Ni http://aip2014.org.au/cms/uploads/presentation/elizabeth_williams.pdf Dr. Elizabeth Williams Department of Nuclear Physics The Australian National University, Canberra, ACT, Australia AIP Congress, Canberra, ACT 9 December 2014 22 O.Tarasov, 10-Apr-2015, East Lansing

23. 36S (12 MeV/u) + 12C, 238U 12C 238U 23 O.Tarasov, 10-Apr-2015, East Lansing

24. 40Ar + 208Pb 24 O.Tarasov, 10-Apr-2015, East Lansing

25. Acknowledgements I would like to acknowledge to Profs. D.J.Morrissey, M.Thoennessenn, Z.Kohley (NSCL/MSU), Dr.G.Knyazheva (FLNR/Dubna), for fruitful discussions. 25 O.Tarasov, 10-Apr-2015, East Lansing