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Photons in the lab and in stars: a tedious route from experimental data to stellar reaction rates

Photons in the lab and in stars: a tedious route from experimental data to stellar reaction rates. Peter Mohr Diakonie-Klinikum, D-74523 Schwäbisch Hall, Germany ATOMKI, H-4001 Debrecen, Hungary. ECT Workshop – Trento – November 2018. A provocative question at the beginning….

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Photons in the lab and in stars: a tedious route from experimental data to stellar reaction rates

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  1. Photons in the lab and in stars:a tedious route from experimental data to stellar reaction rates Peter MohrDiakonie-Klinikum, D-74523 Schwäbisch Hall, GermanyATOMKI, H-4001 Debrecen, Hungary ECT Workshop –Trento – November 2018

  2. A provocative question at the beginning… • What is a direct experiment? • Relevant quantity: reaction rate at stellar conditions- NA < σv >* for particle-induced reactions- λ* for photon-induced reactions • A direct experiment should measure NA < σv >* or λ*(may become feasible in laser-induced plasma) • All other experiments measure NA < σv >lab or λlabunder lab conditions (T ≈ 0; no thermally excited states) and are thus – more or less – indirect! • Resulting question: What is the relation between the stellar rates and the laboratory rates (cross sections)? Peter Mohr ECT-Workshop Trento, November 2018

  3. Outline of this presentation (1): formalism • Difference between:NA < σv >* and NA < σv >labfocus on λ* and λlab for photon-induced reactions • A very simple example:16O(α,γ)20Ne and 20Ne(γ,α)16O in the lab and in starsP. Mohr et al., EPJA 27, s01, 75 (2006) • Reciprocity for time-reversed cross sectionsσ(1+2↔3+γ) for partial cross sectionse.g. 16Og.s.(α0,γ1)20Ne2+ and 20Ne2+(γ1,α0)16Og.s. • Detailed balance between stellar reaction ratesfor photons: NA < σv >*(1+2→3+γ) and λ*(3+γ→1+2) Peter Mohr ECT-Workshop Trento, November 2018

  4. Outline of this presentation (2): applications • Thermalization of isomers via intermediate states: 180Ta, 176Lu, 186Re, 92Nb- various scenarios: s-process, p-process, ν-process • Rate of capture reactions between light nuclei from photodisintegration- various scenarios: BBN, H-, He-burning • γ-induced reactions in the p(γ)-process: (γ,n), (γ,α) • (n,γ) rates from (γ,n) experiments- branching points in the s-process • Suggestions for ELI-NP (and other photon facilities) Peter Mohr ECT-Workshop Trento, November 2018

  5. Some recent work in literature • T. Rauscher,Photonuclear Reactions in AstrophysicsNuclear Physics News 28, 12 (2018) • R. Reifarthet al.,Neutron-induced cross sectionsFrom raw data to astrophysical ratesEurop. Phys. J. Plus 133:424 (2018) Peter Mohr ECT-Workshop Trento, November 2018

  6. 16O(α,γ)20Ne: Full level scheme of 20Ne (to scale) • For simplicity:- discussion restricted to:16O: 0+ ground state20Ne: 0+ ground state20Ne: 2+ state at 1634 keV20Ne: 1-state at 5788 keVappears as resonance in 16O(α,γ)20Ne at 1058 keV- partition functs. neglected:G(16O) ≈ G(20Ne) ≈ 1.0 Peter Mohr ECT-Workshop Trento, November 2018

  7. Time scale for thermalization: 20Ne (0+ ↔ 2+) Time scale for thermalization is essentially defined by the lifetime of the 2+ state First important message of this talk:thermalization is fast, compared to typical timescales in stars(at least for allowed intra-band transitions; isomers will require special consideration) Fast transition between 0+ ground state and 2+:T1/2 = 0.73 psГγ = 0.63 meV Peter Mohr ECT-Workshop Trento, November 2018

  8. Some (trivial) definitions… • Breit-Wigner cross section σ(E) in a resonance: • Resonance strength ωγ: • Total and partial widths Г,Гα, Гγfor 16O(α,γ)20Ne: • γ-branching ratio: Peter Mohr ECT-Workshop Trento, November 2018

  9. Reaction rate of 16O(α,γ)20Ne Stellar rate < σ v >* isproportional to total resonance strength ωγ and to exp(-ERα/kT) 0+ ground state:ωγ0 = 0.18 ωγ 2+ excited state:ωγ1634 = 0.82 ωγ Peter Mohr ECT-Workshop Trento, November 2018

  10. Reaction rate of 20Ne(γ,α)16O: formalism • Rate λ from folding of thermal photons nγ(E,T) and photon-induced cross section σ(E): • Photon (Planck) distribution: • σ(E) from (narrow) B-W resonance (using reciprocity): Peter Mohr ECT-Workshop Trento, November 2018

  11. Reaction rate of 20Ne(γ,α)16O: (a) 0+ ground state Rate from 0+g.s.:proportional to partial resonance strength ωγ0 and to exp(-ERγ/kT) Peter Mohr ECT-Workshop Trento, November 2018

  12. Reaction rate of 20Ne(γ,α)16O: (b) 2+ excited state Rate from excited 2+:proportional to partial res. strength ωγ1634 and to exp[-(ERγ-Ex)/kT] enhancement by factor exp(+Ex/kT) for excited state because of lower γ-transition energy ERγ-Ex! Peter Mohr ECT-Workshop Trento, November 2018

  13. Reaction rate of 20Ne(γ,α)16O: (c) stellar rate λ* Stellar rate λ*from weighted summation (Boltzmann factors): Peter Mohr ECT-Workshop Trento, November 2018

  14. Reaction rate of 20Ne(γ,α)16O: (c) stellar rate λ* Stellar rate λ*from weighted summation (Maxwell-Boltzmann): proportional to total resonance strength ωγand to exp(-ERγ/kT) 0+g.s. 2+(1634) Boltzmann suppression Eγ enhancement proportional to total ωγand exp(-5788 keV/kT) exactly cancel each other!!! Peter Mohr ECT-Workshop Trento, November 2018

  15. Reaction rate of 20Ne(γ,α)16O: (c) stellar rate λ* Stellar rate λ* ≥ λlab proportional to total resonance strength ωγand to exp(-ERγ/kT) exact cancellation between enhancement from lower Eγ and Boltzmann suppression λ*/λlab = (ωγ)/(ωγ0) ≥ 1 λ*/λlab = (ωγ)/(ωγ0) >> 1 Peter Mohr ECT-Workshop Trento, November 2018

  16. Reaction rate of 20Ne(γ,α)16O: (c) stellar rate λ* Stellar rate λ* ≥ λlab proportional to total resonance strength ωγand to exp(-ERγ/kT) ratio λ*/λlabdepends only on nuclear properties, but not on stellar temperature! λ*/λlab = (ωγ)/(ωγ0) ≥ 1 Peter Mohr ECT-Workshop Trento, November 2018

  17. Detailed balance betw. 16O(α,γ)20Ne and 20Ne(γ,α)16O • stellar 16O(α,γ)20Ne capture rate: • stellar 20Ne(γ,α)16O photodisintegration rate: • Detailed balancebetween stellar forward (α,γ) and backward (γ,α) rates: Peter Mohr ECT-Workshop Trento, November 2018

  18. Summary of formalism: three important messages • Thermalization is fast • Detailed balance between stellar forward and backward rates (not for cross sections!) • Significant (often: dramatic!) enhancement for stellar rates of photon-induced reactions:λ*/λlab = (ωγ)/(ωγ0) = 1/B0 ≥ 1 • lab experiments miss contributions of excited states • lab experimts.miss resonances without gs branchingsimilar results for non-resonant reactions:λlab provides only the (typically minor) ground state contribution Peter Mohr ECT-Workshop Trento, November 2018

  19. Stellar enhancement factor vs. ground state contribution • Stellar enhancement factor fSEF(T):fSEF(T) := < σv >*/< σv >labin words: ratio between stellar rate at temperature T and rate at target temperature T=0 (laboratory rate) • Ground state contribution X0(T):X0(T):= < σv >lab/ [ G0 ∙ < σv>*]in words: contribution of the experimentally accessible ground state rate (T=0) to the stellar rate at temp. TG0(T): partition function For further details: see Rauscher et al., ApJ738:143 (2011) Peter Mohr ECT-Workshop Trento, November 2018

  20. fSEF(T) vs. X0(T) for capture reactions: T = 0 • Stellar enhancement factor fSEF(T):fSEF(T) := < σv >*/< σv >labfSEF(T=0) = 1:by definition • Ground state contribution X0(T):X0(T) := < σv >lab / [ G0 ∙ < σv >*]X0(T=0) = 1 Peter Mohr ECT-Workshop Trento, November 2018

  21. fSEF(T) vs. X0(T) for capture reactions: T> 0 • Stellar enhancement factor fSEF(T):fSEF(T) := < σv >*/< σv >labfSEF(T)≈ 1 : remains close to unity (as long as the cross sections of excited states are not too different) • Ground state contribution X0(T):X0(T):= < σv >lab/ [ G0 ∙ < σv>*]X0(T) ≈ 0.1 – 1.0 for kT = 30 keV (s-process)X0(T) ≈ 0.02 – 1.0 for T9= 2.5 (γ-process)already at s-process temperatures many rates are affected by theory (although fSEF(T) ≈ 1 !!!) Peter Mohr ECT-Workshop Trento, November 2018

  22. fSEF(T) vs. X0(T) for capture reactions: T> 0 • Example: 187Os(n,γ)188Os at kT = 30 keVfor simplicity: only 1/2-g.s. and 3/2- at 10 keVMACS (lab): < σ>lab ≈ 1000 mb and fSEF(30 keV) ≈ 1.3MACS (stellar): < σ>*≈ 1300 mbnaive, but wrong interpretation:excited state contributes with 300 mb (or 30%) • but: Boltzmann factor n(3/2-)/n(1/2-) ≈ 1.5 at 30 keV1/2- ground state contribution to < σ >* ≈ 400 mb3/2- excited state contribution to < σ >* ≈ 900 mbcorrect interpretation:ground state contribution X0(30 keV) ≈ 0.3 Peter Mohr ECT-Workshop Trento, November 2018

  23. fSEF(T) vs. X0(T) for photodisintegration reactions • Stellar enhancement factor fSEF(T):fSEF(T) := λ*/ λlabfSEF(T) ≈ 100 – 1000 ( >> 1 ) : much larger than unity because of significant contributions of excited states • Ground state contribution X0(T):X0(T):= λlab / [ G0 ∙ λ* ]X0(T) ≈ 10-2 – 10-3at all temperatures the ground state contribution X0(T) is very small; contributions from thermally excited states dominate even for low temperatures Peter Mohr ECT-Workshop Trento, November 2018

  24. Gamow-like window for photon-induced reactions ? first presentation of a Gamow-like window:P. Mohr et al., PLB 488, 127 (2000) chosen example:192Pt(γ,n)191Pt similar for (γ,α) react. Gamow-like window shifted by Q-value of (X,γ) reaction:E0(γ,X) = E0(X,γ) + Q(X,γ) potentially misleading:E0(γ,X) is a window in excitation energies Exin the compound nucleus (but not in Eγ!!!) Peter Mohr ECT-Workshop Trento, November 2018

  25. Outline of this presentation (2): applications • Thermalization of isomers via intermediate states: 180Ta, 176Lu, 186Re, 92Nb- various scenarios: s-process, p-process, ν-process • Rate of capture reactions between light nuclei from photodisintegration- various scenarios: BBN, H-, He-burning • γ-induced reactions in the p(γ)-process: (γ,n), (γ,α) • (n,γ) rates from (γ,n) experiments- branching points in the s-process • Suggestions for ELI-NP (and other photon facilities) Peter Mohr ECT-Workshop Trento, November 2018

  26. Mystery of nature’s rarest isotope: properties of 180Ta • heavy odd-odd nucleus (Z=73, N=107) • lowest absolute abundance: 2.6 x 10-6 (rel. to Si =106)K. Lodders, ApJ591, 1220 (2003) • very low isotopic abundance: 0.01201%J. R. de Laeteret al., PRC 72, 025801 (2005) • unstable Jπ = 1+ ground state (T1/2 = 8.152 h)T. B. de Ryves, JPG 6, 763 (1980) • exists as long-lived Jπ = 9- isomer (T1/2> 7.1 x 1015yr) at Ex = 77.2 ± 1.2 keVEx from: T. Wendelet al., PRC 65, 014309 (2001) T. Cousins et al., PRC 24, 911 (1981) quasi-stable E. Wardeet al., PRC 27, 98 (1983) isomer aboveK. S. Sharma et al., PLB 91, 211 (1980) ground state!T1/2from: M. Hultet al., PRC 74, 054311 (2006) } Peter Mohr ECT-Workshop Trento, November 2018

  27. Nucleosynthesis of 180Ta Peter Mohr ECT-Workshop Trento, November 2018

  28. Nucleosynthesis of 180Ta: r-process • stable 180Hf shields 180Ta from the r-process→ no 180Ta is made in the r-process Peter Mohr ECT-Workshop Trento, November 2018

  29. Nucleosynthesis of 180Ta: s-process • s-process bypasses 180Ta→ no 180Ta is made in the s-process Peter Mohr ECT-Workshop Trento, November 2018

  30. Nucleosynthesis of 180Ta: p(γ)-process • (γ,n) much faster on n-odd 180Ta than on n-even 181Ta→ practically no 180Ta is made in the γ-process Peter Mohr ECT-Workshop Trento, November 2018

  31. Nucleosynthesis of 180Ta: p(γ)-process • up to the late 1970s:no 180Ta in any major nucleosynthesis process ??? Peter Mohr ECT-Workshop Trento, November 2018

  32. Nucleosynthesis of 180Ta: r-process • β-decay path along isomers in A=180 nuclei→ branchings too small: no 180Ta in the r-process Peter Mohr ECT-Workshop Trento, November 2018

  33. Nucleosynthesis of 180Ta: s-process • isomer branching at A=180 and β-decay of highly ionized 179Hf→ 180Ta is made in the s-process Peter Mohr ECT-Workshop Trento, November 2018

  34. Nucleosynthesis of 180Ta: p(γ)-process • low-T9 window with sufficiently slow 180Ta(γ,n) rate→ 180Ta is made in the γ-process Peter Mohr ECT-Workshop Trento, November 2018

  35. Nucleosynthesis of 180Ta: ν-process • huge neutrino flux in CC-SN: 180Hf(νe,e-)180Ta→ 180Ta is made in the ν-process Peter Mohr ECT-Workshop Trento, November 2018

  36. Nucleosynthesis of 180Ta: early summary • until 1970s: no 180Ta is made in the major processes (s-, r-, p(γ)-process) • 1980s – 1990s: several new ideas for production:-s-process- p(γ)-process- ν-processall processes claim to make sufficient 180Ta→ now we have a factor of 3 too much 180Ta • but: what is the role of isomeric nature of 180Ta?- short-lived low-K 1+ ground state- quasi-stable high-K 9- isomeric state Peter Mohr ECT-Workshop Trento, November 2018

  37. Isomers under stellar conditions: 180Ta • Relevant quantity: stellar rate λ* for the transition from the isomer to the ground state • Direct transition (9- → 1+) highly suppressed • Search for intermediate states (IMS) which connect:9- isomer → intermediate Jπ IMS → 1+ ground state • Widely used method: photoactivationZs. Nemeth et al., ApJ392, 277 (1992)J. J. Carroll et al., ApJ344, 454 (1989)C. B. Collins et al., PRC 42, R1813 (1990)E. B. Norman et al., ApJ281, 360 (1984)D. Belicet al., PRL 83, 5242 (1999); PRC 65, 035801 (2002) • Improved analysis:P. Mohr et al., PRC 75, 012802(R) (2007)T. Hayakawa et al., PRC 81, 052801(R) (2010); PRC 82, 058801 (2010) Peter Mohr ECT-Workshop Trento, November 2018

  38. Photoactivation of 180Ta (under stellar conditions?!) Fig.1 of Belic-2002 • excitation of IMS • decay of IMS- back to 9-isom.- down to 1+g.s. (direct/cascade) Peter Mohr ECT-Workshop Trento, November 2018

  39. Photoactivation of 180Ta (under stellar conditions?!) Fig.1 of Belic-2002 • excitation of IMS • decay of IMS- back to 9-isom.- down to 1+g.s. (direct/cascade) But:What is the role of further excited states in 180Ta? Peter Mohr ECT-Workshop Trento, November 2018

  40. Isomers under stellar conditions: formalism (1) • similar to photon-induced (γ,α) reactions:resonance strength (ωγ) → integrated cross section Iσ • stellar rate λ* from sum over intermediate states (IMS)most relevant: typically the lowest IMS • (energy)integrated cross section Iσ for transition j→k: Peter Mohr ECT-Workshop Trento, November 2018

  41. Isomers under stellar conditions: formalism (2) • Iσlabfor photoactivation in the lab:JIMS→k (exit channel): sum over all low-K cascadesJIMS→j (entr. ch.): only direct high-K transition j=9-→IMS • Iσ*under stellar conditions:JIMS→k (exit channel): sum over all low-K cascadesJIMS→j (entr. channel): all high-K transitions j→IMS including cascades! • λ*/λlab = Iσ*/ Iσlab= 1/Bj ≥ 1laboratory experiment provides only a lower limit! Peter Mohr ECT-Workshop Trento, November 2018

  42. Intermediate states (IMS) in 180Ta (Mohr-2007) photoactivation in the lab IMS1 under stellar condition new IMS2 missed in lab!!! Peter Mohr ECT-Workshop Trento, November 2018

  43. Tentative lowest case-C IMS in 180Ta: 5+, E = 594 keV • band head of Kπ = 5+ band: state with intermediate K between Kπ = 1+g.s. band and Kπ = 9- isomer band • experimentally known properties:- half-life T1/2 = 16.1 ± 1.9 ns- dominating decay to 4+ state at 520 keV (cascading down towards 1+ ground state) • assumed weak E2 branch to 7+ at 357 keV: 1%(cascading down towards 9- isomer):leads to dramatically stronger coupling between ground state and isomer under stellar conditions,but cannot be measured by photoactivation in the lab! • 1% branch corresponds to less than 0.01 W.u. Peter Mohr ECT-Workshop Trento, November 2018

  44. Effective stellar half-life of 180Ta for cases A, B, C effective half-lifeof180Ta reducesfromabout1 yr (case A)toabout11 hours (case C) at kT = 26 keV survivalof180Ta in the s-processdepends on con-vectivemixing! Peter Mohr ECT-Workshop Trento, November 2018

  45. Transition rates from 9- isomer to 1+ ground state stellar rate λ*byfarexceeds 1/s for explosive environments(kT > 100 keV) experimentallyconfirmedcase Aissufficientforthisresult Peter Mohr ECT-Workshop Trento, November 2018

  46. Transition rates from 9- isomer to 1+ ground state survivalof180Ta depends on freeze-out atλ* ≈ 1/s occurs at kT ≈ 40 keV survivalofabout 35% of180Ta as isomer, indepen-dentofproduction Peter Mohr ECT-Workshop Trento, November 2018

  47. Summary for 180Ta • Significantly stronger coupling between ground state and isomer from new tentative low-lying IMS (case C) • Case C states (without direct branching to initial state) cannot be measured by photoactivation! • s-process: - effective half-life of 180Ta reduces by 3 orders of magnitude from 1 year to 11 hours at kT = 26 keV- survival of 180Ta depends on convective mixing • explosive nucleosynthesis: p(γ)-process or ν-process- thermalization of 180Ta at production (kT > 100 keV)- already ensured by existing experimental data- survival at freeze-out (kT ≈ 40 keV): about 35% Peter Mohr ECT-Workshop Trento, November 2018

  48. Final conclusions for 180Ta • 180Ta can be made in 3 processes:- s-process: yield reduced by short effective half-life- p(γ)-process: yield reduced to 35% (at freeze-out)- ν-process: yield reduced to 35% (at freeze-out) • Most likely solution:- 180Ta is made in all 3 processes- early claims of sufficient production in each process probably not so bad- coupling between 9- isomer and 1+ ground state reduces all yields by approx. a factor of 3 • 3 different processes are needed for the nucleo-synthesis of the rarest isotope in nature Peter Mohr ECT-Workshop Trento, November 2018

  49. Another interesting nucleus with isomers: 176Lu • nucleosynthesis in the s-processbranching at 176Lu:isomer(short-lived):towards 176Hfground state(quasi-stable):towards 177Lucouplingbetweeng.s. and isomer?P. Mohr et al., Phys. Rev. C 79, 045804 (2009) Peter Mohr ECT-Workshop Trento, November 2018

  50. … turns out to be a better example … (?) • high-K ground state • low-K isomer • IMS at 839 keV:branchings knownstrong branch to 7-g.s.abs. strength uncertainperfect candidate for experiment at ELI-NPbut also complications:- IMS with smaller Ex?- internal conversion?couplingbetweeng.s. and isomer? Peter Mohr ECT-Workshop Trento, November 2018

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