1. ECT Workshop – Trento – November 2018
Photons in the lab and in stars: a tedious route from experimental data to stellar reaction rates
Peter Mohr Diakonie-Klinikum, D Schwäbisch Hall, Germany ATOMKI, 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 < σ v >* for particle-induced reactions - λ* for photon-induced reactions
A direct experiment should measure NA < σ v >* or λ* (may become feasible in laser-induced plasma)
All other experiments measure NA < σ v >lab or λlab under 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 < σ v >* and NA < σ v >lab focus 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 stars P. Mohr et al., EPJA 27, s01, 75 (2006)
Reciprocity for time-reversed cross sections σ(1+2↔3+γ) for partial cross sections e.g. 16Og.s.(α0,γ1)20Ne2+ and 20Ne2+(γ1,α0)16Og.s.
Detailed balance between stellar reaction rates for photons: NA < σ v >*(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 Astrophysics Nuclear Physics News 28, 12 (2018)
R. Reifarth et al., Neutron-induced cross sections From raw data to astrophysical rates Europ. 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 state 20Ne: 0+ ground state 20Ne: 2+ state at 1634 keV 20Ne: 1- state at 5788 keV appears 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 ps Гγ = 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, Гγ for 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 >* is proportional 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 ωγ and to exp(-ERγ/kT)
0+ g.s.
2+ (1634)
Eγ enhancement
Boltzmann suppression
exactly cancel each other!!!
proportional to total ωγ and exp(-5788 keV/kT)
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 ωγ and 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 ωγ and to exp(-ERγ/kT)
ratio λ*/λlab depends 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 balance between 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 branching similar 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) := < σ v >* / < σ v >lab in words: ratio between stellar rate at temperature T and rate at target temperature T=0 (laboratory rate)
Ground state contribution X0(T): X0(T) := < σ v >lab / [ G0 ∙ < σ v >* ] in words: contribution of the experimentally accessible ground state rate (T=0) to the stellar rate at temp. T G0(T): partition function
For further details: see Rauscher et al., ApJ 738:143 (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) := < σ v >* / < σ v >lab fSEF(T=0) = 1 : by definition
Ground state contribution X0(T): X0(T) := < σ v >lab / [ G0 ∙ < σ v >* ] 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) := < σ v >* / < σ v >lab fSEF(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) := < σ v >lab / [ G0 ∙ < σ v >* ] 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 keV for simplicity: only 1/2- g.s. and 3/2- at 10 keV MACS (lab): < σ >lab ≈ 1000 mb and fSEF(30 keV) ≈ 1.3 MACS (stellar): < σ >* ≈ 1300 mb naive, but wrong interpretation: excited state contributes with 300 mb (or 30%)
but: Boltzmann factor n(3/2-)/n(1/2-) ≈ 1.5 at 30 keV 1/2- ground state contribution to < σ >* ≈ 400 mb 3/2- excited state contribution to < σ >* ≈ 900 mb correct 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*/ λlab fSEF(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 – at 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 ?
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 Ex in the compound nucleus (but not in Eγ !!!)
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.
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, ApJ 591, 1220 (2003)
very low isotopic abundance: % J. R. de Laeter et al., PRC 72, (2005)
unstable Jπ = 1+ ground state (T1/2 = h) T. B. de Ryves, JPG 6, 763 (1980)
exists as long-lived Jπ = 9- isomer (T1/2 > 7.1 x 1015 yr) at Ex = 77.2 ± 1.2 keV Ex from: T. Wendel et al., PRC 65, (2001) T. Cousins et al., PRC 24, 911 (1981) quasi-stable E. Warde et al., PRC 27, 98 (1983) isomer above K. S. Sharma et al., PLB 91, 211 (1980) ground state! T1/2 from: M. Hult et al., PRC 74, (2006) }
Peter Mohr ECT-Workshop Trento, November 2018

27. Peter Mohr ECT-Workshop Trento, November 2018
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-process all 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: photoactivation Zs. Nemeth et al., ApJ 392, 277 (1992) J. J. Carroll et al., ApJ 344, 454 (1989) C. B. Collins et al., PRC 42, R1813 (1990) E. B. Norman et al., ApJ 281, 360 (1984) D. Belic et al., PRL 83, 5242 (1999); PRC 65, (2002)
Improved analysis: P. Mohr et al., PRC 75, (R) (2007) T. Hayakawa et al., PRC 81, (R) (2010); PRC 82, (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)
Iσlab for photoactivation in the lab: JIMS→k (exit channel): sum over all low-K cascades JIMS→j (entr. ch.): only direct high-K transition j=9-→IMS
Iσ* under stellar conditions: JIMS→k (exit channel): sum over all low-K cascades JIMS→j (entr. channel): all high-K transitions j→IMS including cascades!
λ*/λlab = Iσ* / Iσlab = 1/Bj ≥ 1 laboratory 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-life of 180Ta reduces from about 1 yr (case A) to about 11 hours (case C) at kT = 26 keV
survival of 180Ta in the s-process depends on con-vective mixing!
Peter Mohr ECT-Workshop Trento, November 2018

45. Transition rates from 9- isomer to 1+ ground state
stellar rate λ* by far exceeds 1/s for explosive environments (kT > 100 keV)
experimentally confirmed case A is sufficient for this result
Peter Mohr ECT-Workshop Trento, November 2018

46. Transition rates from 9- isomer to 1+ ground state
survival of 180Ta depends on freeze-out at λ* ≈ 1/s
occurs at kT ≈ 40 keV
survival of about 35% of 180Ta as isomer, indepen-dent of production
Peter Mohr ECT-Workshop Trento, November 2018

47. Peter Mohr ECT-Workshop Trento, November 2018
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-process branching at 176Lu: isomer (short-lived): towards 176Hf ground state (quasi-stable): towards 177Lu coupling between g.s. and isomer? P. Mohr et al., Phys. Rev. C 79, (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 known strong branch to 7- g.s. abs. strength uncertain perfect candidate for experiment at ELI-NP but also complications: - IMS with smaller Ex? - internal conversion? coupling between g.s. and isomer?
Peter Mohr ECT-Workshop Trento, November 2018

51. Transition rates from 7- ground state to 1- isomer
IMS at 839 keV: integrated cross section from nuclear data in conflict with astrophysical “best case” by Heil et al., ApJ 673, 434 (2008): nuclear: Iσ = 1.2 eV fm2 astrophysical: Iσ = 0.07 eV fm2
Peter Mohr ECT-Workshop Trento, November 2018

52. Transition rates from 7- ground state to 1- isomer
rate further enhanced by IMS with lower Ex
minor contributions from most candidates
huge uncertainty from possible K-mixing between two 7- states at and keV V. Gintautas et al., PRC 80, (2009)
Peter Mohr ECT-Workshop Trento, November 2018

53. K-mixing of 7- states around 725 keV?
V. Gintautas et al., PRC 80, (2009)
low-K 7- at keV and high-K 7- at keV
K-mixing allows transitions between low-K and high-K
high-K
high-K
low-K
Peter Mohr ECT-Workshop Trento, November 2018

54. K-mixing of 7- states around 725 keV?
V. Gintautas et al., PRC 80, (2009)
no direct branch from 7- states to 7- ground state
stellar rate not measurable by photoactivation!
high-K
high-K
low-K
Peter Mohr ECT-Workshop Trento, November 2018

55. Peter Mohr ECT-Workshop Trento, November 2018
Summary for 176Lu
Known 5-;4 IMS at 839 keV: - dominating branching to 7- ground state - absolute strength uncertain - excellent candidate for ELI-NP - resolve conflicting numbers: Iσ = 1.2 eV fm2 from nuclear data (Mohr et al.) Iσ = 0.07 eV fm2 from astrophysics (Heil et al.)
Candidates for IMS with lower Ex: - not accessible by photoactivation - very uncertain: K-mixing of two 7- states at 725 keV
Peter Mohr ECT-Workshop Trento, November 2018

56. Conclusion (1): Thermalization of isomers
most important: intermediate states (IMS) at low excitation energies
typically: lowest IMS for transitions between low-K and high-K states have intermediate Jπ
consequence: branching from IMS to ground state (with either high-K or small-K) very small (or even negligible)
in such cases: experiments under laboratory conditions cannot provide the stellar transition rate λ* between low-K and high-K states (e.g., 180Ta)
experimental data are very useful to analyze the structure of IMS
Peter Mohr ECT-Workshop Trento, November 2018

57. Capture reactions between light nuclei
Stellar rate of capture reactions betw. light nuclei can – in principle – be estimated from photodisintegration
essential prerequisite: dominating ground state branching in capture reaction
alternatively: ground state contribution sufficiently strong and well-known from other experiments
in general: requirements fulfilled only for light nuclei
Peter Mohr ECT-Workshop Trento, November 2018

58. Capture reactions between light nuclei: 12C(α,γ)16O
very important reaction!
ground state transitions are dominating
cascade contributions about 10-20% Matei et al., PRL 97, (2006)
excellent case for ELI-NP !
Peter Mohr ECT-Workshop Trento, November 2018

59. Capture reactions between light nuclei: 2H(α,γ)6Li
important for BBN and 6Li abundance
only one bound state (1+ g.s.)
excellent case for ELI-NP, but…
direct data available for many energies: Robertson et al., PRL 47, 1867 (1981) Mohr et al., PRC 50, 1543 (1994) Anders et al., PRL 113, (2014)
Peter Mohr ECT-Workshop Trento, November 2018

60. Capture reactions between light nuclei: 3H(α,γ)7Li
important for BBN and 7Li abundance
two bound states (3/2- g.s. and 1/2-)
branching ratio R : R = σ1/σ0 ≈ experimentally known at low energies < 1.2 MeV Brune et al., PRC 50, 2205 (1994) - theoretically expected up to about 10 MeV
good case for ELI-NP
Peter Mohr ECT-Workshop Trento, November 2018

61. Capture reactions between light nuclei: 15N(α,γ)19F
many bound states in 19F
resonances with minor branching to 1/2+ g.s. Wilmes et al., PRC 66, (2002)
no ground state branch f. lowest (7/2+) resonance
bad case for ELI-NP
Tilley et al., NPA 595, 1 (1995)
Peter Mohr ECT-Workshop Trento, November 2018

62. Capture reactions between light nuclei: 20Ne(α,γ)24Mg
many bound states in 24Mg
most resonances with strong branching to 2+ (1369 keV) Schmalbrock et al., NPA 398, 273 (1983) Kölle, NIMA 431, 160 (1999)
no ground state branching for 0+ and J > 3 resonances
bad case for ELI-NP
Schmalbrock et al., NPA 398, 273 (1983)
Peter Mohr ECT-Workshop Trento, November 2018

63. Conclusion (2): capture reactions
Stellar rate of capture reactions between light nuclei can be estimated from photodisintegration
essential prerequisite: dominating ground state branching in capture reaction
alternatively: ground state contribution sufficiently strong and well-known from other experiments
few good examples: 2H(α,γ)6Li, 3H(α,γ)7Li, 12C(α,γ)16O
ground state contribution minor for many cases
many bad examples: 15N(α,γ)19F, 20Ne(α,γ)24Mg, …
Peter Mohr ECT-Workshop Trento, November 2018

64. Conclusion (3): (γ,n) and (γ,α) in the γ-process
relevant: heavy nuclei (A > 100)
typically: ground state contribution in (n,γ) and (α,γ) reactions small or even negligible
experimental (γ,X) data cannot provide stellar (γ,X) reaction rates
experimental (γ,X) data are essential to constrain model parameters (gamma-ray strength function)
above arguments also hold for (n,γ) rates from (γ,n) experiments (for branching points in the s-process)
Peter Mohr ECT-Workshop Trento, November 2018

65. What can be learnt from (γ,n) or (γ,α) experiments?
example: 86Kr(γ,n)85Kr
σlab(n,γ) ~ Tn,0 Tγ / Ttot ≈ Tγ σlab(n,γ) mainly depends on the γ-strength function fγ,down at ≈ (2-7) MeV
Raut et al., PRL 111, (2013)
Peter Mohr ECT-Workshop Trento, November 2018

66. What can be learnt from (γ,n) or (γ,α) experiments?
γ-spectrum:
γ-spectrum: continuous and discrete
Peter Mohr ECT-Workshop Trento, November 2018

67. What can be learnt from (γ,n) or (γ,α) experiments?
example: 86Kr(γ,n)85Kr
σlab(γ,n) ~ Tn Tγ,0 / Ttot ≈ Tγ,0 σlab(γ,n) mainly depends on the γ-ray strength function fγ,up at ≈ 10 MeV
Raut et al., PRL 111, (2013)
Peter Mohr ECT-Workshop Trento, November 2018

68. What can be learnt from (γ,n) or (γ,α) experiments?
example: 86Kr(γ,n)85Kr
σlab(γ,γ’) ~ Tγ,0 σlab(γ,γ’) mainly depends on the γ-strength function fγ,up at lower energies
Raut et al., PRL 111, (2013)
Peter Mohr ECT-Workshop Trento, November 2018

69. What can be learnt from (γ,n) or (γ,α) experiments?
(γ,n) : provides fγ,up above threshold (0 → ≈10 MeV)
(γ,γ’) : provides fγ,up at lower energies (0 → few MeV)
(n,γ) : requires fγ,down for few MeV (≈10 → 8-3 MeV)
experimental (γ,X) data, complemented by (γ,γ’), are essential to constrain the γ-ray strength function
we still have to rely on the assumption: fγ,up = fγ,down
we still have to rely on the Brink-Axel hypothesis
we still have to use some model for the energy dependence of the γ-ray strength function seems to work: Renstrom et al., Utsunomiya et al., Phys. Rev. C, in press
Peter Mohr ECT-Workshop Trento, November 2018

70. What can be learnt from (γ,n) or (γ,α) experiments?
σlab(γ,α) ~ Tα Tγ,0 / Ttot = Tα Tγ,0 / (Tα+Tp+Tn+Tγ) σlab(γ,α) sensitive to all ingredients of statistical model
at astrophysically relevant low energies: often: Tα << Tγ and Tp << Tγ (Coulomb barrier) for p(γ)-process: often: Tn = 0 (high neutron separation energy)
σlab(γ,α) ~ Tα Tγ,0 / Ttot ≈ Tα Tγ,0 / Tγ = Tα Bγ,0 : σlab(γ,α) sensitive to Tα and g.s. branch Bγ,0 = Tγ,0 / Tγ but (γ,α) cross sections are tiny…
Peter Mohr ECT-Workshop Trento, November 2018

71. What can be learnt from (γ,p) and (γ,α) experiments?
σlab(γ,α) ~ Tα Tγ,0 / Ttot
σlab(γ,p) ~ Tp Tγ,0 / Ttot
ratio σlab(γ,α) / σlab(γ,p) scales with Tα / Tp for any Eγ
simultaneous measurement of several channels provides further constraints for the parameters of statistical model calculations!
combined (γ,α) and (γ,p) measurements are feasible Lan et al. (ELI-NP), Phys. Rev C 98, (2018)
Peter Mohr ECT-Workshop Trento, November 2018

72. Thank you very much for your attention!
Final conclusion
Significant difference between (γ,X) in the lab and (γ,X) under stellar conditions
Reason: thermally excited states in the target nucleus in the hot stellar plasma
Bad news: determination of stellar (γ,X) reaction rates from (γ,X) experiments not possible in most cases
Good news: experimental (γ,X) data are essential to constrain theoretical models
Thank you very much for your attention!
Peter Mohr ECT-Workshop Trento, November 2018

73. Thank you very much for your attention!
Peter Mohr ECT-Workshop Trento, November 2018