A selected overview of stellar effects and reaction mechanisms with relevance
to the prediction of astrophysical reaction rates far off stability is
provided.Comment: 4 pages, 2 figures (contining 2 subfigures each); Proceedings of 10th
  Intl. Conference on Nucleus-Nucleus Collisions, Beijing, China, August 2009;
  to appear in Nuclear Physics 

Abbondanno

Avrigeanu

Bonneau

Chloupek

Descouvemont

Fedoseyev

Fülöp

Goriely

Kiss

Koehler

Litvinova

Loens

Mocelj

Mohr

Rauscher

Somorjai

T. Rauscher

Yalçin

Nuclear Physics A

English

arXiv

A selected overview of stellar effects and reaction mechanisms with relevance to the prediction of astrophysical reaction rates far off stability is provided

Rauscher, T.

University of Hertfordshire Research Archive

arXiv:0911.0262v1  [astro-ph.HE]  2 Nov 2009Astrophysical Rates for Explosive Nucleosynthesis: Stellar andLaboratory Rates for Exotic NucleiT. Rauschera∗aDepartment of Physics, University of Basel,Klingelbergstr. 82, 4056 Basel, SwitzerlandA selected overview of stellar effects and reaction mechanisms with relevance to theprediction of astrophysical reaction rates far off stability is provided.1. INTRODUCTIONNuclear theory is important in the determination of reaction cross sections and ratesfor astrophysics in several respects. Firstly, a large number of reactions in astrophysicalenvironments involve highly unstable nuclei which are unaccessible in laboratory mea-surements. This is especially true for the high temperature plasmas of stellar explosions.Secondly, despite of high plasma temperatures, the relevant particle interaction energyis low by nuclear physics standards. This is a challenge for experimentalists, especiallywhen studying charged-particle reactions at or below the Coulomb barrier. Very smallcross sections at low energy may even prevent a measurement and have to be predicted inthis case. Thirdly, the nuclei occur in excited states because they are in thermal equilib-rium with the stellar plasma. This modifies the reaction cross sections and has importantconsequences for the determination of stellar reaction rates. Laboratory measurementsonly account for a fraction of the possible transitions and the actual plasma corrections(stellar enhancement factors, SEF) can only be provided by theory. (Electron screeningis also important but will not be discussed here.)Large-scale predictions of reaction cross sections across the chart of nuclei are requiredto provide the rates needed for reaction networks applied to nucleosynthesis. In astro-physical applications usually different aspects are emphasized than in pure nuclear physicsinvestigations. Reliable predictions of the nuclear properties and optical model ingredi-ents, like optical potentials for particle and α transmission coefficients [ 1, 2, 3, 4, 5, 6],nuclear level densities (NLD) [ 7, 8], resonance energies, and γ-transition strengths [9, 10], are needed far from stability. Even at stability, there are still considerable un-certainties, especially in the optical potential for charged particles which is not well con-strained at low energy. In addition to the well-known difficulty in predicting α-potentials[ 3, 11, 12, 13, 14], it was recently found that also the optical potential for protons mayrequire special attention [ 1, 2, 15, 16].∗Supported by the Swiss NSF, grant 200020-122287.2 T. Rauscher 0 2 4 6 8 10 12 14 16 18 100  105  110  115  120  125  130  135  140  145  150Energy [MeV]mass number ASnmaximum 1 2 3 4 5 6 7 8 9 10 195  200  205  210  215  220  225  230mass number ASnmaximumFigure 1. The maximally contributing γ energies when capturing 60 keV neutrons onisotopes of Sn (left) and Pb (right) are compared to the neutron separation energies Sn inthe compound nuclei [ 9]. The mass number A is the one of the final (compound) nucleus.2. STELLAR ENHANCEMENTThe SEFs, given by the ratio of stellar rate to ground state rate r∗/rg.s. and beinga result of thermal population of nuclear excited states, are mainly important at thecomparatively high temperatures of explosive burning (r−, p−, rp−, νp-processes), al-though they can play a role in the s−process in some cases, when low-lying (a few keVexcitation energy) states are present. Because the number of possible transitions to themore strongly bound nucleus is larger, it is generally assumed that stellar effects are lesspronounced in the direction of positive Q−value and measurements should preferrablybe performed in this reaction direction to obtain rates closer to the stellar value. How-ever, recently we showed that the general Q−value rule does not apply for a number ofcases due to the suppression of low-energy transitions in the exit channel by an additionalbarrier (Coulomb or centrifugal) [ 1, 2]. effectively reducing the number of contributingtransitions. The application of detailed balance implies that the populations of targetand final nucleus are in equilibrium. It has to be noted, however, that the validity ofdetailed balance cannot be taken for granted in all cases. This is well known for nucleihaving isomeric states but may also become problematic in nuclei with low NLD or formulti-particle emission channels.3. γ-RAY ENERGIESIn particle capture reactions, γ rays with energies in the range 0 < Eγ ≤ Sparticle +Eparticle can be emitted. Due to the fact that the number of accessible levels is increasingexponentially with excitation energy Ex but the γ strength is decreasing with Ex (becauseEγ = Sparticle + Eparticle − Ex), only a limited range of Eγ will significantly contribute tothe cross section, described by a peak around an energy of highest impact Esig [ 9]. Thisenergy Esig is shown in Fig. 1 for sequences of Sn and Pb isotopes. It is interesting toAstrophysical Rates for Explosive Nucleosynthesis 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0  0.5  1  1.5  2  2.5  3  3.5  4DC/(DC+HF)Sn [MeV]TiCrFeSnPb10-710-610-510-410-310-2 75  80  85  90  95  10030 keV MACS [barn]neutron numberHFmod. HFDCFigure 2. Left: Relation between direct neutron capture and (unmodified) compoundcapture as function of neutron separation energy [ 23]. Right: Comparison between directcapture with energy-dependent spectroscopic factor, modified Hauser-Feshbach capture,and standard Hauser-Feshbach capture on even Sn isotopes (preliminary results).note that it remains mostly in the interval of 2 − 4 MeV despite large differences in theneutron separation energy Sn. (This is for 60 keV neutrons; Esig ≃ (2 − 4) + En MeV [10].) The exceptions are nuclei with very low NLD, where the transition to the groundstate dominates and Esig = Sparticle + Eparticle. (Note, however, that in this case directcapture may be dominating; see below). For further details see [ 9].4. DIRECT CAPTUREMost astrophysically relevant reactions can be described in the Hauser-Feshbach statis-tical model (HF). Due to the low particle separation energies and/or NLDs encounteredin very neutron- (or proton-) rich nuclei, direct reactions will also become important, evenat very low energies (in the keV region) [ 7, 8, 17, 18, 19, 20, 21, 22, 23]. Figure 2 (left)compares direct capture (DC) with the regular HF [ 23]. It is clearly seen that the rela-tive importance of DC increases with decreasing Sn. This is because the number of finallevels for γ transitions from HF capture becomes lower. The Sn isotopes have the lowestNLD of the isotopes shown here and consequently the highest relative importance of DC.This comparison was made by simply comparing the DC and HF 30 keV MaxwellianAveraged Cross Section (MACS). Regular HF calculations assume a compound formationprobability independent of the NLD at the compound formation energy. The availabilityof compound states and doorway states defines the applicability of the HF model [ 7].Relying on an average over resonances the HF model is not applicable with a low NLDat compound formation. On average it will then overpredict the resonant cross section(unless single resonances dominate) because it will overestimate the compound formationprobability. This can be treated by introducing a modification of the formation cross sec-tion which includes the NLD dependence. For the parity dependence, this was discussedin [ 24]. A similar modification but also including the full NLD is available as an option4 T. Rauscherin NON-SMOKERWEB since version 4.0w [ 25]. The new code SMARAGD [ 26, 27, 28]will have an improved version of this as default and thus implicitly account for low NLDat the compound formation energy. Preliminary results with this modification are shownin Fig. 2 (right). The code SMARAGD will also include a global DC treatment using anaveraged DC model and energy-dependent spectroscopic factors [ 22, 23, 27]. This aver-age DC approach aims at providing robust predictions despite of considerable differencesbetween microscopic predictions [ 21]. Preliminary results for this DC are shown in Fig.2 (right), too.The final rate (or cross section) is the sum of the modified HF value and the DC one.Interestingly, for the isotopes shown here (except for N = 92) this sum is approximatedby the unmodified HF result within a factor of 10. This is in accordance with [ 29] (seefig. 3 therein). This shows that it seems justified to use unmodified HF rates as crudeestimate of the total rates for exotic nuclei.REFERENCES1. G. G. Kiss, et al., Phys. Rev. Lett. 101 (2008) 191101.2. T. Rauscher, et al., Phys. Rev. C 80 (2009) 035801.3. C. Yalçin, et al., Phys. Rev. C 79 (2009) 065801.4. Zs. Fülöp, et al., Phys. Rev. C 64 (2001) 065805.5. V. N. Fedoseyev, et al., Z. Phys. A 353 (1995) 9.6. T. Rauscher, Phys. Rev. C 73 (2006) 0158047. T. Rauscher, F.-K. Thielemann, and K.-L. Kratz, Phys. Rev. C 56 (1997) 1613.8. D. Mocelj, et al., Phys. Rev. C 75 (2007) 045805.9. T. Rauscher, Phys. Rev. C 78 (2008) 032801(R).10. E. Litvinova, et al., Nucl. Phys. A823 (2009) 26.11. P. Mohr, et al., Phys. Rev. C 55 (1997) 1523.12. E. Somorjai, et al., Astron. Astrophys. 333 (1998) 1112.13. P. Koehler, et al., Phys. Rev. C 69 (2004) 015803.14. M. Avrigeanu and V. Avrigeanu, Phys. Rev. C 79 (2009) 027601.15. G. G. Kiss, et al., Phys. Rev. C 76 (2007) 055807.16. T. Rauscher, Proc. Nuclear Physics in Astrophysics 4, J. Phys. Conf. Ser., in press.17. F. R. Chloupek, et al., Nucl. Phys. A652 (1999) 391.18. U. Abbondanno, et al., Nucl. Instr. Meth. Phys. Res. A 538 (2005) 692.19. T. Rauscher and F.-K. Thielemann, At. Data Nucl. Data Tables 75 (2000) 1.20. P. Descouvemont, T. Rauscher, Nucl. Phys. A777 (2006) 137.21. T. Rauscher, et al., Phys. Rev. C 57 (1998) 2031.22. L. Bonneau, T. Kawano, T. Watanabe, and S. Chibo, Phys. Rev. C 75 (2007) 054619.23. T. Rauscher, J. Phys. G 35 (2008) 014026.24. H. P. Loens, et al., Phys. Lett. B 666 (2008) 395.25. http://nucastro.org/websmoker.html; (current version: v5.8.1w; 12-Jan-2007: v4.0w)26. T. Rauscher, code SMARAGD, unpublished.27. T. Rauscher, Int. J. Mod. Phys. E, in preparation.28. R. H. Cyburt, et al., Astrophys. J., submitted.29. S. Goriely, S. Hilaire, and N. Chamel, AIP Conf. Ser. 1090 (2009) 33.

Astrophysical Rates for Explosive Nucleosynthesis : Stellar and Laboratory Rates for Exotic Nuclei

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Astrophysical Rates for Explosive Nucleosynthesis: Stellar and Laboratory Rates for Exotic Nuclei

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Astrophysical Rates for Explosive Nucleosynthesis: Stellar and
  Laboratory Rates for Exotic Nuclei

Astrophysical Rates for Explosive Nucleosynthesis: Stellar and Laboratory Rates for Exotic Nuclei

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