Rate Analysis or a Possible Interpretation of Abundances

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1 Rate Aalysis or a Possible Iterpretatio of Abudaces Berze High School/Gyögyösi Berze agy Jáos Gimázium H-00 Gyögyös, Kossuth u.., Hugary kiss-m@chello.hu Heavy elemets are formed i ucleosythesis processes. Abudaces of these elemets ca be classified as elemetal abudace, isotopic abudace, ad abudace of uclei. I this work the uclei are idetified by (Z,), which allows readig out ew iformatio from the measured abudaces. We are iterested i the eutro desity required to reproduce the measured abudace of uclei assumig equilibrium processes. This is oly possible whe two stable uclei are separated by a ustable ucleus. At these places we ivestigated the eutro desity required for equilibrium ucleosythesis both isotopically ad isotoically at temperatures of AGB iterpulse ad thermal pulse phases. We obtaied a estimate for equilibrium ucleosythesis eutro desity i most of the cases. ext we ivestigated the possibility of partial formatio of uclei. We aalyzed the meaig of the brachig factor. We foud a mathematical defiitio for the uified iterpretatio of a brachig poit closed at isotoic case ad ope at isotopic case. We itroduce a more expressive variat of brachig ratio called partial formatio rate. With these we are capable of determiig the characteristic eutro desity values. We foud that all experieced isotope ratios ca be obtaied both at 0 8 K 8 temperature ad at 0 K temperature ad at itermediate eutro desity ( 0 cm ). XIII uclei i the Cosmos 7- July, 04 Debrece, Hugary Speaker

2 Rate Aalysis or a Possible Iterpretatio of Abudaces. Itroductio early sixty years after BBFH [], it is possible ad ecessary to review ad rethik our kowledge about the eutro capture ucleosythesis. The result of the formatio of the uclei is show i the abudaces. It is importat to metio that the formed ustable uclei have decayed ito stable uclei ad we are oly able to see the resultig stable uclei. "The success of ay theory of ucleosythesis has to be measured by compariso with the abudace patters observed i ature." say Käppeler, Beer ad Wisshak [], that is, we eed to create such model that gives back the observed abudace. Because of the formatio of uclei takes place i a variety of coditios, the experieced abudace is a result of more processes. Therefore more models are ecessary for the alterate coditios. Accordig to the coditios of the models the uclei are classified ito categories as s-uclei, r-uclei etc. It seems that the reverse approach is also useful: the abudace is the preserver of the uclei s formatio coditios. So istead ivestigatig whether the theoretical model fits the observed abudace, we look for the circumstaces whe the observed abudace is available. To do this we eed suitable data: the half-life of ustable uclei ad the eutro capture cross sectio of uclei. These data are ot costat always. At some uclei the half-lives deped o the temperature [,,4]. Fortuately, the reactio rate per particle pair is costat betwee 0 ad00 kev because of the eergy depedece of σ [,]. So we ca use the σ values at 0 kev [5]. The possible resoaces oly improve the capture capabilities.. The required eutro desity Chage the ucleo idetificatio from the usual (Z,A) to (Z,) ad see the idividual abudaces as well. We took the abudace of uclei from [6]. This will allow us to read ew iformatio from the various measured abudaces. We use the followig rate equatios accordig to the requiremets of the idividual uclei formatio: Z, (t)z, (t) Z, +λz,+ (t) + λαz+,+ (t) (t) (t) λ (t) λ (t) +K Z, Z, We also assume the equilibrium formatio of uclei. From the correspodig rate equatios we ca get the eutro desity as i isotopic as i isotoic cases.. Isotopic case.. Two stable eighbor isotopes First let us we cosider two stable eighbor isotopes (see Fig. ), applyig the ew idetificatio. v < σ Z, α Z,

3 Rate Aalysis or a Possible Iterpretatio of Abudaces ( σ σ ) v Fig.. Two stable eighbor isotopes If we suppose the equilibrium that is 0, we got σ σ, what is well kow i classical idetificatio. So there is o iformatio about the formatio coditios. But it is importat to metio that this relatio is ot true i geeral about the experieced abudaces ad eutro capture cross sectios. The mai cause is the existeces of other rates from other chaels through ustable uclei... Two stable isotopes are separated by a ustable isotope A more iterestig case is, whe two stable isotopes are separated by a ustable isotope (see Fig. ). I this isotopic case the rate equatios for the ustable ucleus: λ About the equilibrium 0, so ( 0 ) λ λ ( ) Fig.. The isotopic chael λ v(σ σ)

4 Rate Aalysis or a Possible Iterpretatio of Abudaces λ v( σ σ) If the third ucleus ca form oly from the secod ucleus About the equilibrium 0, so such as the previous case we have σ σ σ σ σ λ v( σ σ) σ λ + σ v σσ σ σσ λ ( + σ) σ v σ σ λ λ σ + + σ v This expressio cotais the specific eutro desity value. We must refer to σ v costat at low ad itermediat coditios, so it is eough to kow the 0 kev eutro capture cross sectios ad average velocity. From this formula, we ca get the eutro desity value. Of coure resoaces may occure, but these oly improve the capture capabilities v( σ λ σ σ σ ) or λ v σ σ ( σ σ ) (See the required eutro desities at differet stellar temperature i Appedix ad.) From the tables we ca see that the isotopic equilibrium is ot always possible. This meas that the formatio of third uclei has at least aother chael.. Isotoic case I this isotopic case (see Fig. ) the rate equatios for the ustable ucleus: λ If there is equilibrium, the 0, so + λ 4

5 Rate Aalysis or a Possible Iterpretatio of Abudaces Fig.. The isotoic chael If the third ucleus ca form oly from secod ucleus λ < σ Beacause of the equilibrium 0 we get < σ The two equatios about these v λ λ v < σ σv v λ < +λ λ λ From this formula, we ca get the eutro desity value for equilibrium ucleosythesis. +λ Because of σ λ λ σ λ or σ v σ v costat it is eough to take the eutro capture values at 0keV. (See the required eutro desities at differet stellar temperature i Appedix ad 4.). The role of eutro desity We have the possible equilibrium eutro desity at isotopic ad isotoic cases as well. There is a big differece betwee the two cases. I isotopic case the icremet of eutro desity icreases the amout of the third uclei, but i isotoic case the icremet of eutro 5

6 Rate Aalysis or a Possible Iterpretatio of Abudaces desity decreases the amout of the third uclei. These result the shift of capture path (or capture bad) toward eutro rich uclei.. Partial formatio of uclei We ca see i the previous sectio that ot all of the third uclei ca form from the first uclei. But how much ca be formed o this way? Suppose that from the abudace of the first uclei ( ) the k-s the abudace of third uclei ( k ) are formed ( 0 < k). What eutro desity is required i this case? (Here k is the Partial Formatio Ratio so PFR.) If k the all of the third uclei are formed as i the previous sectio. The required eutro desity at the two chaels i isotopic ad i isotoic cases: λ 4. Give eutro desity v σ σ σ ( σ k ) λ vσ σ σ k After this theoretic ivestigatio it is ecessary to take a realistic approach. We ca cosider the iverse questio: what part of third uclei abudace is formed from the first uclei abudace at give eutro desity? ( k?) 4. I isotopic case: k Z g(x) λ σ R ( λ + λ ) σ Z x σ R (x + ) σ λ σ ( λ + λ ) σ x R f (x + ) (x) λ λ λ + λ λ x λ 4. I isotoic case: k g(x) λ σ R ( λ + λ ) σ σ R (x + ) σ λ σ ( λ + λ ) σ R f (x + ) (x) λ + λ λ x λ Where f ad f are the classical brachig factors for eutro capture ad beta decay. So we have uiform fuctios i both isotopic ad isotoic cases. 6

Rate Aalysis or a Possible Iterpretatio of Abudaces 5. Mathematical aalysis It might be better to see these fuctios i logarithmic represetatio. O Fig.

The we take the two logarithmic tagets at ξ 0 or x. Where these tagets take the value zero the isotopic formatio of uclei opes, ad the isotoic formatio of uclei closes.

7 Rate Aalysis or a Possible Iterpretatio of Abudaces 5. Mathematical aalysis It might be better to see these fuctios i logarithmic represetatio. O Fig. 4 the two brachig fuctios are: f (x) ad f (x), where ξ lgx: Fig. 4. The two brachig fuctios i logharitmic scale I this logarithmic represetatio the two fuctios become symmetric. The we take the two logarithmic tagets at ξ 0 or x. Where these tagets take the value zero the isotopic formatio of uclei opes, ad the isotoic formatio of uclei closes. Similarly, where the taget takes value oe, the isotopic formatio is o ad the isotoic formatio is off. So we have got well-defied characteristics for both of the opeig ad closig cases. We foud a mathematical defiitio for the uified iterpretatio of a brachig poit closed at the isotoic case ad ope at the isotopic case. 6. The eutro desity rage From the mathematical aalysis we get the ext values: Tab.. brachig ratio chael ξ x f f isotopic isotoic , opeig closig 0,87 7, opeed closed The isotopic chael is begiig to ope ad isotoic chael is begiig to close whe λ 0, 5 λ. Isotoic chael is early closed ad isotopic chael is almost fully opeed whe λ 7, 9 λ T 8 ad T8 cases..we have reviewed the appropriate three uclei cases ad examied both of 7

Rate Aalysis or a Possible Iterpretatio of Abudaces At these cases we have got the maximum of all eutro desity

Upper lies refer to isotoic cases; the bottom lies refer to isotoic cases.

The rage of eutro capture ucleosythesis about eutro desity.

This process is m-process (i-process) (medium or itermediate) [7,8,9,0,]. 7. Brachig i a ew poit of view 0 Fig.

8 Rate Aalysis or a Possible Iterpretatio of Abudaces At these cases we have got the maximum of all eutro desity ot more tha 4 0 cm. Some details are show o the Fig. 5. Upper lies refer to isotoic cases; the bottom lies refer to isotoic cases. The temperature depedece of half-lives we took from [4]. Fig. 5. The rage of eutro capture ucleosythesis about eutro desity. All uclei formatio is available at a eutro desity rage betwee s-process ad r- process. This process is m-process (i-process) (medium or itermediate) [7,8,9,0,]. 7. Brachig i a ew poit of view 0 Fig. 6. Partial formatio ratio from Ru as the fuctio of eutro desity. Here we ca the 0 temperature depedece of the formatio ratio as well. At Ru there is o isomer. The brachig factor does ot give the correct formatio ratio. It gives the partial formatio ratio: k R f. (Data from KADoiS [], DC [].) The k is determied by f 8

Rate Aalysis or a Possible Iterpretatio of Abudaces ad R, where σ R.

σ 0 0 6 shows the k as a fuctio of eutro desity i the cases of Ru Rh ad 0 04 Ru Ru as well.

The bad of eutrocapture ucleosythesis at AGP TP phase ad at IP after TP We ca see i oe uified model the

Here we ca chage the eutro desity ad other parameters. But more data is required here [5].

9 Rate Aalysis or a Possible Iterpretatio of Abudaces ad R, where σ R. The PFR is chagig the amout of formed uclei. The graph o Fig. σ shows the k as a fuctio of eutro desity i the cases of Ru Rh ad 0 04 Ru Ru as well. These are both simple cases with oly oe icomig chael. 8. Full etwork model Fig. 7. The bad of eutrocapture ucleosythesis at AGP TP phase ad at IP after TP We ca see i oe uified model the etire possible eutro capture ad decay processes [,4]. Here we ca chage the eutro desity ad other parameters. But more data is required here [5]. The formatio of uclei rather occurs alog a bad tha alog a path (see Fig. 7). The eutro capture bad is oly visible i logarithmic represetatio. The structure of bad at Z 50, at ti isotopes is visible o Fig. 8. Fig. 8. The profil of eutro capture bad at ti isotopes. ( cm ) 9

Rate Aalysis or a Possible Iterpretatio of Abudaces 9. What does path mea at arbitrary eutro desity? Fig. 9. The differet paths at differet eutro desity.

10 Rate Aalysis or a Possible Iterpretatio of Abudaces 9. What does path mea at arbitrary eutro desity? Fig. 9. The differet paths at differet eutro desity. The maximum values we took from isotoically (p) or isotopically (). Here p8 ad 8 refer to the cm eutro desity. Istead of the classical paths the paths are more like the ridge of the σvalue at give eutro desity, i case of the eutro capture ucleosythesis. There is s-path, r-path ad betwee them are the m-paths o the Fig. 9 at differet eutro desity by the uified model [4]. The s-path is the theoretical edge of the paths at very low eutro desity. 0. Experimetal costraits: tellurium ad techetium ad iro The isotope aomalies at tellurium [] ad xeo [5] or the presece or absece of the techetium i AGB stars [6,7] ca be explaied with m-process. These deped o where the 8 path is. We have foud that the two r-oly isotopes of tellurium ( Te maily i the m-process at AGB coditios []. 60 Fe 60 Fe 60 The existece of Fe 58 radioisotope is also importat. The stable Fe 0, Te) are formed is separated from 59 by the ustable isotope Fe. The case is the same o the Fig.. The third uclei are 59. The rate equatio for the Fe: λ λ 0

Rate Aalysis or a Possible Iterpretatio of Abudaces 59 60 Fig. 0. The Co ad Feabudace at differet eutrodesity.

so it is egligible [8,9]. v σ x σ x σ f f f,6 f λ + x σ + x σ σ 5,5 σ + v 60 At a give eutro desity the amout of Fe is early three s what we get from the simple brachig ratio (see Fig. 0).

11 Rate Aalysis or a Possible Iterpretatio of Abudaces Fig. 0. The Co ad Feabudace at differet eutrodesity. The figure shows the differece beetve PFR ad the brachig factor I the case of equilibrium comes: σ λ σ σ x f λ λ λ + λ λ + x σ + σ + σ + v v v 60 λ 6 Because of the half-life of Fe ( T,5 0 y ) << σ, so it is egligible [8,9]. v σ x σ x σ f f f,6 f λ + x σ + x σ σ 5,5 σ + v 60 At a give eutro desity the amout of Fe is early three s what we get from the simple brachig ratio (see Fig. 0). We used data from KADoiS.0 [9]. 59 Co 60 This explais the high abudace of i, which is four s (4.4 s) the amout of σ, The formatio of i uclei occurs maily through the Fe chael.. Coclusio All experieced isotope ratios ca be obtaied both at K temperature ad at 0 K temperature at itermediate eutro desity ( cm ), so the m-process ad the AGB stars are probably oe of the mai places of ucleosythesis. It seems that the so-called r-uclei ca form i itermediate processes as well. Refereces [] E. M. Burbidge, G. R. Burbidge, W. A. Fowler, ad F. Hoyle (957). "Sythesis of the Elemets i Stars". Reviews of Moder Physics 9 (4): 547. Bibcode:957RvMP B. doi:0.0/revmodphys

12 Rate Aalysis or a Possible Iterpretatio of Abudaces [] F. Käppeler, H. Beer ad K. Wisshak, s-process ucleosythesis-uclear physics ad the classical model: Rep. Prog. Phys. 5 (989) [] C. E. Rolfs, W. S. Rodey: Cauldros i the Cosmos, The Uiv. of Chicago Press, 988 [4] K. Takahashi, K. Yokoi: BETA-DECAY RATES OF HIGHLY IOIZED HEAVY ATOMS I STELLAR ITERIORS, ATOMIC DATA AD UCLEAR DATA TABLES 6, (987)] [5] M. Kiss ad Z. Trócsáyi, Pheomeological Descriptio of eutro Capture Cross Sectios at 0 kev, ISR Astroomy ad Astrophysics, vol. 0, Article ID 70954, 8 pages, 0. doi:0.55/0/70954 [6] D Arett: Superovae ad ucleosythesis, Priceto Uiversity Press, 996 [7] J. J. Cowa ad W. K. Rose: PRODUCTIO OF 4 C AD EUTROS I RED GIATS, The Astrophysical Joural, :49-58, 977 February 5 [8] R. A. Malaey, Heavy -elemet sythesis i AGB ad post-agb stars of low mass, Mo. ot. R. astr. Soc. (986), [9] M. Lugaro, A. I. Karakas Sara Bisterzo Models ad observatios of the s process i AGB, PoS(IC X)04, 008: [0] P. Prado, L. Dardalet, E. Heriger, C. Higgs, C. Ritter, S. Joes, M. Pigatari, M. Bertolli, P. Woodward, Falk Herwig, i process ad CEMP-s+r stars IC XIII. 04 [] M. Kiss, PhD Thesis/Egyetemi doktori (PhD) értekezés, Debrecei Egyetem Debrece 0 [] [] [4] Kiss M., Trócsáyi Z. A uified model for ucleosythesis of heavy elemets i stars, Joural of Physics: Coferece Series (00) 004 doi:0.088/ /0//004 [5] J. D. Gilmour ad G. Turer, COSTRAITS O UCLEOSYTHESIS FROM XEO ISOTOPES I PRESOLAR MATERIAL, The Astrophysical Joural, 657:600Y608, 007 March [6] T. Lebzelter, J. Hro, Techetium ad the third dredge up i AGB stars I. Field stars, A&A 4, 5-54 (00) doi: 0.05/ :00458 [7] R. A. MALAEY: Productio of techetium i red giats by γ- ray-iduced fissio, ature 7, ( February 989); doi:0.08/778a0 [8] [9] Kadois.0:

13 Rate Aalysis or a Possible Iterpretatio of Abudaces Appedix. Isotopic equilibrium eutro desity at a temperature of 0 8 K uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg. 6i,55, 6i 00, Y 66,7 64i 8,4,76,E+06 6,. 68Z,69 0,7 69Z 56,4 m 75,4 70Z 0,9 0,89,8E+,5. 68Z,69 0,7 69Z m,76 d* 0,9 70Z 0,9 0,89,5E+08 8, Ga,58 8,7 70Ga,4 d 0,5 7Ga 04,6,76 6,4E+09 9, Ge,68 7,6 75Ge 8,78 m 0, 76Ge 4,4 0,965 4,0E+, Se,64 6, 79Se,95E+05 y 6 80Se 8,49-4,E+04 /a 7. 80Se,49 8 8Se 8,45 m 8, 8Se 8,4 0,757,E+, Se,49 8 8Se m 57,8 m* 8, 8Se 8,4 0,757,8E+, Br 0, Br,77E+0 m 790,0 8Br 9 0,766,8E+, Br 0, Br m 4,4E+00 h* 790,0 8Br 9 0,766,E+,08. 84Kr,408,6 85Kr 96,8 D 7 86Kr 4,76 0,89 4,8E+06 6,68. 84Kr,408,6 85Kr m 4,48 h 78,6% 7 86Kr 4,76 0,89,0E+,0. 85Rb 0, Rb 8,64 d 0 87Rb 5,7 0,6,E+08 8,4 4. 9Zr 0,09 7,8 9Zr,5E+06 Y 96 94Zr 7, 0,09,E+0, 5. 94Zr 0,97 7, 95Zr 64,0 D 79 96Zr 0, -0,496,8E+08 8, Mo -0,8 70,5 99Mo,7489 D 40 00Mo 80,5-0,609,9E+0 0, Ru -0, 5 0Ru 9,6 D 4 04Ru 54-0,46 9,5E+0 0, Pd -0, Pd 6,50E+06 Y 0 08Pd 8-0,4 7,4E+0, Pd -0,4 8 09Pd,700 H 6, 0Pd 57-0,785,0E+, Ag -0, Ag,7 m 788,0 09Ag 79-0,67,0E+4 4,9. 07Ag -0, Ag m 48 y*ec 8,0 09Ag 79-0,67,6E+06 6,4. 4Cd -0, 5, 5Cd 5,46 H 90 6Cd 76, -0,94 7,9E+09 9,90. 4Cd -0, 5, 5Cd m 44,56 d 4 6Cd 76, -0,94 5,E+08 8,7 4. I -, I 7,9 s 08,0 5I 776-0,754 -,8E+ /a 5. I -, I m 49,5 d* 595 5I 776-0,754 -,4E+08 /a 6. 0S 0,097 6, S 7,0 H 67 S,6-0,745 9,E+09 9, S 0,097 6, S m 4,9 y % 75,4 S,6-0,745 6,E+05 5,79 8. S -0,745,6 S 9, D 6 4S 5,7-0,644,9E+,59 9. S -0,745,6 S m 40,06 m 6 4S 5,7-0,644,8E+5 5,6 0. Sb -0,75 5 Sb D 894 Sb 0-0,879 9,0E+09 9,95. 6Te -0,046 8, 7Te 9,5 H 56,8 8Te 44,4 0,85,9E+,59. 6Te -0,046 8, 7Te m 09 d,4% 668,6 8Te 44,4 0,85,E+,05. 8Te 0,85 44,4 9Te 69,6 M 7,5 0Te 4, 0,,4E+,7

14 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg 4. 8Te 0,85 44,4 9Te m,6 d* 49,6 0Te 4, 0, 9,5E+08 8,98 5. Xe 0,086 6,8 Xe 5,4 D 7 4Xe, -0, 7,E+09 9, Xe -0,, 5Xe 9,4 H 65,6 6Xe 0,98-0,405 4,7E+0 0, Ce 0,004,7 4Ce,508 D 76 4Ce 9,9-0,9 5,6E+09 9, d -0,845 9, 47d 0,98 D d 46,6 -,4 5,7E+09 9, d -,4 46,6 49d 7,8 H 5, 50d 56, -, -,9E+ /a Sm -,77 4, 5Sm 90 Y 040 5Sm 464,8 -,6 -,7E+05 /a 4. 5Sm -,6 464,8 5Sm 46,84 H Sm 6,9 -,,0E+0 0, Gd -,086,6 59Gd 8,479 H 455, 60Gd 78 -,4 7,6E+0 0, Er -, Er 9,9 D 65,0 70Er 70, -,48,E+09 9, Yb -,0 50,5 75Yb 4,85 D Yb 5,9 -,5 6,7E+09 9, W -, W 75, D 6 86W 6 -,4 8,8E+09 9, Re -,77 48,5 86Re,786 D 74 87Re 84 -,475 -,5E+0 /a Re -,77 48,5 86Re m,00e+05 y* 74 87Re 84 -,475 -,8E+0 /a Os -0, Os 5,4 D 90 9Os 60-0,558,4E+0 0, Ir -0, Ir 7,87 D 080 9Ir 994-0,8 -,0E+09 /a 50. 9Ir -0, Ir m 4 y*ec 080 9Ir 994-0,8-8,6E+05 /a 5. 96Pt -0,47 67,4 97Pt 9,895 H 79,7 98Pt 94 -,05 8,6E+0 0,9 5. 0Hg -0,996 6, 0Hg 46,594 D 98 04Hg 4 -,6 5,7E+0 0, Tl -,65 70,5 04Tl,78 y 5 05Tl 5-0,866,4E+08 8,5 8. Isotopic equilibrium eutro desity at a temperature of 0 K uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg. 6i,55, 6i 00, Y 66,7 64i 8,4,76,E+07 7,09. 68Z,69 0,7 69Z 56,4 m 75,4 70Z 0,9 0,89,8E+,5. 68Z,69 0,7 69Z m,76 d* 0,9 70Z 0,9 0,89,5E+08 8, Ga,58 8,7 70Ga,4 d 0,5 7Ga 04,6,76 6,4E+09 9, Ge,68 7,6 75Ge 8,78 m 0, 76Ge 4,4 0,965 4,0E+, Se,64 6, 79Se,95E+05 y 6 80Se 8,49-7,6E+07 /a 7. 80Se,49 8 8Se 8,45 m 8, 8Se 8,4 0,757,E+, Se,49 8 8Se m 57,8 m* 8, 8Se 8,4 0,757,6E+, Br 0, Br,77E+0 m 790,0 8Br 9 0,766,E+, Br 0, Br m 4,4E+00 h* 790,0 8Br 9 0,766 7,9E+0 0,90. 84Kr,408,6 85Kr 96,8 D 7 86Kr 4,76 0,89 4,9E+06 6,69 4

15 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg. 84Kr,408,6 85Kr m 4,48 h 78,6% 7 86Kr 4,76 0,89,0E+,0. 85Rb 0, Rb 8,64 d 0 87Rb 5,7 0,6,E+,6 4. 9Zr 0,09 7,8 9Zr,5E+06 Y 96 94Zr 7, 0,09 4,8E+0, Zr 0,97 7, 95Zr 64,0 D 79 96Zr 0, -0,496,8E+08 8, Mo -0,8 70,5 99Mo,7489 D 40 00Mo 80,5-0,609 5,8E+0 0, Ru -0, 5 0Ru 9,6 D 4 04Ru 54-0,46,E+, Pd -0, Pd 6,50E+06 Y 0 08Pd 8-0,4 5,E+05 5, Pd -0,4 8 09Pd,700 H 6, 0Pd 57-0,785,0E+, Ag -0, Ag,7 m 788,0 09Ag 79-0,67,7E+4 4,. 07Ag -0, Ag m 48 y*ec 8,0 09Ag 79-0,67,E+06 6,6. 4Cd -0, 5, 5Cd 5,46 H 90 6Cd 76, -0,94 7,9E+09 9,90. 4Cd -0, 5, 5Cd m 44,56 d 4 6Cd 76, -0,94 5,E+08 8,7 4. I -, I 7,9 s 08,0 5I 776-0,754 -,8E+ /a 5. I -, I m 49,5 d* 595 5I 776-0,754 -,4E+08 /a 6. 0S 0,097 6, S 7,0 H 67 S,6-0,745 4,6E+09 9, S 0,097 6, S m 4,9 y % 75,4 S,6-0,745,0E+05 5,48 8. S -0,745,6 S 9, D 6 4S 5,7-0,644,4E+,8 9. S -0,745,6 S m 40,06 m 6 4S 5,7-0,644,E+6 6,04 0. Sb -0,75 5 Sb D 894 Sb 0-0,879,4E+0 0,5. 6Te -0,046 8, 7Te 9,5 H 56,8 8Te 44,4 0,85,4E+,5. 6Te -0,046 8, 7Te m 09 d,4% 668,6 8Te 44,4 0,85 9,6E+0 0,98. 8Te 0,85 44,4 9Te 69,6 M 7,5 0Te 4, 0,,E+,5 4. 8Te 0,85 44,4 9Te m,6 d* 49,6 0Te 4, 0, 9,0E+08 8,95 5. Xe 0,086 6,8 Xe 5,4 D 7 4Xe, -0, 9,4E+09 9, Xe -0,, 5Xe 9,4 H 65,6 6Xe 0,98-0,405 4,7E+0 0, Ce 0,004,7 4Ce,508 D 76 4Ce 9,9-0,9 5,6E+09 9, d -0,845 9, 47d 0,98 D d 46,6 -,4 5,7E+09 9, d -,4 46,6 49d 7,8 H 5, 50d 56, -, -,9E+ /a Sm -,77 4, 5Sm 90 Y 040 5Sm 464,8 -,6-9,8E+06 /a 4. 5Sm -,6 464,8 5Sm 46,84 H Sm 6,9 -,,6E+0 0, Gd -,086,6 59Gd 8,479 H 455, 60Gd 78 -,4 7,6E+0 0, Er -, Er 9,9 D 65,0 70Er 70, -,48,E+09 9, Yb -,0 50,5 75Yb 4,85 D Yb 5,9 -,5,0E+0 0, W -, W 75, D 6 86W 6 -,4 9,5E+09 9, Re -,77 48,5 86Re,786 D 74 87Re 84 -,475 -,8E+0 /a Re -,77 48,5 86Re m,00e+05 y*ec 74 87Re 84 -,475 -,9E+0 /a Os -0, Os 5,4 D 90 9Os 60-0,558,6E+0 0,4 5

16 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg 49. 9Ir -0, Ir 7,87 D 080 9Ir 994-0,8 -,4E+09 /a 50. 9Ir -0, Ir m,4e+0 y* 080 9Ir 994-0,8 -,E+06 /a 5. 96Pt -0,47 67,4 97Pt 9,895 H 79,7 98Pt 94 -,05 9,9E+0, Hg -0,996 6, 0Hg 46,594 D 98 04Hg 4 -,6 8,E+0 0,9 5. 0Tl -,65 70,5 04Tl,78 y 5 05Tl 5-0,866 6,8E+0 0,8. Isotoic equilibrium eutro desity at a temperature of 0 8 K uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg. 58Fe,47, 44,4495 d 59Fe 6,4 59Co 40,,5 -,4E+0 /a. 59Co,5 40, 95,8 d 60Co,64 60i 9,9 4, -,E+09 /a. 6i,55, 00, y 6i 66,7 6Cu 5,7,558,8E+07 7, i,76 8,57 h 65i, 65Cu 9,07 -,E+ /a 5. 65Cu,07 9 5, m 66Cu 6,6 66Z 6,4,544-4,E+ /a 6. 68Z,69 0,7 56,4 m 69Z 75,4 69Ga 8,7,58 7,9E+, Z,69 0,7,76 h* 69Z m 0,9 69Ga 8,7,58,7E+, Z 0,89 0,9,45 m 7Z 48,6 7Ga 06,4,76 -,4E+4 /a 9. 70Z 0,89 0,9,96 h 7Z m 48,6 7Ga 06,4,76 -,5E+ /a 0. 69Ga,58 8,7,4 m 70Ga 0,5 70Ge 89,,87,6E+,. 7Ga,76 06,4 4,095 h 7Ga 67,6 7Ge 5,,5 -,7E+0 /a. 74Ge,68 7,4 8,78 m 75Ge 0, 75As 55 0,87-7,7E+ /a. 75As 0,87 55,094 d 76As 469,6 76Se 68 0,748 4,9E+, Se,64 6,,95E+05 y 79Se 6 79Br 6 0,775-7,8E+0 /a 5. 80Se,49 8 8,45 m 8Se 9 8Br 9 0,766 -,6E+ /a 6. 80Se, ,8 m* 8Se m 9 8Br 9 0,766-5,E+ /a 7. 79Br 0, ,68 m 80Br Kr 74 0,009,6E+, Br 0, ,405 h* 80Br m Kr 90,4 0,009 7,8E+, Br 0, ,8 h 8Br 90,5 8Kr 9 0,76,0E+, Kr,408,6 96,8 d 85Kr 7 85Rb 4 0,709 -,E+07 /a. 84Kr,408,6 4,78 h79% 85Kr m 7 85Rb 4 0,709-6,E+ /a. 86Kr 0,89 4,76 76, m 87Kr 8 87Rb 5,7 0,6 4,5E+,65. 85Rb 0, ,64 d 86Rb 0 86Sr 6,5 0,65 5,6E+0 0, Rb 0,6 5,7 7,77 m 88Rb 0 88Sr 6,6,88 -,5E+ /a 5. 88Sr,88 6,6 50,57 d 89Sr 9 89Y 9, 0,667,0E+0 0,0 6

17 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg 6. 89Y 0,667 9, 90 y 90Y 49,9 90Zr 9, 0,769 -,E+06 /a 7. 9Zr 0,99 7,8,5E+06 y 9Zr 96 9b 65,7 0,99-4,4E+0 /a 8. 9b -0,56 65,7,0E+04 y 94b 48 94Mo 09,6-0,66,0E+09 9,0 9. 0Ru -0, 5 9,6 d 0Ru 4 0Rh 80-0,46 -,E+0 /a 0. 0Rh -0, , s 04Rh 54 04Pd 74-0,88,E+5 5,5. 0Rh -0, ,4 m* 04Rh m 54 04Pd 74-0,88,6E+4 4,56. 06Pd -0,4 44 6,60E+06 y 07Pd 0 07Ag 787-0,60-5,7E+00 /a. 08Pd -0,4 8,70 h 09Pd 6, 09Ag 79-0,67 -,E+ /a 4. 07Ag -0,60 787,7 m 08Ag Cd 0 -,85 6,8E+4 4, Ag -0, y* 08Ag m 8,0 08Cd 0 -,85 9,E+06 6, Ag -0, ,6 s 0Ag 7 0Cd 9,9-0,70,E+4 4, Ag -0, ,76 d 0Ag m 7 0Cd 9,9-0,70,E+08 8, 8. 4Cd -0, 5, 5,46 h 5Cd 90 5I 776-0,754 -,5E+0 /a 9. 4Cd -0, 5, 44,56 d* 5Cd m 4 5I 776-0,754 -,6E+09 /a 40. I -,0 9 7,9 s 4I 08 4S 4,4 -,599 -,E+ /a 4. I -, ,5 d* 4I m 595 4S 4,4 -,599 8,E+07 7,9 4. 5I -0, , s 6I 77 6S 9, -0,6-6,E+ /a 4. 5I -0, ,9 m 6I m 77 6S 9, -0,6 6,7E+, S 0,097 6, 7,0 h S 67 Sb 5-0,75 -,E+0 /a 45. 0S 0,097 6, 4,9 y* S m 75,4 Sb 5-0,75 -,E+06 /a 46. S -0,745,6 9, d S 6 Sb 0-0,879-4,0E+0 /a 47. S -0,745,7 40,06 m S m 6 Sb 0-0,879 -,9E+4 /a 48. Sb -0,75 5,78 d Sb 894 Te 95,4-0,98,E+0 0, 49. Sb -0, , d 4Sb 94,0 4Te 55-0,654,E+, Te -0,046 8, 9,5 h 7Te 56,8 7I 66-0,046 -,6E+ /a 5. 6Te -0,046 8, 09 d* 7Te m 668,6 7I 66-0,046 -,6E+08 /a 5. 7I -0, ,99 m 8I 679,5 8Xe 6,5 0,99 -,8E+ /a 5. Xe 0,086 6,8 5,4 d Xe 7 Cs 50-0,49 -,7E+0 /a 54. Cs -0,49 50,065 y 4Cs 74 4Ba 76-0,96,5E+09 9, Ba 0,508 4, 8,06 m 9Ba 9,7 9La,4-0,5 -,0E+ /a 56. 9La -0,5,4,67855 d 40La 7,8 40Ce,7 0,004,E+0 0, Ce 0,004,7,508 d 4Ce 76 4Pr,4-0,777-4,4E+09 /a 58. 4Pr -0,777,4 9, h 4Pr 6,4 4d 5, -0,65 5,4E+0 0, Sm -,77 4, 90 y 5Sm 040 5Eu 556 0,5 -,8E+05 /a 60. 5Sm -,6 464,8 46,84 h 5Sm 095 5Eu 567 -,94 -,E+0 /a 6. 5Eu -, ,59 y 54Eu Gd 08 -,49 8,8E+07 7, Gd -,086,6 8,479 h 59Gd 455, 59Tb 87 -, -6,E+0 /a 7

18 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb) uc T uit σ (mb) uc σ (mb) log y (cm - ) lg 6. 59Tb -, 87 7, d 60Tb 40 60Dy 890 -,044,6E+09 9, Dy -0,955,4 h 65Dy 84,5 65Ho 7 -,05-8,4E+ /a Ho -,05 7 6,8 h 66Ho 6,0 66Er 700 -,077,E+09 9, Ho -,05 7,0E+0 y 66Ho m 5, 66Er 700 -,077 5,4E+0, Er -,68 9 9,9 d 69Er 65 69Tm 065 -,4 -,5E+09 /a Tm -, ,6 d 70Tm Yb 768, -,4 7,E+08 8, Yb -,0 50,5 4,58 d 75Yb Lu 9 -,449 -,E+0 /a Lu -, ,6475 d 77Lu 794,9 77Hf 544 -,545-5,8E+09 /a 7. 76Lu -, ,44 d 77Lu m 48, 77Hf 544 -,545-5,5E+08 /a 7. 76Lu -, m 77Lu m 48, 77Hf 544 -,545 -,E+ /a 7. 80Hf -,65 56,6 4,9 d 8Hf 94 8Ta 766 -,684 -,E+09 /a 74. 8Ta -, ,4 d 8Ta 0 8W 85 -,455,0E+06 6, W -, ,4 d 85W 6 85Re 48,5 -,77-4,5E+08 /a W -,4 6,7 h 87W 8 87Re 84 -,475 -,E+ /a Re -,77 40,786 d 86Re 74 86Os 44 -,06 7,0E+0 0, Re -,77 8,5,00E+05 y* 86Re m 74 86Os 44 -,06-4,9E+0 /a Re -, ,00 h 88Re 4 88Os 94 -,047 9,0E+09 9, Os -0, ,4 d 9Os 90 9Ir 50-0,607 -,4E+09 /a 8. 9Os -0, , h 9Os 95,6 9Ir 994-0,8 -,E+ /a 8. 9Ir -0, ,8E+0 d 9Ir 080 9Pt 48 -,979,E+0 0,0 8. 9Ir -0,607 50,4E+0 y* 9Ir m 080 9Pt 48 -,979,E+07 7, Ir -0, ,8 h 94Ir 97,8 94Pt 8-0,56,E+, Pt -0,47 67,4 9,895 h 97Pt 75,4 97Au 6,8-0,78 -,0E+ /a Au -0,78 6,8,70E+00 d 98Au Hg 7 -,46,5E+, Hg -0,996 6, 46,594 d 0Hg 98 0Tl 70,5 -,65-9,8E+0 /a Hg -,6 4 5,4 m 05Hg,7 05Tl 5,6-0,886-5,6E+4 /a 89. 0Tl -,65 70,5,78 y 04Tl 5 04Pb 8,7 -,07 7,8E+07 7, Tl -0,866 5,6 4, m 06Tl 4, 06Pb 4,7-0,77 -,E+ /a 9. 08Pb 0,65 0,76,5 h 09Pb,6 09Bi,6-0,84 5,E+, Isotoic equilibrium eutro desity at a temperature of 0 K uc log y σ (mb T uit uc σ (mb) uc σ (mb) log y (cm - ) lg. 58Fe,47, 44,4495 d 59Fe 6,4 59Co 40,,5 -,4E+0 /a. 59Co,5 40, 95,8 d 60Co,64 60i 9,9 4, -,85E+0 /a. 6i,55, 00, y 6i 66,7 6Cu 5,7,558 9,50E+07 7,98 8

19 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb T uit uc σ (mb) uc σ (mb) log y (cm - ) lg 4. 64i,76 8,57 h 65i, 65Cu 9,07 -,8E+ /a 5. 65Cu,07 9 5, m 66Cu 6,6 66Z 6,4,544-4,4E+ /a 6. 68Z,69 0,7 56,4 m 69Z 75,4 69Ga 8,7,58 7,89E+, Z,69 0,7,76 h* 69Z m 0,9 69Ga 8,7,58,67E+, Z 0,89 0,9,45 m 7Z 48,6 7Ga 06,4,76 -,7E+4 /a 9. 70Z 0,89 0,9,96 h 7Z m 48,6 7Ga 06,4,76 -,48E+ /a 0. 69Ga,58 8,7,4 m 70Ga 0,5 70Ge 89,,87,64E+,. 7Ga,76 06,4 4,095 h 7Ga 67,6 7Ge 5,,5-7,8E+0 /a. 74Ge,68 7,4 8,78 m 75Ge 0, 75As 55 0,87-7,49E+ /a. 75As 0,87 55,094 d 76As 469,6 76Se 68 0,748,40E+, Se,64 6,,95E+05 y 79Se 6 79Br 6 0,775 -,9E+07 /a 5. 80Se,49 8 8,45 m 8Se 9 8Br 9 0,766 -,48E+ /a 6. 80Se, ,8 m* 8Se m 9 8Br 9 0,766-4,78E+ /a 7. 79Br 0, ,68 m 80Br Kr 74 0,009,4E+, Br 0, ,405 h* 80Br m Kr 90,4 0,009 5,5E+,7 9. 8Br 0, ,8 h 8Br 90,5 8Kr 9 0,76,05E+, Kr,408,6 96,8 d 85Kr 7 85Rb 4 0,709 -,E+07 /a. 84Kr,408,6 4,78 h79% 85Kr m 7 85Rb 4 0,709-6,5E+ /a. 86Kr 0,89 4,76 76, m 87Kr 8 87Rb 5,7 0,6 4,48E+,65. 85Rb 0, ,64 d 86Rb 0 86Sr 6,5 0,65 5,60E+0 0, Rb 0,6 5,7 7,77 m 88Rb 0 88Sr 6,6,88 -,4E+ /a 5. 88Sr,88 6,6 50,57 d 89Sr 9 89Y 9, 0,667,0E+0 0, Y 0,667 9, 90 y 90Y 49,9 90Zr 9, 0,769 -,6E+06 /a 7. 9Zr 0,99 7,8,5E+06 y 9Zr 96 9b 65,7 0,99 -,58E+0 /a 8. 9b -0,56 65,7,0E+04 y 94b 48 94Mo 09,6-0,66 4,04E+0 0,6 9. 0Ru -0, 5 9,6 d 0Ru 4 0Rh 80-0,46 -,59E+0 /a 0. 0Rh -0, , s 04Rh 54 04Pd 74-0,88,7E+5 5,4. 0Rh -0, ,4 m* 04Rh m 54 04Pd 74-0,88,80E+4 4,45. 06Pd -0,4 44 6,60E+06 y 07Pd 0 07Ag 787-0,60-4,0E+04 /a. 08Pd -0,4 8,70 h 09Pd 6, 09Ag 79-0,67 -,4E+ /a 4. 07Ag -0,60 787,7 m 08Ag Cd 0 -,85 5,96E+4 4, Ag -0, y* 08Ag m 8,0 08Cd 0 -,85 7,9E+06 6, Ag -0, ,6 s 0Ag 7 0Cd 9,9-0,70,0E+4 4, Ag -0, ,76 d 0Ag m 7 0Cd 9,9-0,70,8E+08 8, Cd -0, 5, 5,46 h 5Cd 90 5I 776-0,754 -,47E+0 /a 9

20 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb T uit uc σ (mb) uc σ (mb) log y (cm - ) lg 9. 4Cd -0, 5, 44,56 d* 5Cd m 4 5I 776-0,754 -,60E+09 /a 40. I -,0 9 7,9 s 4I 08 4S 4,4 -,599 -,6E+ /a 4. I -, ,5 d* 4I m 595 4S 4,4 -,599 8,07E+07 7,9 4. 5I -0, , s 6I 77 6S 9, -0,6-5,9E+ /a 4. 5I -0, ,9 m 6I m 77 6S 9, -0,6 6,5E+, S 0,097 6, 7,0 h S 67 Sb 5-0,75 -,40E+0 /a 45. 0S 0,097 6, 4,9 y* S m 75,4 Sb 5-0,75 -,60E+06 /a 46. S -0,745,6 9, d S 6 Sb 0-0,879 -,00E+ /a 47. S -0,745,7 40,06 m S m 6 Sb 0-0,879 -,40E+5 /a 48. Sb -0,75 5,78 d Sb 894 Te 95,4-0,98 7,76E+0 0, Sb -0, , d 4Sb 94,0 4Te 55-0,654 5,00E+, Te -0,046 8, 9,5 h 7Te 56,8 7I 66-0,046 -,E+ /a 5. 6Te -0,046 8, 09 d* 7Te m 668,6 7I 66-0,046 -,06E+08 /a 5. 7I -0, ,99 m 8I 679,5 8Xe 6,5 0,99 -,8E+ /a 5. Xe 0,086 6,8 5,4 d Xe 7 Cs 50-0,49 -,64E+0 /a 54. Cs -0,49 50,065 y 4Cs 74 4Ba 76-0,96 9,5E+0 0, Ba 0,508 4, 8,06 m 9Ba 9,7 9La,4-0,5 -,0E+ /a 56. 9La -0,5,4,67855 d 40La 7,8 40Ce,7 0,004 4,E+0 0, Ce 0,004,7,508 d 4Ce 76 4Pr,4-0,777-4,5E+09 /a 58. 4Pr -0,777,4 9, h 4Pr 6,4 4d 5, -0,65,60E+0 0, Sm -,77 4, 90 y 5Sm 040 5Eu 556 0,5-7,E+06 /a 60. 5Sm -,6 464,8 46,84 h 5Sm 095 5Eu 567 -,94 -,8E+0 /a 6. 5Eu -, ,59 y 54Eu Gd 08 -,49,08E+0 0, Gd -,086,6 8,479 h 59Gd 455, 59Tb 87 -, -6,09E+0 /a 6. 59Tb -, 87 7, d 60Tb 40 60Dy 890 -,044,5E+, Dy -0,955,4 h 65Dy 84,5 65Ho 7 -,05-8,4E+ /a Ho -,05 7 6,8 h 66Ho 6,0 66Er 700 -,077,6E+0 0, Ho -,05 7,0E+0 y 66Ho m 5, 66Er 700 -,077,0E+04 4, Er -,68 9 9,9 d 69Er 65 69Tm 065 -,4 -,40E+09 /a Tm -, ,6 d 70Tm Yb 768, -,4 7,95E+08 8, Yb -,0 50,5 4,58 d 75Yb Lu 9 -,449 -,64E+0 /a Lu -, ,6475 d 77Lu 794,9 77Hf 544 -,545-8,8E+09 /a 7. 76Lu -, ,44 d 77Lu m 48, 77Hf 544 -,545-7,7E+08 /a 7. 76Lu -, m 77Lu m 48, 77Hf 544 -,545 -,98E+ /a 7. 80Hf -,65 56,6 4,9 d 8Hf 94 8Ta 766 -,684-5,6E+0 /a 74. 8Ta -, ,4 d 8Ta 0 8W 85 -,455 5,E+08 8, W -, ,4 d 85W 6 85Re 48,5 -,77-4,8E+08 /a 0

21 Rate Aalysis or a Possible Iterpretatio of Abudaces uc log y σ (mb T uit uc σ (mb) uc σ (mb) log y (cm - ) lg W -,4 6,7 h 87W 8 87Re 84 -,475 -,4E+ /a Re -,77 40,786 d 86Re 74 86Os 44 -,06 7,48E+0 0, Re -,77 8,5,00E+05 y* 86Re m 74 86Os 44 -,06-5,E+0 /a Re -, ,00 h 88Re 4 88Os 94 -,047 9,50E+09 9, Os -0, ,4 d 9Os 90 9Ir 50-0,607 -,58E+09 /a 8. 9Os -0, , h 9Os 95,6 9Ir 994-0,8 -,05E+ /a 8. 9Ir -0, ,8E+0 d 9Ir 080 9Pt 48 -,979,76E+0 0,4 8. 9Ir -0,607 50,4E+0 y* 9Ir m 080 9Pt 48 -,979,47E+07 7, Ir -0, ,8 h 94Ir 97,8 94Pt 8-0,56,47E+, Pt -0,47 67,4 9,895 h 97Pt 75,4 97Au 6,8-0,78 -,9E+ /a Au -0,78 6,8,70E+00 d 98Au Hg 7 -,46 9,5E+, Hg -0,996 6, 46,594 d 0Hg 98 0Tl 70,5 -,65 -,40E+ /a Hg -,6 4 5,4 m 05Hg,7 05Tl 5,6-0,886-5,59E+4 /a 89. 0Tl -,65 70,5,78 y 04Tl 5 04Pb 8,7 -,07,55E+0 0, Tl -0,866 5,6 4, m 06Tl 4, 06Pb 4,7-0,77 -,E+ /a 9. 08Pb 0,65 0,76,5 h 09Pb,6 09Bi,6-0,84 5,0E+,7 Leged /a: ot all third uclei ca be achieved i that process log y i : D. Arett: Superovae ad ucleosythesis, Priceto Uiversity Press, 996 at σ i: bold: KADoiS.0 ormal: KADoiS 0. (MACS) italic: B. Pritycheko, S.F. Mughabghab: eutro Thermal Cross Sectios, Westcott Factors, Resoace Itegrals, Maxwellia Averaged Cross Sectios ad Astrophysical Reactio Rates Calculated from the EDF/B-VII., JEFF-.., JEDL-4.0, ROSFOD- 00, CEDL-. ad EAF-00 Evaluated Data Libraries uderlied:

Structure and evolution of AGB stars

Structure and evolution of AGB stars Structure ad evolutio of AGB stars M bol T eff The mai s-process s i AGB stars H 12 C(p,γ) 13 N(β + υ) 13 C 13 C(α,) He-flash eutro source 13 C(α,) 16 dy 13 dt dy dt C = Y = x 13 Y C X Y 4 Y He ρ N ρ N