Data needs for the astrophysical p-process

Nuclear Physics A 758 (2005) 90c–97c

Data needs for the astrophysical p-process Zs. F¨ ul¨opa, Gy. Gy¨ urkya , E. Somorjaia a

ATOMKI, H-4001 Debrecen, POB.51., Hungary

A status report is given on the experimental aspects of the astrophysical p-process that is responsible for the production of the heavy proton rich nuclei known as p-nuclei. The numerical modelling of the p-process scenario involves the knowledge of photodisintegration cross sections, mostly calculated through the Hauser-Feshbach statistical model approach. Recent experiments test the reliability of the model calculations in the proton rich region as well as providing indirect experimental information on the cross sections relevant to the p-process. 1. INTRODUCTION Although the nucleosynthesis of heavy elements is well described by neutron capture during the s- and r-processes there are some isotopes not reachable by the above processes. These stable neutron-deficient isotopes of the elements with charge number Z≥34 are classically referred to as p-nuclei. The aim of this paper is to give a status report on the nuclear physics problems regarding the nucleosynthesis of the p-nuclei. A short introduction to the overall status of light and heavy element nucleosynthesis can be found in [1]. The solar and isotopic abundances of p-nuclei are listed in Table 1. The p-nuclei have been observed only in the solar system and here they represent 0.1% to 1% of the abundance of the bulk isotopes, made predominantly of the more neutron-rich s- and r-nuclei. The stellar process synthesizing the p-nuclei is called the p-process. Several models have been developed for describing the p-process. There are differences in the details (astrophysical site, temperature, time scale, reactions involved, etc.), however, the generally accepted main process involves sequential (γ,n) reactions starting from sand r-nuclei and driving the nuclei towards the neutron-deficient region [2–4]. Along this isotopic path, the binding energy of neutrons becomes gradually larger, the reaction flow slows down and, at a branching point, is deflected by (γ,α) and/or (γ,p) reactions. The branching points are the p-nuclei themselves (lower mass region) or their progenitors (heavier mass region). The importance of the nuclear physics aspects of the p-process is also emphasized in the Long Range Plan of NuPECC expert committee [5]. A recent overview on p-process studies can be found in [6]. In the following sections the contribution of experimental nuclear physics to the understanding of the p-process is described. 0375-9474/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2005.05.168

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Table 1 List of p–nuclei with their solar and isotopic abundances [7]. Nucleus 74

Se Kr 84 Sr 92 Mo 94 Mo 96 Ru 98 Ru 102 Pd 106 Cd 108 Cd 113 In 112 Sn 114 Sn 115 Sn 120 Te 124 Xe 126 Xe 130 Ba 78

Abundance [Si = 106 ] 0.55 0.153 0.132 0.378 0.236 0.103 0.035 0.0142 0.0201 0.0143 0.0079 0.0372 0.0252 0.0129 0.0043 0.00571 0.00509 0.00476

Isotopic abundance (%) 0.88 0.34 0.56 14.84 9.25 5.52 1.88 1.02 1.25 0.89 4.3 0.97 0.66 0.34 0.09 0.12 0.11 0.11

Nucleus 132

Ba La 136 Ce 138 Ce 144 Sm 152 Gd 156 Dy 158 Dy 162 Er 164 Er 168 Yb 174 Hf 180 Ta 180 W 184 Os 190 Pt 196 Hg 138

Abundance [Si = 106 ] 0.00453 0.000409 0.00216 0.00284 0.008 0.00066 0.000221 0.000378 0.000351 0.00404 0.000322 0.000249 2.48 · 10−6 0.000173 0.000122 0.00017 0.00052

Isotopic abundance (%) 0.10 0.09 0.19 0.25 3.10 0.20 0.06 0.10 0.14 1.61 0.13 0.16 0.01 0.13 0.02 0.01 0.15

2. DATA NEEDS The modelling of p-process nucleosynthesis requires a large network of nuclear reactions involving stable nuclei as well as unstable, proton-rich nuclides. The relevant astrophysical reaction rates (calculated from the cross sections) are inputs to this network, therefore their knowledge is essential for the p-process calculations. While there are compilations of neutron capture data along the line of stability above the iron region, there are still very few charged-particle cross sections determined experimentally, despite big experimental efforts in recent years. Thus, the p-process rates involving charged particles are still based mainly on (largely untested) theoretical cross sections obtained from modern HauserFeshbach statistical model calculations [8,9]. Recently, Rapp et al [10] studied the effect of cross section uncertainties on the p-nuclei overabundance for the relevant (γ,n), (γ,p) and (γ,α) reactions. The result underlines the importance of (γ,p) experiments at the lower mass region, while the (γ,α) reaction uncertainties are dominating the higher mass region. Using the latest reaction rate compilations the p-process branching points can be reanalyzed as was done by Rauscher [11]. The primary aim of the present p-process experiments is the test of statistical model calculations in the mass and energy range relevant to the astrophysical p-process. Because of the limited intensity of available gamma sources instead of the (γ,α) or (γ,p) exper-

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iments usually the inverse (α,γ) or (p,γ) cross sections are determined experimentally. However, due to the fast developments of high intensity gamma sources it is expected that in the near future the first gamma induced charged particle emitting reactions in the p-process region can be investigated [12]. 2.1. Radiative capture cross sections The existing cross section database of (α,γ) and (p,γ) reactions relevant to the p-process networks was built up mostly during the last decade. Predominantly (p,γ) reactions were studied, because of the higher expected cross sections. Different experimental methods were used for the (p,γ) studies, for example, inbeam gamma spectrometry detecting the individual transitions with angular distributions (e.g. [13]), summing spectroscopy using 4π scintillator setups (e.g. [14]) and the activation method (e.g. [15,16]). In contrast to the in-beam methods, during the activation method, the irradiation is separated in time from the gamma-detection. The advantage of this method is that capture reactions on different isotopes of an element can be studied simultaneously using natural targets, and the in-beam background is reduced to the laboratory background that can be shielded well. On the other hand, because of the possible longer half-lives of the residual nuclei new targets should be prepared for each irradiation, or longer cooling periods should be applied. In addition, this method can be used only in a limited range of residual nuclei: the half-life of the residual nucleus should be reasonable, too short or too long lived isotopes cannot be measured. Also, the γ branching of the decay is a limiting factor. A recent study reveals the sensitivity of the statistical model calculations on several input parameters in case of (p,γ) cross sections at various Se isotopes [16]. The result shows that the investigated models are able to reproduce the experimental data within about a factor of two and the predictions are not very dependent on the input parameters. In the case of (α,γ) reactions, however, there are only limited number of reaction cross sections available, and mostly from the low mass region [17–19]. The only exception is the 144 Sm(α,γ)148 Gd reaction [20] measured by the activation method detecting the alphadecay of the residual 148 Gd. In the case of (α,γ) reactions the statistical model calculations are more sensitive to the optical potential parameters, therefore recent efforts aim at the determination of a reliable global optical potential to be used for astrophysical purposes [21–24]. To gain more experimental data on (α,γ) reactions a new project on the determination of the cross section of the 106 Cd(α,γ)110 Sn reaction in the Gamow window has been started [25]. Here, the abundance ratios of the stable proton rich 106 Cd and 108 Cd isotopes are affected by the 110 Sn(γ,α)106 Cd photo-induced reaction, which can be studied indirectly via radiative alpha capture. The relevant p-process reaction flow can be seen in Fig.1. Since the 110 Sn is radioactive (T1/2 = 4.11 h, Eγ = 280 keV) the activation method is applicable. As it can be seen in Fig. 2, in addition to the 106 Cd(α,γ) cross section, 106 Cd(α,n) and 106 Cd(α,p) reactions can be studied simultaneously, and those cross sections can be compared to statistical model calculations, too. In order to reduce the systematic errors, parallel measurements were started in ATOMKI, Hungary, and at Notre Dame, USA [25]. The activation method implies the knowledge of the half-life of the residual nucleus,

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(J,n)

112Te

2.0 m

15.2 m

4.11 h

)

0.65%

(J ,D

)

E

(J,n)

108C d

1.25%

114Sn

0.97%

(J ,D 106C d

(J,n)

112Sn

(J ,D )

E

(J ,D

(J ,D

(J,n)

110Sn

10.3 m

(J,n)

0.89%

116Te

2.49 h

E

)

(J ,D )

E

(J,n)

108Sn

(J,n)

114Te

)

(J,n)

(J,n)

110C d

12.5%

Figure 1. Reaction flows in the region of proton rich tin and cadmium isotopes. The dominant reactions are denoted by solid, the weaker ones by dashed lines. Stable nuclides are indicated by bold squares in which the natural abundance is given. For the unstable nuclei the half-life is indicated. Only the even-even nuclei are shown, hence the (γ,n) arrow corresponds to subsequent emission of two neutrons.

109Sn

10.14 M eV

2

T 1/2

T 1/

1. 13

M

eV

h 4.1

m 18

=

=

110In

Q

=

109In

=

(D ,J)

T 1/2

1 M eV

h 4.2

(D,n)Q = -

110Sn

= -5.5 (D,p)Q 106C d

109C d

Figure 2. Alpha-induced reactions with the relevant Q-values on the residual nuclei are also indicated

106

Cd. The decays of

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1.005 148

measured data exponential fit

Sn activity [a.u.]

1.000

0.995

0.990

1000

110

normalized

148

241

Gd/ Am yield/month

Gd, T1/2= 74.5 +/- 3.7 y

0.985 100

0.980 0

100

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Figure 3. Decay of 148 Gd with exponential fit. Measured by a silicon detector and normalized to the decay of 241 Am [26].

0

5

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elapsed time [hours]

Figure 4. Decay curve of 110 In measured by a shielded HPGe detector. The preliminary result is T1/2 = 4.17 ± 0.02 h.

and the error of the half-life in question directly affects the error in the reaction rate. Therefore in selected cases a complementary measurement on the half-lives can reduce the systematic errors in the cross sections. Some examples are the half-life of the alphaemitting isotope 148 Gd [26] for the 144 Sm(α,γ)148 Gd reaction (see Fig.3) and the half-life of 110 Sn for the 106 Cd(α,γ)110 Sn reaction (see Fig.4). 2.2. Refined optical potential parameter sets for the statistical model Of the many nuclear properties (ground state properties, level densities, gamma strength functions, optical potentials) entering the statistical model calculation, the uncertainty in the α particle width is the dominating one. This particle width is obtained by employing an α+nucleus optical potential. One method to obtain optical potential parameters is to study (α,α) elastic scattering angular distributions over a wide angular range. Another possibility for studying the alpha-nucleus potential is using the sensitivity of (n,α) reactions, for which details can be found in [27,28]. The determination of the α-nucleus potential at energies below the Coulomb barrier is limited in general because the experimental data show only small deviations from the Rutherford cross section, and the optical potentials have ambiguities. The (γ,α) and (α,γ) reaction rates show a strong dependence on the chosen α-nucleus potential. Recently, systematic folding potentials [29] have been determined by elastic α scattering experiments on different proton-rich nuclei (144 Sm, 92 Mo, 112 Sn [30–34]). In those experiments complete angular distributions have been measured, and the corresponding α–nucleus potentials for 144 Sm, 92 Mo and 112 Sn have been fully determined at the measured energies. These potentials can be used to predict (α,γ) reaction cross sections, and their inverse (γ,α) reaction rates can be calculated using detailed balance. The lack of experimental cross section data has meant that a comparison between measured (α,γ) cross sections and statistical model predictions using experimentally determined optical model parameters has been possible only for the 144 Sm(α,γ)148 Gd reaction. However, the ongoing experi-

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Figure 5. Elastic scattering cross sections normalized to the Rutherford cross section for 124 Sn(α,α) at Eα = 19 MeV, 112 Sn(α,α) at Eα = 19 MeV and 112 Sn(α,α) at Eα = 14 MeV. The solid lines are the results of the optical model analysis [34].

ments on 92 Mo [35] and 112 Sn [36] will provide further possibilities for direct comparisons. Since a long isotopic range can be studied in the case of tin isotopes, to understand the

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systematic behavior of optical potentials the neutron rich 124 Sn was also studied to reveal the differences between the proton-rich 112 Sn and the neutron rich 124 Sn (See Fig.5). 3. SUMMARY To understand the nature of the astrophysical p-process, the various astrophysical scenarios should provide reliable abundance values for the p-nuclei. The lack of experimental data necessitates the use of extensive reaction rate calculations using cross sections based on statistical model. Therefore the sensitivity of Hauser-Feshbach statistical model calculations to various input parameters should be studied especially in the proton rich region. Further (p,γ) and (α,γ) cross section experiments are needed to cover especially the heavy ion region. In order to establish a reliable global alpha potential further low energy elastic scattering experiments are also needed. The first steps have been made towards an experimental nuclear database for the p-process, but the most important and most difficult part —determination of alpha capture cross sections close to the heaviest p-nuclei— is still missing. 4. ACKNOWLEDGEMENTS This work was supported by OTKA (T034259, T042733, F043408 and D048283). Gy. Gy. and Zs. F. are Bolyai fellows. The authors thank D. Galaviz for providing his preliminary results on 112,124 Sn(α,α) elastic scattering. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

G. Wallerstein et al. Rev. Mod. Phys. 69 (1997) 995. M. Arnould, Astronomy and Astrophysics 46 (1976) 117. S.E. Woosley and W.M. Howard, Ap. J. Suppl. 36 (1978) 285. M. Rayet, Astronomy and Astrophysics 227 (1990) 271. M.Harakeh et al. (eds), NuPECC Long Range Plan 2004. M. Arnould and S. Goriely, Phys. Rep. 384 (2003) 1. E. Anders, N. Grevesse, Geochim. Cosmochim. Acta 53 (1989) 197. T. Rauscher and F. K. Thielemann, At. Data Nucl. Data Tables 79 (2001) 47. and At. Data Nucl. Data Tables 75 (2000) 1. S. Goriely, in Nuclei in the Cosmos V, Edition Frontieres Paris, (1998) 314. W. Rapp, Nucl. Phys. A this issue T. Rauscher, Nucl. Phys. A this issue H. Utsunomiya et al. Nucl. Phys. A in press. doi:10.1016/j.nuclphysa.2004.06.025. S. Galanopoulos et al. Phys. Rev. C 67 (2003) 015801. P. Tsagari et al. Phys. Rev. C 70 (2004) 015802. Gy. Gy¨ urky et al. Phys. Rev. C 64 (2001) 065803. Gy. Gy¨ urky et al. Phys. Rev. C 68 (2003) 055803. Zs. F¨ ul¨op et al. Z. Phys. A 355 (1996) 203. W. Rapp et al., Phys. Rev. C 66 (2002) 015803. ¨ N. Ozkan et al., Nucl. Phys. A 710 (2002) 469. E. Somorjai, Astron. Astrophys. 333 (1998) 1112.

Z. Fülöp et al. / Nuclear Physics A 758 (2005) 90c–97c

21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

P. Mohr, Phys. Rev. C 61 (2000) 045802. P. Demetriou et al., Nucl. Phys. A 707 (2002) 253. V. Avrigeanu et al., Nucl. Phys. A 723 (2003) 104. T. Rauscher et al., Nucl. Phys. A 719 (2002) 73c, Nucl. Phys. A 725 (2003) 295. Gy. Gy¨ urky et al. Nucl. Phys. A this issue Zs. F¨ ul¨op et al., Nucl. Phys. A 718 (2003) 688. Yu. M. Gledenov et al., Phys. Rev. C 62 (2000) 042801R. P.E. Koehler, et al., Phys. Rev. C 69 (2004) 015803. U. Atzrott et al., Phys. Rev. C 53 (1996) 1336. P. Mohr et al., Phys. Rev. C 55 (1997) 1523. Zs. F¨ ul¨op et al., Phys. Rev. C 64 (2001) 065805. D. Galaviz et al., Nucl. Phys. A 718 (2003) 578c. D. Galaviz et al., Nucl. Phys. A 719 (2003) 111c. D. Galaviz, et al. Phys. Rev. C, to be submitted. S. Harissopulos, Nucl. Phys. A this issue W. Rapp, Ph.D. Thesis, TH Karlsruhe (2003)

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