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Indirect measurement of radiative capture cross sections relevant in astrophysical scenarios
Progress in Particle and Nuclear Physics 59 (2007) 183–192 www.elsevier.com/locate/ppnp
Review
Indirect measurement of radiative capture cross sections relevant in astrophysical scenarios Ushasi Datta Pramanik ∗ Saha Institute of Nuclear Physics (SINP), Kolkata, India Gesellschaft f¨ur Schwerionenforschung (GSI), Darmstadt, Germany
Abstract Radiative capture cross sections play a significant role in many cosmic phenomena, e.g. galactic evolution, star formation and planet formation etc. In explosive stellar burning scenarios, a large number of unstable nuclei play a crucial role, and reliable reaction cross sections are necessary for astrophysical model calculations, which will help in turn to understand the phenomena. A number of indirect methods are being explored by experimental nuclear physicists to avoid radioactive targets and other difficulties of direct measurements of radiative capture cross sections. The Coulomb dissociation of radioactive ion beams at intermediate energy is one of the most powerful indirect methods for measuring capture cross sections, and is being explored at various laboratories in the world. Here, a brief current status report is presented. This indirect method has a number of advantages compared to direct measurements, but there are also a number of limitations to this method with the presently available experimental facilities. A discussion on these aspects is given, together with an outlook on future experimental prospects. c 2007 Elsevier B.V. All rights reserved.
1. Introduction Nuclear radiative capture reactions, in which the incident projectile is absorbed by a target nucleus followed by γ -ray emissions, are important in various branches of fundamental as well as applied physics. A wide range of nuclear properties, such as spectroscopic properties, collective band structure, and various modes of nuclear motions [1] have been extensively ∗ Corresponding address: Saha Institute of Nuclear Physics (SINP), Kolkata, India. Tel.: +91 33 23375346 49; fax: +91 33 23374637. E-mail address: [email protected].
c 2007 Elsevier B.V. All rights reserved. 0146-6410/$ - see front matter doi:10.1016/j.ppnp.2006.12.005
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studied with these types of reactions. Polarized cold neutron capture on protons is used for a precision measurement of the parity violation asymmetry [2]. Besides this, the radiative capture of α, p, n, and d by nuclei at very low relative energies plays an important role in understanding the nucleosynthesis as well as the chemical evolution of stars and planets, and the relative abundances in stellar burning processes in various astrophysical sites [3–8]. Astrophysical models on these cosmological phenomena require the rate and energy released by the relevant nuclear reactions as critical inputs, in addition to a good understanding of the underlying hydrodynamics, radiation transfer and other aspects of stellar evolution. Nuclear models play a central role in providing the information needed for astrophysical calculations. But often, depending upon the mass region with different neutron to proton ratios, and hence different effective nucleon–nucleon interactions, the results of these calculations vary by a factor of 23 or more. Therefore, reliable experimental data are essential. Until recently, the only reliable method was to measure them in the laboratory directly with a low energy beam and eventually extrapolate the results down to astrophysical energies. The principal difficulty of measuring radiative capture cross sections directly arises due to a very low cross section (∼µb, pb, nb). The cross section is small because the electromagnetic force is weak compared to the nuclear force. The decay of unbound nuclear states by the emission of a particle is 103 –106 times more probable than its decay via γ -ray emission. Moreover, due to a very low-energy beam, the target must be thin considering the energy loss of the projectile. In addition to that, in a large number of astrophysical sites, such as nova explosions, explosive supernovae (core collapse), solar fusion, explosive hydrogen burning, and the r-process (see Table 1), where the temperature is high enough (>108 K), the interaction time can be so short (∼ seconds) that the unstable nuclei formed in the reaction can undergo subsequent nuclear processes before they decay to stable nuclei. In these scenarios, a study of the capture cross sections of unstable nuclei, using radioactive targets would be necessary. Particularly, direct measurements of neutron capture cross sections of unstable nuclei with a very short life time is practically impossible. In order to overcome all these limitations, various indirect measurements are being explored in the recent years at various laboratories in the USA, Europe and Asia. These indirect measurements use the Coulomb Dissociation method [9,10], the ANC method (Asymptotic normalization coefficient) [11,12], the Trojan–Horse method [13,14], and the Surrogate Nuclear reaction method [15,16]. In the following subsection, a brief introduction to these methods will be presented. Finally, a review of indirect measurements at different laboratories through the Coulomb dissociation will be presented, with a focus on their advantages and limitations. 2. Indirect methods for measurements of radiative capture cross sections A. The ANC has been explored for low energy radiative capture reactions A(a, γ )B, which are dominated by processes occurring well outside the nuclear radii. The cross section of such a reaction depends on the asymptotic behavior of the overlap function for B → A + a, which can be determined via a peripheral transfer reaction [11,12]. B. The Trojan–Horse method provides a mechanism which eliminates the problem of the Coulomb barrier for low energy the two body charge particle reaction cross section A(a,b)B. It can be done by selecting a reaction d + A → b + B + c with d = a + c, and c can be considered a spectator in the reaction between A and a (‘quasi-free scattering’). Hence, from the reaction cross section of three body reaction, one can link to the reaction cross section of the two-body reaction of interest [13,14].
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U. Datta Pramanik/ Progress in Particle and Nuclear Physics 59 (2007) 183–192 Table 1 Explosive nucleosynthesis in supernovae Fuel
Main product
Secondary product
T(109 ) K
Time (s)
Main reaction
Inner most ejecta Si, O O, Ne
r-process
–
>10
1
(n, γ ), β −
56 Ni
Iron-gr Na, Al, P p-process
>4 2-3
0.1 5 5
(α, γ ) (γ , α) (γ , n)
O, Ne, Mg
C. The Surrogate Nuclear reaction technique is an indirect method (a + A → B∗ → c + C) which combines experiment with reaction theory to obtain ‘desired’ reaction cross sections that proceeds through a compound nuclear state B∗ [15,16]. D. The Coulomb dissociation method is the main topic of the present Review, which will be presented in the following subsection: 3. Coulomb dissociation (CD) of unstable nuclei at intermediate energy and capture cross sections When a projectile (A) moving with high velocity passes a target of high nuclear charge Z , it may be excited by absorbing virtual photons from the time-dependent Coulomb field [17,9]. The projectile may be excited to its unbound state and decay into core (B) and particle (x i,e n dσ or p or α etc.). This Coulomb dissociation cross section dE ∗ is related to the photo dissociation cross section σ (γ , x), which in turn is related to the inverse reaction σ (x, γ ) via the principle of detailed balance [9]. σ (x, γ ) = where kγ2 =
Eγ h¯ c
kγ2 2(2 j A + 1) σ (γ , x) (2J B + 1)(2J X + 1) k 2
, k2 =
(1)
2µ Bx E c.m. . h¯ 2
3.1. Advantages of this method Intermediate-energy beams of unstable nuclei will solve the problem of radioactive targets. Since the beam’s energy is high enough; moreover, one can use thick targets, which provide more yield. The CD cross section is by orders of magnitude larger than the capture cross section, due to the phase space factor. In addition to that, the CD data obtained from one particular projectile energy provide capture cross sections in center of mass energy i.e, up to 5–20 MeV depending on the adiabacity cutoff. Since the decay products are kinematically forward focused, small-size detectors cover a large solid angle of the reaction product. At the high beam energies, the reaction’s mechanism can be approximated as a sudden process. With this indirect method, one can thus measure capture cross sections of unbound nuclei which will not be accessible with the direct method. 3.2. Radiative proton capture reactions from Coulomb dissociation A successful first benchmark experiment to study radiative capture via the Coulomb dissociation is 7 Be (p.γ ) [18–22]. The main interest behind this measurement was the socalled solar neutrino problem, which has now been resolved by considering neutrino flavor
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oscillations [24]. A large number of both direct and indirect measurements have been performed in the last 30 years. A critical assessment of all these measurements by Gai [23] showed that direct and indirect measurements (CD) are in good agreement. However, as pointed out by Bahcall et al. [24], a precise measurement of this reaction is necessary, which will reduce the uncertainty of solar neutrino flux to around 4.8%. Other than this reaction, a number of experiments were performed to study proton capture cross sections which are relevant to hot-pp mode nuclear burning in hydrogen rich massive objects through the CD of 9 C, 12 N, 13 O [25]. It is interesting to note that the astrophysical Sfactor of the 8 B(p, γ )9 C reaction at low energy is not in agreement with the ANC method. The proton capture reaction rate of the heavier system 22 Mg(p, γ ), which might play a role in the rp process, has been measured at RIKEN. Togano et al., [26] have studied the 26 Si(p, γ ) reaction through the CD of 27 P, and the result indicates a non-negligible effect of this reaction on nuclear burning in novae and X-ray bursts. 3.3. Radiative neutron capture cross-section of neutron-rich nuclei from CD So far, CD as an indirect method has been used for charged particle capture cross sections at low energy as far as relevant to astrophysical scenarios. This was proposed by Baur et al. [9]. But to establish the indirect measurement of neutron capture cross sections in astrophysical scenarios is more essential, because a neutron target is not available and short-lived unstable nuclei targets are also not possible. We have shown for the first time that the CD method is also very successful in measuring neutron capture cross sections. 14 C(n, γ ) is the only reaction where both direct and indirect measurements are available. Before discussing the result, a short presentation of the experimental setup and procedure is given. The secondary beams of neutronrich isotopes B, C and F at an energy of 400–600 MeV/A were produced by the fragmentation of an 40 Ar beam obtained from the SIS facility at GSI, Darmstadt. Secondary beams with a particular A/Z ratio were separated by the FRS and transferred to the secondary reaction target area where the LAND setup [27] was placed. The ions were identified on an event by event basis by means of energy loss and time-of-flight methods. In a secondary-secondary reaction, the projectile was excited and the decay neutron(s), which were kinematically forward focused, were detected by a large area neutron detector (LAND). Decay γ transitions of the fragment(s) were measured to identify the core excited states. The Coulomb dissociation cross section was measured using a Pb target. Breakup data were also taken for a Carbon target to determine the nuclear contributions, and an empty target was used for information on background reactions, which could take place in various detector materials. By measuring the momenta of all decay products of the projectile after inelastic scattering followed by breakup, the excitation energy of the nucleus was determined. The electromagnetic excitation in energetic (several hundred of MeV/nucleon) heavy ion collisions is dominated by dipole excitation. Hence, the non-resonant direct breakup dσ/dE ∗ cross section due to the Coulomb interaction can be expressed as X X dσ 16π 3 2 π ∗ = N (E ) C S(I , nl j) × |hq|(Z e/A)r Ym1 |ψnl j i|2 , E1 c dE ∗ 9h¯ c m nl j
(2)
ψnl j (E r ) represents the single-particle wave function of the valence neutron in the projectile ground state, and C 2 S(Icπ , nl j) its spectroscopic factor with respect to a particular core state (Iπc ). The final-state wave function hq| of the valence neutron in the continuum may be approximated by a plane wave or distorted waves. The distorted wave calculation was performed with an
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optical potential taken from systematics. Alternatively, an effective-range approach was used [28] to calculate the reduced transition probabilities (matrix elements). The single-particle wave functions have been derived from a Woods-Saxon potential. N E1 (E ∗ ) is the number of equivalent dipole photons of energy E ∗ . For details see [27,29,30]. The Coulomb dissociation data have been fitted with such direct breakup model calculations. From the fitted results, the values of the capture cross section can be obtained. 14 C(n, γ ) 15 C:
Beer et al. [31] measured this capture cross section directly with a 14 C target and a neutron beam. with a special interest in understanding the influence of this reaction in the nucleosynthesis of A > 14 in homogeneous big bang nucleosynthesis. Recently, Terasawa et al., [32] showed that with the inclusion of light neutron-rich nuclei (including this reaction) in the reaction network of the wind model of massive Type II supernova explosions, the r-process nuclei abundances are enhanced by an order of magnitude. Wiescher et al. pointed out the possibility of the role of this reaction in the break out of the neutron induced hot CNO cycle [33]. However, the direct measurement by Beer et al. [31] at neutron energy 23 keV was found to be a factor of five smaller than that obtained from direct capture model calculations. In contrast, as it was discussed above, the capture cross-section obtained from the CD (GSI) is in agreement with the calculations, and thus disagrees with direct measurements. In later from repeated measurements of the direct reaction [34,35], the capture cross section was found to be in agreement with the value of that obtained from the CD of 15 C [29,30]. Fig. 1 shows the capture cross-sections obtained from various calculations and the experimental data. It is very clear that the recent calculations of this capture cross section by Timofeyuk et al. [37] using the charge symmetry of mirror nuclei is in agreement with the re-analyzed direct measurement data [35] and that obtained from the Coulomb dissociation data of GSI [29,30], but this is not in agreement with the CD data of MSU [38]. The CD data of MSU are also not in agreement with the direct model calculation considering both the shape and absolute value of the capture cross section data with the neutron energy. It is interesting to note that in AGB stars [39], a relatively large amount of 14 C on the top of the layer of 13 C pocket exists, and 14 C(n, γ ) can act as neutron poison. However, inclusion of this reaction with the reaction rate obtained from the experimental data [30] in the model calculation of 3 solar mass [40] does not change the result of the earlier calculation [39]. But, it would be interesting to check the effects of this reaction in low metallicity stars. 15 C(n, γ ) 16 C:
As pointed out by Herndl et al. [41], neutron-rich C nuclei may play an important role in the stellar helium and carbon burning stages. There are a large number of theoretical calculations available [36,41,42] and their values vary in a wide range. Not only for astrophysical interest, but also to check the validation of theoretical calculations, experimental data are necessary. Fig. 2 shows the Coulomb dissociation spectra of 16 C, which break up into 15 C and neutron. The excited states’ contribution of 15 C and nuclear breakup has been subtracted. Fig. 2 shows that the CD data of this isotope are in good agreement with the direct model calculation using a valence neutron in the s orbital, and for the outgoing wave, a distorted wave approximation has been considered [30]. It is not in agreement with the plane wave calculation for the continuum state of the breakup neutron [30]. It was already noticed earlier that the CD of a deeply bound nucleus is not in agreement with direct breakup calculations using a plane wave for outgoing particles. Fig. 3 shows the reaction rate obtained from the CD experimental data for 14 C(n, γ ), and 15 C(n, γ ). The error is around 10%. Direct model calculations by Rauscher et al. [42] are shown as well. Clearly, a larger neutron capture reaction rate of 14 C than 15 C indicates the
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Fig. 1. Experimental data and theoretical values of σn,γ E−1/2 for the 14 C(n, γ ) reaction with variation of neutron energy. The dotted line represents the calculation by the microscopic cluster model [36]. The upper two shaded regions (filled with tilted straight lines) correspond to calculations based on charge symmetry of mirror nuclei [37]. The thick solid line within the lower shaded region was obtained from the direct breakup model calculation fitted to the experimental data of the CD of 15 C at GSI [29,27]. The shaded region around that line filled with vertical lines represents the error corresponding to that measurement. The square data points represent data of MSU [38] obtained from the CD and triangle, the circle and star marked data points were obtained from measurements of direct capture [31,34,35].
Fig. 2. Spectrum of Coulomb dissociation of 16 C (lead target) into 15 C and neutron [30]. Contributions from excited states in 15 C and from nuclear breakup (diffraction dissociation)contribution are subtracted. The dashed and dotdashed curves represent calculated CD with the direct breakup model where the valence neutron is in s and d orbitals, respectively and the outgoing particle is approximated as a plane wave.
dependence of direct capture on the asymptotic part of p wave neutron. For 15 C, the neutron separation energy (Sn = 1.2 MeV) is much lower than that (sn = 4.2 MeV) of 16 C. In a similar way, we [30] have also measured the capture cross section of 13 B(n, γ )14 B, 23 F(n, γ )24 F, which may influence the reaction network in the r-process nucleosynthesis calculation [32].
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Fig. 3. Reaction rates in variation with temperature (109 K). The thick solid line and thin solid line represent the reaction rates of neutron capture for (with 10% error) 14 C and 15 C, respectively, obtained from the CD data of GSI [30]. The thick and thin dashed lines represent the same, respectively, obtained from direct model calculations by Rauscher et al. [42].
3.4. Unbound nuclei, nuclei beyond the drip line The two neutron capture cross sections could play an important role in r-process nucleosynthesis. But the only possible way to get reliable experimental data is by using indirect approaches. Aumann et al. studied the Coulomb breakup of 6 He [43]. Fig. 4 shows the relative energy spectra of the α–n and n–n subsystems in the three body decay of 6 He after inelastic scattering on a Pb target. The lower panel of the figure shows the ratio of the measured two body relative energy distribution, and the simulated phase space distribution for α–n and n–n. From the excess cross section in α–n, a rough estimation of the photo absorption cross section of 6 He(γ , n)5 He was obtained, which is of the same order as that given by the theoretical calculations. 3.5. Present limitations of the CD method In the first part of this section, the discussion will be focused on the limitations of the indirect measurement by Coulomb dissociation. With the present experimental facilities at GSI, RIKEN, MSU, the energy resolution of the Coulomb breakup experiment above the particle threshold is around 150–200 keV, whereas as astrophysical scenarios often demand cross sections at an energy of few tens of keV. As another limitation, this method provides only partial information on σcap , namely information on radiative capture to the ground state only. Fortunately, most of the light nuclei after the capture reaction populate predominantly the ground state. So far, CD has been successful as an indirect measurement for radiative capture cross sections of light loosely bound nuclei, where E1 transitions are dominant and the nuclear contribution is around 10%. However, in some deeply bound nuclei, the E2 transition is dominant over E1, and in this case the nuclear contribution is predominant in the dissociation process. Therefore, it will be very difficult to disentangle the nuclear and Coulomb parts of the dissociation, and hence to extract capture cross sections. The higher-order effects in CD are important when projectile beam energy is slower (v c) i.e. the interaction time is larger. Then these effects are particularly important at low relative Energy, which is relevant in the astrophysical scenario. However, it
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Fig. 4. Top: spectra of relative energy between α and neutron (left) and between two neutrons (right), observed after the breakup of 6 He with a Pb-target. The solid line represents the calculated phase space distributions. The lower panels show the ratio between the measured α–n and n–n relative-energy spectra and the spectra simulated (histograms) according to standard phase-space distributions. Figure reprinted from [43]. c 1999, by the American Physical Society.
is difficult, if not impossible, to study these effects with the presently available experimental facilities. For deeply bound heavier nuclei, the density of states will be much higher, so CD will not give reliable results for direct capture cross-sections. In that scenario, the Hauser–Feshbach calculation will be applicable for capture cross sections. However, for loosely bound heavier nuclei where density of states is low, direct capture through CD will be applicable. It would be interesting to check the validity of this prediction. A more interesting situation is when the nuclei are neither very loosely bound nuclei nor deeply bound nuclei. For example, nuclei close to doubly magic 132 Sn region will be ideal to disentangle these two processes. It is interesting to note that the low-lying dipole strength of odd-A Sn isotopes (close to 132 Sn) is much greater than the direct breakup model calculation predicts [44]. 4. Conclusion The main aim of this review was to offer a flavor of the indirect measurement of capture cross sections, with special attention to the Coulomb dissociation of unstable nuclei at intermediate
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energies. These methods are particularly useful for very loosely bound nuclei with very short half lives, and for unbound nuclei beyond the drip line. This indirect method is especially important for neutron-rich nuclei because of the non-availability of a neutron target. When a nuclear reaction plays a crucial role in cosmic phenomena and accurate reaction cross sections are needed, then it is very important to measure it utilizing various methods, both the direct and indirect way, if possible, keeping in mind the limitations of all these methods. In this way, the systematic errors of the methods will be different. As we can see in the case of the 14 C(n, γ ) 15 C, the capture cross section measured by the direct method improved the results from 1.1µb to 7.1µb (at neutron energy 23 keV) after comparing them with the results from the indirect method through CD. Coulomb dissociation as an indirect method for measurements of capture cross sections is opening up a new channel, with upcoming facilities such as FAIR, RIA, RIKEN, now available to explore cosmological phenomena in an exclusive way. However, to establish this method in a more general and fruitful way, a more detailed theoretical and experimental investigation is necessary, spanning over a wide range of nuclear masses. Acknowledgments I am grateful to H. Emling, T. Aumann, S. Bhattacharya, G. Baur, G. Muenzenberg, C. Rolf, B.M. Sherrill, K. Suemmerer for stimulating discussions, as well as to Stefan Typel for providing theoretical calculations, and to my S188 LAND-FRS-CB collaborators for the experimental studies which have been presented here. I am indebted to the Alexander von Humboldt (AvH) foundation for financial support during my stay at GSI. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
K.A. Snover, Annu. Rev. Nucl. Part. Sci. 36 (1986) 545. B. Lauss, et al., arXiv:nucl-ex/0601004 v1. E.M. Burbidge, G.R. Burbidge, W.A. Fowler, F. Hoyle, Rev. Modern Phys. 29 (1957) 547. C. Rolf, Annu. Rev. Nucl. Part. Sci. 40 (1992) 45. M.S. Smith, K.E. Rehm, Annu. Rev. Nucl. Part. Sci. 51 (2001) 91. M. Wiescher, H. Shartz, Nucl. Phys. A 693 (2001) 269. B.M. Sherrill, Nucl. Phys. A 751 (2005) 494c. F. Kappeler, Nucl. Phys. A 752 (2005) 500c. G. Baur, C.A. Bertulani, H. Rebel, Nucl. Phys. A 458 (1986) 188. G. Baur, K. Henchen, D. Trautmann, Prog. Part. Nucl. Phys. 51 (2003) 487. H.M. Xu, et al., Phys. Rev. Lett. 73 (1994) 2027. A.M. Mukhamedzhanov, et al., Euro. Phys. J. A 27 (2006) 205. G. Baur, Phys. Lett. B 178 (1986) 135. C. Spitaleri, et al., Phys. Rev. C 69 (2004) 055806. W. Younes W, H.C. Britt, Phys. Rev. C 67 (2003) 024610. J. Escher, et al., J. Phys. G 31 (2005) s1687. E. Fermi, Z. Phys. A 29 (1924) 315. T. Motobayashi, et al., Phys. Rev. Lett. 73 (1994) 2680. B. Davids, et al., Phys. Rev. Lett. 86 (2001) 2750. B. Davids, et al., Phys. Rev. C 63 (2003) 065806. F. Schuemann, et al., Phys. Rev. Lett. 90 (2003) 232501. F. Schuemann, et al., PRC 73 (2006) 015806. M. Gai, Phys. Rev. C 74 (2006) 025810. J.N. Bahcall, C. Pena-Garay, New J. Phys. 6 (2004) 63. T. Motobayashi, Nucl. Phys. A 734 (2004) 623. Y. Togano, et al., Euro. Phys. J. A 27 (2006) 233. U. Datta Pramanik, et al., Phys. Lett. B 551 (2003) 63.
192 [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]
U. Datta Pramanik/ Progress in Particle and Nuclear Physics 59 (2007) 183–192 S. Typel, G. Baur, Phys. Rev. Lett. 93 (2004) 142502. U Datta Pramanik, et al., Prog. Theor. Phys. Suppl. 146 (2002) 427. U. Datta Pramanik, et al.. Manuscript under preparation. H. Beer, et al., Astro. Phys. J. 387 (1992) 258. M. Terasawa, et al., Astro. Phys. J. 562 (2001) 470. M. Wiescher, et al., J. Phys. G 25 (1999) R133. R. Reifarth, et al., Nucl. Phys. A 758 (2005) 787c. R. Reifarth, et al. (in press). P. Descouvemont, Nucl. Phys. A 675 (2000) 559. N.K. Timofeyuk, et al., Phys. Rev. Lett. 96 (2006) 162501. A. Horvath, et al., Astro. Phys. J. 570 (2002) 926. M. Lugaro, et al., Astro. Phys. J. 586 (2003) 1305. M. Lugaro. Private communication. H. Herndl, et al., Phys. Rev. C 60 (1999) 064614. T. Rauscher, et al., Astro. Phys. J. 429 (1994) 499. T. Aumann, et al., Phys. Rev. C 59 (1999) 1252. A. Klimkiewicz, Ph.D. Thesis (to be submitted).
Review
Indirect measurement of radiative capture cross sections relevant in astrophysical scenarios Ushasi Datta Pramanik ∗ Saha Institute of Nuclear Physics (SINP), Kolkata, India Gesellschaft f¨ur Schwerionenforschung (GSI), Darmstadt, Germany
Abstract Radiative capture cross sections play a significant role in many cosmic phenomena, e.g. galactic evolution, star formation and planet formation etc. In explosive stellar burning scenarios, a large number of unstable nuclei play a crucial role, and reliable reaction cross sections are necessary for astrophysical model calculations, which will help in turn to understand the phenomena. A number of indirect methods are being explored by experimental nuclear physicists to avoid radioactive targets and other difficulties of direct measurements of radiative capture cross sections. The Coulomb dissociation of radioactive ion beams at intermediate energy is one of the most powerful indirect methods for measuring capture cross sections, and is being explored at various laboratories in the world. Here, a brief current status report is presented. This indirect method has a number of advantages compared to direct measurements, but there are also a number of limitations to this method with the presently available experimental facilities. A discussion on these aspects is given, together with an outlook on future experimental prospects. c 2007 Elsevier B.V. All rights reserved.
1. Introduction Nuclear radiative capture reactions, in which the incident projectile is absorbed by a target nucleus followed by γ -ray emissions, are important in various branches of fundamental as well as applied physics. A wide range of nuclear properties, such as spectroscopic properties, collective band structure, and various modes of nuclear motions [1] have been extensively ∗ Corresponding address: Saha Institute of Nuclear Physics (SINP), Kolkata, India. Tel.: +91 33 23375346 49; fax: +91 33 23374637. E-mail address: [email protected].
c 2007 Elsevier B.V. All rights reserved. 0146-6410/$ - see front matter doi:10.1016/j.ppnp.2006.12.005
184
U. Datta Pramanik/ Progress in Particle and Nuclear Physics 59 (2007) 183–192
studied with these types of reactions. Polarized cold neutron capture on protons is used for a precision measurement of the parity violation asymmetry [2]. Besides this, the radiative capture of α, p, n, and d by nuclei at very low relative energies plays an important role in understanding the nucleosynthesis as well as the chemical evolution of stars and planets, and the relative abundances in stellar burning processes in various astrophysical sites [3–8]. Astrophysical models on these cosmological phenomena require the rate and energy released by the relevant nuclear reactions as critical inputs, in addition to a good understanding of the underlying hydrodynamics, radiation transfer and other aspects of stellar evolution. Nuclear models play a central role in providing the information needed for astrophysical calculations. But often, depending upon the mass region with different neutron to proton ratios, and hence different effective nucleon–nucleon interactions, the results of these calculations vary by a factor of 23 or more. Therefore, reliable experimental data are essential. Until recently, the only reliable method was to measure them in the laboratory directly with a low energy beam and eventually extrapolate the results down to astrophysical energies. The principal difficulty of measuring radiative capture cross sections directly arises due to a very low cross section (∼µb, pb, nb). The cross section is small because the electromagnetic force is weak compared to the nuclear force. The decay of unbound nuclear states by the emission of a particle is 103 –106 times more probable than its decay via γ -ray emission. Moreover, due to a very low-energy beam, the target must be thin considering the energy loss of the projectile. In addition to that, in a large number of astrophysical sites, such as nova explosions, explosive supernovae (core collapse), solar fusion, explosive hydrogen burning, and the r-process (see Table 1), where the temperature is high enough (>108 K), the interaction time can be so short (∼ seconds) that the unstable nuclei formed in the reaction can undergo subsequent nuclear processes before they decay to stable nuclei. In these scenarios, a study of the capture cross sections of unstable nuclei, using radioactive targets would be necessary. Particularly, direct measurements of neutron capture cross sections of unstable nuclei with a very short life time is practically impossible. In order to overcome all these limitations, various indirect measurements are being explored in the recent years at various laboratories in the USA, Europe and Asia. These indirect measurements use the Coulomb Dissociation method [9,10], the ANC method (Asymptotic normalization coefficient) [11,12], the Trojan–Horse method [13,14], and the Surrogate Nuclear reaction method [15,16]. In the following subsection, a brief introduction to these methods will be presented. Finally, a review of indirect measurements at different laboratories through the Coulomb dissociation will be presented, with a focus on their advantages and limitations. 2. Indirect methods for measurements of radiative capture cross sections A. The ANC has been explored for low energy radiative capture reactions A(a, γ )B, which are dominated by processes occurring well outside the nuclear radii. The cross section of such a reaction depends on the asymptotic behavior of the overlap function for B → A + a, which can be determined via a peripheral transfer reaction [11,12]. B. The Trojan–Horse method provides a mechanism which eliminates the problem of the Coulomb barrier for low energy the two body charge particle reaction cross section A(a,b)B. It can be done by selecting a reaction d + A → b + B + c with d = a + c, and c can be considered a spectator in the reaction between A and a (‘quasi-free scattering’). Hence, from the reaction cross section of three body reaction, one can link to the reaction cross section of the two-body reaction of interest [13,14].
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U. Datta Pramanik/ Progress in Particle and Nuclear Physics 59 (2007) 183–192 Table 1 Explosive nucleosynthesis in supernovae Fuel
Main product
Secondary product
T(109 ) K
Time (s)
Main reaction
Inner most ejecta Si, O O, Ne
r-process
–
>10
1
(n, γ ), β −
56 Ni
Iron-gr Na, Al, P p-process
>4 2-3
0.1 5 5
(α, γ ) (γ , α) (γ , n)
O, Ne, Mg
C. The Surrogate Nuclear reaction technique is an indirect method (a + A → B∗ → c + C) which combines experiment with reaction theory to obtain ‘desired’ reaction cross sections that proceeds through a compound nuclear state B∗ [15,16]. D. The Coulomb dissociation method is the main topic of the present Review, which will be presented in the following subsection: 3. Coulomb dissociation (CD) of unstable nuclei at intermediate energy and capture cross sections When a projectile (A) moving with high velocity passes a target of high nuclear charge Z , it may be excited by absorbing virtual photons from the time-dependent Coulomb field [17,9]. The projectile may be excited to its unbound state and decay into core (B) and particle (x i,e n dσ or p or α etc.). This Coulomb dissociation cross section dE ∗ is related to the photo dissociation cross section σ (γ , x), which in turn is related to the inverse reaction σ (x, γ ) via the principle of detailed balance [9]. σ (x, γ ) = where kγ2 =
Eγ h¯ c
kγ2 2(2 j A + 1) σ (γ , x) (2J B + 1)(2J X + 1) k 2
, k2 =
(1)
2µ Bx E c.m. . h¯ 2
3.1. Advantages of this method Intermediate-energy beams of unstable nuclei will solve the problem of radioactive targets. Since the beam’s energy is high enough; moreover, one can use thick targets, which provide more yield. The CD cross section is by orders of magnitude larger than the capture cross section, due to the phase space factor. In addition to that, the CD data obtained from one particular projectile energy provide capture cross sections in center of mass energy i.e, up to 5–20 MeV depending on the adiabacity cutoff. Since the decay products are kinematically forward focused, small-size detectors cover a large solid angle of the reaction product. At the high beam energies, the reaction’s mechanism can be approximated as a sudden process. With this indirect method, one can thus measure capture cross sections of unbound nuclei which will not be accessible with the direct method. 3.2. Radiative proton capture reactions from Coulomb dissociation A successful first benchmark experiment to study radiative capture via the Coulomb dissociation is 7 Be (p.γ ) [18–22]. The main interest behind this measurement was the socalled solar neutrino problem, which has now been resolved by considering neutrino flavor
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oscillations [24]. A large number of both direct and indirect measurements have been performed in the last 30 years. A critical assessment of all these measurements by Gai [23] showed that direct and indirect measurements (CD) are in good agreement. However, as pointed out by Bahcall et al. [24], a precise measurement of this reaction is necessary, which will reduce the uncertainty of solar neutrino flux to around 4.8%. Other than this reaction, a number of experiments were performed to study proton capture cross sections which are relevant to hot-pp mode nuclear burning in hydrogen rich massive objects through the CD of 9 C, 12 N, 13 O [25]. It is interesting to note that the astrophysical Sfactor of the 8 B(p, γ )9 C reaction at low energy is not in agreement with the ANC method. The proton capture reaction rate of the heavier system 22 Mg(p, γ ), which might play a role in the rp process, has been measured at RIKEN. Togano et al., [26] have studied the 26 Si(p, γ ) reaction through the CD of 27 P, and the result indicates a non-negligible effect of this reaction on nuclear burning in novae and X-ray bursts. 3.3. Radiative neutron capture cross-section of neutron-rich nuclei from CD So far, CD as an indirect method has been used for charged particle capture cross sections at low energy as far as relevant to astrophysical scenarios. This was proposed by Baur et al. [9]. But to establish the indirect measurement of neutron capture cross sections in astrophysical scenarios is more essential, because a neutron target is not available and short-lived unstable nuclei targets are also not possible. We have shown for the first time that the CD method is also very successful in measuring neutron capture cross sections. 14 C(n, γ ) is the only reaction where both direct and indirect measurements are available. Before discussing the result, a short presentation of the experimental setup and procedure is given. The secondary beams of neutronrich isotopes B, C and F at an energy of 400–600 MeV/A were produced by the fragmentation of an 40 Ar beam obtained from the SIS facility at GSI, Darmstadt. Secondary beams with a particular A/Z ratio were separated by the FRS and transferred to the secondary reaction target area where the LAND setup [27] was placed. The ions were identified on an event by event basis by means of energy loss and time-of-flight methods. In a secondary-secondary reaction, the projectile was excited and the decay neutron(s), which were kinematically forward focused, were detected by a large area neutron detector (LAND). Decay γ transitions of the fragment(s) were measured to identify the core excited states. The Coulomb dissociation cross section was measured using a Pb target. Breakup data were also taken for a Carbon target to determine the nuclear contributions, and an empty target was used for information on background reactions, which could take place in various detector materials. By measuring the momenta of all decay products of the projectile after inelastic scattering followed by breakup, the excitation energy of the nucleus was determined. The electromagnetic excitation in energetic (several hundred of MeV/nucleon) heavy ion collisions is dominated by dipole excitation. Hence, the non-resonant direct breakup dσ/dE ∗ cross section due to the Coulomb interaction can be expressed as X X dσ 16π 3 2 π ∗ = N (E ) C S(I , nl j) × |hq|(Z e/A)r Ym1 |ψnl j i|2 , E1 c dE ∗ 9h¯ c m nl j
(2)
ψnl j (E r ) represents the single-particle wave function of the valence neutron in the projectile ground state, and C 2 S(Icπ , nl j) its spectroscopic factor with respect to a particular core state (Iπc ). The final-state wave function hq| of the valence neutron in the continuum may be approximated by a plane wave or distorted waves. The distorted wave calculation was performed with an
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optical potential taken from systematics. Alternatively, an effective-range approach was used [28] to calculate the reduced transition probabilities (matrix elements). The single-particle wave functions have been derived from a Woods-Saxon potential. N E1 (E ∗ ) is the number of equivalent dipole photons of energy E ∗ . For details see [27,29,30]. The Coulomb dissociation data have been fitted with such direct breakup model calculations. From the fitted results, the values of the capture cross section can be obtained. 14 C(n, γ ) 15 C:
Beer et al. [31] measured this capture cross section directly with a 14 C target and a neutron beam. with a special interest in understanding the influence of this reaction in the nucleosynthesis of A > 14 in homogeneous big bang nucleosynthesis. Recently, Terasawa et al., [32] showed that with the inclusion of light neutron-rich nuclei (including this reaction) in the reaction network of the wind model of massive Type II supernova explosions, the r-process nuclei abundances are enhanced by an order of magnitude. Wiescher et al. pointed out the possibility of the role of this reaction in the break out of the neutron induced hot CNO cycle [33]. However, the direct measurement by Beer et al. [31] at neutron energy 23 keV was found to be a factor of five smaller than that obtained from direct capture model calculations. In contrast, as it was discussed above, the capture cross-section obtained from the CD (GSI) is in agreement with the calculations, and thus disagrees with direct measurements. In later from repeated measurements of the direct reaction [34,35], the capture cross section was found to be in agreement with the value of that obtained from the CD of 15 C [29,30]. Fig. 1 shows the capture cross-sections obtained from various calculations and the experimental data. It is very clear that the recent calculations of this capture cross section by Timofeyuk et al. [37] using the charge symmetry of mirror nuclei is in agreement with the re-analyzed direct measurement data [35] and that obtained from the Coulomb dissociation data of GSI [29,30], but this is not in agreement with the CD data of MSU [38]. The CD data of MSU are also not in agreement with the direct model calculation considering both the shape and absolute value of the capture cross section data with the neutron energy. It is interesting to note that in AGB stars [39], a relatively large amount of 14 C on the top of the layer of 13 C pocket exists, and 14 C(n, γ ) can act as neutron poison. However, inclusion of this reaction with the reaction rate obtained from the experimental data [30] in the model calculation of 3 solar mass [40] does not change the result of the earlier calculation [39]. But, it would be interesting to check the effects of this reaction in low metallicity stars. 15 C(n, γ ) 16 C:
As pointed out by Herndl et al. [41], neutron-rich C nuclei may play an important role in the stellar helium and carbon burning stages. There are a large number of theoretical calculations available [36,41,42] and their values vary in a wide range. Not only for astrophysical interest, but also to check the validation of theoretical calculations, experimental data are necessary. Fig. 2 shows the Coulomb dissociation spectra of 16 C, which break up into 15 C and neutron. The excited states’ contribution of 15 C and nuclear breakup has been subtracted. Fig. 2 shows that the CD data of this isotope are in good agreement with the direct model calculation using a valence neutron in the s orbital, and for the outgoing wave, a distorted wave approximation has been considered [30]. It is not in agreement with the plane wave calculation for the continuum state of the breakup neutron [30]. It was already noticed earlier that the CD of a deeply bound nucleus is not in agreement with direct breakup calculations using a plane wave for outgoing particles. Fig. 3 shows the reaction rate obtained from the CD experimental data for 14 C(n, γ ), and 15 C(n, γ ). The error is around 10%. Direct model calculations by Rauscher et al. [42] are shown as well. Clearly, a larger neutron capture reaction rate of 14 C than 15 C indicates the
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Fig. 1. Experimental data and theoretical values of σn,γ E−1/2 for the 14 C(n, γ ) reaction with variation of neutron energy. The dotted line represents the calculation by the microscopic cluster model [36]. The upper two shaded regions (filled with tilted straight lines) correspond to calculations based on charge symmetry of mirror nuclei [37]. The thick solid line within the lower shaded region was obtained from the direct breakup model calculation fitted to the experimental data of the CD of 15 C at GSI [29,27]. The shaded region around that line filled with vertical lines represents the error corresponding to that measurement. The square data points represent data of MSU [38] obtained from the CD and triangle, the circle and star marked data points were obtained from measurements of direct capture [31,34,35].
Fig. 2. Spectrum of Coulomb dissociation of 16 C (lead target) into 15 C and neutron [30]. Contributions from excited states in 15 C and from nuclear breakup (diffraction dissociation)contribution are subtracted. The dashed and dotdashed curves represent calculated CD with the direct breakup model where the valence neutron is in s and d orbitals, respectively and the outgoing particle is approximated as a plane wave.
dependence of direct capture on the asymptotic part of p wave neutron. For 15 C, the neutron separation energy (Sn = 1.2 MeV) is much lower than that (sn = 4.2 MeV) of 16 C. In a similar way, we [30] have also measured the capture cross section of 13 B(n, γ )14 B, 23 F(n, γ )24 F, which may influence the reaction network in the r-process nucleosynthesis calculation [32].
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Fig. 3. Reaction rates in variation with temperature (109 K). The thick solid line and thin solid line represent the reaction rates of neutron capture for (with 10% error) 14 C and 15 C, respectively, obtained from the CD data of GSI [30]. The thick and thin dashed lines represent the same, respectively, obtained from direct model calculations by Rauscher et al. [42].
3.4. Unbound nuclei, nuclei beyond the drip line The two neutron capture cross sections could play an important role in r-process nucleosynthesis. But the only possible way to get reliable experimental data is by using indirect approaches. Aumann et al. studied the Coulomb breakup of 6 He [43]. Fig. 4 shows the relative energy spectra of the α–n and n–n subsystems in the three body decay of 6 He after inelastic scattering on a Pb target. The lower panel of the figure shows the ratio of the measured two body relative energy distribution, and the simulated phase space distribution for α–n and n–n. From the excess cross section in α–n, a rough estimation of the photo absorption cross section of 6 He(γ , n)5 He was obtained, which is of the same order as that given by the theoretical calculations. 3.5. Present limitations of the CD method In the first part of this section, the discussion will be focused on the limitations of the indirect measurement by Coulomb dissociation. With the present experimental facilities at GSI, RIKEN, MSU, the energy resolution of the Coulomb breakup experiment above the particle threshold is around 150–200 keV, whereas as astrophysical scenarios often demand cross sections at an energy of few tens of keV. As another limitation, this method provides only partial information on σcap , namely information on radiative capture to the ground state only. Fortunately, most of the light nuclei after the capture reaction populate predominantly the ground state. So far, CD has been successful as an indirect measurement for radiative capture cross sections of light loosely bound nuclei, where E1 transitions are dominant and the nuclear contribution is around 10%. However, in some deeply bound nuclei, the E2 transition is dominant over E1, and in this case the nuclear contribution is predominant in the dissociation process. Therefore, it will be very difficult to disentangle the nuclear and Coulomb parts of the dissociation, and hence to extract capture cross sections. The higher-order effects in CD are important when projectile beam energy is slower (v c) i.e. the interaction time is larger. Then these effects are particularly important at low relative Energy, which is relevant in the astrophysical scenario. However, it
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Fig. 4. Top: spectra of relative energy between α and neutron (left) and between two neutrons (right), observed after the breakup of 6 He with a Pb-target. The solid line represents the calculated phase space distributions. The lower panels show the ratio between the measured α–n and n–n relative-energy spectra and the spectra simulated (histograms) according to standard phase-space distributions. Figure reprinted from [43]. c 1999, by the American Physical Society.
is difficult, if not impossible, to study these effects with the presently available experimental facilities. For deeply bound heavier nuclei, the density of states will be much higher, so CD will not give reliable results for direct capture cross-sections. In that scenario, the Hauser–Feshbach calculation will be applicable for capture cross sections. However, for loosely bound heavier nuclei where density of states is low, direct capture through CD will be applicable. It would be interesting to check the validity of this prediction. A more interesting situation is when the nuclei are neither very loosely bound nuclei nor deeply bound nuclei. For example, nuclei close to doubly magic 132 Sn region will be ideal to disentangle these two processes. It is interesting to note that the low-lying dipole strength of odd-A Sn isotopes (close to 132 Sn) is much greater than the direct breakup model calculation predicts [44]. 4. Conclusion The main aim of this review was to offer a flavor of the indirect measurement of capture cross sections, with special attention to the Coulomb dissociation of unstable nuclei at intermediate
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energies. These methods are particularly useful for very loosely bound nuclei with very short half lives, and for unbound nuclei beyond the drip line. This indirect method is especially important for neutron-rich nuclei because of the non-availability of a neutron target. When a nuclear reaction plays a crucial role in cosmic phenomena and accurate reaction cross sections are needed, then it is very important to measure it utilizing various methods, both the direct and indirect way, if possible, keeping in mind the limitations of all these methods. In this way, the systematic errors of the methods will be different. As we can see in the case of the 14 C(n, γ ) 15 C, the capture cross section measured by the direct method improved the results from 1.1µb to 7.1µb (at neutron energy 23 keV) after comparing them with the results from the indirect method through CD. Coulomb dissociation as an indirect method for measurements of capture cross sections is opening up a new channel, with upcoming facilities such as FAIR, RIA, RIKEN, now available to explore cosmological phenomena in an exclusive way. However, to establish this method in a more general and fruitful way, a more detailed theoretical and experimental investigation is necessary, spanning over a wide range of nuclear masses. Acknowledgments I am grateful to H. Emling, T. Aumann, S. Bhattacharya, G. Baur, G. Muenzenberg, C. Rolf, B.M. Sherrill, K. Suemmerer for stimulating discussions, as well as to Stefan Typel for providing theoretical calculations, and to my S188 LAND-FRS-CB collaborators for the experimental studies which have been presented here. I am indebted to the Alexander von Humboldt (AvH) foundation for financial support during my stay at GSI. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
K.A. Snover, Annu. Rev. Nucl. Part. Sci. 36 (1986) 545. B. Lauss, et al., arXiv:nucl-ex/0601004 v1. E.M. Burbidge, G.R. Burbidge, W.A. Fowler, F. Hoyle, Rev. Modern Phys. 29 (1957) 547. C. Rolf, Annu. Rev. Nucl. Part. Sci. 40 (1992) 45. M.S. Smith, K.E. Rehm, Annu. Rev. Nucl. Part. Sci. 51 (2001) 91. M. Wiescher, H. Shartz, Nucl. Phys. A 693 (2001) 269. B.M. Sherrill, Nucl. Phys. A 751 (2005) 494c. F. Kappeler, Nucl. Phys. A 752 (2005) 500c. G. Baur, C.A. Bertulani, H. Rebel, Nucl. Phys. A 458 (1986) 188. G. Baur, K. Henchen, D. Trautmann, Prog. Part. Nucl. Phys. 51 (2003) 487. H.M. Xu, et al., Phys. Rev. Lett. 73 (1994) 2027. A.M. Mukhamedzhanov, et al., Euro. Phys. J. A 27 (2006) 205. G. Baur, Phys. Lett. B 178 (1986) 135. C. Spitaleri, et al., Phys. Rev. C 69 (2004) 055806. W. Younes W, H.C. Britt, Phys. Rev. C 67 (2003) 024610. J. Escher, et al., J. Phys. G 31 (2005) s1687. E. Fermi, Z. Phys. A 29 (1924) 315. T. Motobayashi, et al., Phys. Rev. Lett. 73 (1994) 2680. B. Davids, et al., Phys. Rev. Lett. 86 (2001) 2750. B. Davids, et al., Phys. Rev. C 63 (2003) 065806. F. Schuemann, et al., Phys. Rev. Lett. 90 (2003) 232501. F. Schuemann, et al., PRC 73 (2006) 015806. M. Gai, Phys. Rev. C 74 (2006) 025810. J.N. Bahcall, C. Pena-Garay, New J. Phys. 6 (2004) 63. T. Motobayashi, Nucl. Phys. A 734 (2004) 623. Y. Togano, et al., Euro. Phys. J. A 27 (2006) 233. U. Datta Pramanik, et al., Phys. Lett. B 551 (2003) 63.
192 [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44]
U. Datta Pramanik/ Progress in Particle and Nuclear Physics 59 (2007) 183–192 S. Typel, G. Baur, Phys. Rev. Lett. 93 (2004) 142502. U Datta Pramanik, et al., Prog. Theor. Phys. Suppl. 146 (2002) 427. U. Datta Pramanik, et al.. Manuscript under preparation. H. Beer, et al., Astro. Phys. J. 387 (1992) 258. M. Terasawa, et al., Astro. Phys. J. 562 (2001) 470. M. Wiescher, et al., J. Phys. G 25 (1999) R133. R. Reifarth, et al., Nucl. Phys. A 758 (2005) 787c. R. Reifarth, et al. (in press). P. Descouvemont, Nucl. Phys. A 675 (2000) 559. N.K. Timofeyuk, et al., Phys. Rev. Lett. 96 (2006) 162501. A. Horvath, et al., Astro. Phys. J. 570 (2002) 926. M. Lugaro, et al., Astro. Phys. J. 586 (2003) 1305. M. Lugaro. Private communication. H. Herndl, et al., Phys. Rev. C 60 (1999) 064614. T. Rauscher, et al., Astro. Phys. J. 429 (1994) 499. T. Aumann, et al., Phys. Rev. C 59 (1999) 1252. A. Klimkiewicz, Ph.D. Thesis (to be submitted).