Astrophysical S-factors for the p+16O and n+16O captures from the analysis of 16O(d,n)17F and 16O(d,p)17O transfer reactions

AIP Conference Proceedings 884, 158 (2007); https://doi.org/10.1063/1.2710573 884, 158 © 2007 American Institute of Physics. Astrophysical S-factors for the p+16O and n+16O captures from the analysis of 16O(d,n)17F and 16O(d,p)17O transfer reactions Cite as: AIP Conference Proceedings 884, 158 (2007); https:// doi.org/10.1063/1.2710573 Published Online: 22 February 2007 M. Assunção, R. Lichtenthäler, V. Guimarães, A. Lépine-Szily, and A. M. Moro ARTICLES YOU MAY BE INTERESTED IN Light radioactive nuclei capture reactions with phenomenological potential models AIP Conference Proceedings 1245, 30 (2010); https:// doi.org/10.1063/1.3448012 Astrophysical S-factors for the p+16 Oand n+16 Ocaptures from the analysis of 16O(d,n)17F and 16O(d,p)17Otransfer reactions M. Assunção∗, R. Lichtenthäler∗, V. Guimarães∗, A. Lépine-Szily∗and A. M. Moro† ∗Departamento de Física Nuclear, Instituto de Física da Universidade de São Paulo, CP 66318, 05315-970 São Paulo SP, Brazil. †Departamento de Física, Instituto Superior Técnico, Taguspark, 2780-990 Porto Salvo, Portugal and Departamento de FAMN, Universidad de Sevilla, Apdo. 1065, E-41080 Sevilla, Spain. Abstract. Coupled reaction channels calculations were performed for the 16O(d,n)17Fand 16O(d,p)17Otransfer reactions for the ground and first excited states at several energies from Elab=2.29 MeV up to 3.27 MeV. A strong polarization effect between the entrance channel and the transfer, 16O(d,n)17F(1/2+,0.495) and 16O(d,n)17O(1/2+,0.87), channels was observed. This polarization effect had to be taken into account to all orders for obtainingrealistic spectroscopic factors from these reactions. The 16O(p, γ )17Fand 16O(n, γ )17Odirect captures were calculated using the Asymptotic Normalization Coefficients (ANC) values from these transfer reactions analysis. The astrophysical S-factors were compared to measurements. The Maxwellian-averaged neutron capture cross section at kT=30 keV was 22(3) μ barn. Keywords: direct reaction, coupled-channel, distorted-wave model, capture cross section, astrophysical S-factor PACS: 24.10.Eq, 24.50.+g, 25.70.-z, 25.45.-z INTRODUCTION The interest in the experimental and theoretical study of few nucleon transfer reactions has been renewed in the last years mainly due to the possibility of obtaining astrophysical relevant information from these reactions [1, 2, 3, 4, 5]. The direct measurements of capture reactions at energies of astrophysical interest are, in some cases, nearly impossible due to low reaction yield, especialy if the capture involves exotic nuclei. Alternative indirect methods such as the asymptotic normalization coefficient (ANC) method, based on the analysis of breakup [6] or transfer reaction [1] have been used as a tool for obtaining astrophysical S-factors. The advantage of the indirect approach comes from the fact that the transfer and breakup reactions can be measured at higher energies, where the cross sections are much larger. However, in order to obtain useful information from transfer reactions one needs to understand, as clear as possible, the reaction mechanism therein involved. In this paper, we investigate the importance of considering the CRC (coupled reaction channel) calculation in the analysis of the 16O(d,n)17Fand 16O(d,p)17Otransfer reactions, at incident deuteron energies from Ed=2.279 MeV to Ed=3.155 MeV, for which experimental data exist [7]. By performing CRC calculations and comparing to DWBA 158 CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER CP884, VI Latin American Symposium on Nuclear Physics and Applications, edited by O. Civitarese, C. Dorso, G. García Bermúdez, A. J. Kreiner, A. J. Pacheco, and N. N. Scoccola © 2007 American Institute of Physics 978-0-7354-0388-8/07/$23.00 (distorted wave Born approximation) and CCBA (coupled channel Born approximation) results, we show that if realistic spectroscopic information is to be obtained from these reactions one hasto go beyond the Born approximation.We use the spectroscopic factors obtained from a full CRC calculation to evaluate the p+16 Oand n+16 Ocapture cross sections. In particular, the large 16O(n, γ )17Ocross section obtained has implications for nucleosyntesis theories, especially in metal-defficient massivestars as an important neutron poison [8]. DWBA AND CCBA ANALYSIS Firstly, the transfer reactions were analyzed in terms of the DWBA approach. The distorting potential for the entrance channel was considered as a variation of the Satchler parametrization [9] slightly modified to improve the fit to the d+16 Oangular distribution. The optical potentials in the exit channels were obtained from parametrization of Rosen [10]. These potentials are listed in Table 1 and the spin-orbit contributions are VS0=6.0 MeV, rS0=1.4 fm and aS0=0.7 fm for the d+16O system. Both n+17F and p+17O systems have been considered the values ofVS0=5.5 MeV, rS0=1.25 fm and aS0=0.65 fm. TABLE 1. Optical potential parameters used in DWBA and CCBA analysis. System V0r0a0Wdriai (MeV) (fm) (fm) (MeV) (fm) (fm) d+16O 110.0 1.012 0.876 9.3 1.837 0.356 n+17F -49.3+0.33Ec.m.1.25 0.65 5.75 1.25 0.70 p+17O -53.8+0.33Ec.m.1.25 0.65 7.5 1.25 0.70 Set(CRC) 104 1.25 0.65 24.9 1.25 0.233 The DWBA calculation is in good agreement with the ground state for (d,n0)and (d,p0)reactions at forward angles, while a clear overestimation for the first excited state for (d,n1)and (d,p1)is observed in lower pannels of Figure 1.(a) and 1.(b). In these cases, the spectroscopic factor of about 0.6 would be required to fit the data what is not consistent with the single-particle character expected for the 17Fand 17Onuclei. In all calculations, a compound nucleus contributionsobtained by Dietzch et al. [7] were subtracted from experimental data. One of the main sources of ambiguity in the DWBA calculations presented above is the optical potential for the exit channels (n+17 For p+17 O) for which no experimental data exists. In the former case, the weakly bound nature of the 17F(1/2+,0.495) stateproduces a longtailin thebound statewave function, making the system more diffuse than the ground state. Therefore, the different character of these two states might cast doubt on the validity of the global parametrization [10] usedto describe then+17F∗elasticscattering.In addition, couplings between theground and excited states of 17Fare neglected in the DWBA calculations. These effects can be properly taken into account by using the CCBA formalism. By performing the CCBA calculations, we noted that the results are very similar to the DWBA results, indicating that the final state interaction arising from target excitation plays a negligible role in this reaction [11]. 159 CRC CALCULATIONS Previous section has shown that both DWBA and CCBA calculations do not quite reproduce the transfer cross section for the 16O(d,n)17F∗and 16O(d,p)17O∗reactions, unless unreasonably small spectroscopic factors are used for the 17F∗|16Oand 17O∗|16O overlaping wave functions. The accuracy of both, the DWBA and CCBA approaches, rely on the validity of the Born approximation. In the CRC approach, the optical potentialsfor the entrance and exit channels couldbe understood as bare potentials. Once the transfer couplings are set in both directions, the bare potentials is defined as to reproduce the elastic scattering of the respective channel. We used the search version SFRESCO [12] code to determine the bare potential in the entrance channel by varying V0,Wd,aiand the spectrosopic amplitude in order to fit simultaneously the elastic (d+16 O)data and transfer channels at 2.85 MeV. The obtained values of V0,Wdand aiare listed in the Table 1. The optical potentials in the exit channels were kept fixed to the Rosen parametrization. The best fit for Set(CRC) is listed in Table 1. Results using this set of parameters, are presented in Figure 1.(a), 1.(b) and 1.(c). For comparison purposes,The DWBA prediction,assumingunitspectroscopic factor, is also included in the figure. The CRC (d,d) (solid lines in Figure 1.(c)) is in very good agreement with the data. Futhermore, the CRC calculation produces a reduction of the cross section at forward angles for the (d,n1)and (d,p1)reactions, improving significantly the agreement with the experimental data using spectroscopic factors close to one. FIGURE 1. (a) CRC calculations (solid line) for the 16O(d,n)17Fand (b) 16O(d,p)17Oreactions for the ground (upper pannels) and first excited (lower pannels) states at 2.85 MeV, using the Set(CRC) of parameters (see Table 1). (c) Experimental and calculated elastic angular distributions for d+16 O at Ed=2.85 MeV. The experimental data were obtained by Diezsch et al. and CN contributions [7] are included. We have extended the CRC analysis to other energies, i.e., from Ed= 2.29 to Ed= 3.186 MeV for the (d,n)reaction and from Ed= 2.279 to Ed= 3.155 MeV for the (d,p) reaction. The average spectroscopic factors obtained from this analysis are summarized in Table 2. The standart deviation specified as the error of the spectroscopic factors were 160 obtained from the average of four analyzed energies. Except for the (d,p1)channel, all spectroscopic factors are close to one. The small value for the 17O∗|16Ospectroscopic factor should be considered as an open problem in our analysis. TABLE 2. Average spectroscopic factors and ANC values from CRC calculations. (d,p0)(d,p1)(d,n0)(d,n1) Spectroscopic Factor 1.19(5) 0.69(17) 0.93(11) 0.96(12) ANC Values (fm−1) 0.88(3) 6(1) 0.85(7) 6017(493) PROTON AND NEUTRON CAPTURE CROSS SECTIONS In order to get reliable ANC values from the spectroscopic factors it is necessary to assure that the transfer reactions are peripheral. For this purpose we performed tests in our previous DWBA calculations by varying the lower cut in the DWBA integrals and observing the sensitivity to the calculations. The results of these tests indicated that one calculations were practically insensitive to cuts until rcut ∼5 fm and become very sentiveabove rcut=6 fm showingthat the transfer reactions are quite peripheral [13]. The obtained ANC values for p+16 Oand n+16 Oare shown in Table 2. FIGURE 2. (a)AstrophysicalS- factorfrom 16O(d,n)17Ftransfer reaction and (b)neutroncapture cross section from 16O(d,p)17Otransfer reaction performedby CRC analysis. The solid lines are our results and the dashed lines are error bands. The dotted line in (b) was obtained using the spectroscopic factor equal to one. The experimental data were obtained by Morlock et al. [15] and by Igashira et al.[8] (resonance effect are included), respectively. The astrophysical S-factors for the 16O(p, γ )17Fand 16O(n, γ )17Ocapture cross sections were determined using the program Radcap [14]. The results are shown in Figure 2 (a) and (b) compared to experimental data of Morlock et al. [15] and Igashira et al. [8], respectively. The zero energy S-factor for the first excited state 16O(p, γ )17F∗was obtained as 9.6±0.8 keVbarn and it is in agreement with the value of Gagliardi et al [4]. For the ground state in both S-factor calculations underestimate the experimental data, 161 however, Morlock et al. [15] suggest that the ground experimental data could have been contaminated by the background [15]. The neutron captures to the ground and first excited states of the 17Onucleus are shown in Figure 2.(b). The Maxwellian-averaged direct cross section at kT=30 keV was calculated as 22±3 μ barn from our transfer reaction analysis. Igashira et al. [8] reported a 34±4 μ barn from experimental data with the resonance effect subtracted. This large cross section result could have implications for nucleosynthesis theories and inhomogeneous models [8]. CONCLUSIONS We investigated in detail the mechanism of the 16O(d,n)17Fand 16O(d,p)17Otransfer reactions at very low energies. We have shown that standard DWBA and CCBA calculations do not reproduce the (d,n1)and (d,p1)reactions unless very small spectroscopic factors are used, while the CRC calculations greatly improve the agreement with the (d,n1)and (d,p1)channels. The spectroscopic factor obtained from the CRC analysis is close to unit in agreement with theoretical predictions. The obtained astrophysical S-factors for the 16O(p, γ )17F∗and 16O(n, γ )17Ogs capture reactions are in good agreement with the experimental measurements. The 16O(p, γ )17Fgs and 16O(n, γ )17O∗cross sections obtained in this work underestimate the experimental data. The Maxwellianaveraged cross section at kT=30keV for the total (gs+1st exc)16O(n, γ )17Ocapture, has been determined to be 22(3) μ b. The present results demonstrate the possibilityof determining astrophysical S-factors from transfer reaction measurements. ACKNOWLEDGMENTS The authors woud like to thank FAPESP and CNPq for financial support. REFERENCES 1. H.M. Xu et al. Phys. Rev. Lett.,73,(1994), 2027. 2. A.M. Mukhamedzhanovet al. Phys. Rev. C56,(1997) 1302. 3. J. C. Fernandes, R. Crespo, and F. M. Nunes Phys. Rev. C64, (2001) 062801(R). 4. C. A. Gagliardi et al. Phys. Rev. C59, 1149 (1999). 5. L.Trache et al. Phys. Rev. Lett. 87, 271102 (2001). 6. N. Imai et al. Nucl. Phys. A688, 281c-284c (2001). 7. O. Dietzsch et al. Nucl. Phys. A114, 330 (1968). 8. M. Igashira et al. Astrophys. J. Lett.,441, L89-L92 (1995). 9. G.R. Satchler Nucl.Phys. 85, 273 (1966). 10. L. Rosen Proceedings of the 2nd International Symposium on Polarization Phenomena of Nucleons, Birkhauser Verlag, Basel, 1966, p. 253. 11. M. Assunção et al. Phys. Rev. C70, 054601 (2004). 12. I.J. Thompson, Computer Physics Reports 7, 167-212 (1988). 13. R. Lichtenthäler et al. DFN-081/IFUSP-1568,(2003) 14. C. A. Bertulani, MSUCL 1267, (2003). 15. R. Morlock et al. Phys. Rev. Lett. 79, 3837 (1997). 162