Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the

Abstract

A new analysis of the modern astrophysical S factors for the direct-capture 3 He(α, γ ) 7 Be reaction, precisely measured in recent works [B.S. Nara Singh et al., Phys. Rev. Lett. 93, 262503 (2004); D. Bemmerer et al., ibid. 97, 122502 (2006); F. Confortola et al., Phys. Rev. C 75, 065803 (2007), Gy. Gyrky et al., ibid. 75, 035805 (2007), T. A. D. Brown et al., ibid. 76, 055801 (2007), and A. Di Leva, et al., Phys. Rev. Lett. 102, 232502], has been carried out within the modified two-body potential approach. New estimates are obtained for the "indirectly determined" values of the asymptotic normalization constants and the respective nuclear vertex constants for 3 He + α → 7 Be(g.s.) and 3 He + α → 7 Be(0.429 MeV) as well as the astrophysical S factors S 34 (E) at E 90 keV, including E = 0. The values of asymptotic normalization constants have been used to obtain the values of the ratio of the α-particle spectroscopic factors for the mirror ( 7 Li 7 Be) pair.

Indirect methods of determination of the asymptotic normalization coefficients and their application for nuclear astrophysics

“…In works [28] and [29], to determine the ANC values for α + 3 He → 7 Be(E * =0.0 MeV; J π =3/2 − ), α + 3 He → 7 Be(E * =0.429 MeV; J π =1/2 − ) and p + 7 Be → 8 B the analysis has been performed within the MTBPA for the precisely measured modern experimental astrophysical S factors for the direct capture 3 He(α, γ) 7 Be and 7 Be(p, γ) 8 B reactions (see, references in the recent review [24]). The scrupulous analysis, performed in [28] and [29], has quantitatively shown that these reactions are strongly peripheral. Therefore, the expression (4) can be used for determination of the aforementioned ANCs since the calculated function R(E, b Aa ) does not depend practically from the free parameter b Aa .…”

“…In [28] and [29], the new estimations have been obtained for the ANC values for α + 3 He → 7 Be(g.s. ), α + 3 He → 7 Be(0.429 MeV) and p + 7 Be → 8 B, respectively, which have then been used for extrapolating the S 43 (E) and S 17 (E) to solar energies, including E=0.…”

“…), α + 3 He → 7 Be(0.429 MeV) and p + 7 Be → 8 B, respectively, which have then been used for extrapolating the S 43 (E) and S 17 (E) to solar energies, including E=0. The weighed means for square of the ANCs recommended in [28,29] for α + 3 He → 7 Be(g.s. ), α + 3 He → 7 Be(0.429 MeV) and p + 7 Be → 8 B are equal to 23.3±1.7, 15.9±1.1 [28] and 0.628±0.017 fm −1 [29], respectively.…”

“…The weighed means for square of the ANCs recommended in [28,29] for α + 3 He → 7 Be(g.s. ), α + 3 He → 7 Be(0.429 MeV) and p + 7 Be → 8 B are equal to 23.3±1.7, 15.9±1.1 [28] and 0.628±0.017 fm −1 [29], respectively. The ANC value for p + 7 Be → 8 B deduced in [29] differs noticeably from that of 0.465±0.041 fm −1 recommended in [30], which was obtained from the analysis of the peripheral proton transfer reactions performed in the "post"-form of the modified DWBA but without correctly taking into account the threebody Coulomb dynamics in the transfer mechanism.…”

“…All the more, the reactions considered in [30] are related to the "dramatic" case [6] and, consequently, as it was noted in [2,5], the modified DWBA applied in [30] cannot be used for a correct determination of the ANC for p + 7 Be → 8 B from the analysis done. The weighed ANC means recommended in [28,29] allowed to estimate the S 43 (0) and S 17 (0) values, which are equal to 0.613±0.045 keV b [28] and 23.4±0.6 eV b [29], respectively. One notes that these results for S 43 (0) and S 17 (0) are more (about of ±9.5% and ±30% ) than those recommended in [24] and [30], which were determined by the model dependent ways [28,29].…”