Elsevier

Physics Letters B

Volume 514, Issues 3–4, 16 August 2001, Pages 226-232
Physics Letters B

Determination of the astrophysical S factor of the 8B(p,γ)9C capture reaction from the d(8B,9C)n reaction

https://doi.org/10.1016/S0370-2693(01)00828-0Get rights and content

Abstract

The asymptotic normalization coefficients for the virtual decay 9C8B+p have been determined by measuring the cross-section of the 8B(d, n)9C reaction in inverse kinematics at 14.4 MeV/u, using the RIPS facility. The deduced astrophysical S factor S18 of the 8B(p,γ)9C capture reaction in the center of mass energy range 1–100 keV is S18=45±13 eVb.

Introduction

Radiative capture such as (p,γ) reactions are of crucial interest in astrophysics, since they play an important part in basic processes such as hydrogen burning. The thermonuclear energies relevant for such astrophysical processes are well below the Coulomb barrier, typically where cross-sections are very small. The measurement of such cross-sections is even more complicated when short-lived radioactive nuclides are involved in the entrance channel. This has lead to the implementation of indirect methods allowing the experimental difficulties inherent to the direct measurements of capture cross-section to be circumvented.

A few years ago, such an indirect approach based on measurements of peripheral proton transfer cross-sections on 7Be was proposed [1], [2] as yet another way to determine S17(0), the astrophysical S factor of the long-studied 7Be(p,γ)8B reaction at solar energies [3]. This method relies on the very peripheral character of this capture process at solar energies. It consists in extracting nuclear quantities called Asymptotic Normalization Coefficients (ANC) from peripheral transfer cross-sections, through a Distorted Wave Born Approximation (DWBA) analysis. Knowing these quantities, the S factor of the capture reaction can then be reliably calculated.

From the experimental point of view, the obvious advantage of such method lies in the cross-section magnitudes, which allow to make a measurement within a few days with secondary beams nowadays available. So far, this method (to which we shall refer as the ANC method) has only been applied to the above mentioned 7Be(p,γ)8B solar reaction [4], [5], [6], and also to some test cases, the 16O(p,γ)17F [7] and the 12C(n,γ)13C [8] reactions. For these two test cases the S factors obtained from the ANC method were found in good agreement with those extracted from a direct capture measurement.

In this Letter, we report on an experimental study of the 8B(d, n)9C proton transfer reaction from which the S factor of the 8B(p,γ)9C capture reaction can be derived using the ANC method. The 8B(p,γ)9C capture at astrophysical energies represents a case similar to the 7Be(p,γ)8B reaction, predicted to be non-resonant (direct) and strongly dominated by an electric dipole (E1) transition in the energy range of interest [9]. Nevertheless, the peripheral character of the capture is expected to be less pronounced than for the former reaction, due to the larger proton separation energy in 9C, 1.256 MeV instead of 0.137 MeV in 8B.

The 8B(p,γ)9C is of interest for the nucleosynthesis in stars (such as supermassive stars [10]) where temperatures and densities are such that it can compete with the β decay of 8B, becoming a possible alternative path to the synthesis of CNO elements (the so-called hot proton–proton chain). A recent calculation of the S factor for this reaction (which we will note S18) was performed [9] and the result was found to be in disagreement with a previous evaluation [10]. On the experimental side, only a preliminary estimate was determined from a Coulomb dissociation measurement of 9C [11]. This estimate was found to be consistent with the prediction of  [9], but smaller by a factor three to four than the calculated value of [10].

Section snippets

Experiment and results

The experiment was performed at the RIKEN Accelerator Research Facility where we have measured the cross-section of the 8B(d, n)9C reaction at 14.4 MeV/u. The 7Be(d, n)8B cross-section was also measured in the same run but in this Letter, we restrict ourselves to the results obtained for the former reaction.

The radioactive 8B beam was produced by fragmentation of a 70 A MeV 12C primary beam, using the RIPS [12] fragment separator. As mentioned above, a relatively low incident energy is required in

DWBA analysis

The spin and parity values of 8B and 9C are respectively 2+ and 3/2. Two components contribute to the 8B(d, n)9C cross-section, corresponding to (l=1, j=3/2) and (l=1, j=1/2) transfers. When the reaction is peripheral, transfer cross-sections can be factorized in terms of ANC's instead of spectroscopic factors. These ANC's can then be determined by normalizing DWBA cross-sections to the data, but without the large uncertainties inherent to spectroscopic factors due to the ambiguities on the

Calculation of S18 from the ANC's

The astrophysical S factor S18 can be deduced from the ANC's by calculating the matrix elements for the electromagnetic transition induced by the capture process. We have already mentioned that in the present case (just as in the case of the calculation of S17), the largely dominant contribution to the transition is of electric dipole character. In a potential model, the matrix elements for E1 transitions are: Q(E1)c→b=ΨcT̂E1‖Φb, where we have indicated with subscript c the proton in the

Acknowledgements

We wish to thank the RIKEN RARF and Orsay tandem accelerator staffs. We acknowledge Dr. N. Smirnova for shell-model calculations, and Dr. Y. Blumenfeld, Dr. S. Galès and Dr. J.P. Thibaud for careful reading of the manuscript. Part of this work was achieved within the IN2P3-RIKEN agreements and supported by the Science and Technology Agency of the Japanese government.

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