[Paper Review] Asymptotic normalization coefficient of ^{8}B from breakup reactions and the S_{17} astrophysical factor

L. Trache, F. Cârstoiu+2 more|OakTrust (Texas A&M University Libraries)|Aug 1, 2001

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents a novel indirect method to determine the asymptotic normalization coefficient (ANC) of $^8$B from one-proton breakup reactions at 30–300 MeV/u using an extended Glauber model with non-eikonal corrections. The extracted ANC of $C_{\text{tot}}^2 = 0.450 \pm 0.039\ \text{fm}^{-1}$ yields an astrophysical S-factor for the $^7$Be(p,γ)$^8$B reaction of $S_{17}(0) = 17.4 \pm 1.5\ \text{eV} \cdot \text{b}$, in excellent agreement with direct and indirect measurements.

ABSTRACT

We show that asymptotic normalization coefficients (ANC) can be extracted from one nucleon breakup reactions of loosely bound nuclei at 30-300 MeV/u. In particular, the breakup of ^{8}B is described in terms of an extended Glauber model. The 8B ANC extracted for the ground state of this nucleus from breakup data at several energies and on different targets, C^2 = 0.450+/-0.039} fm^-1, leads to the astrophysical factor S_{17}(0)= 17.4+/-1.5 eVb for the key reaction for solar neutrino production 7Be(p,gamma)8B. The procedure described here is more general, providing an indirect method to determine reaction rates of astrophysical interest with beams of loosely bound radioactive nuclei.

Motivation & Objective

• To develop a reliable indirect method for determining the astrophysical S-factor $S_{17}(0)$ for the $^7$Be(p,γ)$^8$B reaction, a key process in solar neutrino production.
• To extract the asymptotic normalization coefficient (ANC) of $^8$B from one-nucleon breakup data at intermediate energies (30–300 MeV/u), avoiding direct low-energy measurements.
• To validate the extended Glauber model with non-eikonal corrections for peripheral reactions involving loosely bound halo nuclei like $^8$B.
• To provide an alternative, complementary approach to direct measurements, reducing systematic uncertainties and improving redundancy for critical astrophysical S-factors.

Proposed method

• The extended Glauber model in the eikonal approximation with second-order non-eikonal corrections is used to calculate one-proton breakup cross sections and momentum distributions of the $^7$Be core.
• The model treats the $^8$B projectile as a core ($^7$Be) and a valence proton, with the overlap function described by the ANC in the asymptotic region where nuclear forces are negligible.
• The ANC is extracted by fitting the model to experimental data on breakup cross sections and core momentum distributions across multiple targets (Be, C, Al, Cu, Pb) and energies (30–300 MeV/u).
• The calculation accounts for stripping, diffraction dissociation, and Coulomb dissociation contributions via impact-parameter-dependent probabilities.
• A weighted average of ANCs extracted from multiple data sets is performed, with systematic uncertainties from optical model renormalization, $b_p$ dependence, and excited-state contributions included.
• The ANC is then used to compute the astrophysical S-factor $S_{17}(0)$ via the formalism of Ref. [8], and the rms radius of the $^8$B proton halo is estimated.

Experimental results

Research questions

• RQ1 Can the asymptotic normalization coefficient (ANC) of $^8$B be reliably extracted from one-proton breakup reactions at intermediate energies?
• RQ2 Does the extended Glauber model with non-eikonal corrections accurately describe the peripheral dynamics of $^8$B breakup on various targets?
• RQ3 What is the resulting value of the astrophysical S-factor $S_{17}(0)$ for the $^7$Be(p,γ)$^8$B reaction derived from the extracted ANC?
• RQ4 How does the ANC-based $S_{17}(0)$ compare with results from direct measurements and other indirect methods?
• RQ5 To what extent can the ANC be used to infer spectroscopic properties like the rms radius of the $^8$B proton halo?

Key findings

• The asymptotic normalization coefficient for the $^8$B ground state is extracted as $C_{\text{tot}}^2 = 0.450 \pm 0.039\ \text{fm}^{-1}$ from breakup data across 30–300 MeV/u and multiple targets.
• The astrophysical S-factor for the $^7$Be(p,γ)$^8$B reaction is determined to be $S_{17}(0) = 17.4 \pm 1.5\ \text{eV} \cdot \text{b}$, consistent with recent direct and indirect measurements.
• The extended Glauber model with non-eikonal corrections provides an excellent description of the core momentum distribution in $^8$B breakup at 41 MeV/u on $^9$Be, including the large-momentum tails.
• The extracted ANC is in excellent agreement with the value obtained from $^7$Be($p$,$^8$B) transfer reactions at 12 MeV/u, validating the method's consistency.
• The rms radius of the $^8$B proton halo is calculated as $r_h = 4.20 \pm 0.21\ \text{fm}$, consistent with halo nucleus behavior.
• Excluding two $^{12}$C data points at 40 and 142 MeV/u, which show inconsistent energy dependence, yields $C_{\text{tot}}^2 = 0.456 \pm 0.028\ \text{fm}^{-1}$, confirming robustness of the result.