Comment on the7Li(p, γ)8Be reaction at energies of astrophysical interest

The results of two recent publication are reconsidered. These papers argue that the p-wave effects seen in the⁷ Li(p, ) ⁸ Be reaction belowE _p=80 keV can be accounted for by considering the low-energy tail of the p-wave resonance atE _p=441 keV. It is shown that the cross section and analyzing power data require an order-of-magnitude more p-wave strength when considered together.This work was supported by the U.S. Department of Energy, Office of High Energy and Nuclear Physics, under Contract No. DEFG05-91-ER40619.     

Microscopic study of the low-energy 7Be(p,γ)8B reaction

We have performed a microscopic study of the ⁷Be(p,γ)⁸B reaction at low energies within the framework of the resonating group method. At solar energies, E=20 keV, we find an astrophysical S-factor of 0.0254 keV b which is in agreement with the value currently adopted in solar model calculations.     

New determination of the ~7Be ground state spectroscopic factor and the ~6Li(p,γ)~7Be astrophysical S(E) factors

The 'lithium problem, in Big Bang nucleosynthesis(BBN) has recently focused on reactions involving ~7 Be.The ~6 Li(p,γ)~7 Be reaction can provide us not only with information about ~6 Li destruction but also with information about ~7 Be production. In the present work, the proton spectroscopic factor in ~7 Be is extracted to be 0.70 ± 0.17 from the angular distribution of ~7 Be(d, ~3 He)~6 Li at E_(c.m.) = 6.7 MeV. This value is then used to compute the direct component of the astrophysical ~6 Li(p,γ)~7 Be_(g.s.) S(E) factors and determine the resonance parameters from the total S(E) factors.     

Breakup of 8B and the 7Be(p, γ)8B reaction

The calculated rate of events in some of the existing solar neutrino detectors is directly proportional to the rate of the ⁷Be(p, γ)⁸B reaction measured in the laboratory at low energies. However, the low-energy cross sections of this reaction are quite uncertain as various measurements differ from each other by 30–40%. The Coulomb dissociation process which reverses the radiative capture by the dissociation of ⁸B in the Coulomb field of a target, provides an alternate way of accessing this reaction. While this method has several advantages (like large breakup cross sections and flexibility in the kinematics), the difficulties arise from the possible interference by the nuclear interactions, uncertainties in the contributions of the various multipoles and the higher order effects, which should be considered carefully. We review the progress made so far in the experimental measurements and theoretical analysis of the breakup of ⁸B and discuss the current status of the low-energy cross sections (or the astrophysical S-factor) of the ⁷Be(p, γ)⁸B reaction extracted therefrom. The future directions of the experimental and theoretical investigations are also suggested. Work supported by EPSRC, UK, grant nos J/95867 and L/94574.     

Determination of the ~(12)C(p, γ)~(13)N reaction rates fromthe ~(12)C(~7Li,~6He)~(13)N reaction

The angular distribution of the 12C(7Li,6He)13N reaction at E(7Li) = 44.0 MeV was measured at the HI-13 tandem accelerator of Beijing, China. The asymptotic normalization coefficient (ANC) of 13N → 12C + p was derived to be (1.64 ± 0.11) fm-1/2 through the distorted wave Born approximation (DWBA) analysis. The ANC was then used to deduce the astrophysical S (E) factors and reaction rates for the 12C(p,γ)13N direct capture reaction at energies of astrophysical relevance.     

Effects of 8B size on the low-energy 7Be(p,γ)8B cross section

We calculate several “size-like” ⁸B observables within the microscopic three-cluster model and study their potential constraints on the zero-energy astrophysical S₁₇(0) factor of the ⁷Be(p,γ)⁸B reaction. We find within our three-cluster model that a simultaneous reproduction of the experimental data for the ⁸B radius and quadrupole moment and of the ⁸B⁸Li Coulomb displacement energy implies S₁₇(0) = (23–25) eV b.     

Extrapolation of theS(E) factor in7Be(p, γ0)8B: the7Li(p, γ0)8Be case

The observed M1 capture amplitude in⁷Li(p,_o)⁸Be At E_p=80–0 keV originates predominantly from the low-energy tail of a resonance at 441 keV, thue removing a recent criticism on the extrapolation of S(E) data such as for⁷Be(p,)⁸B.     

New determination of the astrophysical 13C( p, γ) 14N S(E) factors and reaction rates via the 13C(7Li, 6He) 14N reaction

The ¹³C(⁷Li, ⁶He) ¹⁴ N_0,1 reactions were measured at E (⁷Li) = 34 MeV with the Q3D magnetic spectrometer of the HI-13 tandem accelerator, and the first peaks of the angular distributions were obtained for the first time. The ¹⁴N_0,1 proton spectroscopic factors were extracted to be 0.67±0.09 and 0.73±0.10 , respectively. Using the ¹³C(p, ??) ¹⁴N direct capture S _dc(E) factors derived by the spectroscopic factors, the direct measurement data for both 1^? and 0^? resonances were well fitted via updating the resonance parameters, and then the total astrophysical ¹³C(p, ??) ¹⁴N S(E) factors and reaction rates were determined at stellar energies. The present work offers an independent examination to the existing results of the ¹³ C(p, ??) ¹⁴N reaction.     

The S(E) factor of7Li(p, γ)8Be and consequences for S(E) extrapolation in7Be(p, γ0)8B

Excitation functions and forward-backward anisotropies have been measured for the⁷Li(p, )⁸Be capture reaction over the proton energy rangeE _p =100 to 1500 keV, using a 4 summing crystal and Ge(Li) detectors, respectively. The data show at all energies the presence of El and M1 capture amplitudes arising from the direct capture (DC) process and theE _R =441 and 1030 keV resonances, respectively. Due to the observed DC process, the present data increase significantly the reaction rates (up to a factor of 110) compared to values given in the compilation. The data and their analyses remove the recent criticism on DC model calculations, which had implied a significant reduction in the extrapolated S(E) factor for⁷Be(p,)B and thus in the predicted flux of high-energy solar neutrinos; thus, the solar neutrino problem is still with us.Supported in part by the Deutsche Forschungsgemeinschaft (Ro429/21-3 and Ro429/21-4) and the German-Hungarian Collaboration (X238.6 and OTKA3808)     

Correlation features of the reaction 9Be(d, pγ)10Be at Ed=15.3 MeV and structure of the 10Be nucleus

Double-differential cross sections for the reaction ⁹Be(d, pγ)¹⁰Be at E _d=15.3 MeV are measured for proton emission into the forward hemisphere. All even spin-tensor components of the density matrix for the 2⁺ 3.37-MeV state of the residual nucleus are reconstructed in a model-independent way. The angular distributions of the populations of the magnetic substates and of the tensors of the angular-momentum orientation for the state in question are also obtained. The experimental results are compared with the results of the calculations performed by the coupled-channel method under the assumption of the neutron-stripping mechanism. The calculated correlation features are found to be highly sensitive to the wave functions for the participant nuclei, especially the ¹⁰Be nucleus. The importance of taking into account multistep processes in the reaction being considered is demonstrated.     

Measurement of the astrophysical S factor for the low energy 2H(d,γ)4He reaction

The y-rays and protons from an Ed = 20 keV deuteron beam incident on a D-Ti target were measured. A branching ratio of the 2H(d,T)4He reaction versus the 2H(d,p)aH reaction of F.v/l'p = (1.06+ 0.34) x 10-7 has been obtained, and the astrophysical S factor of the 2H(d,T)aHe reaction at the center of mass energy Ecru ≈ 7 keV of (6.0+2.4) x 10-8 keV.b was deduced.     

Electron screening in the 7Be + p → 8B + γ reaction

We evaluate the effect of screening by bound electrons in the ⁷Be(p,γ)⁸B reaction, where the ⁷Be target contains bound electrons, in the framework of the adiabatic representation of the three-particle problem. A comparison with two other approximations (united atom and folding) is presented. A good agreement between the “united atom” approximation and the exact solution is found. We also discuss the screening corrections induced by two K-shell electrons on a ⁷Be target. The consequences of bound electron screening for ⁷Be and ⁸B solar neutrino fluxes are discussed.     

Astrophysical ~(22)Mg(p,γ)~(23)Al reaction rates from asymptotic normalization coefficient of ~(23)Ne→~(22)Ne+n

The radionuclide ~(22)Na generates the emission of a characteristic 1.275 MeV γ-ray. This is a potential astronomical observable, whose occurrence is suspected in classical novae. The ~(22)Mg(p, γ)~(23)Al reaction is relevant to the nucleosynthesis of ~(22)Na in Ne-rich novae. In this study, employing the adiabatic distorted wave approximation and continuum discretized coupled channel methods, the squared neutron asymptotic normalization coefficients(ANCs)231 for the virtual decay of Ne → ~(22)Ne + n were extracted, and determined as(0.483 ± 0.060) fm~(-1) and(9.7 ± 2.3) fm~(-1) for the ground state and the first excited state from the experimental angular distributions of ~(22)Ne(d, p)~(23)Ne populating the ground state and the first excited state of ~(23)Ne, respectively. Then, the squared proton ANC of ~(23)Al_(g.s.) was obtained as C_(d5/2)~(2)(~(23)Al)(2.65 ± 0.33) × 10~3 fm~(-1) according to the charge symmetry of the strong interaction. The astrophysical S-factors and reaction rates for the direct capture contribution in ~(22)Mg(p, γ)~(23)Al were also presented. Furthermore, the proton width of the first excited state of ~(23)Al was derived to be(57 ± 14) eV from the neutron ANC of its mirror state in ~(23)Ne and used to compute the contribution from the first resonance of ~(23)Al. This result demonstrates that the direct capture dominates the ~(22)Mg(p, γ)~(23)Al reaction at most temperatures of astrophysical relevance for 0.33 T_9 0.64.     

Microscopic multicluster description of the 7Li7Be, 8Li8B and 9Li9C mirror nuclei

The ⁹Li and ⁹C mirror systems are investigated in a microscopic α+³H+n+n and α+³He+p+p multicluster framework using the stochastic variational method. Possibility of existence of neutron (proton) halo structure is studied. The quadrupole moment of ⁹C is predicted to be −5.04 e fm².     

The mechanism of the 7Li(d, 2α)n reaction from Ed = 3 to 15 MeV

The ⁷Li(d, 2α)n reaction proceeds almost entirely through excitation and sequential decay of the 16.63 and 16.92 MeV levels in ⁸Be, for incident energies 1 to 13 MeV above their threshold. The energy dependence for forming these levels with the neutron emitted at 0° is approximately that predicted assuming the neutron is a spectator from the incident deuteron. None of the individual spectra, the angular dependence of the cross section at fixed E_d, or the bombarding-energy-dependence of the cross section for forming the levels is consistent with the involvement of a spectator neutron from the ⁷Li target.     

Measurement of Angular Distribution for the ^8Li（p,d）^7Li Reaction

The ^8Li（p, d）^7 Li reaction plays an important role in the inhomogeneous Big Bang nucleosynthesis and in the seed-nuclide production phase for the r-process. For the first time, its angular distribution at backward angles was measured in inverse kinematics at Ec.m.=4.0 MeV by using an ^8Li secondary beam. The result of measurement includes the contributions of ^8Li（p, d0）^7Li and ^8Li（p, d1）^7Li^＊. The ^8Li（p, d0）^7Li component is estimated to be 40%-58% in the mixture angular distribution by analysing the measured result.     

Triple correlation in the 10B(n, αγ)7Li reaction

The formally T-odd triple correlation between the directions of the momenta of α particle and γ quantum and the polarization pseudovector of a thermal neutron was examined for the ¹⁰B+n=⁷Li+⁴He+γ reaction. Such T-odd correlations can be directly used for checking time reversal invariance in the elastic scattering of particles. In more complex reactions, this correlation can occur as a result of particle interactions in the entrance and exit channels of the reaction and, being a background effect, requires correct theoretical or direct experimental estimation. Our experiments gave an upper limit of 3.2×10^?4 (90% confidence level) for the possible T-odd asymmetry parameter in the reaction under study.