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.     

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.     

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.     

Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Relaxation of the analyzing power of the (p, τX) and (p, αX) reactions in the continuum

The observed continuous decrease of the analyzing power for the reactions ($\text{p}$, τX) and ($\text{p}$, αX) on ⁹⁰Zr and ²⁰⁹Bi at E_p = 72 MeV as a function of the excitation energy of the final nucleus is described by a phenomenological relaxation process.     

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.     

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.     

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)     

Pion scattering on 3H and 3He nuclei in the Δ33(1232) region

Elastic scattering of π ^± mesons on ³H and ³He nuclei at energies around the Δ₃₃(1232) resonance is considered. The amplitudes for single and double scattering are calculated on the basis of the nonrelativistic diagram technique. The spin and isospin structure of pion-nucleon amplitudes is fully taken into account. The resulting theoretical predictions for the differential cross sections are compared with available experimental data.     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Three-Body Calculation of the 4He（aH,γ）7Li and 4He（aHe,γ）7Be Reactions and Structure of the 7Li and 7Be at Solar Energies

The two 3H＋4He and 3He＋4He fusion reactions at low energies are usually viewed as an approximate external capture process. We study the 4He（3H,γ）rLi and 4He（SHe,γ）7Be reactions in a cluster model, which can take into account two- and three-body electromagnetic currents, using minimal substitution in the explicit momentum dependence of the two- and three-cluster interactions. Our main goal is to explore how the cross section of the low-energy 3H＋4He or 3He＋4He capture reactions depends on energy. The astrophysical S-factors for these reactions are calculated at very low energies. We construct the conserved realistic Argonne v18 for two nucleons and Urbana IX or Tucson-Melbourne three-cluster interactions, which are considered for calculation. We also calculate the binding energies and the structural properties of a Hq-4He or 3He＋4 He systems. The binding energies are found to be -37.72 （-36.32） MeV and -39.35 （-37.43） MeV, with （without） three-body interactions for 7Be and 7 Li, in satisfactory agreement with other theoretical results and experimental data, respectively.     

Determination of astrophysical ~7Be(p,γ)~8B reaction rates from the ~7Li(d,p)~8Li reaction

The7Be(p,γ)8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars.Study of this reaction requires the asymptotic normalization coefficient(ANC) for the virtual decay8 Bg.s.→7Be + p.By using the charge symmetry relation,we obtain this proton ANC with the single neutron ANC of8 Lig.s.→7Li + n,which is determined with the distorted wave Born approximation(DWBA) and adiabatic distorted wave approximation(ADWA) analysis of the7Li(d,p)8Li angular distribution.The astrophysical S-factors and reaction rates of the direct capture process in the7Be(p,γ)8B reaction are further deduced at energies of astrophysical relevance.The astrophysical S-factor at zero energy for direct capture,S17(0),is derived to be(19.9±3.5) e V b in good agreement with the most recent recommended value.The contributions of the1+and 3+resonances to the S-factor and reaction rate are also evaluated.The present result demonstrates that the direct capture dominates the7Be(p,γ)8B reaction in the whole temperature range.This work provides an independent examination to the current results of the7Be(p,γ)8B reaction.     

AstrophysicalS(E) factor of10B(p, α1)7Be at low energies

The absolute cross section of the fusion reaction ¹⁰B(p, ₁)⁷ has been measured at the c.m. energy range E=48 to 159 keV via the 429 keV secondary -ray transition. The studies involved high proton currents and thick solid ¹⁰Btargets. The resulting cross sections have the same energy dependence as those of the ¹⁰B(p,₀)⁷Bereaction but they are lower by a factor 600.Supported in part by the Deutsche Forschungsgemeinschaft (Ro429/18-2 and Ro429/21-3), the Landesamt Nordrhein Westfalen (IVA5-10600387), and the Comision Intel-ministerial de Ciencia y Technologia (AEN90-0932).     

Determination of 8B(p, γ )9C Reaction Rate From 9C Breakup

The astrophysical factor of the ⁸B(p, γ )⁹C reaction at zero energy, S ₁₈(0), is determined from three-body model analysis of ⁹C breakup processes. The elastic breakup ²⁰⁸Pb(⁹C,p ⁸B)²⁰⁸Pb at 65 MeV/nucleon and the one-proton removal reaction of ⁹C at 285 MeV/nucleon on C and Al targets are calculated with the continuum-discretized coupled-channels method (CDCC) and the eikonal reaction theory (ERT), respectively. As a result of the present analysis, S ₁₈(0) extracted from the two reactions shows good consistency, in contrast to in the previous studies.     

Cumulative protons in the 9Be(12C,p)X reaction at 0.2–3.2 GeV/nucleon

The spectra of protons were measured in fragmentation of ¹²C ions in the cumulative region at energies of 0.2–3.2 GeV/nucleon. The energy dependence of the slope parameters in the obtained spectra was traced. The probability of the existence of two- and three-nucleon clusters in the carbon nucleus was estimated within the model of quark-gluon strings.     

Numerical Simulation of the Yield of α Particles and Neutrons from the 11B(p, 3α) and 11B(p,n)11C Nuclear Reactions Induced by Intense Picosecond Laser Radiation

Journal of Experimental and Theoretical Physics - The yields of alpha particles and neutrons from the promising 11B(p, 3α) fusion reaction and the reference 11B(p, n)11C nuclear reaction,...     

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.