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.     

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.     

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)     

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.     

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.     

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.     

The 3He(α, γ)7Be and 3He(α, γ)7Li reactions at astrophysical energies

The radiative capture cross sections for ³He(α, γ)⁷Be and ³He(α, γ)⁷Li at astrophysical energies have been studied microscopically in terms of the resonating group method. It was found that the astrophysical S-factors correlate strongly to the nuclear size and deformation of ⁷Be and ⁷Li. With the help of measured nuclear properties of these nuclei, a safety range of the absolute values of the S-factor was determined; the most recommended S(0)-values are 0.50 ± 0.03 keV · b for the ³He(α, γ)⁷Be reaction and 0.098 ± 0.006 keV · b for the ³H(α, γ)⁷Li reaction.     

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.     

Microscopic calculation of the 3He(α,γ)7Be and 3H(α,γ)7Li capture cross sections using realistic interactions

The radiative capture cross sections for the 3He(α,γ)7Be and 3H(α,γ)7Li reactions are calculated in the fully microscopic fermionic molecular dynamics approach using a realistic effective interaction that reproduces the nucleon-nucleon scattering data. At large distances bound and scattering states are described by antisymmetrized products of 4He and 3He/3H ground states. At short distances the many-body Hilbert space is extended with additional many-body wave functions needed to represent polarized clusters and shell-model-like configurations. Properties of the bound states are described well, as are the scattering phase shifts. The calculated S factor for the 3He(α,γ)7Be reaction agrees very well with recent experimental data in both absolute normalization and energy dependence. In the case of the 3H(α,γ)7Li reaction the calculated S factor is larger than available experimental data by about 15%.     

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.     

Spectroscopy of 88Sr with the 87Sr(n, γ) and 87Sr(d,p) reactions

The γ-ray spectrum emitted after thermal neutron capture in ⁸⁷Sr was studied at the ILL high flux reactor with pair- and intrinsic Ge-spectrometers. 661 transitions were assigned to the reaction ⁸⁷Sr(n, γ)⁸⁸Sr and 205 of them were placed into a ⁸⁸Sr level scheme of 47 levels. This represents 88% of the observed intensity. The level energies were determined with a precision of better than 20 ppm; the neutron binding energy was determined as 11 112.69 (22) keV. To aid the analysis high resolution particle spectra of the reaction ⁸⁷Sr(d, p)⁸⁸Sr were measured at 20 MeV deuteron energy with the Munich Q3D spectrometer. 85 states were observed with this reaction. The data helped to establish newly found levels and to differentiate between primary and secondary transitions in the (n, γ) data. The observed level densities and primary transition strengths are compared with statistical model predictions and non-statistical effects are discussed.     

Study of the187W states excited in the (n, γ) reaction

A singles-ray spectrum and a spectrum of summed amplitudes of coinciding pulses (SACP) were measured in the¹⁸⁶W(n, )¹⁸⁷W reaction experiment on the thermal neutron beam. It was for the first time that the data on¹⁸⁷W-transitions were obtained in the excitation energy region from 1500–2500 keV. The neutron binding energy was determined to beB _n=5467.25 (4) keV (statistical error only). In result the level scheme of¹⁸⁷W was developed in the excitation energy interval 1E _f < 3.4=" mev,=" which=" contained=" 105=" levels=" with=" about=" 70=" of=" them=" being=" identified=" for=" the=" first=" time.=" the=" experimental=" values=" for=" summed=" intensities=" of=" two-step=" cascades=" were=" established=" to=" exceed=" those=" predicted=" by=" the=" modern=" statistical=" theory=" (by=" 36±6%).=" this=" is=" explained=" by=" a=" considerable=" contribution=" of=" few-quasiparticle=" components=" to=" wave=" functions=" of=" compound=" and=" intermediate=">     

(α, n) reactions in cascade γ-transitions

The ratios of the cross sections for the formation of the ground and isomeric states in reactions on¹⁰⁷Ag,¹⁰⁹Ag, and¹¹³In are calculated based on the assumption that at low energies the (, n) reaction proceeds via a) formation of the compound nucleus, b) evaporation of a neutron, and c) cascade -transitions. The number of cascade -quanta and the distribution of the excitation energy between the -quanta and the neutron is not postulated beforehand (as is usually done), but is calculated based on the statistical theory. By comparing with experiment, the parameter of the spin-dependence of the density of nuclear states is found. It is shown that the average number of -quanta in the cascade increases approximately linearly with the energy of the particles. The energy spectrum of the -quanta in the (, n) reaction is calculated. The distribution of -quanta has a maximum at low energies (1 MeV), which, as the energy of the primary particles is increased, moves slowly into the higher energy range while broadening at the same time.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 77–81, August, 1984.     

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.     

Level structure of 87Sr from the 86Sr(n, γ) and 86Sr(d,p) reactions

The γ-ray spectrum emitted after thermal neutron capture in ⁸⁶Sr was studied at the ILL high flux reactor with pair- and intrinsic Ge spectrometers. 759 transitions were assigned to the reaction ⁸⁶Sr(n, γ)⁸⁷Sr and 385 of them were placed into a ⁸⁷Sr level scheme of 80 levels. This represents 90% of the observed intensity. The level energies were determined with a precision of better than 20 ppm; the neutron binding energy was determined to be 8428.16 (17)keV. In a second set of experiments high resolution particle spectra of the reactions ⁸⁶Sr(d, p)⁸⁷Sr and ⁸⁸Sr(d, t)⁸⁷Si were recorded at 20 MeV deuteron energy with the München Q3D spectrometer. These data were used to establish newly found levels and to differentiate between primary and secondary transitions in the (n, γ) data. The observed level densities and primary transition strengths are compared with statistical models.