Coulomb dissociation of 8B and solar neutrino problem

We measured the cross section for Coulomb dissociation of ⁸B using a radioactive ⁸B beam of 46.5 MeV/u energy with a ²⁰⁸Pb target. The corss section for the ⁷Be(p,γ)⁸B capture reaction was deduced at E_cm = 0.6 – 1.7 MeV. The extracted astrophysical S₁₇ factors were consistent with the values measured by Vaughn et al. and Filippone et al. Possible corrections due to ⁷Be excited state population, E1 and M2 contribution, nuclear contribution and post acceleration effects are considered.     

Coulomb breakup of light nuclei in the field of a heavy ion at relativistic collision energies

A simple method for calculating the amplitude and the cross section for the Coulomb breakup of a light nucleus into two fragments in the field of a heavy ion at relativistic collision energies is proposed on the basis of time-dependent perturbation theory. It is shown that the resulting amplitude for the process in question has a correct nonrelativistic limit. The contribution of the longitudinal component of the Coulomb field of a heavy ion tends to zero in the ultrarelativistic limit. A specific implementation of the method is demonstrated by taking the example of the Coulomb breakup reaction ²⁰⁸Pb(⁸B, ⁷Bep)²⁰⁸Pb at various collision energies. The results are found to be in agreement with experimental data.     

Further measurement of the 7Be(p,γ)8B cross section at low energies with the coulomb dissociation of 8B

We have measured the dissociation of ⁸B in the Coulomb field of ²⁰⁸Pb at E_in=51.9 MeV/nucleon and extracted the cross section of the ⁷Be(p,γ)⁸B reaction at 0.4 ≤ E_rel≤ 3 MeV, which is of importance for the ⁸B solar-neutrino production rate. The extracted astrophysical S₁₇ factors are consistent with our earlier Coulomb dissociation measurement, and agree with the values deduced from the direct capture measurements by Filippone et al., Vaughn et al. and Hammache et al. The S factor at zero energy was extracted to be 18.9±1.8 eV-b with the help of theoretical energy-dependence. Received: 15 August 1998     

Sub-barrier interaction between deuterons and 58, 62Ni nuclei

The interaction between deuterons and ^{58, 62}Ni nuclei at energies of E _d = 3.5, 4.5 and 5.16 MeV is investigated. The discrepancy between measured scattering elastic cross section and the Rutherford ones is higher than the value calculated theoretically by considering deuterons polarization and Coulomb breakup. Analysis of measured cross section of ^{58, 62}Ni(d, p) reaction and the results of calculation of Coulomb breakup cross section integrated over neutron emission angles shows that that the dominant mechanism of proton formation is the reaction of neutron transfer to the target nucleus.     

12C1 and 8Be production in 12C + 208Pb collisions

The mechanisms involved in the production of fast α-particles in ¹²C-induced reactions have been studied for the ¹²C + ²⁰⁸Pb system at the bombarding energies of E_12c = 132, 187 and 230 MeV. Absolute cross sections for the reactions ²⁰⁸Pb(¹²C. ¹²C¹→α + ⁸Be), ²⁰⁸Pb(¹²C, ⁸Be(g.s.)) and ²⁰⁸Pb(¹²C, ⁸Be(2.94 MeV)) have been determined by coincidence measurement of two or three correlated α-particles. Inclusive α-particle production cross sections were also measured at E_12c = 187 MeV. It is found that the inelastic process (¹²C, ¹²C¹→α + ⁸Be) does not contribute significantly to fast α-particle production but that the production of ⁸Be by projectile fragmentation is an important source of α-particles. At the highest bombarding energy (230 MeV) it appears that the ¹²C → 3α fragmentation reaction becomes more prominent at the expense of the ¹²C→α + ⁸Be fragmentation channel.     

Asymptotic three-particle approach to the Coulomb breakup process <Superscript>6</Superscript>Li + <Superscript>208</Superscript>Pb → <Superscript>208</Superscript>Pb + α + <Emphasis Type="Italic">d</Emphasis>

On the basis of the distorted-wave method, experimental data on the triple-differential cross section for the Coulomb breakup reaction ²⁰⁸Pb(⁶Li, αd)²⁰⁸Pb are analyzed by employing a correct expression for the final-state ²⁰⁸Pb–α–d three-particle Coulomb wave function. It is shown that the effect of final-state three-particle Coulomb dynamics can be used to assess the kinematical condition of clean Coulomb breakup processes. New values of the astrophysical S factor for the direct-radiative-capture reaction d(α, γ)⁶Li at ultralow energies in the range of 70 ≤ E _dα ≤ 600 keV were extracted from experimental data. The value of S(0) = 1.60 ± 0.17 MeV nb was obtained.     

Total cross-section measurements for the production of nuclear gamma rays from light nuclei by low-energy deuterons

The thick target yields of the reactions ⁶Li, ⁹Be, ¹⁰B(d, nγ) for specific final nucleus γ-rays have been measured between deuteron bombarding energies of 48 and 170 keV. The measured thick target yields are used, together with recently published values of the stopping power of low-energy deuterons in matter, to infer the total reaction cross sections for the production of the specific γ-rays between deuteron energies of 65 and 160 keV. The cross sections are compared to appropriate Coulomb barrier penetration probabilities and the astrophysical functions S(E) are deduced.     

Fragmentation of the total cross section in the reaction16O+208Pb

The fragmentation of the total reaction cross section was investigated for¹⁶O +²⁰⁸Pb atE _c.m.=84 MeV andE _c.m.=92 MeV. Total cross sections for the inelastic, transfer and fission channels were measured. The sum of the inelastic and transfer channels accounts for 30% of the total reaction cross section; the residual strength is found in a compoundfission process.     

Final state three-body Coulomb effects in the 208Pb(8B,7Bep)208Pb Coulomb breakup reaction

We present results of the first calculation of the double differential cross section for the 208Pb(8B,(7)Bep)208Pb Coulomb breakup reaction which treats the postdecay acceleration of the ejectiles within a genuine three-body approach. From this we conclude that, in order to minimize postdecay Coulomb acceleration effects, experiments should be performed at as small as possible scattering angles, not too low 7Be-p relative energies, and high incident energy.     

Alpha-nucleus elastic scattering at intermediate energies

Elastic scattering of 288,340,480 and 699 MeV Alpha-particles was measured on ²⁰⁸Pb, ¹¹⁶Sn and ⁵⁸Ni. The data were analysed in terms of a phenomenological optical model. The optical potentials obtained were found to vary consistently with the target nucleus and the incident energy. The radial zone where the potentials are well determined was studied in detail. The data for ²⁰⁸Pb were also analysed with a folding model. The energy dependence of the strong-absorption radius and of the reaction cross section shows that the nuclear surface becomes slightly transparent for incident energies above 150 MeV per nucleon.     

Two-neutron pickup strengths on the even lead isotopes the transition from single-particle to “collective”

The (p, t) reaction on ²⁰⁸Pb, ²⁰⁶Pb, and ²⁰⁴Pb has been studied with 35 MeV protons. It is observed that the L = 0 ground-state cross section rapidly increases as one changes targets from ²⁰⁸Pb to ²⁰⁶Pb to ²⁰⁴Pb while the cross section for other natural-parity transitions decreases. The observed cross sections are compared with predictions of the shell model and the pairing-vibration model. Both models are seen to describe some features of the data.     

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.     

Dynamic polarization in the Coulomb breakup of loosely bound F

Angular distributions of the Coulomb breakup of radioactive ¹⁷F were measured by impinging a 10 MeV/nucleon beam on ²⁰⁸Pb and on ⁵⁸Ni to study the dynamic polarization effects. The breakup products, oxygen and a proton, were detected in coincidence. First-order perturbation theory significantly overpredicts the breakup cross section for the ²⁰⁸Pb target. Dynamical calculations with a dynamic polarization as the leading order correction were performed. The calculations reproduce the data for ¹⁷F on ⁵⁸Ni but overpredict the breakup of ¹⁷F on ²⁰⁸Pb by a factor of two at forward angles.     

The accuracy of semiclassical approximations in extracting spectroscopic information from direct transfer reactions

The diffraction model amplitude for transfer reactions, previously developed by the author, is extended to energies below the Coulomb barrier. In this way, the spectroscopic factors for various transitions in the reaction ²⁰⁸Pb(d, p)²⁰⁹Pb are extracted. Comparison is made between our results and the predictions of the zero-range DWBA treatment, and good agreement is obtained. The observed cross sections at θ_L = 135° for various incident energies are also correctly reproduced within our treatment.     

Effects of non-orthogonality and virtual excitations in direct reactions (III)

Formulae are presented concerning the effects of virtual Coulomb excitation on the transfer of nucleons between heavy ions at energies below the Coulomb barrier. These formulae are applied towards calculation for the ²⁰⁸Pb(¹⁶O, ¹⁷O)²⁰⁷Pb reaction at 69.1 MeV. Generally, the effect is found to be of the order of 10% but it is not discernable owing to the small reaction cross sections. Suggestions are presented for extending the analysis to higher energies where the situation is more favourable.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

基于ImIQMD模型对近垒重系统准裂变反应的研究

利用改进的同位旋相关的量子分子动力学(ImIQMD)模型程序,对能量在库仑位垒附近的48Ca+208Pb反应系统进行了模拟。 计算得到的俘获截面、 准裂变截面和碎片分布及其发生的时间分布等结果与实验数据符合较好。 同时还得到了准裂变过程中发射第三个较大碎片的截面, 并简单讨论了它们的发射机制。Based on the improved isospin dependent quantum molecular dynamics (ImIQMD) model,the reaction of 48Ca+208Pb at energies near the Coulomb barrier was investigated systematically. The capture cross section,the quasi fission cross section, the mass distribution of the quasi fission fragments and the time for quasi fission happened were obtained. According to the comparison with experimental data,the calculated capture cross sections and the fragment distributions of the quasi fission were reasonable. Additionally,we got the cross sections of the third largest fragment,and the emission mechanism was also discussed briefly.     

Low-energy behavior of the 3He(α, γ)7Be cross section

Cross sections for the ³He(α, γ)⁷Be reaction have been measured at several energies from E_c.m. = 165 to 1169 keV by counting prompt γ-rays from a windowless, differentially pumped, recirculating, ³He gas target. The cross-section factor S₃₄(E_c.m.) and branching ratio γ₁/γ₀ were determined at each energy. Cross sections were also measured at E_c.m. = 947 and 1255 keV by counting the γ-rays from the ⁷Be produced in a ³He gas cell with a Ni entrance foil. Combining the results of these two independent experiments yields a zero-energy intercept for the cross-section factor of S₃₄(0) = 0.53 ± 0.03 keV · b. The relationship between these measurements and several theoretical calculations, and the import of the extrapolated cross section for the solar-neutrino problem are discussed.     

Evaporation residue studies for 58,64Ni ON 58Ni near the Coulomb barrier

Evaporation residue excitation functions are presented for ^64,58Ni projectiles on ⁵⁸Ni targets. The results support the large subbarrier cross sections found by another group with a different setup. Above the Coulomb barrier, the evaporation residue cross section is significantly lower than that obtained by barrier penetration calculations.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.