Low-energy fusion cross sections of D + D and D + 3He reactions

The D(d, n)³He and D(d, p)T reactions have been investigated at E_c.m = 2.98 to 162.5 keV and the ³He(d, p)⁴He reaction at E_c.m. = 6.95 to 141.8 keV. The studies involved high-current accelerators with well-known beam characteristics and windowless gas target systems of the extended and quasi-point supersonic jet type. The measurement of absolute cross sections, angular distributions and excitation functions is reported. The data extend into the thermal energy region of future fusion reactors. The results for the D(d, n)³He and D(d, p)T reactions are in good agreement with previous work, while substantial differences are found for ³He(d, p)⁴He.     

Isotopic dependence of electron screening in fusion reactions

The fusion reactions⁶Li(p, )³He,⁶Li(d, )⁴He, and⁷Li(p, )⁴He have been studied over the c.m. energy rangeE=10 to 1450 keV. Each reaction involved the use of hydrogen projectiles and LiF solid targets as well as Li projectiles and hydrogen molecular gas targets. In all cases the effects of electron screening on the low-energy fusion cross sections (exponential enhancement) have been observed; the effects are somewhat stronger in the case of atomicp ord projectiles compared to the case of molecularH ₂ orD ₂ gas targets. If isotopic effects on electron screening are negligible, all three reactions should exhibit the same enhancements for each set of experimental techniques. The measurements confirmed this expectation to a large extent.Supported in part by the Landesamt Nordrhein-Westfalen (IVA5-10600387), the Deutsche Forschungsgemeinschaft (Ro429/ 18-2 and Ro429/21-1), and the Comision Interministerial de Ciencia y Tecnologia (AEN90-0932)     

The3He(d,p) α reaction at astrophysical energies

We have performed a microscopic study of the³He(d,p) α reaction at astrophysical energies within the framework of the Resonating Group Method adopting three different effective nucleon-nucleon interactions. The calculations suggest that the low-energy³He(d,p) α cross section is in good approximation given by the contribution arising from the 3/2⁺ resonant state atE _R =245 keV. In fact, the low-energy data can be better (and more physically) described by a single Breit-Wigner resonance parametrization than by a polynomial fit. Our fit to the³He(d,p) α cross section results in a noticeable reduction in the uncertainties of the resonance parameters of the 3/2⁺ resonant state as well as in a significantly improved extrapolation of the data to astrophysically important energies. On the basis of this extrapolation we were able to quantitatively deduce the enhancement of the low-energy cross section due to electron screening effects from the data of Krauss et al. and Engstler et al. These experimental enhancement factors were compared with various theoretical models which are all based on the Born-Oppenheimer approximation. As the models underestimate the observed enhancement we suggest that the theoretical study of electron screening effects requires a dynamical treatment.     

The (p, 2p) reaction on 2H, 3He and 4He

The (p, 2p) cross sections on ²H, ³He and ⁴He were measured at 65, 85 and 100 MeV. The experimental data show rather strong energy and target mass dependence, particularly for ⁴He.     

The3He(α,γ)7Be reaction and the solar neutrino problem

The capture reaction³He(α,γ)⁷Be has been investigated in the energy range ofE _c.m. =107 to 1,266 keV. The⁴He or³He beams of up to 300 μA particle current were incident on³He or⁴He gas targets, respectively. The gas target systems were all of the windowless and recirculating type. Excitation functions have been obtained with the use of an extended-static gas target, while the measurements ofγ-ray angular distributions involved a quasi-point supersonic jet system. The determination of absolute cross sections has been carried out with both types of gas target systems. Theγ-ray yields in the³He(α,γ)⁷Be reaction were detected using 80 cm³ Ge(Li) detectors. The data lead to a zero-energy intercept of the astrophysicalS(E) factor ofS(0)=0.30±0.03 keV-b. This result reduces the calculated solar neutrino rate by a factor of 1.76.     

4He fragmentation induced by 46–400 GeV Protons

Inclusivep, d and³He cross sections have been obtained using experimental data on p⁴He collisions over an incident proton energy range of 46-400 GeV. Considering the slopes of spectra, the effective nuclear temperature has been found to be T₀=11 MeV, which is in good agreement with experimental results for lower energies and heavier targets. The shape of the³He inclusive spectrum suggests the existence of two different³He production mechanisms. The experimental³He cross section is compared with theoretical predictions assuming fragment formation as a result of the spectator and cluster knockout mechanisms. The⁴He→³He +n vertex constant has been found to be G²=10.9±0.2 fm.     

Above-barrier enhancement of fusion in the 6He + 209Bi nuclear reaction

The fission cross sections for the ⁶He + ²⁰⁹Bi reaction as functions of the ⁶He-beam energy are measured. The experimental excitation functions for the reaction ²⁰⁹Bi(⁶He, 4n)²¹¹ At are also presented. The ⁶He secondary ion beam is obtained on the basis of the extracted-beam transport system of the U400-M accelerator (the Q4DQ spectrometer). A comparison of the experimental data obtained with available results for the ⁶He + ²⁰⁹Bi reaction shows that a pronounced enhancement of the fission cross sections in the above-barrier energy region is observed in the case of the reaction with the ⁶He beam. In order to fit the results of theoretical calculations to the experimental data, it is necessary to reduce the Coulomb barrier by 15% (20%). This corresponds to an increase of 1.5 (1.6) fm in the parameter r ₀ of the nuclear potential.     

Energy loss of deuterons in 3He gas: a threshold effect

The energy loss of deuterons in ³He gas was measured at E _d = 15 to 100 keV using the ³He pressure dependence of the ³He(d,p)⁴He cross-section at a given incident energy. At the highest energies, the observed energy loss is in good agreement with a standard compilation. However, with decreasing energy the experimental values drop steadily below the theoretical values and near E _d = 18 keV they drop sharply (within 1 keV) reaching the domain of nuclear stopping power. This threshold behavior is due to the minimum 1s → 2s electron excitation of the He target atoms, i.e. it is a quantum effect. Some consequences are discussed.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Absolute cross section of the3He(α,γ)7Be reaction

The absolute cross section σ(E) of the³He(α, γ)⁷Be reaction has been measured fromE _c.m. =195 to 686 keV. The studies employed both a supersonic jet gas target and an extended gas target, and were carried out by the observation of the prompt capture γ-ray transitions as well as the⁷Be residual nuclei. The absolute cross sections deduced from the capture γ-rays are in good agreement with most previous work and remove a discrepancy with other earlier work. In comparison, the σ(E) values obtained from the⁷Be residual nuclei are systematically higher, suggesting a small production of additional⁷Be by contaminant reactions.     

Theoretical Study of the 4He(γ, p)3H and 4He(γ, n)3He Reactions

Ab initio calculation of the total cross section for the reactions ⁴He(γ, p)³H and ⁴He(γ, n)³He is presented, using state-of-the-art nuclear forces. The Lorentz integral transform (LIT) method is applied, which allows exact treatment of the final state interaction (FSI). The dynamic equations are solved using the effective interaction hyperspherical harmonics method. In this calculation of the cross sections the three-nucleon force is fully taken into account, except in the source term of the LIT equation for the FSI transition matrix element.     

Measurements of photoionization cross sections from the 4p, 5d and 7s excited states of potassium

New measurements of the photoionization cross sections from the 4p ²P_1/2,3/2, 5d ²D_5/2,3/2 and 7s ²S_1/2 excited states of potassium are presented. The cross sections have been measured by two-step excitation and ionization using a Nd:YAG laser in conjunction with a thermionic diode ion detector. By applying the saturation technique, the absolute values of the cross sections from the 4p ²P_3/2 and 4p ²P_1/2 states at 355 nm are determined as 7.2±1.1 and 5.6±0.8 Mb, respectively. The photoionization cross section from the 5d ²D_5/2,3/2 excited state has been measured using two excitation paths, two-step excitation and two-photon excitation from the ground state. The measured values of the cross sections from the 5d ²D_5/2 state by two-photon excitation from the ground state is 28.9±4.3 Mb, whereas in the two-step excitation, the cross section from the 5d ²D_3/2 state via the 4p ²P_1/2 state and from the 5d ²D_5/2,3/2 states via the 4p ²P_3/2 state are determined as 25.1±3.8 and 30.2±4.5 Mb, respectively. Besides, we have measured the photoionization cross sections from the 7s ²S_1/2 excited state using the two-photon excitation from the ground state as 0.61±0.09 Mb.     

Cross sections of fusion and transfer reactions in interactions between 3He and Pt and 197Au nuclei in the subbarrier energy region

The reactions of complete and incomplete fusion, along with nucleon transfer reactions in the range of ³He energies from 10 to 24.5 MeV, are investigated by irradiating gold and platinum targets with an accelerated ³He ion beam on the U-120M cyclotron at the Institute of Nuclear Physics, Czech Academy of Sciences, ?e?. Activation is used to determine the yield of nuclides resulting from nuclear reactions. The γ-activity induced in the targets is measured using a with high-resolution HPGe detector. Despite the low binding energy of ³He and the reactions with positive Q values, the measured cross sections of fusion reactions exhibit no specific features, compared to reactions conducted using beams of other light stable particles. Transfer neutron reactions in the subbarrier energy region have relatively high cross sections. These cross sections continue to grow as the energy of ³He rises. When a neutron is captured by a nucleus of ³He, the cross sections of these reactions reach their maximum values in the Coulomb barrier region.     

Stopping power of low-energy deuterons in 3He gas

The stopping power of atomic and molecular deuterons in ³He gas was measured over the range E _d = 10 to 100 keV using the ³He pressure dependence of the ³He(d,p) ⁴He reaction yield. At energies above 30 keV, the observed stopping power values are in good agreement with a standard compilation. However, near 18 keV the experimental values drop by a factor 50 below the extrapolated values of the compilation. In a simple model, the behavior is due to the minimum 1s↦2s electron excitation of the He target atoms (= 19.8 eV, corresponding to E _d = 18.2 keV), i.e. it is a quantum effect, by which the atoms become nearly transparent for the ions.     

The4He(12C, γ)16O reaction at stellar energies

The capture reaction⁴He(¹²C, γ)¹⁶O (E _c.m.= 1.34–3.38 MeV) as well as the elastic scattering process⁴He(¹²C,¹²C)⁴He (E _c.m.=1.44–3.38 MeV) have been investigated with the use of an intense¹²C beam and a windowless and⁴He recirculating gas target system. The measurements involved two large NaI(T1) crystals in close geometry to an extended gas target, whereby angle-integrated γ-ray yields were obtained. A large area plastic detector was used for the suppression of time-independent background. A search for cascade γ-ray transitions was carried out by coincidence techniques. The measurement of absolute cross sections is also reported. Theoretical fits of the excitation function for the groundstate γ-ray transition requireE1 as well asE2 capture amplitudes, which are of equal importance at stellar energies. This result increases significantly the stellar burning rate of⁴He(¹²C, γ)¹⁶O and leads to¹⁶O as the dominant product at the end of helium burning in massive stars. The observed capture yield to the 6.92 MeV state is dominated by the direct capture mechanism and plays a small role at stellar energies.     

Screening effects in secondary electron production by equal velocity H+, H+2, He+, He++ions

Electron spectra produced by equal velocity (0.75 MeV/amu) H⁺, H⁺₂, He⁺ and He ⁺⁺ ions are shown. Screening effects are observed for He⁺ ions but not for H⁺₂. He⁺⁺ cross sections scale like Z² = 4 when compared to H⁺ cross sections.     

Cross sections for slow ion production and charge transfer in H+3(D+3)−H2(D2) collisions

Slow ion production cross sections for collisions of H⁺₃ and D⁺₃ ions with H₂ and D₂ have been measured at collision energies between 100 eV and 500 eV. The values vary from 2 × 10^-17 cm² to 6 × 10^-17 cm². The smaller cross sections for D₃ projectiles may be explained as an internal energy effect.     

Excitation functions for 44Sc, 46Sc, and 47Sc radionuclides produced in the interaction of 45Sc with deuterons and 6He

Experimental excitation functions are presented for ⁴⁵Sc(d, p)⁴⁶Sc, ⁴⁵Sc(d, t)⁴⁴Sc, ⁴⁵Sc(⁶He, ⁵He*)⁴⁶Sc and ⁴⁵Sc(6He, α)⁴⁷Sc reactions at projectile energies near the Coulomb barrier. The obtained excitation functions for reactions ⁴⁵Sc(d, p)⁴⁶Sc and ⁴⁵Sc(⁶He, ⁵He*)⁴⁶Sc have similar behavior and have a maxima near the Coulomb barriers of these reactions. The compilation of the available experimental data, obtained at deuteron- and ⁶He-energies near the Coulomb barrier, showed that the values of the cross sections at the maxima of the excitation functions obtained in (d, p) reactions and the reactions for one-neutron pickup from the ⁶He projectiles have a different Z-dependence.     

Differential cross sections and analyzing powers for pd elastic scattering below 1.0 MeV

Differential cross sections for the elastic pd scattering were measured at seven energies between 0.4 and 1.0 MeV for scattering angles from θ_c.m. = 44.5° to 149.2°. A mixture of D₂ and Kr was used as target gas and the pd differential cross sections were determined relative to those of pKr scattering with a statistical error of $\text{Δσ}\text{σ}$ ～5 × 10^?3. Analyzing powers for $\text{p}$d scattering were measured at 0.8, 0.9 and 1.0 MeV with a statistical error of ΔA_y ～5 × 10^?4.