Measurement of astrophysical S factors and electron screening potentials for d(d, n)3He reaction In ZrD2, TiD2, D2O, and CD2 targets in the ultralow energy region using plasma accelerators

The paper is devoted to study electron screening effect influence on the rate of d(d, n)³He reaction in the ultralow deuteron collision energy range in the deuterated polyethylene (CD₂), frozen heavy water (D₂O) and deuterated metals (ZrD₂ and TiD₂). The ZrD₂ and TiD₂ targets were fabricated via magnetron sputtering of titanium and zirconium in gas (deuterium) environment. The experiments have been carried out using high-current plasma pulsed accelerator with forming of inverse Z pinch (HCEIRAS, Russia) and pulsed Hall plasma accelerator (NPI at TPU, Russia). The detection of neutrons with energy of 2.5MeV from dd reaction was done with plastic scintillation spectrometers. As a result of the experiments the energy dependences of astrophysical S factor for the dd reaction in the deuteron collision energy range of 2?C7 keV and the values of the electron screening potential U _e of interacting deuterons have been measured for the indicated above target: U _e (CD₂) ? 40 eV; U _e (D₂O) ? 26 eV; U _e (ZrD₂) = 157 ± 43 eV; U _e (TiD₂) = 125±34 eV. The value of astrophysical S factor, corresponding to the deuteron collision energy equal to zero, in the experiments with D₂O target is found: S _b (0) = 58.6 ± 3.6 keV b. The paper compares our results with other available published experimental and calculated data.     

Investigation of temperature dependence of neutron yield and electron screening potential for the d(d, n)3He reaction proceeding in deuterides ZrD2 and TiD2

The temperature dependence of the enhancement factor for the dd reaction proceeding in TiD₂ and ZrD₂ is investigated. The experiments were carried out at the Hall pulsed ion accelerator (INP, Polytechnic University, Tomsk, Russia) in the deuteron energy interval 7.0?C12.0 keV and at temperatures ranging from 20 to 200°C. The values obtained for the electron screening potentials indicate that the dd reaction enhancement factor does not depend on the target temperature in the range 20?C200°C. This result contradicts the conclusions drawn by the LUNA Collaboration from their work.     

On electron screening effects in the low-energy 3He(d,p)4He data

We have calculated the screening effects of the two electrons in the atomic ³He gas target on the low-energy³He(d, p)⁴He data. The nuclear degrees of freedom have been described within the microscopic multi-channel Resonating Group Method, while the two electrons have been treated in Born-Oppenheimer approximation deriving the exact screening potential within the Path Integral Monte Carlo method. Our model underestimates the observed screening effects implying the need to consider the coupling of nuclear and electronic degrees of freedom.     

Formalism for the T(d,n)4He and 3He(d,p)4He reactions

The formalism required to describe the T(d, n)⁴He or ³He(d, p)⁴He reaction when all particles may be polarized is discussed. The relation among the various sets of spin-1 tensors is stated explicitly, so that the formulas applying to a particular experiment may be written easily in terms of any desired system.     

Effects of electron screening on the 3He(d,p)4He low-energy cross sections

The reaction ³He(d, p)⁴He has been investigated for E_CM = 5.9−41.6 keV with the use of D projectiles and ³He atomic gas target nuclides as well as with ³He projectiles and D₂ molecular gas target nuclides. These studies show for the first time the effects of electron screening on low-energy fusion cross sections, i.e. a nearly exponential enhancement of the cross sections compared to the case of bare nuclei. The enhancement is about a factor 2 smaller for the case d(³He, p)⁴He due to the molecular nature of the D₂ target nuclides.     

Simulation of the d + 3 H →3 He + 2 n; 2 n → n + n Reaction

Results of a simulation of setups intended to search for excited states of few-nucleon systems decaying into two clusters are presented.     

Complete determination of the transition amplitudes from a comprehensive data analysis of the fusion reactions D(d,p)3H and D(d,n)3He for Ed<500 keV

All relevant low-energy transition amplitudes for the D(d,n)³He and D(d,p)³H reactions were determined from a fit to Legendre expansion coefficients of the available experimental data. A simple barrier penetrability model was used. Quintet S-wave transitions are found to contribute strongly thus obliterating the idea of neutron-lean “polarized” fusion energy production. The D+D interaction radius was determined with good accuracy for both reactions individually. The astrophysical S functions show a small S-wave enhancement and P-wave suppression of the D(d,p)³H branch.     

Longitudinal polarization transfer in the D(d,n)3He reaction at 0°

We have measured the longitudinal neutron polarization in the $\text{D(}\text{d}\text{,}\text{n}\text{)}{}^3\text{He}$ reaction, at θ=0°, for an incident longitudinally polarized deuteron beam. A deuteron energy range of 3.3–14.9 MeV was covered. The polarization transfer from the deuteron to the neutron is found to be large, and the reaction is potentially useful as a source of polarized neutrons.     

厚靶D（d,n）^3He反应加速器中子源的产额、能谱和角分布

给出一种计算氘钛厚靶D(d,n)3He反应加速器中子源的产额、能谱和角分布的方法,并发展了一个计算机模拟程序,程序能够计算氘束流能量小于1.0 MeV的中子源的产额、能谱和角分布.计算时使用推荐的D(d,n)3He反应截面数据和来自SRIM-2003程序的氘在氘钛靶中的阻止本领数据.给出一些典型计算结果,包括中子积分产额、中子能谱和角分布.     

The (3He,n) reaction in the lower 2s1d shell

The two-proton transfer reaction (³He, n) has been measured on four gas targets, ¹⁶O, ¹⁸O, ²⁰Ne, and ²²Ne, with an incident ³He energy of 18.3 MeV. The data were taken with a neutron time-of-flight spectrometer in the angular range 0° to 40° c.m. The results for selected transitions are compared to DWBA predictions using shell-model spectroscopic amplitudes. In addition, the data for the ¹⁸O(³He, n)²⁰Ne reaction are compared to predictions of the SU(3) strong coupling model.     

Ab initio many-body calculations of the (3)H(d,n)(4)He and (3)He(d,p)(4)He fusion reactions

We apply the ab initio no-core shell model combined with the resonating-group method approach to calculate the cross sections of the (3)H(d,n)(4)He and (3)He(d,p)(4)He fusion reactions. These are important reactions for the big bang nucleosynthesis and the future of energy generation on Earth. Starting from a selected similarity-transformed chiral nucleon-nucleon interaction that accurately describes two-nucleon data, we performed many-body calculations that predict the S factor of both reactions. Virtual three-body breakup effects are obtained by including excited pseudostates of the deuteron in the calculation. Our results are in satisfactory agreement with experimental data and pave the way for microscopic investigations of polarization and electron-screening effects, of the (3)H(d,γn)(4)He bremsstrahlung and other reactions relevant to fusion research.     

Large-space cluster model calculations for the 3He(3He,2p)4He and 3H(3H,2n)4He reactions

The ³He(³He,2p)⁴He and ³H(³H,2n)su4He reactions are studied in a microscopic cluster model. We search for resonances in the ³He+³He and ⁴He + p + p channels using methods that treat the two- and three-body resonance asymptotics correctly. Our results show that the existence of a low-energy resonance or virtual state, which could influence the ⁷Be and ⁸B solar neutrino fluxes, is rather unlikely. Our calculated ³He(³He,2p)⁴He and ³H(³H,2n)⁴He cross sections are in a good general agreement with the experimental data.     

Electron screening effect in the reactions He(d, p)He and d(He, p)He

The cross section of the reactions ³He(d, p)⁴He and d(³He, p)⁴He has been measured at the center-of-mass energies E=5 to 60 keV and 10 to 40 keV, respectively. The experiments were performed to determine the magnitude of the electron screening effect leading to the respective electron-screening potential energy U_e=219±7 and 109±9 eV, which are both significantly higher than the respective values from atomic physics models, U_e=120 and 65 eV.     

On the (3He,n) reaction in theA ≈ 100 region

The available experimental data on the (³He,n) reaction between the ground states of even-even nuclei and lowest 1/2^? levels of odd-A nuclei in theA ≈ 100 region are analyzed in a systematic way by the DWBA. The deduced relative intensities of these two-proton transfers, and their uncertainties, are compared to the predictions of various nuclear models. In particular, the influence of the finite dimension of the configuration space available to the transferred protons, and of the blocking effect of a 2p 1/2^? proton, are examined.     

Comparison of analyzing powers for the charge symmetric reactions 2H(d,n)3He and 2H(d,p)3H below 5.5 MeV

Analyzing powers for these charge symmetric reactions were measured at low energies where symmetry breaking effects due to the Coulomb interaction should be enhanced. Differences in the magnitudes exist and must be explained if charge symmetry holds; a simple energy shift, proposed earlier, is not adequate for this purpose.     

Stability of (3)He(2)(4)He(n) and (3)He(3)(4)He(n) L=0 clusters

We have studied the stability of mixed (3)He/(4)He clusters in L=0 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu He-He potential. The clusters (3)He(4)He(N) and (3)He(2)(4)He(N) are stable for N>1. The lighter atoms tend to move to the surface of the cluster. The minimum number of 4He atoms able to bind three 3He atoms in a L=0 state is nine. Two of three fermionic helium atoms stay on the surface, while the third one penetrates into the cluster.     

Microscopic study of the low-energy3He(3He, 2p)4He and3H(3H, 2n)4He fusion cross sections

We have calculated the³He(³He, 2p)⁴He and³H(³H, 2n)⁴He reaction cross sections at low energies within the microscopic multichannel resonating group method. For both reactions, we find good agreement with experiment. For the³H(³H, 2n)⁴He reaction, our calculated energy dependence reproduces that of each individual low-energy experimental data set, except for a normalization constant. Using this fact, we derive at a low-energy³H(³H, 2n)⁴He rate by taking the averaged mean of these fits.This work has been supported in part by the National Science Foundation, Grants PHY86-04197 and PHY88-17296.     

Anisotrope D (d,n)3He-Reaktionsausbeute in Kupfereinkristallen

A selftarget of deuterium (0.5 atomic-% D) in a single copper crystal is produced by a 75 keV deuteron beam. The neutron yield from the D(d, n) ³He reaction shows a 30% increase compared with the yield in polycrystalline copper, if the crystal is oriented in 〈110〉 to the beam. This result is discussed in terms of the channelling behaviour of the penetrating deuterons parallel to the 110 lattice rows.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

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.