Experimental determination of the electron screening potential energy for the d(d, n)3He Reaction in ZrD2 and D2O in the ultralow energy region

This work is devoted to measuring of the values of the astrophysical S-factors and electron screening potential energy for a d(d,n)³He reaction occurring at ultralow energies in zirconium deuteride ZrD₂ (3.5–7.0 keV) and heavy water D₂O (2.2–6.0 keV). The experiment was performed on the Hall pulsed plasma accelerator at the TPU Nuclear Physics Institute (Tomsk) with ZrD₂ and D₂O targets produced by the magnetron sputtering of zirconium in a deuterium environment and heavy water freezing-out on a copper support, respectively. A χ ² analysis of the dependence of the neutron yields and astrophysical S-factors for the dd reaction on the deuteron collision energy E revealed that the upper bounds of the electron screening potential energy for interacting deuterons in ZrD₂ and D₂O and of the astrophysical S-factors at the deuteron collision energy E = 0 were U _e (ZrD₂) < 30 eV, U _e (D₂O) < 25 eV, S(0) = (57.2 ± 3.9) keV · b (ZrD₂), S(0) = (58.6 ± 3.6) keV · b (D₂O) at the 90% confidence level.     

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.     

Measurement of the astrophysical S factor for dd interaction at ultralow deuteron-collision energies using the inverse Z pinch

This paper is devoted to measurement of the astrophysical S factor and cross sections of the d + d → ³He + n reaction at ultralow deuteron-collision energies. Formation of the flow of the accelerated deuterons incident on the CD₂ solid-state target was made within the scheme of the inverse Z pinch. The liner in the initial state was a hollow supersonic deuterium jet of radius of 15 mm and length of 20 mm. The experiment was carried out at the pulsed high-current accelerator (I=950 kA, τ=80 ns) of the Institute of High-Current Electronics (Tomsk, Russia). Measurement of the deuteron energy distribution was performed through an analysis of the time distributions of the intensity of the liner radiation (H_α and H_β lines) generated during the liner radial movement from the axis. Recording of this radiation was carried out by optical detectors placed along the direction of the liner moving from its axis. The measured value of the astrophysical S factor for the dd reaction at the average deuteron collision energy E _coll=3.69 keV was equal to S(E _coll=3.69 keV)=58.2±18.1 keV b. The dd-reaction cross section calculated using the found value of the S factor and known representation of the reaction cross section as the product of the barrier factor and the astrophysical S factor was σ _dd ⁿ (E _coll=3.69 keV)=(1.33±0.41)×10^?30 cm².     

Absolute cross sections for the 6Li(p, 3He)4He reaction at energies below 1 MeV

Total cross sections and angular distributions in the ⁶Li(p,³He)⁴He reaction have been measured over the energy range E_p = 100?700 keV. The extrapolation of the cross section to the energy region which is of interest in controlled thermonuclear reactors is given. The values of the “astrophysical S-function” are deduced from the cross sections.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of T(<Superscript>4</Superscript>He, γ)<Superscript>7</Superscript>Li reaction at <Emphasis Type="Italic">E</Emphasis><Subscript>cm</Subscript> = 15.7 keV

The astrophysical S-factor of the reaction T(⁴He, γ)⁷Li is measured for the first time at the center of mass energy E _cm = 15.7 keV, lower than the energy range of the Standard Big Bang Nucleosynthesis (SBBN) model. The experiment is performed on a Hall pulsed accelerator (TPU, Tomsk). An acceleration pulse length of 10 μs allows one to suppress the background of cosmic radiation and the ambient medium by five orders of magnitude. A beam intensity of ~ 5 × 10^{14 4}He⁺ ions per pulse allows one to measure an extremely low reaction yield. The yield of γ-quanta with the energies E _γ ⁰ = 2483.7 keV and E _γ ¹ = 2006.1 keV is registered by NaI(Tl) detectors with the efficiency ε = 0.331 ± 0.026. A method for direct measurement of the background from the chain of reactions T(⁴He, ⁴He)T→T(T, 2n)X→(n, γ) and/or (n, n′γ) which ends by neutron activation of materials surrounding the target is proposed and implemented in this study. The value of the astrophysical S-factor of the reaction T(⁴He, γ)⁷Li S _αt (E _cm = 15.7 keV) = 0.091 ± 0.032 keV b provides the choice from the set of experimental data for the astrophysical S _αt -factor in favor of experimental data [4] with S _αt (E _cm = 0) = 0.1067 ± 0.0064 keV b.     

The 18O(p, α)15N cross section at low energies

The ¹⁸O(p, α)¹⁵N reaction cross section has been measured over the energy range 661 keV > E_c.m > 223 keV. The S-function was extrapolated to energies of astrophysical interest using the R-matrix theory. The S-factor, S₀, is estimated to be 46 MeV · b which is a factor of 3 larger than the value used in a recent tabulation of nuclear reaction rates. The effects of broad levels near the proton threshold are discussed.     

Astrophysical S factor for dd interaction at ultralow energies

Experimental results are presented that were obtained by measuring the astrophysical S factor for dd interaction at very low deuteron collision energies by using the liner-plasma technique. The experiment was performed at the high-current generator of the High-Current Electronics Institute (Tomsk, Russia). The values found for the S factor at the deuteron collision energies of 1.80, 2.06, and 2.27 keV are S _dd=114±68, 64±30, and 53±16 keV b, respectively. The corresponding dd cross sections obtained as the product of the barrier factor and the measured astrophysical S factor are σ _dd ⁿ (E _col=1.80 keV)=(4.3±2.6)×10^?33cm², σ _dd ⁿ (E _col=2.06 keV)=(9.8±4.6)×10^?33cm², and σ _dd ⁿ (E _col=2.27 keV)=(2.1±0.6)×10^?32cm².     

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.     

Search for the radiative capture reaction d+d → 4He+γ from the ddμ muonic molecule state

A search for the muon-catalyzed fusion (MCF) reaction d+d → ⁴He+γ in the ddμ muonic molecule was performed using the experimental MCF installation TRITON and NaI(Tl) detectors for γ quanta. A high-pressure target filled with deuterium was exposed to the negative muon beam of the JINR phasotron to detect γ quanta with an energy of 23.8 MeV. The first experimental estimation for the yield of radiative deuteron capture from the ddμ state J=1 was obtained at a level of η_γ≤2×10^?5 per one fusion.     

Low-energy cross section for 6Li(d,n)7Be

Cross sections were determined for the ⁶Li(d, n)⁷Be reaction between 100 and 180 keV deuteron energy using the activation method. Different methods of extrapolation were employed and compared down to the energy region of astrophysical interest.     

Experimental observation of electron screening for the D(p, γ)3He nuclear reaction in titanium Deuteride TiD

Characteristics of the pd reaction (p + d → ³He + γ(5.5 MeV)) in titanium deuteride at astrophysical proton-deuteron collision energies ranging from 5.3 to 10.5 keV are investigated. Experiments are conducted on the pulsed plasma Hall accelerator at Tomsk Polytechnic University (Tomsk, Russia). The number of accelerated protons in a pulse 10 μs long is 5 × 10¹⁴ at a repetition rate of 7 × 10^?2 Hz. Gamma rays with an energy of 5.5 MeV are recorded by eight detectors based on NaI(Tl) crystals (100 × 100 × 400 mm) arranged around the TiD target. The dependence of the astrophysical S factor for the pd reaction on the proton-deuteron collision energy and the electron screening potential of protons interacting with deuterons in titanium deuteride are measured for the first time.     

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.     

Study of the pd reaction at ultralow energies using hydrogen liner plasma

The pd reaction (pd → He + γ (5.5 MeV)) is studied in the astrophysical energy collision range of protons with deuterons using the hydrogen liner in the inverse Z-pinch configuration at the pulsed power generator MIG (HCEI, Tomsk). Fundamental characteristics of this and other light-nucleus reactions at ultralow energies are important for problems of basic physics and astrophysics. The knowledge of the energy distribution of the nuclei participating in these reactions is important due to their exponential type of dependence on the collision energy. Two experimental techniques were designed and tested for recovering the energy distribution of liner protons incident on the CD₂ target by using optical detectors and ion collectors. It is shown that the combined use of these two techniques could provide relevant information on the energy distribution of the accelerated protons in the liner. The estimates of the upper limits for the astrophysical S factor and effective cross section of the pd reaction in the proton-deuteron collision energy range of 2.7–16.7 keV are obtained: $\bar S_{pd} (E_{pd} = 10.2 keV) \leqslant 2.5 \times 10^{ - 7} MeV b;\overline \sigma _{pd} (2.7 \leqslant E_{pd} \leqslant 16.7 keV) \leqslant 4 \times 10^{ - 33} cm^2 $ .     

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.     

First experimental evidence of D(p, γ)3He reaction in titanium deuteride in ultralow collision energy region

The article is devoted to the investigation of a pd-reaction (p + d → ³He + γ(5.5 MeV)) under-going in titanium deuteride in astrophysical collision energy region of protons and deuterons ranging from 5.3 to 10.5 keV. The experiments have been performed using the Hall NR TPU (Tomsk, Russia) pulsed plasma accelerator. The number of accelerated protons in 10 μs pulse was 5 × 10¹⁴ at a repetition rate of 7 × 10^?2 Hz. Detection of 5.5 MeV gamma rays was carried out using eight detectors based on crystals of NaI(Tl) (100 × 100 × 400 mm) placed around the TiD target. For the first time, the dependencies between the astrophysical S-factor and the effective cross section of the pd-reaction from proton-deuteron collision energy, and the potential electronic screening of the interacting protons and deuterons in titanium deuteride have been measured.     

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.     

The investigation of short-range 3He, 3H and deuteron spin structure via the measurement of the angular distributions of the analyzing power in the \vec dd \to {}^3Hen and \vec dd \to Hp reactions at 140, 200 and 270 MeV

The results on the vector A _y and tensor A _yy , A _xx and A _xz analyzing powers of the $\vec dd \to {}^3Hen$ and $\vec dd \to {}^3Hp$ reactions obtained at intermediate energies at RARF(RIKEN, Japan) are presented. The high precision experimental data are compared with the theoretical calculation within the one nucleon exchange model by using standard ³He, ³H and deuteron wave functions. The data demonstrate the sensitivity to the short-range ³He, ³H and deuteron spin structure.     

Measurement of the absolute cross section of the 3He(4He, γ)7Be reaction at Ec.m. = 525 keV

The cross section for the radiative capture reaction ³He(⁴He, γ)⁷Be has been measured at 525 keV in the centre-of-mass by detection of prompt capture γ- rays. The targets were ³He-implanted Nb foils that allowed us to circumvent the experimental difficulties inherent in the use of extended gas cells for absolute measurements. The results give an inferred zero-energy cross-section factor of S₃₄(0) = 0.47 ± 0.04 keV · b. The present result is compared with results from previous capture γ-ray yield and ⁷Be-activity methods of measuring the cross-section factor.     

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.