Electron Screening Potential Research Articles

Electron screening in nickel

In order to investigate the interplay between nuclei and their surroundings, we studied proton-induced nuclear reactions over an energy range from 0.86 to 3.08MeV for different environments: Ni metal and NiO insulator. The measurements were based on the observation of the yields of 59, 61, 63, 64, 65Cu and 58, 60, 62Ni de-excitation $ \gamma$ -rays. Shifts in the resonance energy for the metallic target relative to the insulator one were not observed. Electron screening potential of $ U_{e}=31\pm 13$ keV was deduced for 64Ni $ (p,n\gamma )$ 64Cu reaction, while $ U_{e}=19\pm 4$ keV was deduced for 58Ni $(p,\gamma )$ 59Cu and 60Ni $(p,\gamma )$ 61Cu reactions. The observed electron screening potentials for (p,n) and (p, $\gamma$ ) reactions are the same within error bars, but the comparison with previous measurements raises the question of the independence of the electron screening from the reaction exit channel.

Electron screening effects in (p,α) reactions induced on boron isotopes studied via the Trojan Horse Method

The Trojan Horse Method is a powerful indirect technique allowing one to measure the bare nucleus S(E)-factor and the electron screening potential for astrophysically relevant reactions without the needs of extrapolations. The case of the (p,α) reactions induced on the two boron isotopes 10,11B is here discussed in view of the recent Trojan Horse (TH) applications to the quasi-free 10,11B+2H reactions. The comparison between the TH and the low-energy direct data allowed us to determine the electron screening potential for the 11B(p,α) reaction, while preliminary results on the 10B(p,α) reaction have been extracted.

AN UPDATED6Li(p, α)3He REACTION RATE AT ASTROPHYSICAL ENERGIES WITH THE TROJAN HORSE METHOD

The lithium problem influencing primordial and stellar nucleosynthesis is one of the most interesting unsolved issues in astrophysics. 6Li is the most fragile of lithium's stable isotopes and is largely destroyed in most stars during the pre-main-sequence (PMS) phase. For these stars, the convective envelope easily reaches, at least at its bottom, the relatively low 6Li ignition temperature. Thus, gaining an understanding of 6Li depletion also gives hints about the extent of convective regions. For this reason, charged-particle-induced reactions in lithium have been the subject of several studies. Low-energy extrapolations of these studies provide information about both the zero-energy astrophysical S(E) factor and the electron screening potential, Ue . Thanks to recent direct measurements, new estimates of the 6Li(p, ?)3He bare-nucleus S(E) factor and the corresponding Ue value have been obtained by applying the Trojan Horse method to the 2H(6Li, ? 3He)n reaction in quasi-free kinematics. The calculated reaction rate covers the temperature window 0.01 to 2T 9 and its impact on the surface lithium depletion in PMS models with different masses and metallicities has been evaluated in detail by adopting an updated version of the FRANEC evolutionary code.

Trojan Horse technique to measure nuclear astrophysics rearrangement reactions

The knowledge of nucleosynthesis and of energy production in stars requires an increasingly precise measurement of nuclear fusion reactions at the Gamow energy. Because of the Coulomb barrier reaction cross sections in astrophysics cannot be accessed directly at ultra -low energies, unless very favorable conditions are met. Moreover, the energies characterizing nuclear processes in several astrophysical contexts are so low that the presence of atomic electrons must be taken into account. Theoretical extrapolations of available data are then needed to derive astrophysical S(E)-factors. To overcome these experimental difficulties the Trojan Horse Method (THM) has been introduced. The method provides a valid alternative path to measure unscreened low-energy cross sections of reactions between charged particles, and to retrieve information on the electron screening potential when ultra-low energy direct measurements are available. While the theory has been discussed in detail in some theoretical works, present in the scientific literature, also in relation to different types of excitation functions (e.g. non-resonant and resonant), work on detailed methodology used to extract the events to be considered for the bare nucleus cross section measurements is still on going. In this work we will present some critical points in the application of THM that deserve to be discussed in more detail.

MONTE CARLO SIMULATIONS OF dd REACTION PARAMETERS STUDY AT ULTRA-LOW ENERGY RANGE USING PLASMA HALL ACCELERATOR AND DEUTERIZED TARGETS

This paper presents results of the application Monte Carlo method to analyze data from the interaction of deuteron beams with metallic targets saturated with deuterium. The SRIM software was used to generate energy spectrum of ions passing the target. These spectra were used to calculate the neutron yields from dd reactions in energy range 7–12 keV of incident deuteron beams. The calculated outputs were compared with the experimental data for the determination of the electron screening potential for dd reactions. The calculations were performed using two different values of the beam energy spread (FWHM) equal 1% and 16%. It was shown that plasma beams with a relatively high spread (16%) were almost as good a tool as the traditional accelerator with mono-energy beam related to the study of the reaction within an ultra-low energy region.

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 7.0–12.0 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 20–200°C. This result contradicts the conclusions drawn by the LUNA Collaboration from their work.

Measurement of astrophysical S-factors and electron screening potentials for reaction in ZrD2, TiD2 and TaD0.5 targets in the ultralow energy region using plasma accelerator

Abstract The present paper is devoted to the study of the electron screening effect influence on the rate of d ( d , n ) He 3 reaction in the ultralow deuteron collision energy range in the deuterated metals (ZrD 2 , TiD 2 and TaD 0.5 ). The ZrD 2 , TiD 2 and TaD0.5 targets were fabricated via magnetron sputtering of titanium, zirconium and tantalum in gas (deuterium) environment. The experiments have been carried out using the high-current pulsed Hall plasma accelerator (NSR TPU, Russia). The detection of neutrons with energy of 2.5 MeV from the dd reaction was done with plastic scintillation spectrometers. As a result of the experiments, the energy dependences of the astrophysical S -factor for the dd reaction in the deuteron collision energy range of 2–7 keV and the values of the electron screening potential U e of the interacting deuterons have been measured for the above targets: U e ( ZrD 2 ) = ( 205 ± 35 ) eV ; U e ( TiD 2 ) = ( 125 ± 34 ) eV ; U e ( TaD 0.5 ) = ( 313 ± 58 ) eV . Our results are compared with the other published experimental and calculated data.

Recent evaluation of the7Li(p,α)4He reaction rate at astrophysical energies via the Trojan Horse method

Context. The charged-particle induced reactions on lithium have been studied by several works. In particular, several direct measurements of the 7 Li(p, α) 4 He reaction have been performed to extrapolate its low-energy astrophysical S (E)-factor and evaluate the electron screening potential, Ue. Aims. In view of recent direct measurements, we discuss our estimate of the bare-nucleus S (E)-factor and an evaluation of the corresponding reaction rate. Moreover, we present the extracted electron screening potential. Methods. The Trojan Horse method (THM) allows us to measure the 7 Li(p, α) 4 He bare-nucleus S (E)-factor down to energies of ∼10 keV, rendering unnecessary the extrapolation procedure typically used by the direct measurements. The 7 Li(p, α) 4 He S (E)-factor is deduced from the 2 H( 7 Li, α 4 He)n reaction by selecting the quasi-free contribution to the reaction yield. The planewave impulse approximation has proved an effective approach as distortions appear negligible. Results. The THM enable us to measure the 7 Li(p, α) 4 He S (E)-factor over the energy region of interest for astrophysics, namely 0.01 < Ecm < 0.4 MeV. The zero-energy S (E)-factor and the Ue electron screening potential have been measured and compared with the available direct data. From the TH measure of the 7 Li(p, α) 4 He S (E)-factor, the reaction rate calculation has been performed in correspondence with the temperature window of 0.01 < T9 < 2, which is typical of several astrophysical sites where Li burning could shed light on some open questions, such as mixing phenomena. A variation of ∼13%, with respect the adopted NACRE one, has been found at temperatures of about T9 = 10 −3 , while a variation of ∼5% has been found at higher temperatures. By considering in the calculation the upper and lower limits to the TH reaction rate, no significant variation in the Li abundances of low mass giant stars follows or, if any modification occurs, this is negligible in comparison to the uncertainties in the free parameters considered in the extra-mixing model of Palmerini and collaborators.

Analysis of experimental data on the key thermonuclear reactions going within the low energy range

A comparative analysis of experimental data on hydrogen and helium isotope interaction with deuterons and tritons at low energy is performed. If the energy of an incident particle falls to several keV, the astrophysical factor S(E) rises sharply, indicating that there is an electron screening effect for such interaction. The values of electron screening potentials and enhancement factors are given for key thermonuclear reactions. It is important to allow for the electron screening effect in calculations performed during astrophysical research and in designing different thermonuclear facilities.

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 2–7 keV and the values of the electron screening potential Ue of interacting deuterons have been measured for the indicated above target: Ue(CD2) ⩽ 40 eV; Ue(D2O) ⩽ 26 eV; Ue(ZrD2) = 157 ± 43 eV; Ue(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: Sb(0) = 58.6 ± 3.6 keV b. The paper compares our results with other available published experimental and calculated data.

The Trojan Horse Method in nuclear astrophysics

The study of energy production and nucleosynthesis in stars requires an increasingly precise knowledge of the nuclear reaction rates at the energies of interest. To overcome the experimental difficulties arising from the small cross sections at those energies and from the presence of the electron screening, the Trojan Horse Method has been introduced. The method provides a valid alternative path to measure unscreened low-energy cross sections of reactions between charged particles, and to retrieve information on the electron screening potential when ultra-low energy direct measurements are available.

Studies on p+6Li Fusion Reaction using 3-Parameter Model

The 3-parameter model introduces 3 parame- ters (radius of a square nuclear potential well, the real part and the imaginary part of the nuclear potential depth) to describe the low energy behavior of the fusion cross-sec- tion for light nuclei. It has been justified by the experi- mental data from the National Nuclear Data Center (NNDC) for 3 major fusion reactions (d ? T, d ? D, and d ? 3 He). In the present paper this 3-parameter model has been extended to p? 6 Li fusion reaction. It agrees with the fusion cross-section data from NNDC again. Moreover it is able to calculate the astrophysical S-factor with an electron screening potential for p? 6 Li fusion reaction as well. As a development of the 3-parameter model, the necessary condition for a low energy resonant tunneling through Coulomb barrier is derived. It reveals further the possibility of resonant tunneling at very low energy for p? 6 Li system.

Trojan Horse Method: a useful tool for electron screening effect investigation

Direct measurements in the last decades have highlighted a new problem related to the lowering of the Coulomb barrier between the interacting nuclei due to the presence of the “electron screening” in the laboratory measurements. It was systematically observed that the presence of the electronic cloud around the interacting ions in measurements of nuclear reactions cross sections at astrophysical energies gives rise to an enhancement of the astrophysical S(E)-factor as lower and lower energies are explored [H. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. 327 (1987) 461]. Moreover, at present such an effect is not well understood as the value of the potential for screening extracted from these measurements is higher than the upper limit of theoretical predictions (adiabatic limit). On the other hand, the electron screening potential in laboratory measurement is different from that occurring in stellar plasmas thus the quantity of interest in astrophysics is the so-called “bare nucleus cross section”. This quantity can only be extrapolated in direct measurements. These are the reasons that led to a considerable growth on interest in indirect measurement techniques and in particular the Trojan Horse Method (THM) [G. Baur, Phys. Lett. B 178, (1986) 135; S. Cherubini et al. Ap. J. 457, (1996) 855] Results concerning the bare nucleus cross sections measurements will be shown in several cases of astrophysical interest. In those cases the screening potential evaluated by means of the THM will be compared with the adiabatic limit and results arising from extrapolation in direct measurements.

Trojan Horse Method: A tool to explore electron screening effect

Owing the presence of the Coulomb barrier at astrophysically relevant energies, it is very difficult, or sometimes impossible to measure reaction rates for charged particle induced reactions. Moreover due to the presence of the electron screening effect in direct measurements, the relevant nuclear input for astrophysics, i.e. the bare nucleus S(E)-faetor, can hardly be extracted. This is why different indirect techniques are being used along with direct measurements. The THM is an unique: indirect technique which allows one to measure reactions cross sections of astrophysical interest down the thermal energies typical of the different scenarios. The basic principle and a review of the main applications of the Trojan Horse Method are given. The applications aiming at the extraction of the bare Sb(E) astrophysical factor and electron screening potentials Ue for several two body processes are discussed.

Electron screening in theHe3(d,p)He4reaction

A reanalysis of data for the {sup 3}He(d,p){sup 4}He reaction obtained using the Trojan-horse method, together with data from a direct measurement, leads to an electron-screening potential that is not consistent with the adiabatic limit, but it is consistent with a previous value from different data.

Electron capture rates in strong electron screening

The effect of electron screening on electron capture reactions in the environments of pre-supernova objects is discussed, using the strong electron screening potential derived recently from the linear response theory. Our calculations of the electron capture rates for the nuclei 56Co, 56Fe and 56Mn show that in low-temperature and high-density circumstances, the effect of electron screening on the electron capture reaction is a little less than what was previously given, but it is still quite obvious.

Electron screening in reactions between light nuclei

Values of the electron-screening potential derived from previous fits to measurements of low-energy cross sections of nuclear reactions have generally been much larger than the values estimated from model calculations. Here we refit the data using somewhat different procedures and show that better agreement is possible in some cases.

The3He(d→,p)4Hereaction at low energies

Angular distributions of cross sections and complete sets of analyzing powers for the [sup 3]He([rvec d],p)[sup 4]He reaction have been measured at five energies between E[sub d]=60 and 641 keV. The energy dependence of the cross section was also measured from 245 to 685 keV, and the absolute cross section was determined at E[sub d]=426thinspkeV. The data have been included in an [ital R]-matrix analysis of the [sup 5]Li system. The bare-nuclear cross section derived from the [ital R]-matrix parametrization was used to determine the electron screening potential. [copyright] [ital 1999] [ital The American Physical Society]

Reaction in metal at bombarding energies below 5 keV

In order to study the electron screening effect on low-energy nuclear reactions in metals, the D+D reaction in Ti and Yb was investigated. Yields of protons emitted in the D(d, p)T reactions from the deuteron bombardment of Ti and Yb thick targets with bombarding energies between 2.5 and 7.2 keV were measured. The obtained yields were compared with those predicted by using the parametrization of cross sections at higher energies. It was found that the reaction rates in metals are enhanced over those of the bare nuclei for keV, and the enhancement can be interpreted as caused by the electron screening. The electron screening potentials in Ti and Yb are deduced to be eV and eV, respectively.

Measurement of the D(d, p)T Reaction in Ti for2.5&lt;Ed&lt;6.5keV and Electron Screening in Metal

In order to study the electron screening effect on low-energy nuclear reactions in metals, the D+D reaction in Ti was investigated. Measured were thick target yields of protons emitted in the D(d, p)T reaction from the bombardment of Ti metal with deuteron energies between 2.5 and 6.5 keV. The obtained yields were compared with those predicted by using the parameterization of cross sections at higher energies. It was found that the reaction rates in Ti are slightly enhanced over those of the bare D+D reaction for Ed < 4.3 keV, and the enhancement can be interpreted as caused by the electron screening. The electron screening potential in Ti is deduced for the first time to be 19 ± 12 eV.