Gamow Window Research Articles

Approaching the Gamow Window with Stored Ions: Direct Measurement of ^{124}Xe(p,γ) in the ESR Storage Ring.

We report the first measurement of low-energy proton-capture cross sections of ^{124}Xe in a heavy-ion storage ring. ^{124}Xe^{54+} ions of five different beam energies between 5.5 and 8AMeV were stored to collide with a windowless hydrogen target. The ^{125}Cs reaction products were directly detected. The interaction energies are located on the high energy tail of the Gamow window for hot, explosive scenarios such as supernovae and x-ray binaries. The results serve as an important test of predicted astrophysical reaction rates in this mass range. Good agreement in the prediction of the astrophysically important proton width at low energy is found, with only a 30% difference between measurement and theory. Larger deviations are found above the neutron emission threshold, where also neutron and γ widths significantly impact the cross sections. The newly established experimental method is a very powerful tool to investigate nuclear reactions on rare ion beams at low center-of-mass energies.

Astrophysical SE2 factor of the C12(α,γ)O16 reaction through the C12(B11,Li7)O16 transfer reaction

The ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction plays a key role in the evolution of stars with masses of $M >$ 0.55 $M_\odot$. The cross-section of the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction within the Gamow window ($E_\textrm{c.m.}$ = 300 keV, $T_\textrm9$ = 0.2) is extremely small (about $10^{-17}$ barn), which makes the direct measurement in a ground-based laboratory with existing techniques unfeasible. Up until now, the cross-sections at lower energies can only be extrapolated from the data at higher energies. However, two subthreshold resonances, located at $E_x$ = 7.117 MeV and $E_x$ = 6.917 MeV, make this extrapolation more complicated. In this work, the 6.917 MeV subthreshold resonance in the ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ reaction was investigated via the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$ reaction. The experiment was performed using the Q3D magnetic spectrograph at the HI-13 tandem accelerator. We measured the angular distribution of the ${}^{12}\mathrm{C}({}^{11}\mathrm{B},{}^{7}\mathrm{Li}){}^{16}\mathrm{O}$ transfer reaction leading to the 6.917 MeV state. Based on the FRDWBA analysis, we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeV level in $^{16}$O to be (1.10 $\pm$ 0.29) $\times 10^{10}$ fm$^{-1}$, with which the reduced $\alpha$ width was computed to be $18.0\pm4.7$ keV at the channel radius of 6.5 fm. Finally, we calculated the astrophysical $S_{E2}(300)$ factor of the ground-state transitions to be 46.2 $\pm$ 7.7 keV b. The result for the astrophysical $S_{E2}(300)$ factor confirms the values obtained in various direct and indirect measurements and presents an independent examination of the most important data in nuclear astrophysics.

Determination of the photodisintegration reaction rates involving charged particles: Systematic calculations and proposed measurements based on the facility for Extreme Light Infrastructure–Nuclear Physics

Photodisintegration reaction rates involving charged particles are of relevance to the p-process nucleosynthesis that aims at explaining the production of the stable neutron-deficient nuclides heavier than iron. In this study, the cross sections and astrophysical rates of (g,p) and (g,a) reactions for about 3000 target nuclei with 10<Z<100 ranging from stable to proton dripline nuclei are computed. To study the sensitivity of the calculations to the optical model potentials (OMPs), both the phenomenological Woods-Saxon and the microscopic folding OMPs are taken into account. The systematic comparisons show that the reaction rates, especially for the (g,a) reaction, are dramatically influenced by the OMPs. Thus the better determination of the OMP is crucial to reduce the uncertainties of the photodisintegration reaction rates involving charged particles. Meanwhile, a gamma-beam facility at ELI-NP is being developed, which will open new opportunities to experimentally study the photodisintegration reactions of astrophysics interest. Considering both the important reactions identified by the nucleosynthesis studies and the purpose of complementing the experimental results for the reactions involving p-nuclei, the measurements of six (g,p) and eight (g,a) reactions based on the gamma-beam facility at ELI-NP and the ELISSA detector for the charged particles detection are proposed, and the GEANT4 simulations are correspondingly performed. The minimum required energies of the gamma-beam to measure these reactions are estimated. It is shown that the direct measurements of these photonuclear reactions within the Gamow windows at T_9=2.5 for p-process are fairly feasible and promising at ELI-NP. The expected experimental results will be used to constrain the OMPs of the charged particles, which can eventually reduce the uncertainties of the reaction rates for the p-process nucleosynthesis.

Indirect methods in nuclear astrophysics

It is well known that measuring cross-sections of thermonuclear reactions at the low energies typical of astrophysical sites is very difficult. This is due to the presence of the Coulomb barrier between the interacting nuclei. For non-explosive scenarios at astrophysical sites, the relevant energies typically span from few tens to few hundreds of keV while the Coulomb barrier is in the order of MeV. The fusion processes then proceed via tunnel effect and their cross-sections are strongly depending on the probability of penetration through the barrier. In a first approximation, this probability is given by the Gamow factor. Owing to the exponential decrease in this factor with energy, the cross-section values of thermonuclear fusion processes in stellar systems often reach values as small as micro- and nanobarn and even lower ones. Neutron-induced reactions, in spite of the absence of Coulomb barrier, are also difficult to measure. Indeed, it is the possible presence of a centrifugal barrier that can hinder the measurement of the values of the cross-sections of these processes. In either cases the cross-sections of astrophysical nuclear processes result in experimental difficulties, due to the low signal-to-noise ratio, that have been a challenge for scientists since the setting of this scientific field: Nuclear Astrophysics. In the last two to three decades, experimental improvements, including the construction of underground laboratories, allowed for the first time the measurement of cross-sections of astrophysical nuclear processes in the relevant energy region for astrophysics. Also, indirect methods were developed. As a general and common feature, using these methods it is possible to relate the features --typically the cross-section-- of a process that is experimentally simpler to measure, although not directly linked to astrophysics, to those of another process that is of interest for this latter field. This didactic paper will briefly describe some of these indirect methods with a special emphasis on Trojan Horse and on its application also to reactions that involve the use of radioactive ion beams and to neutron-induced reactions.

Double ionization of water molecules by proton impact: the role of the direct ionization mechanism

The proton-induced double ionization process of water molecules is here theoretically investigated at high impact energy. The current 1st Born perturbative approach refers to an initial collisional state that both includes a target molecular wave function expressed as a single-center linear combination of atomic orbitals and a plane wave for describing the incident proton whereas the final collisional state is characterized by a scattered proton modeled by a plane wave and two ejected electrons modeled by Coulomb wave functions coupled via a Gamow factor. Total and partial cross sections are then provided and compared with existing experimental and theoretical data in considering the various dissociative channels. Additionally, a study of the energy dependence of the double ionization process is reported for impact energies ranging from 300 keV to 10 MeV.

Preparation and characterization of strontium targets for nuclear astrophysics experiments

The present paper describes preparation and characterization of strontium targets for nuclear astrophysical experiments with alpha particles accelerated near the Gamow window energy. SrF2 and SrCO3 targets were obtained by thermal evaporation in similar conditions. Target characteristics (thickness, chemical purity and surface morphology) were determined via α transmission measurements, XRD and SEM/EDX analysis. The results reveal the SrF2 target exhibits better properties compared to the SrCO3 one for our nuclear astrophysics experiments. This result was supported by nuclear activation measurements with an α beam at the Bucharest Tandem 9 MV accelerator.

Direct measurement of astrophysically important resonances in K38(p,γ)Ca39

According to sensitivity studies, the $^{38}\mathrm{K}\left( p, \gamma \right){}^{39}\mathrm{Ca}$ reaction has a significant influence on $\mathrm{Ar}$, $\mathrm{K}$, and $\mathrm{Ca}$ production in classical novae. In order to constrain the rate of this reaction, we have performed a direct measurement of the strengths of three candidate $\ell = 0$ resonances within the Gamow window, at $386 \pm 10~\mathrm{keV}$, $515 \pm 10~\mathrm{keV}$, and $689 \pm 10~\mathrm{keV}$. The experiment was performed in inverse kinematics using a beam of unstable $^{38}\mathrm{K}$ impinged on a windowless $\mathrm{H}_2$ target. The $^{39}\mathrm{Ca}$ recoils and prompt $\gamma$ rays from $^{38}\mathrm{K}\left( p, \gamma \right){}^{39}\mathrm{Ca}$ reactions were detected in coincidence using a recoil mass separator and a BGO array, respectively. For the $689$ keV resonance, we observed a clear recoil-$\gamma$ coincidence signal and extracted resonance strength and energy values of $120^{+50}_{-30}~\mathrm{(stat.)}^{+20}_{-60}~\mathrm{(sys.)}~\mathrm{meV}$ and $679^{+2}_{-1}~\mathrm{(stat.)} \pm 1~\mathrm{(sys.)}~\mathrm{keV}$, respectively. We also performed a singles analysis, extracting a resonance strength of $120 \pm 20~\mathrm{(stat.)} \pm 15~\mathrm{(sys.)}~\mathrm{meV}$, consistent with the coincidence result. For the $386$ keV and $515$ keV resonances, we extract $90\%$ confidence level upper limits of $2.54$ meV and $18.4$ meV, respectively. We have established a new recommended $^{38}\mathrm{K}(p, \gamma){}^{39}\mathrm{Ca}$ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of ${\sim} 250$. Using the rate obtained in this work in model calculations of the hottest oxygen-neon novae reduces overall uncertainties on $\mathrm{Ar}$, $\mathrm{K}$, and $\mathrm{Ca}$ synthesis to factors of $15$ or less in all cases.

α-induced reaction cross sections in the mass range A ≈ 20 − 50: a critical review

In a recent review it was shown that the cross sections of α-induced reactions in the A ≈ 20 − 50 mass range follow a general and smooth trend in most cases. For comparison of cross sections of different targets at various energies the method of reduced cross sections σ red and reduced energies E red was used. Four outliers were identified: 36Ar and 40Ar with unusal small cross sections and 23Na and 33S with unusual huge cross sections. New data for 23Na were presented at this NPA-7 conference; contrary to the previous data, these new data fit into the general systematics. In addition, a relation between the most effective energy E 0 for astrophysical reaction rates (the so-called Gamow window) and the reduced energy E red is presented.

Current from a nano-gap hyperbolic diode using shape-factors: Theory

Quantum tunneling by field emission from nanoscale features or sharp field emission structures for which the anode-cathode gap is nanometers in scale (“nano diodes”) experience strong deviations from the planar image charge lowered tunneling barrier used in the Murphy and Good formulation of the Fowler-Nordheim equation. These deviations alter the prediction of total current from a curved surface. Modifications to the emission barrier are modeled using a hyperbolic (prolate spheroidal) geometry to determine the trajectories along which the Gamow factor in a WKB-like treatment is undertaken; a quadratic equivalent potential is determined, and a method of shape factors is used to evaluate the corrected total current from a protrusion or wedge geometry.

Orientation effect on the secondary-electron distributions for the HCl double ionization

Multiple differential cross sections of the double ionization of hydrogen chloride molecule impacted by electrons are here provided within the first Born approximation. The incident and scattered electrons are represented by plane wave functions, whereas the target is described by means of a single-center molecular wave function. The two ejected electrons are modeled by Coulomb wave functions and a Gamow factor is introduced to take into account the Coulomb repulsion between the two outgoing particles. In this work, we study the relative contributions of the four outermost orbitals of the HCl molecule to the double ionization process in the particular case of two electrons ejected from different subshells. The multiple differential cross sections are analyzed for specific target orientations and compared in terms of magnitude and shape. We report a strong dependence of the cross sections versus the target orientation by pointing out the signature of the well-known double ionizing processes, namely, the shake-off and the two-step 1 mechanisms.

Proton and α capture studies for nuclear astrophysics at GSI storage rings

SynopsisThe 124Xe(p,γ) reaction has been measured for the first time at energies around the Gamow window by using stored ions at the ESR facility. The desired beam energies below 10 MeV/u introduce new experimental challenges like windowless ions detection under UHV conditions, extremely short beam lifetimes and efficient beam deceleration and cooling, all of which have been successfully met.

Electron-induced double ionization of oriented methane molecules

We report here a theoretical study of the target orientation effect on the total cross sections for the double ionization of methane molecules impacted by electrons. The theoretical description is performed within the first Born approximation. The initial state of the collisional system is composed of an electron projectile modeled by a plane wave and a molecular target described by a one-center wave function while the final state is constituted by a scattered electron described by a plane wave and two ejected electrons both represented by a Coulomb wave and coupled with a Gamow factor. Secondary electron energetic distributions and total cross sections are reported for particular target configurations. Strong orientation effects on the double-ionization process are pointed out in particular when scrutinized orbital by orbital.

First spin-parity constraint of the 306 keV resonance in Cl35 for nova nucleosynthesis

Of particular interest in astrophysics is the $^{34}\mathrm{S}(p,\ensuremath{\gamma})^{35}\mathrm{Cl}$ reaction, which serves as a stepping stone in thermonuclear runaway reaction chains during a nova explosion. Though the isotopes involved are all stable, the reaction rate of this significant step is not well known, due to a lack of experimental spectroscopic information on states within the Gamow window above the proton separation threshold of $^{35}\mathrm{Cl}$. Measurements of level spins and parities provide input for the calculation of resonance strengths, which ultimately determine the astrophysical reaction rate of the $^{34}\mathrm{S}(p,\ensuremath{\gamma})^{35}\mathrm{Cl}$ proton capture reaction. By performing the $^{37}\mathrm{Cl}(p,t)^{35}\mathrm{Cl}$ reaction in normal kinematics at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory, we have conducted a study of the region of astrophysical interest in $^{35}\mathrm{Cl}$, and have made the first-ever constraint on the spin and parity assignment for a level at $6677\ifmmode\pm\else\textpm\fi{}15$ keV $({E}_{r}=306$ keV), inside the Gamow window for novae.

First Measurement of the 19F(α, p)22Ne Reaction at Energies of Astrophysical Relevance

Abstract The observational 19F abundance in stellar environments systematically exceeds the predicted one, thus representing one of the unsolved challenges for stellar modeling. It is therefore clear that further investigation is needed in this field. In this work, we focus our attention on the measurement of the reaction in the astrophysical energy range, between 0.2 and 0.8 MeV (far below the Coulomb barrier, 3.8 MeV), as it represents the main destruction channel in He-rich environments. The lowest energy at which this reaction has been studied with direct measurements is ∼0.66 MeV, covering only the upper tail of the Gamow window, causing the reaction-rate evaluation to be based on extrapolation. To investigate lower energies, the reaction has been studied by means of the Trojan horse method, applied to the quasi-free reaction at E beam = 6 MeV. The indirect cross section of the reaction at energies ≲1 MeV was extracted, fully covering the astrophysical region of interest and overlapping existing direct data for normalization. Several resonances have been detected for the first time inside the Gamow window. The reaction rate has been calculated, showing an increase up to a factor of 4 with respect to the literature at astrophysical temperatures. This might lead to potential major astrophysical implications.

Decay branching ratios of excitedMg24

The nuclear reactions $^{12}\mathrm{C}(^{12}\mathrm{C},\ensuremath{\alpha})^{20}\mathrm{Ne}$, $^{12}\mathrm{C}(^{12}\mathrm{C},p)^{23}\mathrm{Na}$, and $^{12}\mathrm{C}(^{12}\mathrm{C},n)^{23}\mathrm{Mg}$ are the primary reactions in carbon burning, which occurs as part of several stellar processes. The Gamow window, which describes the energy range where most of these reactions take place, is typically around 1.5 MeV in the center-of-mass frame. Direct measurements of the cross sections at this energy are difficult due to the large Coulomb barrier present between the carbon nuclei; however, a successful surrogate measurement can provide the branching ratios between these reactions while avoiding the $^{12}\mathrm{C}+\phantom{\rule{0.16em}{0ex}}^{12}\mathrm{C}$ Coulomb barrier. An experiment was performed using inelastic scattering of 40 MeV $\ensuremath{\alpha}$ particles on $^{24}\mathrm{Mg}$ as a possible surrogate for the $^{12}\mathrm{C}+\phantom{\rule{0.16em}{0ex}}^{12}\mathrm{C}$ compound nucleus.

Introduction of the new LUNA experimental setup for high precision measurement of the13C(α,n)16O reaction for astrophysical purposes

The 13 C(α,n)16 O reaction is the prevalent neutron source for the main s-process. The direct measurement of this reaction at stellar temperature (kT =8 keV) has so far not been possible due to the very low cross section at the corresponding energy. The extrapolation of the astrophysical S -factor of this reaction into the Gamow window (Eα,c.m. =140-230 keV) is complicated by the large uncertainties of the low-energy experimental data and the existence of a state of 17 O near the α-threshold that can have a large effect on low energy cross section. The aim of this paper is to introduce the new LUNA experimental setup, dedicated to the investigation of 13 C(α,n)16 O reaction below Eα,lab =400 keV.

Absolute cross sections of the86Sr(α,n)89Zr reaction at energies of astrophysical interest

Absolute cross sections for the 86 Sr(α,n)89 Zr reaction at energies close to the Gamow window are reported. Three thin SrF2 targets were irradiated using the 9 MV Tandem facility in IFIN-HH Bucharest that delivered α beams for the activation process. Two high-purity Germanium detectors were used to measure the induced activity of 89 Zr in a low background environment. The experimental results are in very good agreement with Hauser-Feshbach statistical model calculations performed with the TALYS code.

Feasibility study of the13C(α,n)16O reaction at LUNA

The 13C(α, n)16O reaction determines the dominant neutron source of the sprocess in thermally pulsing, low-mass, asymptotic giant branch (TP-AGB) stars. The temperature during the s-process in the 13C pocket of 90×106 K corresponds to a Gamow window of 140-230 keV. Since this energy is far below the Coulomb barrier, the cross section of this reaction is extremely small and its rate can only be extrapolated from the measurements at higher energies. At present, the cross section at Gamow peak is uncertain by almost one order of magnitude.

Target characterizations for direct measurement of the 13C(α, n)16O reaction at LUNA 400

The 13 C(α , n)16 O reaction is the main neutron source for the s-process in low mass AGB stars. Although several direct measurements have been performed, no dataset reaches the Gamow window due to the low cross section. Moreover a dominant component of systematic uncertainty comes from target behaviour under beam irradiation.This work presents a detailed characterization of enriched 13 C targets in order to test reproducibility and uniformity of the evaporation method, stability and purity of targets under a high intensity proton beam (100-200 uA) for the study of this reaction at the Laboratory for Underground Nuclear Astrophysics (LUNA) facility installed at Laboratori Nazionali del Gran Sasso (LNGS, INFN). A procedure to evaluate the target thickness and to monitor its degradation is discussed and preliminary results are presented.

An accurate analytic representation of the temperature dependence of nonresonant nuclear reaction rate coefficients

Abstract There has been intense interest for several decades by different research groups to accurately model the temperature dependence of a large number of nuclear reaction rate coefficients for both light and heavy nuclides. The rate coefficient, k ( T ) , is given by the Maxwellian average of the reactive cross section expressed in terms of the astrophysical factor, S ( E ) , which for nonresonant reactions is generally written as a power series in the relative energy E . A computationally efficient algorithm for the temperature dependence of nuclear reaction rate coefficients is required for fusion reactor research and for models of nucleosynthesis and stellar evolution. In this paper, an accurate analytical expression for the temperature dependence of nuclear reaction rate coefficients is provided in terms of τ = 3 ( b / 2 ) 2 3 or equivalently, T − 1 3 , where b = B / k B T , B is the Gamow factor and k B is the Boltzmann constant. The methodology is appropriate for all nonresonant nuclear reactions for which S ( E ) can be represented as a power series in E . The explicit expression for the rate coefficient versus temperature is derived with the asymptotic expansions of the moments of w ( E ) = exp ( − E / k B T − B / E ) in terms of τ . The zeroth order moment is the familiar Gaussian approximation to the rate coefficient. Results are reported for the representative reactions D(d, p)T, D(d, n) 3 He and 7 Li(p, α ) α and compared with several different fitting procedures reported in the literature.