Gamow Window Research Articles

TALYS calculation and a short review of the experimental status of proton capture studies on p-nuclei: A guide to future investigation* *The present study was funded by DST, Govt. of India, under the WOS-A scheme (Reference No.: SR/WOS-A/PM-68/2017)

TALYS calculations were performed to obtain the theoretical proton capture cross-sections on the p-nuclei. A short review on the status of related experimental studies was also conducted. Some basic properties such as Q-values, Coulomb barrier, Gamow peak, Gamow Window, and decay properties of the parent and daughter nuclei were studied. Various experimental parameters, e.g., beam energy, beam current, targets, and detectors, used in experimental investigations reported in the literature, were tabulated. The results of the TALYS calculations in the Gamow region were compared with the corresponding experimental values wherever available. This study is expected to facilitate the planning of future experiments.

Astrophysical S-factor and reaction rate for 15N(p,γ)16O within the modified potential cluster model* *Supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP09259174)

We study radiative capture on the ground state of 16O at stellar energies within the framework of a modified potential cluster model (MPCM) with forbidden states, including low-lying resonances. The investigation of the 15N( )16O reaction includes the consideration of resonances due to transitions and the contribution of the scattering wave in the p + 15N channel due to the transition. We calculated the astrophysical low-energy S-factor, and the extrapolated turned out to be within 34.7−40.4 keV·b. The important role of the asymptotic constant (AC) for the 15N( )16O process with interfering (312) and (962) resonances is elucidated. A comparison of our calculation for the S-factor with existing experimental and theoretical data is addressed, and a reasonable agreement is found. The reaction rate is calculated and compared with the existing rates. It has negligible dependence on the variation of AC but shows a strong impact of the interference of (312) and (962) resonances in reference to the CNO Gamow windows, especially at low temperatures. We estimate the contribution of cascade transitions to the reaction rate based on the exclusive experimental data from Phys. Rev. C. 85, 065810 (2012). The reaction rate enhancement due to the cascade transitions is observed from and reaches the maximum factor ~ 1.3 at . We present the Gamow energy window and a comparison of rates for radiative proton capture reactions 12N( )13O, 13N( ) 14O, 14N( )15O, and 15N( )16O obtained in the framework of the MPCM and provide the temperature windows, prevalence, and significance of each process.

Reinvestigating the Gamow Factor of Reactions on Light Nuclei

We present a modified Gamow factor by reinvestigating the conventional assumptions used in its derivation. The conventional Gamow factor, factorized from the total cross section, effectively describes the penetration probabilities (PPs) in low-energy nuclear reactions under the assumption of particle energies significantly lower than the Coulomb barrier. However, we find that the assumption is invalid for light nuclei, resulting in PPs that depend on the nuclear potential depth for such nuclei. By adopting a potential depth fitted to experimental fusion cross sections, we demonstrate that PPs for light nuclei (D+D, D+T, D+3He, p+D, p+6Li, and p+7Li) become higher than those predicted by the conventional form near the Coulomb barrier. This reduces the Gamow peak energy by a factor of 5.3 maximally compared to the conventional form. Furthermore, we show that the enhancement factor due to the Debye screening effects in the solar core can be reduced by approximately 5%–10% due to the modified PP. Our findings hold implications for evaluating the available energy region in low-energy reaction experiments based on the Gamow peak energy region and for understanding electron screening effects in typical astrophysical environments.

The 13C(α,n)16O cross section measurement at low energies at LUNA

One of the main neutron sources for the astrophysical s-process is the 13C(α,n)16O. This reaction takes place in thermally pulsing asymptotic giant branch (TP-AGB) stars in a stellar environmental with temperature of about 90 MK. To model the nucleosynthesis process connected with the reaction, it is important the cross section reaction evaluation inside the so called Gamow peak, in the energy window 150-240 keV. In this work the results of the first 13C(α,n)16O direct measurement performed by the LUNA collaboration in the underground laboratory of LNGS are presented.The measurement covers the energy range 230-300 keV, being the first direct measurement to reach the s-process Gamow window. Lower uncertainties with respect to previous measurements in literature are provided and this allows to reduce overall uncertainties on reaction rates calculation. Selected stellar models have been computed to estimate the impact of our revised reaction rate. Using the lower reaction rate at -2σ, for stars of nearly solar composition, we find sizeable variations for some isotopes, whose production is influenced by the activation of close-by branching points that are sensitive to the neutron density, in particular 60Fe, 205Pb and and 152Gd.

Correction to: Calculable Microscopic Theory for $$^{12}\hbox {C}(\alpha ,\gamma )^{16}\hbox {O}$$ Cross Section near Gamow Window

Correction to: Calculable Microscopic Theory for $$^{12}\hbox {C}(\alpha ,\gamma )^{16}\hbox {O}$$ Cross Section near Gamow Window

First measurement of the 7Li(D, n) astrophysical S-factor in laser-induced full plasma

Nuclear fusion reactions which produce energies and most of the elements in the Universe are the keys to driving the process of the Big Bang nucleosynthesis, as well as the evolution of stars. For fusions in real astrophysical conditions, it is crucial to directly measure them in the plasma environments. However, it is challenging to obtain reaction cross sections quantitatively because of the high instabilities of plasma. Here, an innovative self-calibration method is proposed to eliminate the large uncertainties caused by the plasma instabilities. And for the first time, it is applied to investigating the deuteron-lithium nuclear-fusion reaction 7Li(D,n)8Be in the plasma, which is related to the Big Bang lithium abundance puzzle. Further, the reaction's astrophysical S-factor in the Gamow window around 173 keV in the plasma is measured to be S=(24±8) MeV⋅barn, which demonstrates from an experimental point of view that the coulomb screening effect does not play an essential role in this 7Li consuming reaction related to the Big Bang lithium abundance puzzle. This self-calibration method for nuclear reactions in the plasma can also be applied to exploring other nuclear-fusion reactions, such as 7Li(p,α)4He and 6Li(p,α)3He, as well as providing a new probe for detecting plasma dynamics.

Fast and accurate determination of the curvature-corrected field emission current

The curvature-corrected field emission current density, obtained by linearizing at or below the Fermi energy, is investigated. Two special cases, corresponding to the peak of normal energy distribution and mean normal energy, are considered. It is found that the current density evaluated using the mean normal energy results in errors in the net emission current below 3% for apex radius of curvature Ra≥5 nm and for apex fields Ea in the range of 3–10 V/nm for an emitter having a work function of ϕ=4.5 eV. An analytical expression for the net field emission current is also obtained for local parabolic tips using the generalized cosine law. The errors are found to be below 6% for Ra≥5 nm over an identical range of apex field strengths. The benchmark current is obtained by numerically integrating the current density over the emitter surface and the current density itself computed by integrating over the energy states using the exact Gamow factor and the Kemble form for the WKB transmission coefficient. The analytical expression results in a remarkable speed-up in the computation of the net emission current and is especially useful for large area field emitters having tens of thousands of emission sites.

Direct measurement of the 13C(α,n)16O reaction in the Gamow window of the s-process nucleosynthesis

One of the main neutron sources for the astrophysical s process is the 13C(α,n)16O reaction, which takes place in thermally pulsing asymptotic giant branch (TP-AGB) stars at environmental temperature around 90 MK. To model the nucleosynthesis process connected with the reaction, it is important to know with high accuracy the cross section reaction in the energy window 240-150 keV, the so called Gamow window. At these sub-Coulomb energies, direct cross section measurements are severely affected by the low event rate and low signal-to-noise ratio. In this work, a new study of the astrophysical S(E)-factor for the 13C(α,n)16O reaction is presented.In the framework of the LUNA scientific programme, a direct measurement of the absolute cross section of the 13C(α,n)16O reaction in an energy window from 300 keV down to 230 keV, significantly closer to the Gamow peak, has been performed. Lower uncertainties with respect to literature values are obtained allowing to reduce overall uncertainties on reaction rates calculation. Selected stellar models have been computed to estimate the impact of our revised reaction rate. For stars of nearly solar composition, we find sizeable variations of some isotopes, whose production is influenced by the activation of close-by branching points that are sensitive to the neutron density, in particular 60Fe, 205Pb and and 152Gd.

S-process Nuclear Reaction Rates

In stars the 13C(α, n)16O and 22Ne(α, n)25Mg reactions are the two main sources of neutrons for the so-called slow neutron capture process (s-process), which is one of the main mechanisms for the stellar synthesis of heavy elements. About 13C(α, n)16O, in despite of many efforts in measuring its cross section at the lower energies, only high uncertainty data above the s-process Gamow window (150 keV < Ecm < 230 keV) were available, due mostly to the difficulties on suppress the natural background. Indeed, only recently the LUNA collaboration performed high precision underground measurements of the reaction cross section inside the Gamow window, improving the accuracy of its extrapolation at the lower energies. Again due to natural background, only upper limits for the 22Ne(α, n)25Mg reaction cross section are currently known in the s-process Gamow window (450 keV < Ecm < 750 keV). For this, the ERC founded project SHADES (Unina/INFN) aims to perform high precision and high sensitivity measurements of the 22Ne(α, n)25Mg reaction cross section down to the neutron threshold. A sensitivity improvement of at least two orders of magnitude over the state of the art is expected thanks to the low natural background environment of the INFN-LNGS laboratory in Italy, the high beam current of the new LUNAMV accelerator and the Beam Induced Background events suppression performed by SHADES hybrid detectors array. In this paper I will present the LUNA efforts to estimate nuclear reaction rates for 13C(α, n)16O, with a focus on the R-Matrix analysis performed with the code AZURE2 to extrapolate nuclear reaction rates at stellar energies and the estimate of their uncertainty through Monte Carlo methods. I will also present an overview of the SHADES project to measure 22Ne(α, n)25Mg in the Gamow window and the first results on the setup commissioning.

12C+12C reactions for Nuclear Astrophysics

12C fusion reactions are among the most important in stellar evolution since they determine the destiny of massive stars. Over the past fifty years, massive efforts have been done to measure these reactions at low energies. However, existing data present several discrepancies between sets and large uncertainties specially at the lowest energies. Factors such as beam/environmental backgrounds, extremely low cross sections and insufficient knowledge of the reaction mechanism contribute to these problems. Recently, the ERNA collaboration measured the 12C+12C reactions at Ec.m. = 2.51 - 4.36 MeV with energy steps between 10 and 25 keV in the centre of mass. Representing the smallest energy steps to date. In these measurements, beam induced background was minimised and S-factors for the proton and alpha channels were calculated. Results indicate that a possible explanation for the discrepancies between data sets is the wrongly assumed constant branching ratios and isotropical angular distributions. Given the excellent performance of the detectors for low energy measurements, a collaboration with the LUNA group (LNGS) has started. Background measurements underground are being performed and results indicate it could be possible to measure the 12C+12C reactions directly into the Gamow Window.

Influence of crystal structures on electron screening

For nucleosynthesis calculations, precise reaction rates should be known at energies within the Gamow window. At these energies, electron screening cannot be neglected. Despite the significance of the effect, a huge disagreement between experimental data and theoretical predictions is still not understood. In order to address to this problem, we investigated the dependence of the electron screening potential on the target host lattice structure by measuring the rate of the 2H(19F,p)20F reaction in zirconium, titanium and palladium targets containing deuterium.

Results of total cross-section measurements of the 87Rb(p,γ)88Sr reaction

The existence of a set of stable proton-rich nuclei - the p nuclei - cannot be explained via neutron-capture reactions. Therefore, another mechanism has to exist in order to explain their origin, the most probable, especially at high masses, being photodisintegration reactions. This gives rise to the γ process. Since most photodisintegration reactions involved in the process are not experimentally accessible, reliable statistical model calculations are needed to predict cross sections and reaction rates. To improve these calculations nuclear input parameters need to be constrained and a large experimental database is needed. Via comparison of experimental data to theoretical predictions different models can be tested and constrained. In order to study the 87Rb(p,γ)88Sr reaction, for which previously no experimental data have been available, an in-beam experiment at at the University of Cologne’s high-efficiency HPGe γ-ray spectrometer HORUS was performed. Proton beams with energies between Ep = 2000 to 5000 keV reaching deep into the Gamow window of the reaction were provided by the 10 MV FN Tandem accelerator. Cross-section values at six proton beam energies were determined. The experimental results are in good agreement with statistical model calculations. The obtained results are the first experimental cross-section values for the87Rb(p,γ)88Sr reaction and help to constrain the nuclear physics input for statistical model calculations.

A new 12C+12C reaction rate: Impact on stellar evolution

Among the reactions driving stellar evolution during carbon burning, 12C + 12C fusion provides the key ingredients. This system reveals many resonances, but also regions with suppressed fusion cross-sections. The reaction was recently measured by the STELLA collaboration utilizing the gammaparticle coincidence technique for precise cross-section measurements reaching down to the Gamow window of massive stars. From the experimental data, reaction rates were determined by approximating a hindrance parametrization and by adding on top a resonance at the lowest measured energy. The impact of these reaction rates on the evolution of massive stars was explored with models of 12 and 25 M⊙ using the stellar evolution code GENEC, and a detailed study of the resulting nucleosynthesis with a 1454 elements network was performed. The sensitivity of the STELLA experimental cross-sections on the temperature range for C-burning for the stellar models studied were presented. The final abundances and their impacts on stellar evolution were discussed.

Deep Underground Laboratory Measurement of ^{13}C(α,n)^{16}O in the Gamow Windows of the s and i Processes.

The ^{13}C(α,n)^{16}O reaction is the main neutron source for the slow-neutron-capture process in asymptotic giant branch stars and for the intermediate process. Direct measurements at astrophysical energies in above-ground laboratories are hindered by the extremely small cross sections and vast cosmic-ray-induced background. We performed the first consistent direct measurement in the range of E_{c.m.}=0.24 to 1.9MeV using the accelerators at the China Jinping Underground Laboratory and Sichuan University. Our measurement covers almost the entire intermediate process Gamow window in which the large uncertainty of the previous experiments has been reduced from 60% down to 15%, eliminates the large systematic uncertainty in the extrapolation arising from the inconsistency of existing datasets, and provides a more reliable reaction rate for the studies of the slow-neutron-capture and intermediate processes along with the first direct determination of the alpha strength for the near-threshold state.

Resonance Excitations in ^{7}Be(d,p)^{8}Be^{*} to Address the Cosmological Lithium Problem.

The anomaly in lithium abundance is a well-known unresolved problem in nuclear astrophysics. A recent revisit to the problem tried the avenue of resonance enhancement to account for the primordial ^{7}Li abundance in standard big-bang nucleosynthesis. Prior measurements of the ^{7}Be(d,p)^{8}Be^{*} reaction could not account for the individual contributions of the different excited states involved, particularly at higher energies close to the Q value of the reaction. We carried out an experiment at HIE-ISOLDE, CERN to study this reaction at E_{c.m.}=7.8 MeV, populating excitations up to 22MeV in ^{8}Be for the first time. The angular distributions of the several excited states have been measured and the contributions of the higher excited states in the total cross section at the relevant big-bang energies were obtained by extrapolation to the Gamow window using the talys code. The results show that by including the contribution of the 16.63MeV state, the maximum value of the total S factor inside the Gamow window comes out to be 167MeV b as compared to earlier estimate of 100MeV b. However, this still does not account for the lithium discrepancy.

Constraints on key O17(α,γ)Ne21 resonances and impact on the weak s process

The efficiency of the slow neutron-capture process in massive stars is strongly influenced by neutron-capture reactions on light elements. At low metallicity, $^{16}$O is an important neutron absorber, but the effectiveness of $^{16}$O as a light-element neutron poison is modified by competition between subsequent $^{17}$O$(\alpha,n)^{20}$Ne and $^{17}$O$(\alpha,\gamma)^{21}$Ne reactions. The strengths of key $^{17}$O$(\alpha,\gamma)^{21}$Ne resonances within the Gamow window for core helium burning in massive stars are not well constrained by experiment. This work presents more precise measurements of resonances in the energy range $E_{c.m.} = 612 - 1319$ keV. We extract resonance strengths of $\omega\gamma_{638} = 4.85\pm0.79$ $\mu$eV, $\omega\gamma_{721} = 13.0^{+3.3}_{-2.4}$ $\mu$eV, $\omega\gamma_{814} = 7.72\pm0.55$ meV and $\omega\gamma_{1318} = 136\pm 13$ meV, for resonances at $E_{c.m.} =$ 638, 721, 814 and 1318 keV, respectively. We also report an upper limit for the 612 keV resonance of $\omega\gamma<140$ neV ($95\%$ c.l.), which effectively rules out any significant contribution from this resonance to the reaction rate. From this work, a new $^{17}$O$(\alpha,\gamma)^{21}$Ne thermonuclear reaction rate is calculated and compared to the literature. The effect of present uncertainties in the $^{17}$O$(\alpha,\gamma)^{21}$Ne reaction rate on weak s-process yields are then explored using post-processing calculations based on a rotating $20M_{\odot}$ low-metallicity massive star. The resulting $^{17}$O$(\alpha,\gamma)^{21}$Ne reaction rate is lower with respect to the pre-existing literature and found to enhance weak s-process yields in rotating massive star models.

Proton capture onP30in novae: On the existence of states at 6.40 MeV and 6.65 MeV inS31

We use a high-resolution $^{32}\mathrm{S}(d,t)$ measurement to investigate the claimed existence of a 6401(3) keV state in $^{31}\mathrm{S}$ that may affect the $^{30}\mathrm{P}(p,\ensuremath{\gamma})$ nuclear reaction rate in oxygen-neon (ONe) novae. Our data are shown to exclude the null hypothesis---that the state does not exist---with high significance. Additionally, the data also suggest the existence of a hitherto unreported state at 6648(4) keV. This state corresponds to a $^{30}\mathrm{P}(p,\ensuremath{\gamma})$ resonance at 517(4) keV, located below the higher edge of the Gamow window for peak nova temperatures of about 0.4 GK.

Gamow factors and current densities in cold field emission theory: A comparative study

The factors that contribute to the accuracy of the cold field emission current within the contemporary frameworks are investigated. It is found that so long as the net current is evaluated using an expression for the local current density obtained by linearizing the Gamow factor, the primary source of error is the choice of the energy at which the Taylor expansion is done, but not as much on the choice of the method used to arrive at the approximate Gamow factor. A suitable choice of linearization energy and the implementation of the Kemble correction allow the restriction of errors to below 3% across a wide range of local fields.

Development of a low-background neutron detector array

A low-background neutron detector array was developed to measure the cross section of the $$^{13}$$ C( $$\alpha$$ ,n) $$^{16}$$ O reaction, which is the neutron source for the s-process in AGB stars, in the Gamow window ( $$E_\text {c.m.}$$ = 190 ± 40 keV) at the China Jinping Underground Laboratory (CJPL). The detector array consists of 24 $$^{3}$$ He proportional counters embedded in a polyethylene cube. Owing to the deep underground location and a borated polyethylene shield around the detector array, a low background of 4.5(2)/h was achieved. The $$^{51}$$ V(p, n) $$^{51}$$ Cr reaction was used to determine the neutron detection efficiency of the array for neutrons with energies $$E_\text {n}<$$ 1 MeV. Geant4 simulations are shown to effectively reproduce the experimental results. They were used to extrapolate the detection efficiency to higher energies for neutrons emitted in the $$^{13}$$ C( $$\alpha$$ ,n) $$^{16}$$ O reaction. The theoretical angular distributions of the $$^{13}$$ C( $$\alpha$$ ,n) $$^{16}$$ O reaction were shown to be important in the estimation of the uncertainties of the detection efficiency.

A new 12C + 12C nuclear reaction rate: Impact on stellar evolution

Context. By changing the internal composition of stars, nuclear reactions play a key role in their evolution and spur their contribution to the chemical evolution of galaxies. The STELLA collaboration recently carried out new direct measurements of the 12C + 12C fusion cross section – one of the key reactions occurring in C-burning regions in massive stars. Using a coincidence technique, accurate measurements were obtained for many different energies, with the lowest energy explored according to the Gamow window for massive stars. Aims. This work presents new 12C + 12C reaction rates in the form of numerical tables with associated uncertainty estimations, as well as analytical formulae that can be directly implemented into stellar evolution codes. We also describe the impact of these new rates on C-burning in stars. Methods. We determined reaction rates for two cross section extrapolation models: one based on the fusion-hindrance phenomenon and the other on fusion-hindrance plus a resonance. We then compared our results to prior data. Using the GENEC stellar evolution code, we study how these new rates impact the C-burning phases in two sets of stellar models for stars with 12 M⊙ and 25 M⊙ initial masses, which were chosen to be highly representative of the diversity of massive stars. Results. The effective temperatures of C-burning in both sets of stellar models are entirely covered by the sensitivity of the present experimental data and no extrapolation of the rates is required. Although the rates may differ by more than an order of magnitude for temperatures typical of C-burning, the impacts on the stellar structures during that phase remain modest. This is a consequence of the readjustment of the stellar structure to a change of nuclear reaction rate for reactions that are shown to be important for energy production. For the hindrance case, the C-burning phase is found to occur at central temperatures that are 10% higher than with the hindrance plus resonance rate. Its C-burning lifetime is reduced by a factor of two. This model, nevertheless, loses more entropy than the other one; thus, it enters into the degeneracy regime earlier, which will impact the last stages of the evolution at the pre-core collapse time. The hindrance model produces up to 60% more neon. The impact of the different rates on the s-process occurring during the C-burning phase is modest, affecting the final abundances of s-processed elements by at most 20% (cobalt).