Astrophysical Energies Research Articles

Measurement of the cross section of 12C( α, γ) 16O using the recoil mass separator ERNA

The reaction 12 C( α , γ ) 16 O plays a key role in determining the C/O ratio in the stellar core at the end of helium burning, which in turn influences the further evolution and nucleosynthesis. The determination of the cross section at the relevant astrophysical energy E c m = 0.3 MeV , which is of the order of 10 −17 b, requires extrapolation of the S factor determined from data collected with high precision and accuracy at higher energy. A new experimental approach has been undertaken in order to study this reaction for the first time by the direct detection of the 16 O nuclides using the recoil mass separator ERNA.

Measurement of cross section and astrophysical factor of the d(d,p)t reaction using the Trojan Horse Method

Knowledge about reactions involving deuterium is required for a correct understanding of stellar and primordial nucleosynthesis processes, and also in planning fusion reactors for energy production. We have studied the d(d,p)t reaction in the energy range from 1.5 MeV down to astrophysical energies by means of the Trojan Horse Method applied to the three-body 6 Li(d,pt) α reaction, at a beam energy of 14 MeV. Protons and tritons have been detected in coincidence and identified. Quasi-free events have been kinematically selected, in order to extract the cross section and the astrophysical factor, and compare them with the values measured for the direct d(d,p)t process.

Influence of the electronic chaotic motion on the fusion dynamics at astrophysical energies

We perform semi-classical molecular dynamics simulations of screening by bound electrons in low energy nuclear reactions. In our simulations quantum effects corresponding to the Pauli and Heisenberg principle are enforced by constraints. In addition to the well-known adiabatic and sudden limits, we propose a new “dissipative limit” which is expected to be important not only at high energies but in the extremely low energy region. The dissipative limit is associated with the chaotic behavior of the electronic motion. It affects also the magnitude of the enhancement factor. We discuss also numerical experiments using polarized targets. The derived enhancement factors in our simulation are in agreement with those extracted within the R-matrix approach.

A test of the zero-range DWBA method at astrophysical energies

The DWBA method is tested through a comparison with a microscopic cluster model on the 13C (α, n) 16O reaction in the energy range E = 0-5MeV, relevant for nuclear astrophysics. The conditions of the calculation are as close as possible to the reference model, i.e. the nucleus-nucleus potentials are phase equivalent, and the spectroscopic factors are identical. We find significant differences between both approaches, which means that antisymmetrization effects, missing in the DWBA, are important. Our work also points out the strong sensitivity of the DWBA with input parameters.

σ(γ,p)∕σ(γ,n)ratio, current conservation, and nucleon scattering inHe4

A continuum shell model has been constructed which allows inclusion of any nonspurious states of the core nuclei and any nonspurious states of the composite system. The resulting coupled-channels solutions are antisymmetric and translationally invariant. These wave functions can be used to calculate many nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. The model is used to investigate the $^{4}\mathrm{He}(\ensuremath{\gamma},p)^{3}\mathrm{H}$, $^{4}\mathrm{He}(\ensuremath{\gamma},n)^{3}\mathrm{He}$, and, $^{3}\mathrm{He}(p,p)^{3}\mathrm{He}$ reactions.

The Trojan-Horse Method applied to theLi(p,α)He reaction down to astrophysical energies

The Trojan-Horse Method has been applied to the three-bodyd( 6 Li,α 3 He)n break-up reaction in order to extract the bare nucleus S(E) factor for the 6 Li(p,α) 3 He down to astrophysical energies.

The Trojan-Horse Method applied to theLi(p,α)He reaction down to astrophysical energies

The Trojan-Horse Method has been applied to the three-bodyd( 6 Li,α 3 He)n break-up reaction in order to extract the bare nucleus S(E) factor for the 6 Li(p,α) 3 He down to astrophysical energies.

The Trojan-Horse Method applied to the 6Li(p,α) 3He reaction down to astrophysical energies

The Trojan-Horse Method has been applied to the three-bodyd( 6Li,α 3He)n break-up reaction in order to extract the bare nucleus S(E) factor for the 6Li(p,α) 3He down to astrophysical energies.

Indirect Study of the Astrophysically Relevant6Li(p, α)3He Reaction by Means of the Trojan Horse Method

The Trojan Horse Method was applied to the 2 H( 6 Li,α 3 He)n three-body reaction in order to extract the bare nucleus S(E) factor for the 6 Li(p, α) 3 He reaction. The three-body reaction was performed in two kinematically complete experiments at beam energies of 25 and 14 MeV. The selected quasi-free coincidence yield was compared with the result of a Monte Carlo calculation where the entering two-body cross section was the result of a R-matrix parameterization of the direct two-body cross section. The quite good agreement throughout the investigated region above and below the p- 6 Li Coulomb barrier, allowed for the extraction of the bare S(E) factor in the astrophysical energy region. The S(0) value together with an independent estimate of the screening potential U e were derived and compared with those obtained from direct measurements.

Fission and the r-process: The rates of induced and delayed fission

The most recent fission-barrier calculations based on improved mass formulas indicate that the adopted values are underestimated. We analyze the dependence of the fission rates on the fission barrier and show that an increase in the fission barriers leads not so much to a decrease in the importance of fission as to the possible synthesis of heavier elements in the r-process. The rates of induced fission of most isotopes with Z>80 at astrophysical energies have been calculated for the first time for fission barriers obtained from different theoretical models.

Indirect methods for astrophysical nuclear reaction rates

Astrophysical nuclear reaction rates are usually extremely difficult to measure directly due to the very low relevant astrophysical energies. Thus indirect methods have been proposed, where the reaction can be measured at higher energy and the connection to the astrophysical process is established via direct reaction theory. These approaches are briefly reviewed here. We discuss in more detail the Trojan-Horse Method, which studies the two-body astrophysical reaction as a subprocess of an exclusive three-body breakup reaction. We show the essential features of the approach and discuss recent applications, which shows the promising aspects of the approach.

Validity test of the “Trojan horse” method applied to the6Li(p,α)3Hereaction

The ${}^{6}\mathrm{Li}(p,\ensuremath{\alpha}{)}^{3}\mathrm{He}$ reaction has been studied from ${E}_{\mathrm{c}.\mathrm{m}.}=2.4\mathrm{MeV}$ down to astrophysical energies by means of the indirect Trojan horse method applied to the ${}^{2}\mathrm{H}{(}^{6}\mathrm{Li},\ensuremath{\alpha}$ ${}^{3}\mathrm{He})$ n three-body reaction performed at an incident energy of 25 MeV. Coincidence spectra measured in a kinematically complete experiment show the presence of the quasifree ${}^{6}\mathrm{Li}\ensuremath{-}p$ process. The excitation function for this process was extracted from the three-body reaction cross section at low neutron momentum and compared with the behavior of the free two-body reaction cross section.

Indirect study of the 6Li(p, α) 3He reaction at astrophysical energies

The bare nucleus cross section for the 6Li(p, α) 3He reaction has been extracted in the energy range from 2.3 MeV down to astrophysical energies by means of the Trojan-Horse-Method applied to the three-body d( 6Li,α 3He)n break-up reaction.

Bare astrophysical S(E)-factor for the 6Li( d, α) 4He and 7Li( p, α) 4He reactions at astrophysical energies

The Trojan Horse Method has been applied to study the 7 Li( p, α) 4 He and 6( Li( d, α) 4 He reactions through the 7Li(d, αα)n and 6Li( 6Li, αα) 4He three body processes, respectively. The electron screening potential deduced from these experiments is much larger than the adiabatic approximation prediction for both cases; the systematic discrepancy between data and theoretical predictions is thus confirmed. Astrophysical implications of these measurements are also discussed.

Enhancement of Resonant Thermonuclear Reaction Rates in Extremely Dense Stellar Plasmas

The enhancement factor of the resonant thermonuclear reaction rates is calculated for the extremely dense stellar plasmas in the liquid phase. In order to calculate the enhancement factor we use the screening potential which is deduced from the numerical experiment of the classical one-component plasma. It is found that the enhancement is tremendous for white dwarf densities if the ^{12}C + ^{12}C fusion cross sections show resonant behavior in the astrophysical energy range. We summarize our numerical results by accurate analytic fitting formulae.

Potential resonant screening effects on stellar 12C + 12C reaction rates

The 12C + 12C fusion cross-sections show a resonant behavior down to the lowest energies accessible so far in the laboratory. If this tendency continues into the astrophysical energy range, the stellar 12C + 12C reaction rates have to be corrected for resonant screening effects, in addition to the conventional screening corrections. We estimate the resonant screening effects in the weak electron screening limit for hydrostatic burning and white-dwarf environments.

Direct capture contribution to the [formula omitted]N reaction at astrophysical energies

The contribution of the direct mechanism to the 11 C( p,γ) 12 N capture reaction at astrophysically relevant energies is calculated using the overlap integral 〈 11 C| 12 N〉 and the p– 11 C local effective potential obtained within a microscopic approach. This approach is based on the solution of the inhomogeneous differential equation with the source term calculated within the translation-invariant 0 ℏω shell model. The calculations resulted in a zero-energy astrophysical S-factor S(0) equal to 0.149 keV b. This value was obtained with the two-body effective NN potential, which gives the asymptotic normalization coefficient (ANC) for mirror nucleus 12 B close to the available experimental value. A separate estimation of S(0) based on the ratio of mirror ANCs gave S(0)=0.111 +0.025 −0.020 keV b. This value is about three times larger than the one obtained from the Coulomb breakup of 12 N.

The p-shell with one particle in the continuum

A continuum shell model is now available for p-shell nuclei with exactly the same important properties as a bound-state p-shell model calculation. This means that one can obtain all solutions that correspond to coupling one nucleon to the possible p-shell states of a bound-state calculation. The resulting coupled-channels solutions are antisymmetric and contain no spurious components. This model can be used to describe a very broad range of nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. Example calculations are shown for the compound systems 7Be and 7Li. Here it is demonstrated that agreement between theoretical and experimentally determined elastic and inelastic cross sections and analyzing power values can be improved by coupling to all open channels.

Asymptotic normalization coefficients and astrophysical direct capture rates

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The 10B(7Be, 8B)9Be and 14N(7Be, 8B)13C reactions have been used to measure the ANC appropriate for determining the 7Be(p,γ)8B rate, and the 14N(11C, 12N)13C reaction has been used to measure the ANC required to calculate the 11C(p,γ)12N rate.

First results with the recoil separator ARES

We present here the first results obtained with the new recoil separator ARES. ARES is used for the measurement of (p,gamma) and (alpha,gamma) reactions at astrophysical energies in inverse kinematic using both stable and radioactive beams.