Search

It is known that the calculated values of log(ft) and the half-life of beta decay are less than the measured values when a single-particle approach is used to calculate these quantities. In this article, we discuss the importance of taking into account the spectroscopic factor in the calculation of the half-life and log(ft) beta decay of nuclei containing one nucleon in the outermost shell. We also emphasize the dominant role of the asymptotic normalization coefficient, which takes into account the many-particle effect and allows us to obtain the spectroscopic factor necessary to describe the reaction 13N → 13C + β+ + νe . We find the asymptotic normalization coefficients using the experimental data of the elastic scattering phase-shift of the proton and neutron on 12C. Using overlap functions instead of single-particle functions, we obtain a better comparison with the experimental data. The overlap function is represented as the product of the single-particle function and the root of the corresponding spectroscopic factor.

The total cross-section, astrophysical S-factor, and rate of radiative capture reaction 12C(p, γ)13N are calculated using the potential model. In this work, we take into account the capture of protons through s1/2 → p1/2 and d3/2 → p1/2 single-particle transitions, fine-tune the values of the depth and nuclear radius of the Woods-Saxon potential to achieve better comparison with the measured data. The results for the elastic scattering phase shift, astrophysical S-factor, and rates are compared with the previously reported results of the calculations and experimental data.

Within the framework of the modified potential model, we computed the astrophysical S-factor of the proton radiative capture p + 11C → 12N + γ. At energies bearing astrophysical importance, radiative capture is a key process in the spectroscopic study of 12N. In this work, we consider the radiative capture cross-section for the proton capture by 11C within the framework of the potential model. For the possible electric and magnetic dipole transitions, we computed the partial components of the astrophysical S-factor within the energy range E = (0.01–0.8) MeV. The computed value of the S-factor at zero energy shows satisfactory agreement with the reported results. Furthermore, we computed the radiative capture rates for the selected reaction, which shows a better comparison with the reported data.

Radiative capture $p + {}^{13}\mathrm{C}\rightarrow {}^{14}\mathrm{N}+\gamma $ at energies bearing astrophysical consequences is one of the important processes in the CNO cycle. We focus on the possibility of describing the main contribution to the total cross section of the radiative capture process in the framework of the single-particle potential model without separation into direct and resonant transitions. In case where the single-particle potential model fails to describe other partial components, we use the R-matrix approach. The partial components of the astrophysical S-factor are calculated for all possible electric dipole transitions. The calculated value of the total S-factor at zero energy is in good agreement with earlier reported values. Based on the value of total astrophysical S-factor depending on the collision energy, we calculate the nuclear reaction rates for ${p} + {^{13}\mathrm{C}} \rightarrow {^{14}\mathrm{{N}}}+\gamma $ .

Radiative capture p + 13C → 14N + γ at energies of astrophysical interest is one of the important process in the CNO cycle. We focus the reader’s attention on the possibility of describing this reaction within the framework of a single-particle potential model even when the reaction has a resonant characteristic. The partial components of the astrophysical S-factor are calculated for electric dipole transition. The calculated value of S-factor is in good agreement with experimental data both at low and high energy from the resonance position.

Recently, a new $\Delta$ method for the calculation of asymptotic normalization coefficients (ANC) from phase-shift data has been formulated, proved and used for bound states. This method differs from the conventional one by fitting only the nuclear part of the effective-range function which includes a partial phase shift. It should be applied to large-charge nuclei when the conventional effective-range expansion or the Pad\'e-approximations using the effective-range function $K_l(k^2)$ fitting do not work. A typical example is the nucleus vertex $\alpha+^{12}$C $\longleftrightarrow ^{16}$O. Here we apply the $\Delta$ method, which totally excludes the effective-range function, to isolated resonance states. In fact, we return to the initial renormalized scattering amplitude with a denominator which defines the well-known pole condition. Concrete calculations are made for the resonances observed in the $^3$He-$^4$He, $\alpha$-$\alpha$, and $\alpha$-$^{12}$C collisions. We use the experimental phase-shift and resonant energy data including their uncertainties and find the ANC variations for the states considered. The corresponding results are in a good agreement with those for the $S$-matrix pole method which uses the differing formalism. The simple formula for narrow resonances given in the literature is used to check the deduced results. The related ANC function clearly depends on the resonance energy ($E_0$) and width ($\Gamma$), which is used to find the ANC uncertainty ($\Delta$ANC) through the energy ($\Delta E_0$) and the width ($\Delta\Gamma$) uncertainties.We also discuss the $\Delta$ method differences between bound and resonance states pole conditions., Comment: 9 pages, 3 figures and 3 table

Within the framework of potential cluster model, astrophysical S-factor of radiative capture reaction $^{12}\mathrm{C} (\mathrm{p},\gamma)^{13}\mathrm{N}$ has been calculated in the two body cluster model for the energy range 0–1 MeV. The nuclear interaction in the initial and final states is described by the Woods–Saxon potential. The calculated astrophysical S-factor and rates are compared with known experimental results.

A new algorithm for the asymptotic nuclear coefficients calculation, which we call the $\mathrm{\ensuremath{\Delta}}$ method, is proved and developed. This method was proposed by Ram\'{\i}rez Su\'arez and Sparenberg (arXiv:1602.04082.) but no proof was given. We apply it to the bound state situated near the channel threshold when the Sommerfeld parameter is quite large within the experimental energy region. As a result, the value of the conventional effective-range function ${K}_{l}({k}^{2})$ is actually defined by the Coulomb term. One of the resulting effects is a wrong description of the energy behavior of the elastic scattering phase shift ${\ensuremath{\delta}}_{l}$ reproduced from the fitted total effective-range function ${K}_{l}({k}^{2})$. This leads to an improper value of the asymptotic normalization coefficient (ANC) value. No such problem arises if we fit only the nuclear term. The difference between the total effective-range function and the Coulomb part at real energies is the same as the nuclear term. Then we can proceed using just this $\mathrm{\ensuremath{\Delta}}$ method to calculate the pole position values and the ANC. We apply it to the vertices $^{4}\mathrm{He}+^{12}\mathrm{C}\ensuremath{\leftrightarrow}^{16}\mathrm{O}$ and $^{3}\mathrm{He}+^{4}\mathrm{He}\ensuremath{\leftrightarrow}^{7}\mathrm{Be}$. The calculated ANCs can be used to find the radiative capture reaction cross sections of the transfers to the $^{16}\mathrm{O}$ bound final states as well as to the $^{7}\mathrm{Be}$.

In this article the results of the evaluation of the contribution of nuclear disintegration, based on the basis of diffraction theory in the 208Pb(6Li, αd)208Pb Coulomb breakup at an energy of 156 MeV is presented. Comparison of the results of the calculation with the experimental data of Kiener et al. [Phys. Rev. C 44, 2195 (1991)] gives evidence for the dominance of the Coulomb dissociation mechanism and contribution of nuclear distortion, but essentially smaller than the value reported byHammache et al. [Phys. Rev. C 82, 065803 (2010)] and Summerer [Prog. Part. Nucl. Phys. 66, 298 (2011)].

The experimental result of the neutrino flux produced by the p + p + e → d + ν e reaction (pep) in the Sun at 1 AU was announced for the first time in 2012 by the Borexino collaboration. We use the three-body model for the proton–proton–electron system in the initial state for the calculation of the rate of the pep reaction with various types of nucleon–nucleon potentials.

Deuteron induced quasi-free scattering and reactions have been extensively investigated in the past few decades. This was done not only for the study of the nuclear structure and processes but also for the important astrophysical implication (Trojan Horse Method, THM). In particular the width of the neutron momentum distribution in deuteron will be studied as a function of the transferred momentum. THM applications will also be discussed because the momentum distribution of the spectator particle inside the Trojan horse nucleus is a necessary input for this method. The impact of the width variation on the extraction of the astrophysical S(E)-factor is discussed as well as the relevance of the s and d wave component in the deuteron wave function.

To explore a possible indirect method for $^{8}\mathrm{Be}$ induced astrophysical reactions, the $^{9}\mathrm{Be}=(^{8}\mathrm{Be}+\mathit{n})$ cluster structure has been studied via the Trojan horse method. For the first time a $^{8}\mathrm{Be}$ nucleus having an ultrashort lifetime is studied by the Trojan horse method and a $^{9}\mathrm{Be}$ nucleus in the ground state is used for this purpose. The $^{9}\mathrm{Be}$ nucleus is assumed to have a ($^{8}\mathrm{Be}+\mathit{n}$) cluster structure and used as a Trojan horse nucleus. The $^{8}\mathrm{Be}$ nucleus acts as a participant, while the neutron is a spectator to the virtual $^{8}\mathrm{Be}+\mathit{d}\ensuremath{\rightarrow}\ensuremath{\alpha}+^{6}\mathrm{Li}$ reaction via the 3-body reaction $^{9}\mathrm{Be}+\mathit{d}\ensuremath{\rightarrow}\ensuremath{\alpha}+^{6}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathit{n}$. The experimental neutron momentum distribution inside $^{9}\mathrm{Be}$ has been reconstructed. The agreement between the experimental momentum distribution and the theoretical one indicates that a ($^{8}\mathrm{Be}+\mathit{n}$) cluster structure inside $^{9}\mathrm{Be}$ is very likely. Therefore, the experimental study of $^{8}\mathrm{Be}$ induced reactions, for example, the measurement of the $^{8}\mathrm{Be}+\ensuremath{\alpha}\ensuremath{\rightarrow}^{12}\mathrm{C}$ reaction proceeding through the Hoyle state, is possible.

A new method is proposed for finding the resonance parameters of a nuclear system, obtained from the phase shift analysis of elastic scattering data, by means of a pole representation of an S-matrix in complex momentum space is proposed. This method is based on the expansion of the potential phase shift into a Taylor series within the area of real momentum near the resonance pole. The coefficients of the expansion and resonance parameters are determined by fitting the analytical expression for the experimental phase shift. The proposed method provides reliable values of the energy and width of broad resonances.

3H and 3He nuclei are considered in a two-body model (3H = n + d; 3He = p + d). Two independent approaches are used: in the first, interaction is described by the folding potential, while NN potentials are taken in the Hulthen form with allowance for violations of isotopic invariance. The second approach features phenomenological Hulthen and Yukawa Nd potentials used as Nd interaction. In both approaches, the binding energies, vertex constants, and asymptotic normalization coefficients in the N+d channel are calculated.

Explicit expressions of the vertex constant for the decay of a nucleus into two charged particles for an arbitrary orbital momentum $l$ are derived for the standard expansion of the effective-range function $K_l(k^2)$, as well as when the function $K_0(k^2)$ has a pole. As physical examples, we consider the bound state of the nucleus ${}^3\rm{He}$ and the resonant states of the nuclei ${^2}$He and ${^3}$He in the s-wave, and those of ${}^5\rm{He}$ and ${}^5\rm{Li}$ in the p-wave. For the systems $Np$ and $Nd$ the pole trajectories are constructed in the complex planes of the momentum and of the renormalized vertex constant. They correspond to a transition from the resonance state to the virtual state while the Coulomb forces gradually decrease to zero., Comment: 17 pages, 5 figures

In view of projected experiments on the production of relativistic hypernuclei and the investigation of reactions induced by them, the characteristics of the hypernucleus and low-energy parameters of the Λ 5 He hyperon scattering from 4He were calculated. The interaction of the Λ hyperon and the α particle is described by the effective Λα potential in two different forms. The root-mean-square radius of the Λ hyperon in the Λ 5 He hypernucleus, the vertex constant for the Λ 5 He ↔ 4He + Λ process, and the corresponding asymptotic normalization coefficient of the Λ 5 He wave function were calculated by solving the radial Schrodinger equation. The scattering length and the effective radius for the scattering of Λ from 4He were calculated by two methods. The calculated characteristics turn out to be sensitive to the form of the Λα potential.

Trajectories for the S-wave pole of the scattering amplitude are constructed in the complex planes of the resonance momentum and of the renormalized vertex constant squared. They correspond to transitions from the resonance states to the virtual states of the singlet deuteron and the doublet triton while the Coulomb interaction gradually decreases to zero. The effective-range theory and a Yukawa-potential model are used. Physical reasons for the differences between the corresponding trajectories for Np and Nd systems are found. The results obtained explain why the resonances in the doublet Nd scattering are more difficult to detect in experiments in comparison with the well-studied singlet NN resonances.

A method has been developed for calculating the off-shell wave function by solving the inhomogeneous Schrodinger equation with allowance for the nuclear and Coulomb interactions. The off-shell wave function makes it possible to construct the off-shell scattering amplitude in order to solve the problems for three or more particles. An important application of the method is the Trojan Horse calculations of nuclear reactions that are important in nuclear astrophysics. Specific calculations are performed for neutron and proton scattering on the 7Be nucleus. The Woods-Saxon potential is used and the spin-orbital interaction is taken into account.

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Reqres| > |Imqres|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr−nexp(−μr) if |Imqres| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.

The characteristics of bound states of hypernuclei were calculated in [1] in a wide range of mass numbers within the potential model for three different potentials. In this study, the phase shifts and low-energy parameters for scattering of Λ hyperons from core nuclei, considered in [1], have been calculated for the same potentials. The calculated scattering lengths and effective radii are compared with their values found in [1] on the basis of the data on the binding energies and vertex constants of hypernuclei.

N/D equations taking into account the Coulomb interaction effects are used to consider the phase analysis data on 3He4He scattering and determine the nuclear vertex constants for the 7Be ↔ 3He4He vertex, where the beryllium nucleus is in the ground (3/2−) or first excited (1/2−) states. Information about the asymptotic normalization coefficients of the wave functions of the 7Be nucleus in the noted states is derived. The data obtained are used to calculate the astrophysical S factor for the 4He(3He, γ)7Be reaction.

The vertex constants, asymptotic normalization coefficients, and mean-square radii for a number of Λ hypernuclei have been calculated in a wide range of mass numbers. Interaction of a Λ hyperon with a core nucleus was described by the Woods-Saxon, Hulten, and Yukawa potentials. Geometric parameters of the Woods-Saxon potential were taken from the data in the literature, and the interaction force was fitted to the experimental binding energy of the ground state of this hypernucleus. The parameters of the Hulthen and Yukawa potentials were chosen so as to reproduce simultaneously the binding energy of the hyperon and its mean-square radius calculated with the Woods-Saxon potential. Within the effective-radius approximation, the low-energy parameters for hyperon scattering by the core nucleus are expressed in terms of vertex constants and the numerical values of these parameters are determined.

The $^{17}\text{O}(p,\ensuremath{\alpha})^{14}\text{N}$ and $^{17}\text{O}(p,\ensuremath{\gamma})^{18}\text{F}$ reactions are of paramount importance for the nucleosynthesis in a number of stellar sites, including red giants (RGs), asymptotic giant branch (AGB) stars, massive stars, and classical novae. In particular, they govern the destruction of $^{17}\text{O}$ and the formation of the short-lived radioisotope $^{18}\text{F}$, which is of special interest for $\ensuremath{\gamma}$-ray astronomy. At temperatures typical of the above-mentioned astrophysical scenario, $T=0.01$--0.1 GK for RG, AGB, and massive stars and $T=0.1$--0.4 GK for a classical nova explosion, the $^{17}\text{O}(p,\ensuremath{\alpha})^{14}\text{N}$ reaction cross section is dominated by two resonances: one at about ${E}_{R}^{cm}=65$ keV above the $^{18}\text{F}$ proton threshold energy, corresponding to the ${E}_{X}=5.673$ MeV level in $^{18}\text{F}$, and another one at ${E}_{R}^{cm}=183$ keV $({E}_{X}=5.786$ MeV). We report on the indirect study of the $^{17}\text{O}(p,\ensuremath{\alpha})^{14}\text{N}$ reaction via the Trojan Horse method by applying the approach recently developed for extracting the strength of narrow resonance at ultralow energies. The mean value of the strengths obtained in the two measurements was calculated and compared with the direct data available in literature. This value was used as input parameter for reaction-rate determination and its comparison with the result of the direct measurement is also discussed in the light of the electron screening effect.

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing an important role in nuclear physics and astrophysics. We derive a new useful relationship between ANC of the Gamow radial wave function and the renormalized (due to the Coulomb interaction) Coulomb-nuclear partial scattering amplitude. We use an analytical approximation in the form of a series for the nonresonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. Earlier, this method which we call the $S$-matrix pole method was used by us to find the resonance pole energy. We find the corresponding fitting parameters for the $^5\rm{He},\,^5\rm{Li}$, and $^{16}\rm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei $^5\rm{He}$ and $^5\rm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the $^{16}\rm{O}$ resonances which lie slightly above the threshold for the $\alpha^{12}\rm{C}$ channel., Comment: 8 pages, 3 tables, 5 figures

In recent years, the Trojan Horse Method (THM) has been used to investigate the low-energy cross sections of proton-induced reactions on 17O nuclei, overcoming extrapolation procedures and enhancement effects due to electron screening. We will report on the indirect study of the 17O(p,α)14N reaction via the THM by applying the approach developed for extracting the resonance strength of narrow resonance in the ultralow energy region. Two measurements will be described and the experimental THM cross sections will be shown for both experiments.

The accurate knowledge of thermonuclear reaction rates is important in understanding the energy generation, the neutrinos luminosity and the synthesis of elements in stars. The physical conditions under which the majority of astrophysical reactions proceed in stellar environments make it difficult or impossible to measure them under the same conditions in the laboratory. That is why different indirect techniques are being used along with direct measurements. The Trojan Horse Method (THM) is introduced as an independent technique to obtain the bare nucleus astrophysical S(E)-factor. As examples the results of recent the application of THM to the 2H(11B, ?08Be)n and 2H(10B, ?07Be)n reactions are presented.

International audience; The O-17(p,alpha)N-14 reaction is of paramount importance for the nucleosynthesis in a number of stellar sites, including red giants (RG), asymptotic giant branch (AGB) stars, massive stars and classical novae. We report on the indirect study of the O-17(p,alpha)N-14 reaction via the Trojan Horse Method by applying the approach recently developed for extracting the resonance strength of the narrow resonance at E-c.m.(R) = 65 keV (E-X = 5.673 MeV). The strength of the 65 keV resonance in the O-17(p,alpha)N-14 reaction, measured by means of the THM, has been used to renormalize the corresponding resonance strength in the O-17 + p radiative capture channel.

A simple method for calculating the amplitude and the cross section for the Coulomb breakup of a light nucleus into two fragments in the field of a heavy ion at relativistic collision energies is proposed on the basis of time-dependent perturbation theory. It is shown that the resulting amplitude for the process in question has a correct nonrelativistic limit. The contribution of the longitudinal component of the Coulomb field of a heavy ion tends to zero in the ultrarelativistic limit. A specific implementation of the method is demonstrated by taking the example of the Coulomb breakup reaction 208Pb(8B, 7Bep)208Pb at various collision energies. The results are found to be in agreement with experimental data.

The $^{10}\mathrm{B}(p,{\ensuremath{\alpha}}_{0})^{7}\mathrm{Be}$ bare nucleus astrophysical $S(E)$ factor has been measured for the first time at energies from about 100 keV down to about 5 keV by means of the Trojan Horse method (THM). In this energy region, the $S(E)$ factor is strongly dominated by the 8.699 MeV $^{11}\mathrm{C}$ level (${J}^{\ensuremath{\pi}}={\frac{5}{2}}^{+}$), producing an $s$-wave resonance centered at about 10 keV in the entrance channel. Up to now, only the high--energy tail of this resonance has been measured, while the low-energy trend is extrapolated from the available direct data. The THM has been applied to the quasifree $^{2}\mathrm{H}(^{10}\mathrm{B},{\ensuremath{\alpha}}_{0}$ $^{7}\mathrm{Be}$)n reaction induced at a boron-beam energy of 24.5 MeV. An accurate analysis leads to the determination of the $^{10}\mathrm{B}(p,{\ensuremath{\alpha}}_{0})^{7}\mathrm{Be}$ $S(E)$ factor and of the corresponding electron screening potential ${U}_{e}$, thus giving for the first time an independent evaluation of it.

The 17O(p,α)14N reaction is of paramount importance for the nucleosynthesis in a number of stellar sites, including red giants (RG), asymptotic giant branch (AGB) stars, massive stars and classical novae. We report on the indirect study of the 17O(p,α)14N reaction via the Trojan Horse Method by applying the approach recently developed for extracting the resonance strength of narrow resonance in the ultra-low energy region.

The widths of the spectator momentum distributions in several nuclei, which have been used as Trojan Horses, have been obtained as a function of the transferred momentum. Applications of Trojan Horse method will also be discussed.

The indirect measurement of 17O(p,α)14N cross section was performed by means of the Trojan Horse Method. This approach allowed to investigate the ultra-low energy range ( E c . m . = 0 − 300 keV ) relevant for several astrophysics environments, where two resonant levels of 18F at E c . m . R = 65 keV and E c . m . R = 183 keV play a significant role in the reaction rate determination.

Few-body methods provide very useful tools to solve different problems important for nuclear astrophysics. Some of them are discussed below.

Using expansion of the three-body wave function of the $pep$ system in the initial state on hyperharmonic functions, the rate of the $p+p+e^{-} \rightarrow d+\nu_e$ reaction in the Sun is calculated. The results of calculation of the flux at 1 AU are compared with the results of a measurement made by the Borexino collaboration and Bahcall \textit{et al.} theoretical predictions.

International audience; The role of oxygen in astrophysics is related to different problems as novae nucleosynthesis and gamma-ray astronomy. In particular, owing to the still present uncertainties on its rate, the 17O(p,α)14N is one of the most important reaction to be studied in order to get more information about the fate of oxygen in different astrophysical scenarios.

The Trojan horse method allows one to extract the cross section of a binary reaction by properly selecting the quasi-free component of a suitable surrogate reaction. A crucial point of its application is the discrimination of the quasi-free contribution to the total reaction yield, requiring the study of the experimental momentum distribution of the adopted Trojan horse nucleus. Deuteron has been largely used as Trojan horse nucleus in $p$- and $n$-induced reactions and the extracted experimental momentum distribution compared with the square of the Hulth\'en wave function in momentum space, which accounts for the $s$-wave component of the deuteron wave function. Here, the contribution of the $d$-wave has been evaluated, turning out to be negligibly small, thus corroborating the assumptions made so far in Trojan horse experiments where deuteron has been used.

Deuteron induced quasi-free scattering and reactions have been extensively investigated in the past few decades. This was done not only for nuclear structure and processes study but also for the important astrophysical implication (Trojan Horse Method, THM). In particular the width of the neutron momentum distribution in deuteron will be studied as a function of the transferred momentum. The same will be done for other nuclides of possible use as Trojan Horse particles. Trojan horse method applications will also be discussed because the momentum distribution of the spectator particle inside the Trojan horse nucleus is a necessary input for this method. The impact of the width (FWHM) variation on the extraction of the astrophysical S(E)-factor is discussed.

The triple differential cross section of $^{208}\rm{Pb}(^6\rm{Li};\alpha,\rm{d})^{208}\rm{Pb}$ elastic Coulomb breakup is calculated using the semiclassical method. We fit the parameters of the Woods-Saxon potential using the experimental $\alpha-\rm{d}$ phase shifts for different states to describe the relative motion of $\alpha$-particle and deuteron. In order to check the validity of the two particle approach for $\alpha-d$ system we apply a potential model to describe the $^2\rm{H}(\alpha,\gamma)^6\rm{Li}$ radiative capture. Our results for the Coulomb breakup of $^6\rm{Li}$ show large value of the forward-backward asymmetry of the $\alpha$-particle and deuteron emission around zero energy in the $^6\rm{Li}$ center-of-mass (c.m.) system. Comparison of the results of our calculation with experimental data gives evidence for the dominance of the Coulomb dissociation mechanism at the $\alpha-d$ relative energy larger than $E_{\alpha\,d}>300\,\rm{keV}$ and sufficiently big contribution of nuclear distortion at $E_{\alpha\,d}$ near zero energy, but essentially smaller than the value reported in Ref.[F. Hammache et al. Phys.Rev. C82, 065802 (2010)].

Recently, a new measurement of the $^{6}\mathrm{Li}$ (150 A MeV)dissociation in the field of $^{208}\mathrm{Pb}$ has been reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)] to study the radiative capture $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process. However, the dominance of the nuclear breakup over the Coulomb one prevented the information about the $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process from being obtained from the breakup data. The astrophysical ${S}_{24}(E)$ factor has been calculated within the $\ensuremath{\alpha}\ensuremath{-}d$ two-body potential model with potentials determined from the fits to the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering phase shifts. However, the scattering phase shift, according to the theorem of the inverse scattering problem, does not provide a unique $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential, which is the most crucial input when calculating the ${S}_{24}(E)$ astrophysical factor at astrophysical energies. In this work, we emphasize the important role of the asymptotic normalization coefficient (ANC) for ${}^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, which controls the overall normalization of the peripheral $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process and is determined by the adopted $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential. Since the potential determined from the elastic scattering data fit is not unique, the same is true for the ANC generated by the adopted potential. However, a unique ANC can be found directly from the elastic scattering phase shift, without invoking intermediate potential, by extrapolation the scattering phase shift to the bound-state pole [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)]. We demonstrate that the ANC previously determined from the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering $s$-wave phase shift [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)], confirmed by ab initio calculations, gives ${S}_{24}(E)$, which at low energies is about $38%$ less than the other one reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)]. We recalculate also the reaction rates, which are lower than those obtained in that same study [Hammache et al., Phys. Rev. C 82, 065803 (2010)].

The {sup 17}O(p,{alpha}){sup 14}N reaction is of fundamental relevance in several astrophysical scenarios, such as novae, asymptotic giant branch nucleosynthesis, and {gamma}-ray astronomy. We report on the indirect measurement of the {sup 17}O(p,{alpha}){sup 14}N reaction bare-nucleus cross section in the low-energy region. In particular, the two resonances at E{sub R}{sup c.m.}=65 keV and E{sub R}{sup c.m.}=183 keV, which dominate the reaction rate inside the Gamow window, have been observed, and the strength of the 65 keV resonance has been deduced. The reaction rate determination and the comparison with the results of the previous measurements are also discussed.

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$, Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and 4 tables

The 18O(p,α)15N reaction is of primary importance to pin down the uncertainties affecting present-day models of asymptotic giant branch stars. An indirect measurement of the low-energy region of the 18O(p,α)15N reaction has been performed by means of the Trojan Horse Method. We discuss why the plane wave approximation is justified by evaluating what changes the more correct DWBA approach introduces.

Deuteron induced quasifree scattering and reactions have been extensively investigated in the past few decades as well as {sup 6}Li, {sup 3}H, {sup 3}He, and {sup 9}Be induced reactions. This was done not only for the investigation of nuclear structure and reaction mechanisms but also for important astrophysical applications (Trojan horse method). In particular the widths of the spectator momentum distributions in several nuclei, which have been used as Trojan horses, have been obtained as a function of the transferred momentum. Applications of Trojan horse method will also be discussed because the momentum distribution of the spectator particle inside the nucleus is a important input for this method. This gives hints on distortion effects at low energies important for nuclear astrophysics.

International audience; The 18O(p,α)15N reaction rate has been deduced by means of the Trojan horse method. For the first time the contribution of the 20 keV resonance has been directly evaluated, giving a value about 35% larger than the one in the literature. Moreover, the present approach has allowed to improve the accuracy by a factor 8.5, as it is based on the measured strength instead of spectroscopic measurements. The contribution of the 90 keV resonance has been also determined, which turned out to be of negligible importance to astrophysics.