Few-Body Problems in Experimental Nuclear Astrophysics

The 3α-reaction is one of the key reactions in nuclear astrophysics. Since it is a three-body reaction direct measurement is impossible, and therefore the reaction rate must be estimated theoretically. In this contribution I will discuss uncertainties in this reaction rate both at very low temperatures, temperatures typical for Helium burning in red giant stars, and for very high temperatures.     

Theory of the Trojan-Horse method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.     

ChPT Calculation for Two Pion Production in NN Collision Reaction at Threshold

We investigate the two pion production in NN collision reaction at threshold with Chiral Perturbation Theory (ChPT). The leading-order diagrams are presented and as an example we give the results of complete calculation of the reaction pn → d ππ at threshold. It is found that the leading order diagrams are of equal importance as expected by power counting. The role of initial, intermediate and final state interactions in nucleon-nucleon system is also investigated and found to be very important. The calculations also show that the non-resonant contributions near threshold in the two-pion production in NN collision reaction is sizable and important.     

An investigation of the 144Sm(α, 3He)145Sm reaction

The ¹⁴⁴Sm(α, ³He)¹⁴⁵Sm stripping reaction has been studied up to 3 MeV excitation energy with a 40 MeV α-beam. Angular distributions have been recorded, and spectroscopic factors are deduced using a standard DWBA procedure. The reaction favours high-l transfers, and is found to be very useful for the investigation of large-j states. From a comparison with the spectroscopic factors known from the ¹⁴⁴Sm(d, p)¹⁴⁵Sm reaction the normalization factor for the (α, ³He) reaction is found to depend strongly on the optical model parameters and on the transferred angular momentum l.     

Time-reversal,nuclear reactions and molecular beams

It is pointed out, that very accurate nuclear reaction detailed balance test could be done in a single experiment using molecular beams. The feasibility of these measurements is discussed for the case of the¹³C(d, t)¹²C reaction.     

Ni(CO)4 formation on single Ni crystals: Reaction kinetics and observation of surface facetting induced by the reaction

We have studied the kinetics of the synthesis of nickel carbonyl (Ni + 4 CO → Ni(CO)₄), using single crystalline Ni surfaces of different crystallographic orientation. A dependence of the reaction rate on the crystallographic orientation of the surface has been observed. Scanning electron micrographs showed that a very sharp (111) facetting of the surface takes place during the reaction. A reaction mechanism for the Ni(CO)₄ formation, taking into account recent experimental data of the chemisorption of CO on Ni, is discussed, which may explain the kinetic results and the observed facetting.     

Few-Body Reactions in Nuclear Astrophysics

Nuclear reactions involving light nuclei require few-body models to describe the nuclear structure and the reaction mechanism. The production rates for the α+n+n → ⁶ He+γ and α+n+n+n → ⁶ He+n processes are discussed. Typically only very low relative energies are relevant. For environments with a high density, processes involving more particles could dominate. The use of the adiabatic approach as a method to compute cross sections at very low energies is proposed.     

Production and Parity Determination of Ξ Baryons

To understand the structure of hadrons and their production mechanisms, it is very important to be able to identify their quantum numbers. For investigating the spin and parity quantum numbers of Ξ and Ω, in particular, it is very important to understand strong interactions in the strangeness sector. At present, such quantum numbers are known for only a few of the Ξ baryons, and even the parity of the ground state Ξ(1318) has never been measured. In this article, we present a novel, model-independent way to determine the parity of Ξ baryons solely based on symmetry considerations for the hadronic reaction K? N → K Ξ.     

The contribution of pion absorption with two-nucleon emission to the pion-nucleus optical potential

Four terms in the pion-nucleus optical potential which arise from pion absorption with two nucleon emission are calculated using a model in which the nucleon is treated as a bound state of a pion and a nucleon. The contribution of these terms to the reaction cross section of carbon is considered. Two of the terms give rise to a negative reaction cross section, but it is shown that the sum of the four is positive definite. We find that the absorption reaction cross sections are very sensitive to the off-shell behavior of the free pion-nucleon T-matrix.     

A novel sodium iodide and ammonium molybdate co-catalytic system for the efficient synthesis of 2-benzimidazoles using hydrogen peroxide under ultrasound irradiation

The reaction of aldehydes and o-phenylenediamine for the preparation of 2-benzimidazoles has been studied using hydrogen peroxide as an oxidant under ultrasound irradiation at room temperature in this paper. The combination of substoichiometric sodium iodide and ammonium molybdate as co-catalysts, together with using small amounts of hydrogen peroxide, makes this transformation very efficient and attractive under ultrasound. Thus, a mild, green and efficient method is established to carry out this reaction in high yield.     

The p + p → π+ + d reaction close to threshold at COSY

Differential and total cross sections of the p + p → π⁺ + d reaction close to threshold were measured employing a magnetic spectrograph with track reconstruction, a very thin liquid hydrogen target and an accelerated proton beam with high phase space density. The data resolve a previous discrepancy between the n + p → π⁰ + d and the π⁺ + d → 2p reaction close to threshold indicating that isospin symmetry may be broken in the s-wave part of the cross section.     

Application of the Three-Component-Dual-Deck-Model to the ΛK channel inpp reaction

We have applied the Three-Component Dual-Deck-Model (TCDDM) to the (ΛK) channel inpp reaction. We conclude that our results are very satisfactory and take into account the experience. In this paper we take advantage of the fact that spin-structure is the same as (N π) channel which has been calculated in previous papers [3].     

Calculation of excitation functions of the 5 4 , 5 6 , 5 7 , 5 8 Fe(p,n) reaction from threshold to 30 MeV

The cross-sections for the formation of ^54,56,57,58Co in the ^54,56,57,58Fe(p, n) reaction from threshold to 30 MeV protons have been theoretically calculated using the TALYS-1.4 nuclear model code, whereby we have studied major nuclear reaction mechanisms, including direct, pre-equilibrium and compound nuclear reaction. Subsequently, the level density and shell damping parameters have been adjusted and at the same time, the odd–even effects are well comprehended. The excitation functions have been compared with experimental nuclear data. It is observed that the theoretical cross-sections match fairly well. Proton-induced reaction cross-sections provide clues to understand the nuclear structure and offers a good testing ground for ideas about nuclear forces. In addition, complete information in this field is very much required for application in accelerator-driven subcritical system.     

Statistical model calculations for medium and strong absorption in theA=90 region

Calculations of elastic, inelastic and total neutron cross sections as well as of (p, n) reaction cross sections in theA=90 mass region have been performed, using the statistical model of Hofmann, Richert, Tepel and Weidenmüller. The optical model parameters were obtained by Finckh et al. from the neutron decay of IAR in the⁹¹Zr(p, n)⁹¹ Nb reaction. The calculations are in very good agreement with the published experimental data. The optical model parameters proved to be satisfactory up to aboutE _n=8.0 MeV. The present work might be relevant to the evaluation of neutron data for reactor technology.     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Reaction rates and energy spectra for nuclear reactions in high energy plasmas

Total reaction rates and energy spectra of the generated particles are discussed for fusion reactions in high energy plasmas. Examples, discussed in some detail, concern elliptic and monoenergetic velocity distributions of the plasma. One obtains energy spectra with very typical shapes which should be useful for diagnostic purposes. This is true in particular, of reactions between different particles such as thed-t reaction.     

Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.     

The tensor analyzing power AzzATθ = 0° for the 3He(d, p)4He reaction

The tensor analyzing power f_zz has been measured for the ³He($\text{d}$, p)⁴He reaction at 0 = 0° over an incident deuteron energy range E_d = 6.6–15.8 MeV in steps of 0.5 MeV. The present results agree with and extend the previous measurements of Grüebler et al. The present results indicate that this reaction is a very good tensor analyzer for polarized deuteron beams with energies up to 15.8 MeV.     

Charge and mass transfer in the reaction136Xe+208Pb at energies close to the coulomb barrier

Mass and charge transfer was investigated for the system¹³⁶Xe+²⁰⁸Pb at 5.9 MeV/nucleon incident energy with aΔE —E-time of flight telescope. The angle and energy integrated cross section for the strongly damped events was found to be 510 mb, very close to the total reaction cross section. The width of the mass distribution as function of the total kinetic energy loss was measured and is compared to the width of the corresponding charge distribution. An upper limit of 1 μb has been found for processes with very large mass transfer.     

Local forces and the 16O reaction matrix

It is demonstrated that the G-matrix elements obtained from a solution of the Bethe-Goldstone equation for finite nuclei and a given NN interaction can be very well approximated by an effective local interaction. The local approximation is determined from the reaction matrix in nuclear matter using the same realistic NN interaction. The comparison is performed on the level of RPA calculations for the excited states in ¹⁶O. Very good agreement is found between the results for both interactions except for scalar-isoscalar states. It is shown that this is due to the energy dependence of the reaction matrix and can be cured rather easily. A comparison with experiment for isovector states is very satisfactory.