Quasifree Reaction Research Articles

New Perspectives on Spectroscopic Factor Quenching from Reactions.

The evolution of single-particle strengths as the neutron-to-proton asymmetry changes informs us of the importance of short- and long-range correlations in nuclei and has therefore been extensively studied for the last two decades. Surprisingly, the strong asymmetry dependence of these strengths and their extreme values for highly asymmetric nuclei inferred from knockout reaction measurements on a target nucleus are not consistent with what is extracted from electron-induced, transfer, and quasi-free reaction data, constituting a two-decade old puzzle. This work presents the first consistent analysis of one-nucleon transfer and one-nucleon knockout data, in which theoretical uncertainties associated with the nucleon-nucleus effective interactions considered in the reaction models are quantified using a Bayesian analysis. Our results demonstrate that, taking into account these uncertainties, the spectroscopic strengths of loosely bound nucleons extracted from both probes agree with each other and, although there are still discrepancies for deeply bound nucleons, the slope of the asymmetry dependence of the single-particle strengths inferred from transfer and knockout reactions are consistent within 1σ. Both probes are consistent with a small asymmetry dependence of these strengths. The uncertainties obtained in this work represent a lower bound and are already significantly larger than the original estimates.

Examination of the sensitivity of quasifree reactions to details of the bound-state overlap functions

It is often stated that heavy-ion nucleon knockout reactions are mostly sensitive to the tails of the bound-state wavefunctions. In contrast, (p,2p) and (p,pn) reactions are known to access information on the full overlap functions within the nucleus. We analyze the oxygen isotopic chain and explore the differences between single-particle wave functions generated with potential models, used in the experimental analysis of knockout reactions, and ab initio computations from self-consistent Green's function theory. Contrary to the common belief, we find that not only the tail of the overlap functions, but also their internal part are assessed in both reaction mechanisms, which are crucial to yield accurately determined spectroscopic information.

Sensitivity of analyzing power to distorting potentials in the quasifree reaction Ca40(p,pα)Ar36 at 100 MeV incident energy: Comparison with Be9 and C12 targets

Background: The ($p,p\ensuremath{\alpha}$) knockout reaction is useful for the study of preformed $\ensuremath{\alpha}$ clusters in atomic nuclei. At quasifree kinematic conditions above an incident energy of about 100 MeV the cross section and analyzing-power angular distributions extracted from the ($p,p\ensuremath{\alpha}$) knockout reaction are anticipated to resemble its free two-body counterparts. Several ($p,p\ensuremath{\alpha}$) knockout studies in the incident-energy range of 100--150 MeV on targets up to $^{12}\mathrm{C}$ confirm the predicted equivalence. However, the only experiment on $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ appears to fail the expectation spectacularly.Purpose: The reason for the drastic discrepancy between the experimental analyzing-power angular distribution for $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ and the trend of free elastic scattering of protons from $^{4}\mathrm{He}$ is investigated.Method: Guidance in general from the distorted-wave impulse approximation (DWIA) theory is employed. Specific focused theoretical calculations are performed.Results: As expected, for the ($p,p\ensuremath{\alpha}$) reaction on several light target masses up to $^{12}\mathrm{C}$, comparable cross section and analyzing-power angular distributions resemble free $^{4}\mathrm{He}(p,p)^{4}\mathrm{He}$ elastic scattering to a remarkable extent. The DWIA treatment for the $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ reaction, however, needs a more careful selection of the distortion optical-model parameters in the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ar}$ outgoing channel. Global optical-model potentials used in the published work reproduce neither analyzing-power distribution of the $^{40}\mathrm{Ca}(p,p\ensuremath{\alpha})^{36}\mathrm{Ar}$ reaction, nor $\ensuremath{\alpha}\text{\ensuremath{-}}^{36}\mathrm{Ar}$ elastic scattering cross-section angular distributions. Use of appropriate optical potentials resolves the problem.Conclusions: The use of appropriate optical-model potentials which describe elastic scattering of $\ensuremath{\alpha}$ particles from $^{36}\mathrm{Ar}$ correctly appears to be crucial. The problem reported previously in the literature is resolved to a remarkable extent. There is a need to explore the two-body aspects of the quasifree ($p,p\ensuremath{\alpha}$) reaction for heavier targets further.

Spectroscopy of 16B from quasi-free (p,pn) reaction with 17B

Spectroscopy of 16B plays an essential role in understanding the halo structure in 17B, but very limited knowledge has so far been obtained. We have carried out a kinematically complete measurement on the spectroscopy of 16B by using quasi-free (p,pn) reaction on 17B. The level scheme of 16B up to 5 MeV was made clear for the first time.

Recent Progress of the Trojan Horse Method and Its Application

The Trojan Horse Method(THM) is an important indirect method in experimental nuclear astrophysics. The S(E) factor of a two-body reaction in Gammow energy range related to astrophysics can be extracted from an appropriate three-body reaction measurement above the Coulomb barrier, under the quasi-free reaction condition. The method can overcome the difficulties caused by the Coulomb barrier suppression and the electron screening effect in direct measurement. While no extrapolation is needed, the method can also avoid the uncertainty in the extrapolation process. THM has a wide application in the experimental nuclear astrophysical study, low-energy fusion data measurement, neutron-induced reaction, electron screening effect and other important research fields. After a short introduction of the THM, this paper will focus on some of the most important experimental results in nuclear astrophysics measured by THM recently and the prospect of its future applications. The following key reactions will mainly be discussed: the indirect measurement of the key neutron source reaction \begin{document}$ ^{{\rm{13}}}{\rm{C(\alpha ,n}}{{\rm{)}}^{{\rm{16}}}}{\rm{O}}$\end{document} in the s-process of AGB stars, the indirect measurement of the nuclear reaction related to the fluorine abundance anomaly in AGB stars, as well as the recent hot spot, the indirect measurement results of the carbon burning reaction in medium or massive stars.

Application of Trojan Horse Method to radioactive ion beams induced reactions

In the last decades, many indirect methods have been developed to measure the cross section of nuclear reactions at the low energies interesting in many astrophysical scenarios. The Trojan Horse Method uses a three body reaction, involving by a strong clusterized nucleus, to infer information about a two body reaction of interest, selecting the events that proceed through the quasi-free reaction mechanism. To reconstruct the reaction kinematic and to identify the useful reaction mechanism, the energy and angle of at least two of the three outgoing particles must be carefully measured. Moreover, enough statistics is required, as the quasi-free events usually represent just a small fraction of the acquired statistic.These requirements hardly match with the typical characteristics of radioactive ion beams: low intensity, large divergence and possible presence of contaminants. For this reason, only recently the Trojan Horse Method has been applied to study reactions induced by radioactive beams. This application gives also the opportunity to measure cross section of neutron induced reactions on radioactive isotopes, even if they have a short lifetime.In the following some results obtained in the study of the reactions 18F(p,α)15O and 18F(n,α)15N will be presented.

Resonant reactions of astrophysical interest studied by means of the Trojan Horse Method. Two case studies

Resonant reactions in astrophysics play and important role as un- expected resonances may enhance the astrophysical factor with respect to the direct reaction contribution, altering the predicted nucleosynthesis scenarios by changing, for instance, the expected nucleosynthesis path. They also are of great interest in nuclear structure studies, since the determination of energies, spin-parities and partial widths sheds light on the occurrence of cluster structures, for instance. However, nuclear reactions in most astrophysical environments usually take place at energies below about 1 MeV, leading to an exponential de- crease of the cross sections due to the effect of the penetration of the Coulomb barrier. Also, at energies so low to be comparable with those associated to elec- tronic degrees of freedom, the effect of atomic and/or molecular clouds cannot be neglected, resulting in a shielding of nuclear charges and in an enhancement of the cross sections with respect to the case of bare nuclei (the so called elec- tron screening effect). Owing to vanishingly small cross sections and ambigui- ties in the extrapolation due to the electron screening, supplying accurate cross sections for astrophysical modeling is extremely challenging. Indirect methods have been introduced to explore the energy range of astrophysical interest with no need of extrapolation, even guided by theoretical arguments. In particular, the Trojan Horse Method makes use of quasi-free reactions with three particles in the exit channel,a+A ^ c + C + s,to deduce the cross section of the reaction of astrophysical interest,a + x ^ c + C,under the hypothesis thatAshows a strongx+scluster structure. Even if measurements are carried out above astro- physical energies to be free from Coulomb suppression and electron screening, the range of astrophysical interest can be covered thanks to the x - s intercluster motion and binding energy. In these proceedings we will show the application of the THM, in the case of resonant reactions, using the generalised R-matrix approach introduced by A.M. Mukhamedzhanov. We will discuss the possibil- ity to extract resonance parameters from the Trojan Horse data and perform a full spectroscopic study of low-energy and even sub-threshold resonances. In particular, we will focus on the19F(p, a)16O and the13C(a, n)16O reactions, of particular importance in the case of asymptotic giant branch stars and in the synthesis of heavy elements by means of the s-process.

Scaling in quasifree hadron-nucleus charge-exchange reactions

Scaling in quasifree hadron-nucleus charge-exchange reactions

Astrophysics studies with the Trojan Horse Method

The Trojan Horse Method represents an indirect approach to investigate reactions of astrophysical relevance at the energies of interest, free of Coulomb suppression and electron screening effects. In this review, we will examine how the Trojan Horse Method has evolved from the study of the quasi-free reaction mechanism. We will first present the basic features of the quasi-free reaction mechanism in the framework of the theory of direct reactions, from quasi-free scattering to quasi-free reactions processes, and its evolution towards the Trojan Horse Method with its modern theory. We will review the validity tests to assess the technique, the procedure to analyze the data and to extract the astrophysical factor. Finally, we will discuss some of the most important experimental results recently published related to nuclear astrophysics and applications.

THM applied to the investigation of explosive astrophysical scenarios

The Trojan Horse Method (THM) makes use of quasi-free reactions to deduce the cross section of nuclear reactions relevant for astrophysics at the energies of interest. Thanks to the suppression of the Coulomb barrier, the THM cross section does not exponentially vanishes at astrophysical energies. Here we will briefly summarise the fundamentals of the method, then we will discuss two applications of the method to reactions that have a pivotal role in the latest stages of stellar evolution, leading to explosive scenarios. In particular, we will focus on the indirect investigation of the 18F(p,α)15O reaction, which is the most important 18F destruction channel in novae, and the 12C + 12C reaction, which plays a critical role in astrophysics to understand stellar burning scenarios in carbon-rich environments, including supernovae.

Cross-section Measurement of the Cosmologically Relevant 7Be(n, α)4He Reaction over a Broad Energy Range in a Single Experiment

Abstract Studying interactions of radioactive ions with neutrons is particularly demanding and has been performed only in a few cases. Some of these interactions are crucial in several astrophysical contexts. In the present work, the case of the 7Be destruction induced by the (n, α) reaction is investigated at the energies typical of the primordial nucleosynthesis by means of the Trojan Horse Method applied to the 2H(7Be, αα)p quasi-free reaction. The 7Be(n, α)4He cross-section has been measured in a single experiment from ∼2 MeV down to cosmological energies. The corresponding deduced reaction rate has been adopted to evaluate the impact on big bang nucleosynthesis and on the lithium problem.

Luminosity determination for the proton-deutron reactions using quasi-free reactions with WASA-at-COSY facility

The scientific aim of our research is experimental confirmation of the existence of mesic-nucleus: a new exotic kind of nuclear matter consisting of nucleons and mesons. In this report we present the method of luminosity determination for experiment performed atWASA-at-COSY detector dedicated to search for 3He-η bound state. This method is based on analysis of quasi-free $pd \to ppn_{{\rm{spec}}} $ reaction.

Exclusive quasi-free proton knockout from oxygen isotopes at intermediate energies

The dependence of the single-particle strength on the difference between proton and neutron separation energies is studied for oxygen isotopes in a wide range of isospins. The cross sections of the quasi-free (⁠|$p,2p$|⁠) reaction on |$^{14,16,18,22,24}$|O were measured at intermediate energies. The measured cross sections are compared to predictions based on the distorted wave impulse approximation and shell-model |$psd$| valence-space spectroscopic factors. The reduction factors, which are the ratio of the experimental cross sections to the theoretical predictions, show no apparent dependence on the proton–neutron separation energy difference. The result is compatible with the result of the (⁠|$e,e^{\prime}p$|⁠) reaction on stable targets and with the predictions of recent ab initio calculations.

Maris polarization in neutron-rich nuclei

We present a theoretical study of the Maris polarization effect and its application in quasi-free reactions to assess information on the structure of exotic nuclei. In particular, we explore the dependence of the polarization effect on neutron excess and neutron-skin thickness. We discuss the uncertainties in the calculations of triple differential cross sections and of analyzing powers due the choices of various nucleon–nucleon interactions and optical potentials and the limitations of the method. Our study implies that polarization variables in (p, 2p) reactions in inverse kinematics can be an effective probe of single-particle structure of nuclei in radioactive-beam facilities.

Effectiveness of using a magnetic spectrograph with the Trojan Horse method

The Trojan Horse method relies on performing reactions in a specific kinematic phase space that maximizes contributions of a quasi-free reaction mechanism. The hallmark of this method is that the incident particle can be accelerated to high enough energies to overcome the Coulomb barrier of the target, but once inside the target nucleus the relative motion of the clustered nuclei allows the reaction of interest to proceed at energies below this Coulomb Barrier. This method allows the experimentalist to probe reactions that have significance in astrophysics at low reaction energies that would otherwise be impossible due to the vanishing cross section. Traditionally the Trojan Horse method has been applied with the use of silicon detectors to observe the reaction products. In this study we apply the Trojan Horse method to a well studied reaction to examine the potential benefits of using a splitpole magnetic spectrograph to detect one of the reaction products. We have measure the three body 7Li(d,αn)α reaction to constrain the energy 7Li(d,α)α cross section. Measurements were first made using two silicon detectors, and then by replacing one detector with the magnetic spectrograph. The experimental design, limitations, and early results are discussed.

Analysis of the exclusive final state npe+e- in the quasi-free np reaction

.We report on the investigation of dielectron production in tagged quasi-free neutron-proton collisions by using a deuteron beam of kinetic energy 1.25GeV/u impinging on a liquid hydrogen target. Our measurements with HADES confirm a significant excess of e^{+}e^{-} pairs above the pi^{0} mass in the exclusive channel dp rightarrow npe^{+}e^{-}(p_{spect}) as compared to the exclusive channel ppe^{+}e^{-} measured in proton-proton collisions at the same energy. That excess points to different bremsstrahlung production mechanisms. Two models were evaluated for the role of the charged pion exchange between nucleons and double- Delta excitation combined with intermediate rho-meson production. Differential cross sections as a function of the e^{+}e^{-} invariant mass and of the angles of the virtual photon, proton and electrons provide valuable constraints and encourage further investigations on both experimental and theoretical sides.

On the investigation of resonances above and below the threshold in nuclear reactions of astrophysical interest using the Trojan Horse Method.

The occurrence of resonances in reactions of astrophysical interest might significantly enhance the astrophysical factor with respect to the direct reaction contribution, divert nucleosynthesis path and change the energy production, with significant impact on astrophysics. Moreover, the determination of resonance parameters, that is, energy, spin-parity and partial widths, allows one to perform nuclear structure studies leading, for instance, to determine the cluster structure of the state under investigation. However, nuclear reactions in stars take place at energies well below ~ 1 MeV owing to the typical temperatures characterising these environments. Therefore, the Coulomb barrier exponentially suppressing the cross section and the electron screening effect, due to the shielding of nuclear charges by atomic electrons, make it very difficult to provide accurate astrophysical factors. The THM is an indirect method allowing to overcome such difficulties. It makes use of quasi-free reactions with three particles in the exit channel, a + A → c + C + s, to deduce the cross section of the reaction of astrophysical interest, a + x → c + C, under the hypothesis that A shows a strong x + s cluster structure, right at astrophysical energies. By using a generalised R-matrix approach, the resonance parameters can be deduced from THM data allowing one to perform a full spectroscopic study of low-energy and sub-threshold resonances. In this work, we will discuss two examples of reactions of astrophysical interest, whose cross sections show a resonant behaviour: the19F(p, α)16O cross section that displays resonances at energies above the particle emission threshold and the13C(α, n)16O reaction, dominated by the −3 keV sub-threshold resonance due to the 6.356 MeV level in17O.

At the origins of the Trojan Horse Method

During the seventies and eighties a long experimental research program on the quasi-free reactions at low energy was carried out by a small group of nuclear physicists, where Claudio Spitaleri was one of the main protagonists. Nowadays, a posteriori , the results of these studies can be considered an essential step preparatory to the application of the Trojan Horse Method (THM) in Nuclear Astrophysics.

Coulomb dissociation another “Trojan Horse”

Abstract. Coulomb dissociation is discussed in connection with the Trojan-Horse method and other quasi-free reactions.

The12C(12C,α)20Ne and12C(12C,p)23Na reactions at the Gamow peak via the Trojan Horse Method

A measurement of the 12 C( 14 N, α 20 Ne) 2 H and 12 C( 14 N,p 23 Na) 2 Hreactions has been performed at a 14 N beam energy of 30.0 MeV. The experiment aims to explore the extent to which contributing 24 Mg excited states can be populated in the quasi-free reaction off the deuteron in 14 N. In particular, the 24 Mg excitation region explored in the measurement plays a key role in stellar carbon burning whose cross section is commonly determined by extrapolating high-energy fusion data. From preliminary results, α and proton channels are clearly identified. In particular, ground and first excited states of 20 Ne and 23 Na play a major role.