Quasi Free Research Articles

Exploring the Trojan Horse Method for Nuclear Fusion Data

The Trojan Horse Method (THM) is an indirect technique which extracts a two-body cross-section of interest from a related three-body reaction. The need for the application of the THM for obtaining fusion data is outlined, with a focus on the 93Nb(n, γ)94Nb cross-section. The basic features of THM are explained, with a particular focus on the quasi-free (QF) kinematics and the resulting energy relations, which provide a way to link the spectator momentum to the interaction energy of interest. The QF kinematics are then applied to the 93Nb(d, pγ)94Nb reaction, with some experimental considerations being outlined. A follow-up measurement to validate the THM result using the High-Flux Accelerator Driven Neutron Facility (HF-ADNeF) is proposed.

The $$^3$$He+$$^5$$He$$\rightarrow $$ $$\alpha $$+$$\alpha $$ reaction below the Coulomb barrier via the Trojan Horse Method

For the first time in an application to nuclear astrophysics, a process induced by the unstable $$^5$$ He = ( $$^4$$ He-n) nucleus, the $$^3$$ He+ $$^5$$ He $$\rightarrow $$ 2 $$\alpha $$ reaction, has been studied through the Trojan Horse Method (THM). For that purpose, the quasi-free (QF) contribution of the $$^9$$ Be( $$^3$$ He, $$\alpha \alpha $$ ) $$^4$$ He reaction was selected at $$E_{^{3}\text{ He }}=4$$ MeV incident energy. The reaction was studied in a kinematically complete experiment following a recent publication (Spitaleri et al. in Eur Phys J A 56:18, 2020), where for the quasi free contribution the momentum distribution between $$\alpha $$ and $$^5$$ He particle cluster in the $$^9$$ Be nucleus in the ground state have been extracted. The angular distribution of the QF $$^3$$ He+ $$^5$$ He $$\rightarrow $$ 2 $$\alpha $$ reaction was measured at $$\theta _{cm}$$ = 78 $$^{\circ }$$ –115 $$^{\circ }$$ . The energy dependence of the differential cross section of the $$^3$$ He+ $$^5$$ He $$ \rightarrow $$ 2 $$\alpha $$ virtual reaction was extracted in the energy range $$E_{cm}$$ = 0–650 keV. The total cross section obtained from the Trojan-horse method was normalized to absolute cross sections from a theoretical calculation in the energy range $$E_{cm}$$ =300–620 keV.

Comprehensive measurements of cross sections and spin observables of the three-body break-up channel in deuteron-deuteron scattering at 65\xa0MeV/nucleon

Detailed measurements of five-fold differential cross sections and a rich set of vector and tensor analyzing powers of the ^{2}mathrm{H}({varvec{d}},dp){n} break-up process using polarized deuteron-beam energy of 65 MeV/nucleon with a liquid-deuterium target are presented. The experiment was conducted at the AGOR facility at KVI using the BINA 4pi -detection system. We discuss the analysis procedure including a thorough study of the systematic uncertainties. The results can be used to examine upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights into the dynamics of three- and four-nucleon forces in few-nucleon systems. The results of coplanar configurations are compared with the results of recent theoretical calculations based on the Single-Scattering Approximation (SSA). Through these comparisons, the validity of SSA approximation is investigated in the Quasi-Free (QF) region.

Quasi-free limit in the deuteron-deuteron three-body break-up process

Detailed measurements of vector and tensor analyzing powers of the ^{2}{\rm H}(\vec d,dp){n} break-up process are presented. The data were obtained using a polarized deuteron-beam with an energy of 65 MeV/nucleon impinging on a liquid-deuterium target. The experiment was conducted at the AGOR facility at KVI using the BINA 4\piπ-detection system. The focus of this contribution is to analyze data of the dddd scattering process in the regime at which the neutron acts as a spectator, which we refer to as the quasi-free (QF) limit. To achieve this, events for which the final-state deuteron and proton are coplanar have been analyzed and the data have been sorted for various reconstructed momenta of the missing neutron. In the limit of vanishing neutron momentum and at small deuteron-proton momentum transfer, the data match very well with measured and predicted spin observables of the elastic deuteron-proton scattering process. The agreement deteriorates rapidly with increasing neutron momentum and deuteron-proton momentum transfer. The results of coplanar configurations in four-body phase space are compared with the results of recent available theoretical calculations based on the Single-Scattering Approximation.

The 10B(n,$\alpha$)7Li cross sections at ultra-low energy through the Trojan Horse Method applied to the 2H(10B,$\alpha^{7}$Li)1H

In the framework of the experimental campaign of the ($ p,\alpha$) and ($ n,\alpha$) reactions cross sections measurement involving the 10, 11B isotopes, different ($ n,\alpha$) cross section measurements have been performed at ultra-low energy. In this work, the 10B(n,$ \alpha$)7Li reaction was investigated through the Trojan Horse Method, by means of the Quasi-Free (QF) 2H(10B,$ \alpha^{7}$Li)1H reaction at 30 MeV of beam energy. As in the standard THM approach, the measurement has been performed in inverse kinematics using a 10B beam. The excitation function of the 10B(n,$ \alpha$)7Li reaction has been measured at a center-of-mass energy between 0 and 700 keV. The data were compared with the existing experimental ones. Even if the energy resolution of the present experiment did not allow a separation between the channels ($ n,\alpha_0$) and ($ n,\alpha_1$) the low energy cross section and the angular distribution are presented, pointing out once more the ability of the method in studying neutron induced reactions using deuteron as source of virtual neutrons.

Interplay of dynamical and structure effects in the observables for 12C(p,2p) near 400 MeV with polarized and unpolarized beams

We investigate the interplay of reaction mechanism and structure effects in the calculated cross sections and polarization observables for the direct C12(p,2p) reaction near 400 MeV around the Quasi Free Scattering (QFS) kinematical condition. We do the first consistent comparison between the scattering observables obtained from solutions of three-body Faddeev/Alt-Grassberger-Sandhas (F/AGS) equations and from the Distorted-Wave Impulse Approximation (DWIA). We explore structure effects on the calculated observables, making use of one-nucleon spectroscopic overlaps obtained from the quantum Monte Carlo (QMC) many-body wave functions and using a Woods-Saxon parametrization with parameters adjusted to experimental (p,2p) data. We show, for the first time, that the two reaction formalisms exhibit a distinct behavior depending upon the kinematic conditions. We also show that the agreement between the experimental data and the theoretical results depends on the reaction formalism, kinematical conditions and optical model parametrizations in addition to the spectroscopic factors (SFs). The agreement between the data and predictions using QMC wave functions diminishes prominently for transitions to excited states of 11B.

The Treiman-Yang Criterion: validating the Trojan Horse Method by experimentally probing the reaction mechanism

Proper selection of the quasi-free (QF) break-up channel in a three-body reaction is a key aspect for the applicability of the Trojan Horse Method (THM). The Treiman-Yang (TY) Criterion is a model-independent experimental test for the dominance of the QF mechanism, and hence constitutes one of the strongest validity tests of the THM. An experiment was performed at LNS to apply the test to the d(10B, 7Be α)n reaction. Here, the criterion is described and some preliminary data from the experiment are shown.

Preliminary Studies for Three Experiments at Treiman-Yang Criterion

Nuclear reactions with three bodies in their final state may proceed through different reaction mechanisms. The Feynman graph technique has been widely used to describe such reactions. However, it is very difficult in general to select the graphs that dominate in given process. The Treiman-Yang criterion is one of the most powerful experimental tests for verifying the pole approximation prediction when describing a quasi-free reaction mechanism. We propose the theoretical study of the H 2 (B 10 ,α Be 7 )ns, H 1 (B 11 ,α 1α2)αs, He 3 (Be 9 ,α 1α2)αs reactions at different energies. The preliminary study helps to check the existence of a QF channel by using the TY creterion. The Trojah Horse Method (THM) is a powerful indirect technique that allows to determine the astrophysical factor for rearrangement reactions. The THM involves obtaining the cross section of the binary process 0+T→1+2 at astrophysical energies by measuring the Trojan Horse (TH) reaction (the two-body to three-body process) 0+N→1+2+s in the quasifree (QF) kinematics mode, where the Trojan Horse particle, N = (s+T), which has a dominant cluster structure, is accelerated at energies above the Coulomb barrier. The advantage of the THM is that the extracted cross section of the binary subprocess does not contain the Coulomb barrier suppresion factor and electron screening does not play a role in the cross section. After penetrating the barrier, the TH-nucleus N undergoes breakup leaving particle T

The FINUDA experiment: recent results

A description of the techniques used in FINUDA to perform, by means of global fits, the analysis of some YN (hyperon-nucleon) spectra is reported. The study of the features of many experimental spectra and how they can be decomposed by contributions of Quasi-Free (QF) background reactions is a fundamental issue to achieve a good and reliable description of the K−2N→YN absorptions.

Design of Quasi Free Surface Secondary Optical Lens for LED Auto Taillights

Owing to its high energy efficiency, high color rendering and long life, LED lamps are promising in the field of Lighting. However, it is much more important to design a secondary optical lens for the LED lamps to obtain good output efficiency and a good light distribution pattern than to light the lamps. In the field of auto lamps, LED has more advantages than the traditional lamps. In this paper, we proposed and developed a secondary optical lens design blueprint for LED auto taillights. A quasi free surface based on the cone lens for auto taillights was designed and the desired illumination was achieved. We present the design procedure of the lens. The simulation of the auto tail-lights is carried out in Tracepro 7.0. The results show that the lens can rearrange the luminous flux accurately and reasonably. An auto taillight with a uniform and rectangular luminous flux distribution is obtained

Single photon double ionization of Helium at 800 eV – observation of the Quasi Free Mechanism

In a kinematically complete experiment we have measured the photo double ionization of Helium at a photon energy of 800 eV and observed He2+ ions with 0 momentum, corresponding to a back-to-back-emission of the two electrons. The results are in good agreement with theoretical calculations.

Photoproduction of Mesons on Quasi–Free Nucleons

The investigation of excited baryon states is important to understand the un- derling nature/symmetries of hadronic matter. Historically, the first nucleon excitation experiments have been done using charged pion and kaon secondary beams. Later the antiproton-proton scattering has also been involved. However, since the beginning of the 90's meson photoproduction reactions have been considered as a powerful tool in baryon spectroscopy. In this contribution, we overview our experimental programs conducted at the bremsstrahlung photon beams of the MAMI accelerator in Mainz and the ELSA accelerator in Bonn. The results are differential and total cross sections for photopro- duction of light neutral mesons and of meson pairs off quasi-free nucleons bound in the deuteron (and sometimes other light nuclei). The scientific programs of this experiments also include single and double polarization measurements as well.

Low-energy d+d fusion via the Trojan Horse Method

The 2H(d,p)3H and 2H(d,n)3He reactions have been recently investigated from Edd=1.5 MeV down to 2 keV, by means of the Trojan Horse Method (THM) applied to the Quasi Free 3He+d interaction at 18 MeV [1]. The knowledge of their fusion cross section at low energies is of interest for pure and applied physics. Both reactions belong to the network of processes to fuel the first inertial confinement fusion reactors in the range of kT= 1 to 30 keV. These energies overlap with the burning temperatures of deuterium in the Pre-main sequence of stellar evolution. They are key processes in the Standard Big Bang Nucleosynthesis (SBBN), in an energy region from 50 to 300 keV and experimental data at least up to 1 MeV are required for an accurate calculation of the reaction rate. Providing experimental data for both channels from a single experiment and over the entire energy range of interest is crucial for an accurate calculation of the reaction rates. This is what has been obtained from the present Trojan Horse (TH) investigation with new reaction rates which deviate by more than 20% from available direct data. This represents also the first pioneering experiment in quasi free regime where the charged spectator is detected.

Photoproduction of charged pions from the deuteron

The photoproduction of the charged pions from the deuteron has been studied with the Neutral Kaon Spectrometer (NKS) and the Neutral Kaon Spectrometer 2 (NKS2) at the Research Center for Electron Photon Science, Tohoku University (ELPH) which was previously known as the Laboratory of Nuclear Science (LNS-Tohoku) using the GeV-region tagged photon beam. The total cross section for the quasi-free (QF) π + π − photoproduction from the deuteron was measured with NKS in the energy region from 0.8 to 1.1 GeV. The cross section for the double Δ excitation in the intermediate state was derived in the analysis of the non-quasi-free (NQF) process, in which two nucleons of the deuteron share the energy of the incident photon. The prospect of the measurements of double pion photoproduction with NKS2 and upgraded NKS2 is discussed. The pion photoproduction from the nucleon has been investigated both experimentally and theoreti- cally for the study of the nucleon resonances for tens of years. The contribution of the double pion photoproduction from the proton is dominant in the energy region higher than 0.6 GeV. The π + π − photoproduction cross section accounts for approximately 30 percent of the total photoproduction in this energy region.

Using chiral perturbation theory to extract the neutron-neutron scattering length fromπ−d→nnγ

The reaction ${\ensuremath{\pi}}^{\ensuremath{-}}d\ensuremath{\rightarrow}\mathit{nn}\ensuremath{\gamma}$ is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (${a}_{\mathit{nn}}$). We include all diagrams up to $O({Q}^{3})$. This includes loop effects in the elementary ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\gamma}n$ amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting ${a}_{\mathit{nn}}$ from the shape of the entire ${\ensuremath{\pi}}^{\ensuremath{-}}d\ensuremath{\rightarrow}\mathit{nn}\ensuremath{\gamma}$ spectrum by using our calculation in its present stage would thus be possible at the $\ifmmode\pm\else\textpm\fi{}0.8$ fm level. A fit to the FSI peak only would allow an extraction of ${a}_{\mathit{nn}}$ with a theoretical uncertainty of $\ifmmode\pm\else\textpm\fi{}0.2$ fm. The effects that contribute to these error bars are investigated. The uncertainty in the nn rescattering wave function dominates. This suggests that the quoted theoretical error of $\ifmmode\pm\else\textpm\fi{}0.3$ fm for the most recent ${\ensuremath{\pi}}^{\ensuremath{-}}d\ensuremath{\rightarrow}\mathit{nn}\ensuremath{\gamma}$ measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly---and thus reducing the error---is briefly discussed.

Contribution of the quasifree mechanism to the ratio of double-to-single ionization

We evaluate the contribution of the quasifree (QF) mechanism to the ratio of double-to-single ionization by one photon. This mechanism is expected to take place in the interaction of a high-energy photon with an atom, and results in the mutual sharing of the photon momentum by two electrons, with small momentum transferred to the nucleus. In this case the electrons should be ejected in nearly opposite directions, sharing the energy nearly symmetrically. By using retardation, we show that the QF contribution displays a ${\ensuremath{\omega}}^{\ensuremath{-}5/2}$ energy dependence, in contrast to the well-known ${\ensuremath{\omega}}^{\ensuremath{-}7/2}$ energy dependence of the shake-off term. Our calculation shows that the QF mechanism does not give a leading contribution to the ratio of double-to-single ionization for keV photon energies, and is smaller than previously predicted.