Neutron-induced reactions investigated via the Trojan Horse Method

The Trojan Horse Method has been applied to many neutron-induced reactions using the deuteron as a virtual source of neutrons, to explore wide energy regions of interest for astrophysics and applied physics and to investigate the suppression of the centrifugal barrier, that is one of the key advantages of this Method. The neutron-induced experimental campaign has already concerned 17O(n, α)14C, 6Li(n,α)3H, 7Be(n,p)7Li, 7Be(n,α)4He, 18F(n,α)15O and 14N(n,p)14C, and very recently 25Mg(n,α)22Ne and 27Al(n,p)27Mg, while others are planned to be measured soon, thus influencing different astrophysical scenarios. Particular attention is dedicated to a new measurement regarding the 10B(n,α)7Li reaction, aimed to disentangle the 7Li ground state contribution from its first excited state to the cross section.


Introduction
Dealing with neutron induced reactions measurements is challenging and complex as much as they turn to be always more necessary. Areas of interest of their applications range from pure nuclear physics (nuclear structure and dynamics) to nuclear astrophysics, where n-induced reactions are fundamental basically in any astrophysical scenario. The same holds for applied physics, where these reactions are nowadays used to study and understand our cultural heritage (as an example the european Ancient Charm project [1]). Some of them, as 10 B(n,α) 7 Li, are also used in nuclear energy power plants (to monitor the neutron fluxes in the plant), and in medicine, as it is discussed in section 3.2.

The need of indirect methods
Measuring neutron induced reactions is anyhow challenging. It is not possible to get a pure target of neutrons and the beam is not easy to have. Indeed, a primary neutron producer reaction, such as 7 Li(p,n) 7 Be, is necessary with low energy accelerators, but this will not produce monoenergetical neutrons. Moreover, it is not possible to accelerate neutrons in the usual ionization way. Despite many attempts are done in facilities spread around the world, it seems impossible to get an intense monoenergetical neutron beam.  Also the way to obtain the cross sections with the detailed balance principle applied to the  inverse reactions is problematic, because of the low efficiency problems connected with neutron  detection. For all these reasons, the use of indirect methods is required to achieve results useful for pure and applied physics.

The Trojan Horse approach
The Trojan Horse Method (THM) [2] [3] results to be the best indirect technique for this case. It was born to determine bare nucleus S-factor at astrophysical energies, because it allows to obtain the cross section without the strong suppression at very low energies due to the Coulomb barrier.
This is made selecting the quasi free mechanism by the cross section of an appropriate 3body reaction measured in the lab, where one of the two interacting particles is called the Trojan Horse nucleus, and has a very high probability of clusterization in two particles. In the peculiar circumstances of this mechanism, one of them will partecipate and the other will act as a spectator to the binary reaction, that is the goal of the experiment.
In recent years, THM has also been applied to neutron-involving reactions: for the case of neutron outgoing, it avoids the use of neutron detectors, reconstructing its kinematics by the other two outcoming particles of the reaction: this has been very helpful for the cases of 2 H(d,n) 3 He [4] and 13 C(α,n) 16 O [5], where their cross section have been extracted detecting the charged outcoming particle and the spectator proton and deuteron, respectively. Instead, for the case when neutron is inducing the reaction, using the very well known p+n structure of deuteron, where their intercluster motion in l = 0 is well known and described by the Hultén function.
Using a CD 2 target (plastic and easy to get) has revealed to be a very cheap and simple way to have a perfect virtual neutrons source. Moreover, the use of this indirect method let us need only one beam energy to get a wide energy range for the excitation function.

Reactions measured
The first reaction used to test the Method in the neutron circumstances has been the 6 Li(n,α) 3 H, whose 2-body cross section has been extracted by the 6 Li(d,αp) 3 H measured at Laboratori Nazionali del Sud (LNS) in Italy. This marked the first evidence that deuteron could be rightly used as neutron virtual source and was the first direct insight of the Trojan Horse cross section behaviour about the centrifugal barrier effects: it is evident from data that TH cross section is in agreement with direct results only if it is multiplied for the on-shell centrifugal effects [6] [7].
Another neutron induced reaction stuedied with THM is 17 O(n,α) 14 C, that turns out to be of great interest for the astrophysical scenario of s-process nucleosynthesis, which is all about neutron captures [8]. In that context, reactions as 17 O(n,α) 14 C are called neutron-poisons, because the total amount of neutron available for s-process depends on their reaction rate. With THM a new measurement has been performed in the energy range of astrophysical interest, resulting in a reaction rate quite different from the ones found in literature, and astrophysical consequences have still to be evaluated [9].
Partial results of a preliminary test to get the cross section of 10 B(n,α) 7 Li have been already published [10], while the final ones are going to be subimitted for publication. However, because of the particular importance of this reaction for applications, a new and very precise measurement has been performed and is still under analysis, as reported in section 3.2.

Results under analysis and applications to exotic beams
Great efforts have been put on the measurement of 7 Be(n,α) 4 He and 7 Be(n,p) 7 Li, made in two runs (the first in LNL, Italy and the second at CRIB, Japan) to get these two cross sections  [12] are a proof that TH perfectly suits the needs of measurements involving exotic beams, such as 7 Be. Also 14 N(n,p) 14 C has been measured at LNS, because it is the first n-poison of s-process, mentioned above. Results are still under analysis [13].
Moreover, in the very recent past other two neutron induced reactions have been measured, both at LNS. The first was the 25 Mg(n,α) 22 Ne to get the 22 Ne(α,n) 25 Mg cross section using the detailed balance principle. The latter is, indeed, one of the most influencing reaction for the star nucleosynthsis scenario, which hardly impacts the s-process and all the rest of the life of a star.
The second one is 27 Al(n,p) 27 Mg, that has been the first step of a long term campaign of measurement involving Al isotopes, which will very soon involve also exotic beams. This has been thought to give contraints to reaction rates involving the abundance of 26 Al, very important to trace the active nucleosynthesis in the Galaxy.

The case of 10 B(n,α) 7 Li
This peculiar neutron induced reaction is of interest for the nuclear energy production in power plants, to have control on reactions induced on the percentage of 10 B in the natual boron, considering that 11 B(p,αα) 4 He is the only good candidate for a clean (aneutronic) energy obtained by fusion. Moreover, it is very important for medicine, considering that the cure protocol of eye melanomas and glioblastoma mulltiforme [14] and the synovial ablation for rheumatoid artritis [15] consist in inducing this reaction inside the patient. For purposes of medicine, an energy range from 0 to 100 keV is of interest in the excitation function, while in the energy production case from 0 to 15 MeV. However, cross section measurement available in literature are still not exhaustive for these applications.
This reaction has already been measured using Trojan Horse Method [10], but a new run has been performed in order to separate the two main contributions to this cross section, coming from the ground state and from the first excited state of the 7 Li, separated by 0.477 MeV.
The experimental run has been performed in 2014 in Laboratori Nazionali del Sud (LNS, Catania), using a 28 MeV 10 B beam impinging on a CD 2 target, measuring 10 B(d,α 7 Li)H cross section, as it is sketched in fig. 2. Results obtained cover the sensitive energy range from 0 to 1.5 MeV.  Figure 2. Sketch of the transfer reaction measured at LNS. The deuteron inside the CD 2 target has been the neutron virtual source, while the 10 B was the beam. 7 Li and α particles have been detected, while the spectator proton kinematics has been reconstructed.
The goal of separating the two contributions was achieved using a very thin target (56 µg/cm 2 ), minimizing the energy straggling and loss of the beam and the outcoming particles.
Once α and 7 Li produced have been discerned via their energy loss in isobutane gas inside ionization chambers placed in front of two of the four PSD in the scattering chamber, the Q-value spectrum, reported in [16], clearly shows two separated peaks related to the channels desired. Some details are reported in [16] and [17].
Angular distributions have been extracted thanks to the avoidance of the centrifugal barrier for each level foreseen by literature in the measured E cm range. They result to be well in agreement with what reported in literature, as shown in fig. 3 where the case of 11.600 MeV level is plotted (α 0 data set). In this figure blue and red dots mark different kinematical conditions of the experimental run, while the black line is the theoritical distribution, calculated as [19] for the J π foreseen by literature, namely 5/2+ [18].

Conclusions
The THM extension to neutron induced reactions has proved to be a very powerful instrument to overcome centrifugal barrier effects, helping in the study of levels which are suppressed in direct measurements, allowing the possibility to measure angular distributions and nuclear properties and obtaining the strenght of each level, thanks to the new Modified R-matrix approach [20].
Moreover, it perfectly suits complex situations of measurements (including RI beams case), because the use of deuteron as a virtual neutron source permits the use of simple setups, easy targets and the need of only one beam energy to get a wide energy range in the excitation function, finally making simple and less expensive the research.