The 22 Ne(α,n) 25 Mg reaction at astrophysical energies studied via the Trojan Horse Method applied to the 2 H( 25 Mg, α 22 Ne) 1 H reaction R. Spartà 1, M. La Cognata 1, C. Spitaleri 1,2, S. Cherubini 1,2, A. Cvetinovic 1, G. D Agata 1,2, G.L. Guardo 1, M.Gulino 1,3, I. Indelicato 1, L. Lamia 1, S. Palmerini 4, R. G. Pizzone 1, O. Trippella 4, S.M.R. Puglia 1, G. G. Rapisarda 1, S. Romano 1,2, M.L. Sergi 1, A. Tumino 1,3 1 Laboratori Nazionali del Sud INFN, Catania, Italy 2 Dipartimento di Fisica e Astronomia, Università degli Studi di Catania, Catania, Italy 3 Università di Enna "Kore", Enna, Italy 4 Dipartimento di Fisica, Università di Perugia and INFN Sezione di Perugia, Perugia, Italy 1. Astrophysical motivation and state of the art The 22 Ne(α,n) 25 Mg reaction is the neutron source triggering the production of elements in the weak component of the s- process (60 < A < 90) during the central He- burning and the shell- carbon burning stages in massive stars. Moreover, the 22 Ne(α,n) 25 Mg is considered the most intense neutron source for AGB stars, providing during thermal pulses neutron fluxes (up to 10 10 n/cm 3 ) large enough to allow for the competition between n- capture and β- decay and, therefore, to open branching points along the s- chain. In this way, nuclei traditionally considered as r- process products, such as 86 Kr, 87 Rb and 96 Zr, can be synthesized through slow neutron captures on unstable seeds ( 85 Kr, 86 Rb and 95 Zr) [1]. Precise measurements of the 22 Ne(α,n) 25 Mg cross section may change the predicted weak s- process distribution and help to improve significantly the conjectures on the s- process contribution to the galactic chemical evolution. The 22 Ne(α,n) 25 Mg reaction influences also the relative production of 25 Mg and 26 Mg and can play an important role in other astrophysical environments, such as type II supernova explosions, by altering the amount of 56 Ni produced (i.e., the peak luminosity) in the explosion. More details can be found in [2]. The 22 Ne(α,n) 25 Mg reaction has been the subject of many investigations, focusing on the measurement of its cross section and on the determination of the resonance parameters through indirect approaches, such as capture and transfer reactions [2]. Fig. 1, taken from [3], shows the trend of the excitation function of the 22 Ne(α,n) 25 Mg reaction measured so far. The steep drop in the yield makes it possible to provide only upper limits to the cross section already at center- of- mass energies of the order of 800 kev. This is extremely critical since the center- of- mass energy region of interest to the s- process is at Ecm = 600 ± 300 kev [2]. Indeed, direct measurements at such low energies are very challenging due to the exponential Coulomb damping of the cross section to values less than 1 μb, pushing the signal- to- noise ratio essentially to zero. Indirect measurement at low energy are thus needed to supply resonance parameters such as spectroscopic factors, to be used in the calculation of the reaction rate. Figure 1 Excitation function of the 22 Ne(α,n) 25 Mg reaction at low energies. In the inset, the resonance at lab energy of 832 kev is shown. Open squares are the data from Ref. [3]. More details can be found in this work.
2. Method A possible way to investigate the 22 Ne(α,n) 25 Mg reaction is by means of the Trojan Horse Method (THM). The method has been already successfully applied to study several astrophysically relevant reactions by using appropriate three- body quasi- free (QF) processes [4]. It has proven to be particularly suited for acquiring information on charged- particle induced reaction cross sections at astrophysical energies, since it allows to overcome the Coulomb barrier in the two- body entrance channel. One can briefly describe the method as follows (more details can be found in Ref. [4] and [5]). A projectile a hits a target nucleus A, whose wave function has a large amplitude for a s- b cluster configuration. Under proper kinematical conditions, particle a interacts only with part b (participant) of the target nucleus A, while the other part s behaves as a spectator to the process a+b(+s) à c+d(+s) (QF mechanism). Since the bombarding energy is chosen to overcome the Coulomb barrier in the entrance channel for the a+a à c+d+s reaction, particle b can be brought into the nuclear field of a to induce the a+b à c+d reaction. Moreover, assuming that the beam energy can be compensated for by the b+s binding energy, the two- body reaction can take place at very low a- b relative energy, e.g. in the region of astrophysical relevance. The method has proven to be very useful also in the case of neutron- induced reactions (see the review [4]). In this case, no expensive and complicate facilities delivering neutron beams are necessary and zero energy can be achieved even in the case the cross section is suppressed by the centrifugal barrier. In the plane wave impulse approximation, the three body cross section can be expressed as: dσ/dec dωc dωd (KF) Φ(ps) 2 dσ N /dω where KF is a kinematical factor containing the final state phase space factor, Φ(ps) 2 is the momentum distribution of the spectator s inside A, and dσ N /dω is the differential nuclear cross section for the a+b à c+d two body reaction. The deduced two- body reaction cross- section σ N (E) represents the nuclear part alone, the Coulomb barrier being already overcome in the entrance channel. The absolute cross section is obtained by normalization to the direct data at energies above the Coulomb barrier. In order to compare the two sets of data, it is necessary to correct σ N (E) for the penetration function through the Coulomb barrier. Thus, the obtained energy dependence is comparable to that derived in the direct measurements, except at low energies where the electron screening enhances the direct cross- section. These considerations apply of course to the corresponding S- factors. It is important to stress that the presence of the quasi- free mechanism is a necessary condition for the THM applicability, so that the experimental setup is chosen to optimize the corresponding kinematics. Moreover, the comparison with direct data in the energy region above the Coulomb barrier represents a significant validity test for the method. In this proposal, we discuss the procedure to investigate the 22 Ne(α,n) 25 Mg cross section using the THM and the detailed balance principle. The idea is to measure the 25 Mg(n,a) 22 Ne reaction applying the THM to the 2 H( 25 Mg, α 22 Ne) 1 H three- body reaction, and link the resulting two- body cross section to the relevant 22 Ne(α,n) 25 Mg one by means of the detailed balance principle. The choice of the 25 Mg(n,a) 22 Ne in the place of the 22 Ne(α,n) 25 Mg reaction is motived by the possibility to use a deuteron target to transfer the participant neutron, which makes the application of the THM very reliable owing to the simple p+n deuteron structure. Moreover, the study of the inverse reaction, namely, the 25 Mg(n,a) 22 Ne using the THM would make the LNS tandem and Camera 2000 the optimal setup for gathering unique information on the key astrophysical reaction 22 Ne(α,n) 25 Mg.
3. Experimental procedure To study the 22 Ne(α,n) 25 Mg reaction, we plan to perform an experiment aimed to investigate the 25 Mg(n,a) 22 Ne inverse reaction in the 22 Ne- α energy range between 478 kev (corresponding to the threshold for the 26 Mgà 22 Ne+α process) and ~1.5 MeV, thus covering the window of astrophysical importance and a broad energy region where direct measurements are available for normalization of the THM S- factor. To this purpose, we plan to apply the THM to the 2 H( 25 Mg, α 22 Ne) 1 H 3- body reaction, by using a 74 MeV 25 Mg beam impinging on a CD2 target, 100 μg/cm 2 thick. In this framework, the deuteron will act as THM nucleus because of its obvious p- n structure, its low- binding energy (Bp- n~2.2 MeV), and a very well known l=0 p- n momentum distribution given in terms of the radial Hulthén wave function. The experimental setup is thought to detect the ejected p and α particles, that is, the lighter fragments, because only two particles have to be detected and identified and their energies and angles of emission measured to completely determine the kinematical properties of the reaction. Figure 2 Kinematics plot for the 2 H( 25 Mg, α 22 Ne) 1 H reaction at 74 MeV beam energy. (a) α detection angle as a function of the proton emission angle, assuming the latter larger than 5 for ease of detection. (b) α emission energy as a function of the proton kinetic energy. Fig. 1a and 1b show the angles of emission of the p and α particles (where a cut on the lowest detection angle of α particles of 5 has been introduced) and their kinetic energies, respectively. Kinematics suggest that a setup symmetric with respect to the beam axis can be used, placing two position sensitive detectors (PSD) at forward angles, covering about 15 from 5 to 20, and two additional ones at larger angles, covering about 20 from 65 to 85 degrees. The target has to be rotated to reduce straggling at angles approaching 90 ). The PSDs under consideration are manufactured by Micron Semiconductors and have 50x10 mm 2 sensitive area and 0.5 mm position resolution. Detectors at forward angles are optimized for α particles while those at backward angles for proton detection. Since α particles are emitted with energies larger than 5 MeV, a 20 μm silicon detector can be used as ΔE stage for particle identification by means of the standard ΔE- E technique. Particle full energy will be measured using 1 mm thick PSD detectors. No proton identification will be done since their energies are very small. Offline kinematical identification of both protons and 22 Ne will be performed. The kinematical conditions for the 2 H( 25 Mg, α 22 Ne) 1 H reaction channel are set to favor very low proton momentum values, i.e. pp <50 MeV/c. This kinematical condition strongly underlines the basic feature of the THM, that is, the selection of the QF reaction mechanism in the 3- body coincidence yield.
Figure 3 22 Ne- α center- of- mass energy spectrum, where phase space only has been taken into account With such angular conditions and gating on the relevant kinematics restrictions corresponding to low proton momentum values, one obtains the simulated three- body coincidence spectrum given in Fig.3, projected onto the 22 Ne- α center- of- mass energy. 4. Beam time request For beam time evaluation, we refer to the typical value for the deuteron break- up processes of about 100 mbarn/sr 2 MeV and to a conservative estimate of the QF mechanism contribution (about 10%, assumed from similar reactions studied in the past). Considering a 25 Mg beam intensity of 0.5 pna (~3 10 9 pps), a CD2 target of about 100 μg/cm 2 (~10 19 atoms/cm 2 ) we should expect about 0.01 cps. Thus, aiming at covering the energy range between 0.5-1.5 MeV (including the one for normalization to direct data) with a bin of 10 kev, 10000 events are required for having a statistical error of 10%. This corresponds to about 12 days (36 BTU) of beamtime for the THM measurement. Moreover, we do need 3 days (9 BTU) of beamtime for energy and position calibration of the detectors. Calibration will be performed using α sources and a 6 Li beam at 8, 10 and 12 MeV impinging on a CH2 target. In this way, reactions on 12 C and 2 H will supply α particles for calibration of the forward detectors and scattered protons for calibration of the PSDs placed at larger angles. This leads to a total request of 15 days (45 BTU). 5. References [1] M. Pignatari et al., Nuclear Physics A 758 (2005) [2] R. Longland, C. Iliadis, A. I. Karakas, Physical Review C 85, 065809 (2012) and references therein [3] M. Jaeger et al., Physical Review Letters 87, 202501 (2001) [4] R. Tribble et al., Rep. Progr. Phys. 77, 106901 (2014) [5] C. Spitaleri et al., Phys. Rev. C 69, 055806 (2004)