Recent results for the one-proton transfer reaction in the 18O+48Ti collision at 275 MeV

The 18O+48Ti reaction was studied at the energy of 275 MeV for the first time under the NUMEN and NURE experimental campaigns with the aim to investigate the complete net of reaction channels potentially involved in the 48Ca→48Ti double charge exchange transition. Such a transition is of great interest because of its relevance to the extraction of 48Ca→48Ti double beta decay nuclear matrix element. The relevant experiment was carried out at the MAGNEX facility of INFN-LNS in Catania. Angular distribution measurements for the various reaction products were performed by using the MAGNEX large acceptance magnetic spectrometer. The present contribution is focused on the analysis of the one-proton transfer channel with emphasis on the particle identification technique and the estimation of background contaminations.


Introduction
The interest of the Nuclear Physics community for the Double Charge Exchange (DCE) reactions is still vivid due to their possible relation with the double beta (ββ) decay [1]. Into this context, a novel idea has been recently conceived at Istituto Nazionale di Fisica Nucleare -Laboratori Nazionali del Sud (INFN-LNS), under the NUMEN (NUclear Matrix Elements for Neutrinoless double beta decay) project [2]. This is to use for the first time DCE reactions induced by heavy-ion beams as a mean for the * e-mail: onoufrios.sgouros@lns.infn.it determination of the ββ decay Nuclear Matrix Elements (NMEs). This unique opportunity is based on the fact that the two processes present some interesting similarities. Among them, both processes probe the same initial and final nuclear wave functions and the operators connecting them have a similar spin -isospin mathematical structure [2][3][4]. Thus, even if the two processes are mediated by different interactions, the involved NMEs could be connected and the determination of the DCE reaction cross-sections may provide an important piece of information on the ββ matrix elements. In the present study, which is a part of the NURE project [5], the 18 O+ 48 Ti reaction was investigated by measuring not only the DCE channel, but also Single Charge Exchange (SCE) and multi-step transfer reactions which may lead to the same final states as the DCE one. It is very important to quantify possible contributions from other reaction channels to the DCE one for a precise determination of the absolute DCE cross sections, which may be the key for accessing the information of the NMEs of the ββ decay. In the present contribution, the data analysis of the one-proton transfer reaction 48 Ti( 18 O, 19 F) 47 Sc is presented. The experimental details are presented in Section 2, while the data reduction procedure is reported in Section 3. Our results are summarized in Section 4.

Experimental Setup
The experiment was performed at the MAGNEX facility [6] of INFN-LNS, where an 18 O 8+ beam accelerated by the K800 Superconducting Cyclotron at the energy of 275 MeV impinged onto a TiO 2 target 510 µg/cm 2 thick. An aluminum foil with a thickness of 216 µg/cm 2 was used as a backing for the target material. In order to estimate the background originating from the different target components, two additional runs, one with a pure 27 Al target 226 µg/cm 2 thick and a WO 3 one (284 µg/cm 2 ) evaporated on a thin aluminium foil, were also performed. The various reaction products were momentum analyzed by the MAG-NEX large acceptance magnetic spectrometer whose optical axis was set at θ opt = 9 • with respect to the beam direction, spanning an angular range between 4 • and 15 • in the laboratory reference frame. The vertical slits of the MAG-NEX spectrometer, located 260 mm downstream the target position were set such as to cover a vertical angular range of ±2 • . The various reaction products emerging from the beam-target interaction were detected by the MAGNEX Focal Plane Detector (FPD) [7,8].
The MAGNEX FPD is consisted of a gas section followed by a wall of 60 single silicon detectors. The use of the gas detector is twofold. It serves as a proportional drift chamber providing the energy loss signal (∆E) of the ions inside the gas, but also as a mean to map the ions track. The tracker is divided in six sections each one having at the top a proportional wire (DC) in which the (∆E) signal is measured. The sum of the 6 signals, ∆E tot , is used in the particle identification process. Above the DC wires, a set of 6 segmented anode strips is located where each strip is composed of 224 induction pads allowing the measurement of the horizontal position (X f oc ) and thus, the determination of the horizontal angle (θ f oc ). Moreover, the electron drift time measurements inside the gas allow the determination of the vertical position (Y f oc ) and angle (φ f oc ). With the present gas tracker, the maximum rate that the detector can sustain is limited to a few kHz. However, this will be insufficient for the future NUMEN experiments at the MAGNEX facility with high intensity beams. To this extent, the development of a new configuration [9,10] for the MAGNEX FPD is in progress based on the THick GEM (THGEM) technology for the new tracker.

Data Reduction
The data analysis relies on the accurate identification of the reaction channel of our interest. The particle identification (PID) is the first step of the data analysis which was performed following the prescription of Ref. [11]. The various ion species were well-discriminated using the conventional ∆E-E technique. A typical ∆E tot -E resid spectrum is presented in the top panel of Figure 1 for a single silicon detector. It is evident that the fluorine isotopes, highlighted with the black contour, are well separated from any other ion family. However, we are interested in identifying the one-proton pick up reaction products i.e. 19 F 9+ so, the Z separation is not enough. To this direction, after the identification of the fluorine ions, the mass separation is feasible via the X f oc -E resid (horizontal position versus residual energy measured for each silicon detector) spectra. In a spectrometer, the position along the dispersive axis is analogous to the momentum of the ion. So, the position and the energy are related according to the following expression: where m, q and E resid are the ions' mass, charge state and residual energy, respectively. Ions possessing a different mass over charge state ratio lie on a different region at the X f oc -E resid representation as it is illustrated in the lower panel of Figure 1. Looking at Figure 1 it is obvious that the mass resolution of MAGNEX is excellent. Thus, the ∆E-E technique in conjunction with mass separation method presented above, provide the root for an accurate identification of the one proton pick-up reaction channel.
Once the 19 F 9+ ions were identified, we have proceeded with the analysis of the the final phase space parameters.
A typical θ f oc -X f oc spectrum obtained with the TiO 2 + 27 Al target is presented in Figure 2, where various loci are wellpronounced in the spectrum. Since a compound target was used in the current measurement, background events due to the reaction of the 18 O beam with the oxygen and aluminium components of the target were also present in our spectra. In order to identify the fingerprint of each reaction, dedicated Monte Carlo simulations by taking into account the reaction kinematics but also the complete geometry of the spectrometer and the spatial distribution of the dipole and quadrupole fields were performed. The results of the simulations are compared to the experimental data in the lower panel of Figure 2. It is seen that the simulations describe in an excellent way the experimental data giving further support to the validity of the dipole and quadrupole fields which were adopted in the simulations. The different slope met both in experimental and simulated events is attributed partially to the different kinematics for each reaction and partially to the chromatic aberrations which are present in large-acceptance optical devices like MAGNEX. However, the latter are effectively compensated when a high-order software trajectory reconstruction [12] is applied to the data.  Having identified the background events, the analysis of the data obtained with the pure aluminum target and the WO 3 + 27 Al one was performed in order to estimate and subtract the contaminant events in the data set obtained with the TiO 2 + 27 Al target. A software ray reconstruction was applied to the data and the initial phase space parameters (e.g. θ lab , kinetic energy) were reconstructed from the measured ones (e.g. θ f oc , φ f oc , X f oc ). The excitation energy E x was determined from the missing mass method [6] as: where Q 0 is the ground state (g.s.) to g.s. transition. The reconstructed excitation energy spectrum for the data obtained with aluminum target is presented in Figure 3. Various peaks associated to transition to the states of 19 F and 26 Mg nuclei are well-formed in the spectrum up to the excitation energy of 10 MeV, where a rather continuum shape is observed due to the decay of 26 Mg nucleus ( 26 Mg→ 22 Ne+α). A similar procedure was also followed for the data obtained with the WO 3 + 27 Al target and the excitation energy spectrum corresponding to the 16 O( 18 O, 19 F) 15 N reaction was deduced. After completing the analysis of the background runs, the same trajectory reconstruction technique was applied to the data obtained with the TiO 2 + 27 Al target. The reconstructed θ lab -E x plot is shown in Figure 4. Like in case of Figure 2, we can immediately identify in the spectrum the presence of the reaction contaminants.  47 Sc reaction. In order to isolate the energy spectrum for the one-proton transfer reaction on 48 Ti, after projecting the data of Figure 4 onto the E x axis, we have superimposed to the mixed spectrum the previously analyzed data with the aluminum and oxygen targets, appropriately normalized. Subsequently, the background spectra were subtracted from the mixed one and the energy spectrum corresponding to the 48 Ti( 18 O, 19 F) 47 Sc reaction was deduced. The background subtraction procedure is presented in Figure 5. Given the high density of states of the populated 47 Sc nucleus and the finite experimental energy resolution (about 500 keV FWHM) the measured excitation energy spectrum was rather structure-less. The results of this analysis will be the subject of a forthcoming publication.