Two measurements of the 22 Na + p resonant scattering via thick-target inverse-kinematics method

22Na is an important isotope for the study of extinct radioactivity, meanwhile its sufficiently long half life provides the possibility to observe live 22Na in nearby nova explosions. The 22Na(p,γ)23Mg is one of the key reactions that influence the 22Na abundance in nova ejecta. To study the proton resonant states in 23Mg relevant to the astrophysical 22Na(p,γ)23Mg reaction rates, two measurements have been carried out at the CRIB separator of University of Tokyo, and the RIBLL secondary beamline in Lanzhou, respectively. The 22Na secondary beam was produced via the 1H(22Ne, 22Na)n charge exchange reaction. Thick-target inverse-kinematics method is applied to obtain the excitation function of 22Na+p elastic scattering. Extended gas target and solid state polyethylene foil were used in the two measurements, respectively, to map the different excitation energy region of the compound nucleus 23Mg. Several new resonant levels are observed and their contribution to the 22Na(p,γ)23Mg reaction rate is evaluated.


Introduction
Cosmic γ ray is a powerful tool to trace and locate new cosmic events.Great progress in the field of γ-ray astronomy has been achieved in the past twenty years, brought largely by the Compton Gamma Ray Observatory (CGRO) of NASA [1], and the International Gamma Ray Astrophysics Laboratory(INTEGRAL) of European Space Agency [2].The main motivation of these missions is to a e-mail: ybwang@ciae.ac.cn observe cosmic γ rays from the decay of relatively long-lived 7 Be, 18 F, 22 Na, 26 Al, 44 Ti and 60 Fe isotopes. 22Na has a half life of 2.6 y, and it decays to the first excited state of 22 Ne which emits a 1.275 MeV characteristic γ ray.The stellar sources of radioactive 22 Na are primarily created in neon-rich nova [3,4] and supernova explosions [5,6].In neon-rich novae, the 22 Na is produced by the so-called high-temperature NeNa-MgAl reaction sequences [7,8], i.e. 20 Ne(p, γ) 21 Na(β + ) 21 Ne(p, γ) 22 Na, or 20 Ne(p, γ) 21 Na(p, γ) 22 Mg(β + ) 22 Na alternatively.In 1972, an extraordinarily large 22 Ne/ 20 Ne abundance ratio or nearly pure 22 Ne was found in low-density graphite grains separated from carbonaceous meteorites [9], which indicates the extinct radioactivity of 22 Na [10].In 1974, Clayton and Hoyle predicted the possibility to observe live 22 Na by the 1.275 MeV γ ray from nearby classical nova explosions [11].The COMPTEL experiments on board CGRO observed five recent Ne-type novae, which resulted in an upper limit of 3.7 × 10 −8 M of 22 Na ejected by any nova in the Galactic disk [12].Comparing to its relatively long half life, the main depletion mechanism of 22 Na is through the 22 Na(p,γ) 23 Mg reaction, the reaction rate over a large range of temperatures is thus crucial in deriving ranges of 22 Na production during nova and supernova outbursts.Many experimental investigations have been carried out to reduce the uncertainties of the 22 Na(p,γ) 23 Mg reaction rate, including direct measurements of the reaction rate with radioactive 22 Na targets [13][14][15][16], or indirect measurements for 23 Mg resonance properties via the β decay of 23 Al [17][18][19][20], and various transfer [21][22][23] or fusion-evaporation [24,25] reactions.In these studies new 23 Mg levels were identified in the energy region of astrophysical interest.However, most of the spectroscopic information is still missing due to the very complicated level structure of odd-mass 23 Mg close to the proton threshold.The 22 Na+p entrance channel is sensitive to populate the 23 Mg proton resonance states relevant to the 22 Na(p,γ) 23 Mg reaction; while thick target inverse kinematics (TTIK) technique [26] facilitates the measurement of the excitation function of 22 Na(p, p) elastic scattering.Crucial resonant parameters of 23 Mg can then be deduced for the evaluation of the 22 Na(p,γ) 23 Mg reaction rate.

Experiment
Two measurements using thick-target inverse kinematics method were carried out with intense radioactive 22 Na beams of different energies.Extended gas target and solid state polyethylene foil were used in the two measurements, respectively, to map the different excitation energy region of the compound nucleus 23 Mg.

CRIB experiment
One experiment was carried out at the CNS radioactive ion beam separator (CRIB) [27,28] of the University of Tokyo located in the RIKEN radioactive ion beam factory (RIBF).CRIB is a low-energy in-flight separator which can deliver intense secondary beams of low-and medium-mass nuclei.In the experiment 22 Na was produced via the 1 H( 22 Ne, 22 Na)n reaction.The 22 Ne primary beam of 6.0 AMeV bombarded in a hydrogen gas cell of 80 mm in length, which was confined by Havar foils of 2.5 μm in thickness and cooled with liquid nitrogen to a temperature of about 90 K.A nearly pure 22 Na beam was delivered to the 22 Na+p resonant scattering with an intensity of about 2.5 × 10 5 pps.
The 22 Na beam particles were monitored by two parallel-plate avalanche counters (PPACs) before reaching the secondary hydrogen target.The secondary gas target is semi-cylindrical in shape with a length of 300 mm.The energy of the 22 Na secondary beam after the entrance window of the gas target was 37.1±1.0MeV.During the 22 Na + p measurement, the hydrogen gas target was maintained within 310±2 Torr by a gas-flow system; this pressure was chosen to fully stop the 22  in the gas volume.The lighter recoil particles emerging from the exit window were detected by a silicon-detector telescope (ST) centered at θ lab = 0 • .The ST consists of ΔE and E layers, where the ΔE layer is a double-sided silicon strip detector (DSSD) with orthogonally oriented 16 × 16 readout strips on both sides and the E layer is a single-pad silicon detector.All the silicon detectors have an area of 50 mm×50 mm.The thickness of the ΔE detector is 75 μm and that of the E detectors is about 1.5 mm.

RIBLL experiment
The radioactive ion beam line in Lanzhou (RIBLL) is primarily a double-achromatic anti-symmetry fragment separator [29], which is constructed at the heavy ion research facility of Lanzhou (HIRFL).The operation of RIBLL has been mainly based on the coupling of two cyclotrons together, i.e. a K=69 Sector Focus Cyclotron (SFC) for low-energy ions and a K=450 Separate Sector Cyclotron (SSC) for intermediate-energy ions.In order to obtain low-energy intense secondary beams by transfer reaction, a setup similar to CRIB was recently installed including a gas target system at the entrance position of RIBLL [30].The new setup enables the primary beam from SFC to be transported directly to RIBLL, i.e. to bombard the gas target system.The secondary ions are subsequently separated and delivered by the 35 m-long RIBLL separator.
The production condition for 22 Na secondary beam is similar to that of the CRIB experiment.The 22 Ne primary beam of 7.5 AMeV bombarded in a hydrogen gas cell of 80 mm in length, which was confined by Havar foils of 2.5 μm in thickness and cooled with alcohol to a temperature of about 0 • C. The 22 Na secondary beam was monitored by a time-of-flight (TOF) system made of two plastic scintillators, and by two PPACs in the flight path.A schematic layout of the experimental setup for the 22 Na + p resonant scattering is shown in Fig. 1.In the target position, a polyethylene foil of 100 μm in thickness served as the reaction target, while a 61 μm thick carbon foil was used to evaluate the background.On the same slide, a single-pad silicon detector was also installed for the beam-tuning runs.Downstream from the target, the detector setup for lighter recoil particles is similar to that of the previous CRIB experiment.For the ΔE layer at θ lab = 0 • , a larger DSSD with an area of 70 mm×70 mm was used, which has 32 × 32 readout strips on both sides.During the experiment, a nearly pure 22 Na beam was delivered with an intensity of about 8.5 × 10 4 pps.The energy of the 22 Na secondary beam on the surface of the (CH 2 ) n target was 93.3±1.4MeV.

Results
The complexity in the analysis of a thick-target experimental data lies in the fact that at any individual angle, the proton energy spectrum is continuous over a certain range.By taking the two-body kinematics of 1 H( 22 Na, p) 22 Na elastic scattering and by considering the energy losses of 22 Na and proton along their trajectories, the E c.m. was deduced from the detected proton total energy on an event-by-event basis.After the conversion, the proton yields were added up over different θ lab defined by each pixel of the DSSD.The laboratory averaged differential cross section for the 22 Na + p elastic scattering is deduced from the net proton yield according to where dN p /dE refers to the net proton yield per E c.m. unit, dN t /dE is the energy dependent number of hydrogen atoms, I beam is the total number of incident 22 Na particles, and dΩ is the solid angle.The differential cross section in the center-of-mass frame is obtained by where θ 0 is the averaged laboratory scattering angle.
For the CRIB experiment, the excitation function of the 22 Na(p, p) elastic scattering and the Rmatrix analysis have been published in Ref. [31].Due to the stopping power of the gas target, the excitation function for the 22 Na(p, p) elastic scattering is obtained over a small range of excitation energies, as shown in Fig. 2. Three peaks have been observed at E R = 1.030, 1.212 and 1.335 MeV in the excitation function.The best R-matrix fit to the excitation function includes three resonances with J π = (5/2 to 9/2) − , 7/2 + and 5/2 + , respectively.The proton partial widths of the observed 23 Mg states are also deduced from the R-matrix analysis.The explicit assignments of the spin and parity to the 8.793 and 8.916 MeV resonances in 23 Mg allow for the shell-model calculation of the proton spectroscopic factors and the γ widths.Based on the resonant parameters obtained in this work, the 22 Na(p,γ) 23 Mg reaction rate is re-evaluated.An enhancement of about 5% over the evaluation by NACRE [32] is found for T 9 > 2 owing to the two new s-wave resonant states.For the RIBLL experiment, a similar data analysis has been performed and a preliminary excitation function for the 22 Na(p, p) elastic scattering is shown in Fig. 3.By using a higher-energy 22 Na beam and a solid-state (CH 2 ) n target, the excitation function for the 22 Na(p, p) elastic scattering could be extended up to E c.m. ≈ 4 MeV, quite complicated resonance structure is observed for further decomposition by R-matrix analysis.

Summary
The 22 Na + p resonant scattering has been studied via the thick-target inverse-kinematics method with gas and solid-state targets at different 22 Na beam energies.Excitation function for the 22 Na(p, p) elastic scattering is extended up to E c.m. ≈ 4 MeV, corresponding to an excitation energy of about 11.6 MeV in 23 Mg.Complicated resonance structure is observed, which indicates the possibility to explore new proton resonance levels in 23 Mg relevant to the 22 Na(p,γ) 23 Mg and 19 Ne(α,p) 22 Na reactions.The present work demonstrates that resonance parameters of astrophysical significance can be directly obtained by using the thick-target inverse-kinematics method with secondary beams.

DOI: 10
.1051/ C Owned by the authors, published by EDP Sciences, 201 Na particles EPJ Web of Conferences 04010-p.2

Figure 1 .
Figure 1.Schematic layout of the experimental setup for the 22 Na + p resonant scattering at RIBLL.

Figure 2 .
Figure 2. Excitation function for the 22 Na(p, p) elastic scattering obtained from the CRIB experiment.

Figure 3 .
Figure 3. Preliminary excitation function for the 22 Na(p, p) elastic scattering obtained from the recent RIBLL experiment.