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The d(9Li,p)10Li reaction as a tool to explore the 10Li structure

The ground and low-lying states of the unbound nucleus 10Li were populated by the 9Li + 2H → 10Li + 1H reaction at 11 AMeV incident energy at the ISAC II facility (TRIUMF). In the experimental setup, the outgoing 9Li at forward angles and the recoil protons at backward angles were detected and identified. This setup allows to study the 10Li emitted in the crucial region at forward angles in the centre of mass.


Introduction
The study of the unbound system 10 Li is of great interest since the knowledge of its structure is a crucial ingredient in the description of the two-neutron halo nucleus 11 Li [1,2]. Structure calculations for the weakly bound system 11 Li = 9 Li +2n either in the cluster model or in approaches based on the independent particle model require in fact the interaction between one neutron and the 9 Li core as an important input quantity. This can be deduced directly from the binding energy and states of 10 Li. Despite the significant amount of experimental information gathered during the last years, the properties of the 10 Li continuum remain unclear, to the extent that even the energy and the spin-parity of the ground state are still controversial [4][5][6][7][8][9].
In the case of N = 7 isotones, the energy and ordering of the 2s 1/2 , 1p 1/2 and 1d 5/2 orbitals can be represented as in Fig. 1, according to the excitation energy of the known single particle states. In the case of 15 O, 14 N, 13 C and 12 B ground states, it is well known that the main component of the 1d 5/2 shell lies above the 2s 1/2 , which is in turn above the 1p 1/2 . In the 11 Be (Z = 4) ground state a shell inversion between 2s 1/2 and 1p 1/2 is known to appear [9,11]. If this anomaly is maintained also in the 10 Li (Z = 3) case, the lowest energy state in 10 Li is expected to have a dominant configuration with one neutron in the 2s 1/2 . On the other hand, if one supposes that the presence of shell inversion in 11 Be is related to the 2α cluster structure of Be isotopes, such a structure is not possible for 10 Li and the configuration of the 10 Li ground state is expected to be a 9 Li core + one neutron in the 1p 1/2 . Transfer reactions are essential tools to probe selected components of the nuclear wave functions. Thanks to that they have been used in the past and are still crucial for nuclear spectroscopy purposes. With the advent of radioactive beam facilities, the new opportunity to explore nuclear phenomena far from the stability valley has driven a renewed interest to transfer reactions, to be studied in inverse kinematics. On one hand there is a specific attention to understand how the transfer mechanism is influenced by the reduction of the binding energy of the projectile [3,4]. On the other hand, the measured spectra could reveal unexpected features due to nucleon correlations which are beyond the mean field description of nuclear structure [5]. Examples of such phenomena have been recently found in light neutron rich nuclei such as the Li isotopes.

Past attempts to study the d( 9 Li,p) 10 Li reaction
Recently 10 Li has been the subject of different theoretical and challenging experimental studies [6][7][8], including two attempts to explore the resonant energy spectrum by the d( 9 Li,p) 10 Li transfer reaction at 2.35 AMeV incident energy at REX-ISOLDE and at 20 AMeV at NSCL-MSU, respectively.
In the experiment at 2.35 AMeV of Ref. [6], the energy spectrum of 10 Li was measured up to about 1 MeV excitation energy in an angular range between 100° and 140° in the centre of mass. Due to the low beam intensity of about 5 × 10 4 pps, a relatively thick target of deuterated polyethylene CD2 (660 μg/cm 2 thick) was used in order to maximize the yield, which slightly exceeded 100 events in total. The recoiling protons were detected by large area telescopes of position sensitive silicon detectors located between 18° and 80° in the laboratory. At backward laboratory angles, the energy of the protons was too low to be detected, thus excluding in the collected data the crucial region corresponding to forward angles in the centre of mass. Despite the low statistics and the not optimal angular range explored, an excitation energy resolution of about 300 keV (FWHM) was obtained and the authors could draw some conclusions about the role of the s 1/2 and p 1/2 neutron orbitals in 10 Li around the neutron emission threshold.
In the NSCL-MSU experiment [7], a similar experimental technique was used but at higher incident energy (20 AMeV). The beam intensity was even lower than in the REX-ISOLDE experiment (~ 7 × 10 3 pps) and the emittance considerably worse. The CD2 target was about 2 mg/cm 2 thick. The recoiling protons were measured at backward angles by a series of large area silicon detectors in coincidence with the 9 Li detected by the S800 spectrometer at forward angles. The obtained energy resolution was about 700 keV and the reconstructed 10 Li spectra were measured up to about 4.5 MeV excitation energy. However, due to the poor statistics (less than 100 counts in total) and energy resolution, not much was added to our understanding of 10 Li states. In a recent theoretical study of the 10 Li low energy resonances [4], a state dependent treatment of the pairing interaction, beyond the usual BCS approximation, has proven to be necessary to reproduce the energy spectra measured in the REX-ISOLDE experiment. In addition it was shown that, despite the complications due to the resonant structure of the final states, the cross sections can be accurately described within the DWBA.
Nevertheless, due to the limitations of the existing data, many of the details predicted by the theory were not tested. For example only a measurement of the angular distribution at forward angles in the centre of mass would disentangle contributions from s, p and d orbitals in different portions of the energy spectrum. Also the behaviour of the observed s 1/2 and p 1/2 orbitals should be better addressed, since in both cases the coupling with the p 3/2 proton generates a doublet of 10 Li states, namely 1 -, 2for the s 1/2 and 1 + , 2 + for the p 1/2 , while experimentally there is no indication of such doublets. In addition, according to the theory, p 3/2 and d 5/2 orbitals should generate resonances above 1 MeV, but these have not been observed experimentally, since the MSU data are difficult to be reliably interpreted.
To summarize, many of the key points regarding the 10 Li spectrum are still very uncertain, especially from an experimental point of view. As a consequence the description of the 11 Li halo nucleus is quite deficient, since the binding energy strongly depends on the same n -9 Li interaction responsible for the 10 Li structure.

The experiment
We studied the d( 9 Li,p) 10 Li reaction at 11 AMeV incident energy at the TRIUMF laboratory. At this energy the recoiling protons can be detected at backward laboratory angles, thus allowing the exploration of the crucial region at forward angles in the centre of mass.
A 9 Li beam, produced by the ISAC-II facility with an average current of 10 6 pps, impinged on a CD2 target, 126 μg/cm 2 thick, evaporated at the INFN-LNS laboratory (Catania). The target thickness was chosen to improve the energy resolution maintaining an acceptable count rate. The recoiling protons were detected at backward angles 127° < θ LEDA < 152° by the LEDA array of silicon strip detectors [12], thus allowing the study of the 10 Li emitted at forward angles. Protons were detected in coincidence with the 9 Li fragments produced from the break-up of the corresponding 10 Li. 9 Li fragments were detected and identified by a ΔE-E telescope of annular Double Sided Silicon Detectors located downstream the target. Fig. 2 shows an example of ΔE-E identification plot where the 9 Li locus is well identified and contoured by a solid line. An additional benefit of placing the proton detectors at backward scattering angles is that no background is expected from other reaction channels. In Fig. 3 the calculated kinematics of the outgoing deuteron from for the 9 Li + d elastic and inelastic scattering are shown. Since there may be also a small proton contamination in the CD2 target, the 9 Li + proton scattering reactions are also shown in Fig. 3. In all these cases, the kinematics of the reaction does not allow to produce a light nucleus at backward scattering angles, where the LEDA detector was located.  The 10 Li excitation energy was reconstructed with significant statistics allowing to explore its level structure. Fig. 4 shows the excitation energy spectrum obtained up to 2.5 MeV in the angular region 8.3°< θ CM < 16.2°. The centroid (E 0 = 0.6 MeV) and full width at half maximum (Γ = 0.6 MeV) of the unbound ground state were deduced and also the presence of a structure at higher excitation energy at around 1.5 MeV is visible. The sharp fall down of the tail of the first peak toward zero excitation energy shows that there is no evidence in the present data of the existence of a s 1/2 low lying virtual state as supposed by [6].
The highly segmented detection system also allowed to measure the angular distributions of the observed resonances at forward angles. The analysis of the angular distribution, which is still in progress, would give some indication about the controversial question of the spin-parity of the 10 Li unbound ground state.