LUNA measurement found no evidence of a low-energy resonance in 6 Li(p, γ ) 7 Be reaction

. The 6 Li(p, γ ) 7 Be reaction is mainly at work in three nucleosynthesis scenarios: Big Bang Nucleosynthesis, 6 Li depletion in pre-main and in main sequence stars and cosmic ray interaction with interstellar matter. The 6 Li(p, γ ) 7 Be S-factor trend was poorly constrained at astrophysical energies because of conflicting experimental results reported in literature. A recent direct measurement, indeed, found a resonance-like structure at E c . m . = 195 keV, corresponding to an excited state at E x ∼ 5800 keV in 7 Be which, however, has not been confirmed by either other direct measurements or predicted by theoretical calculations. In order to clarify the existence of this resonance, a new experiment was performed at the Laboratory for Underground Nuclear Astrophysics (LUNA), located deep underground in Gran Sasso Laboratory. Thanks to the extremely low background environment, the 6 Li(p, γ ) 7 Be cross section was measured in the center-of-mass energy range E = 60-350 keV with unprecedented sensitivity. No evidence for the alleged resonance was found. LUNA results was confirmed by latest published indirect determination of 6 Li(p, γ ) 7 Be S-factor and it is supported by a recent theoretical study.


Introduction
Lithium abundance involves mainly three nucleosynthesis scenarios. The Galactic chemical evolution models predict, indeed, that most of the solar lithium was provided by low-mass stars [1] while the rest was produced by Big Bang Nucleosynthesis (BBN) [2,3] or by Galactic cosmic rays interacting with interstellar matter.
The 6 Li/ 7 Li isotopic ratio has been proposed as a tool to constrain non-standard lithium production mechanisms [4] and pollution of stellar atmospheres [5] in the context of the cosmological lithium problem. Recent (re-)observations of metal poor stars either severely reduced or provided only upper limits for the lithium isotopic ratio [6][7][8], suggesting that 6 Li depletion must occur in halo stars, which in turn call into question the 7 Li abundance observed in these stars corresponds to the primordial value [9]. The 6 Li(p,γ) 7 Be reaction (Q value = 5606.85(7) keV) has a crucial role in determining the stellar 6 Li/ 7 Li ratio. The 6 Li(p,γ) 7 Be reaction not only deplete 6 Li but it also convert some of it to 7 Li, through 7 Be radioactive decay.
The slope of the astrophysical S -factor is poorly constrained at low energies given the inconsistent results reported in literature [10,11]. Moreover, a new resonance at E c.m. = 195 keV, corresponding to an excited level at E x ≈ 5800 keV with J π = (1/2 + , 3/2 + ) and Γ p ≈ 50 keV, was claimed by [12]. In a recent comprehensive study of the 3 He( 4 He,γ) 7 Be reaction (Q value = 1587.14(7)) no evidence for such a resonance was found at E c.m. = 4210 keV [13].
None of the theoretical calculations of the 6 Li(p,γ) 7 Be S -factor can reproduce the newlyreported resonance [14,15, and references therein], unless this is added ad-hoc to reproduce the experimental data [16].

Experimental Setup
A new experiment [17] was performed at the Laboratory for Underground Nuclear Astrophysics (LUNA), at Laboratori Nazionali del Gran Sasso (Italy) [18]. The LUNA deepunderground location guarantees the reduction of environmental background by several orders of magnitude with respect to overground laboratories, enabling high-sensitivity measurements to be performed.
A schematic view of the experimental setup is shown in Fig.1  ton beam was provided by LUNA-400 accelerator [19] and it was collimated and delivered through a copper pipe to the target, mounted at 55 • with respect to the beam direction. The Cu tube was used both as a cold trap, to improve the scattering chamber vacuum and prevent carbon build-up on target, and for secondary electron suppression. The evaporated targets were made from 6 Li 2 WO 4 or 6 Li 2 O powder, with thicknesses 100 − 200 µg/cm 2 and 20 µg/cm 2 respectively. The 6 Li isotopic enrichment level was 95% for all targets, which were water cooled to limit target degradation during irradiation [17]. To detect 6 Li(p,γ) 7 Be reaction γ-rays a High-Purity Germanium (HPGe) detector was positioned in close geometry to the target and at 55 • with respect to the beam direction. In addition a Silicon (Si) detector was installed at 125 • from the beam direction to detect the α and 3 He particles from the 6 Li(p,α) 3 He reaction concurrently with the gamma rays from the 6 Li(p,γ) 7 Be reaction. Efficiencies for both detectors were obtained using GEANT simulations, fine tuned through the comparison with experimental results for γ and α standards as well as for known resonances of 14 N(p,γ) 15 O and 18 O(p,α) 15 N reactions [17]. The total uncertainty is 4% and 8% for the HPGe and Si detector efficiency respectively.

Results and Discussion
A measurement of the 6 Li(p,γ) 7 Be and 6 Li(p,α) 3 He excitation functions was performed for each target in the whole dynamic range of the LUNA-400 accelerator in order to make consistency checks and verify results are unaffected by systematic effects [17].
The 6 Li(p,γ) 7 Be experimental yield was calculated as the sum of the contributions from the direct capture to the ground state (γ 0 ) and to the 429 keV excited state of 7 Be (γ 1 ). For the calculation of the 6 Li(p,γ) 7 Be reaction S -factor, we adopted a relative approach [17]: the (p,γ) yield was normalized at each energy to the (p,α) yield. This ratio can be expressed in terms of the ratio between (p,γ) and (p,α) S -factors. We adopted for the 6 Li(p,α) 3 He reaction the S -factor parametrization reported in [20]. For the (p,α) channel, the angular distribution coefficients A k and related uncertainties were taken from [21, and references therein]. For the (p,γ) channel we adopted the theoretical angular distribution described in [14]. The measured S -factor was corrected for electron screening using the approximation in [22] and assuming a screening potential U e = 273 eV [20].
The present S -factor has a monotonic dependence on the energy and show no evidence of the resonance reported in [12], see Fig.3. The measurement covered the center-of-mass energy range 60 − 350 keV and the reported statistical and systematic uncertainty were ≤2% and 12% respectively. Combining current data and the high energy results reported in [23] an R-matrix fit was performed providing an extrapolated S -factor to zero energy S (0) = 95 ± 5 eV b. The R-matrix fit was used to calculate a new 6 Li(p,γ) 7 Be reaction rate, which is 9% lower than NACRE [24] and 33% higher than reported in NACREII [16] at temperatures relevant for 6 Li depletion in pre-main sequence stars. Moreover the reaction rate uncertainty has been significantly reduced [17], see Fig.4.
The result of a subsequent indirect study confirms LUNA extrapolation down to low energies for the 6 Li(p,γ) 7 Be S -factor, reporting an S (0) = 92 ± 12 eV b [25]. A recent theoretical study found a consistent trend for the 6 Li(p,γ) 7 Be S -factor predicting a S -factor to zero energy of 98.3 eV b [26] Figure 3. Astrophysical S-factor for the 6 Li(p,γ) 7 Be reaction as obtained by LUNA in red [17]. Previous experimental data and theoretical evaluations are also shown for comparison. The solid red line represents an R-matrix fit of LUNA data and data from [23].  . Reaction rate for the 6 Li(p,γ) 7 Be reaction, normalized to the NACRE rate [24]. The NACRE II rate [16] is also shown for comparison. Dashed lines represent the uncertainty on the NACRE rate (black), on NACREII rate (blue) and on LUNA rate (red).