The New Deep-Underground Direct Measurement of ²²Ne(α, γ)²⁶Mg with EASγ: A Feasibility Study

Abstract

²²Ne(α, γ)²⁶Mg is pivotal in the understanding of several open astrophysical questions, as the nucleosynthesis beyond Fe through the s-process, but its stellar reaction rate is still subject to large uncertainties. These mainly arise from its extremely low rate in the Gamow energy region, whose measurement is hampered by the unavoidable presence of the cosmic ray background noise. A possibility to overcome this issue is to perform the measurement in a quasi background-free environment, such as that offered by the underground Bellotti Ion Beam Facility at LNGS. This is the key idea of EASγ experiment. In this study, the signal from the de-excitation of the compound nucleus ²⁶Mg has been simulated and its detection has been investigated both on surface and deep-underground laboratories. The simulation results show the enhancement in sensitivity achieved by performing the measurement deep underground and with an additional shielding, yielding to unprecedented sensitivity.

1. Introduction

The ²²Ne(α, γ)²⁶Mg reaction plays a crucial role in nuclear astrophysics, as it influences the isotopic ratios of ^24,25,26Mg, one of the few elements for which we have isotopic information directly from stellar spectroscopic observations of cool dwarfs and giants stars [1,2,3] and the nucleosynthesis of the long-lived γ-ray emitter ⁶⁰Fe [4].

Among the other scenarios, it is pivotal to understand the nucleosynthesis of elements beyond iron through the s-process. Indeed, ²²Ne(α, γ)²⁶Mg is the main competitor of ²²Ne(α, n)²⁵Mg, which has been identified as the primary neutron source of the weak component of the s-process in massive stars with $\mathrm{M}\ge 8{\mathrm{M}}_{\odot }$, and acts as a secondary source of neutrons for the main component in AGB stars, influencing the abundances of s-only isotopes near branching points [5,6].

In AGB stars, s-process nucleosynthesis takes place during the thermal pulsing phase. In this phase, the star consists of a carbon–oxygen core, a thin helium shell seeded through hydrogen burning products from the outer layer, and an extended hydrogen envelope. During the thermal pulses, a series of helium-shell flashes is initiated by the abrupt onset of the triple-alpha (3$\mathsf{\alpha }$) process at the bottom of the He-intershell. In this region, free neutrons are produced through two reactions: ${13}^{\mathrm{C}}{(\mathsf{\alpha }, \mathrm{n})}^{16}\mathrm{O}$ and ²²Ne(α, n)²⁵Mg, the latest contributing towards the end of the phase, when the temperature has risen above ca. 200 MK. While a series of recent studies converge on the reaction rate of the ${13}^{\mathrm{C}}{(\mathsf{\alpha }, \mathrm{n})}^{16}\mathrm{O}$ [7,8,9], the second neutron source is still subject to large uncertainties affecting the nucleosynthesis predictions.

The neutron budget available for the subsequent nucleosynthesis strongly depends upon the availability of ²²Ne and the rate of the two competing open channels of ²²Ne + α fusion reaction. While the formation of ²²Ne via ¹⁴N(α, γ)¹⁸F(β+ν)¹⁸O(α, γ)²²Ne reaction chain is well-understood [10], the open question concerns the rate at which the two reactions proceed.

The ²²Ne(α, n)²⁵Mg reaction channel, with its negative Q-value (${\mathrm{Q}}_{(\mathsf{\alpha },\mathrm{n})}=-478.34\pm 0.05\mathrm{keV}$), activates only at specific temperatures, with T varying within $0.1÷0.6{\mathrm{T}}_9$ according to the stellar burning scenario. At lower temperatures, the $(\mathsf{\alpha },n)$ channel remains closed and ²²Ne is consumed exclusively through ²²Ne(α, γ)²⁶Mg, which is always active due to its positive Q-value (${\mathrm{Q}}_{(\mathsf{\alpha },\mathsf{\gamma })}=\mathrm{10,614.74}\pm 0.03\mathrm{keV}$).

The interplay between the two channels has a huge impact on the neutron budget for nucleosynthesis. Therefore, reliable nucleosynthesis predictions require precise reaction rates for both channels within the astrophysical energy range, also known as the Gamow window [11].

The stellar reaction rate is calculated by summing all the resonance states of the compound nucleus ²⁶Mg within the Gamow window, which corresponds to an ${\mathrm{E}}_{\mathsf{\alpha }}=600÷900\mathrm{keV}$ [12,13]. However, the low energy values and extremely low cross-sections make direct measurements very challenging, and mostly dominated by cosmic ray background [14]. Additionally, the high level density of ²⁶Mg near the particle threshold hampers the isolation and identification of all potentially involved states.

In the last 30 years, several measurement campaigns were devoted to the study of both channels, but none of them could collect information below the well-known resonance at $\sim 835\mathrm{keV}$, located on the upper limit of the Gamow window [15,16,17,18,19,20].

Since direct measurements on surface laboratories no longer successful to address this gap, the EASγ project plans a new experimental study of ²²Ne(α, γ)²⁶Mg in the deep-underground environment of LNGS. As part of the LUNA collaboration’s scientific program ([21,22], and the references therein), EASy will directly investigate the ²²Ne(α, γ)²⁶Mg in the energy range with 600–800 keV and remeasure the well-known resonance at 832 keV. Alongside ASFIN [23,24], n-TOF [25,26], ERNA [27,28,29], and PANDORA [30], LUNA is one of the main contributors to nuclear astrophysics research in Italy.

The measurement is proposed to begin in 2025 at the Bellotti Ion Beam Facility of LNGS, and combines advanced beam-induced background reduction techniques with a high-efficiency $\mathsf{\gamma }$-ray spectrometer. As a preliminary work, a Monte Carlo simulation using GEANT4 [31] has been performed to characterize the experimental setup, and will be shown in detail in the next section.

The results of the simulations show a significant enhancement in sensitivity and complete suppression of background above 2.6 MeV. The completely lack of background allows to explore the states so far inaccessible via direct measurements on surface, making this approach promising for obtaining new data in the unexplored energy region.

2. Materials and Methods

2.1. Experimental Setup

EASγ aims at performing a new direct study of the ²²Ne(α, γ)²⁶Mg in the energy range of astrophysical interest. In an attempt to extend our knowledge to the whole Gamow window, the measurement will be conducted deep underground at LNGS, to benefit of the natural shielding provided by the 1400 m of rock overburden of the Gran Sasso massif. The measurement will be carried using the newly commissioned LUNA MV accelerator, capable of delivering a high-stable $\mathsf{\alpha }$ current up to $500 \mathsf{\mu }\mathrm{A}$ [32].

A recirculated, windowless gas target 99% enriched in ²²Ne will be employed, to minimize the beam-induced background and maximize the reaction yield. The same gas target is currently used to study the $(\mathsf{\alpha }, \mathrm{n})$ channel in the framework of SHADES experiment. Details about the gas target can be found in [33].

The $\gamma$-rays resulting from the de-excitation of the compound nucleus ²⁶Mg will be detected using an array of $102\mathrm{mm}\times 102\mathrm{mm}\times 203\mathrm{mm}$ NaI(Tl) crystals.

The final array configuration which maximizes the detection efficiency consists of 6 NaI(Tl) detectors surrounding the target chamber at a distance of 15 cm from its center. In Figure 1, the side and front views of the simulated array are displayed. The estimated full-energy peak efficiency of the entire array is 11% at 4 MeV. Due to this, emitted gamma-ray cascades are not always summed completely and the total spectrum does not only display a single peak at Q + ${\mathrm{E}}_r^{cm}$, but rather multiple additional features corresponding to individual transitions. The operation mode is similar to other such setups like the 4$\pi$ BGO detector at LUNA 400 [34].

2.2. Background Acquisition

Background measurements have been conducted in three different experimental scenarios. The first has been taken with a single NaI(Tl) crystal on the surface and without shielding. The measurement has been performed at Dipartimento di Fisica E. Pancini of the University of Naples Federico II. A second spectrum is obtained placing the detector deep underground at the Bellotti IBF. A third acquisition was ran deep underground and with an additional 15 cm lead shielding surrounding the NaI detector to further reduce the background radiation from the natural radioactivity of the surrounding rock. The total background was estimated as six times the signal from a single NaI(Tl) crystal. However, this approach overestimates the overall background, since it does not account for the mutual shielding that each detector of the array provides to the others. This overestimation allows us to be conservative in the following discussion.

2.3. Simulation

In addition to the experimental setup, the signal from the de-excitation of the compound nucleus ²⁶Mg has been added to the simulation. Since both ²²Ne and $\mathsf{\alpha }$ have $J^{\pi }=0^{+}$, by angular momentum selection rules, only natural-parity states in ²⁶Mg can participate in the reaction. Among all of the natural-parity states lying within the Gamow window, the ones with ${\mathrm{J}}^{\mathsf{\pi }}=0^{+}\mathrm{and}{\mathrm{J}}^{\mathsf{\pi }}=1^{-}$ are expected to substantially contribute to the rate, since $\mathsf{\alpha }$ particles with higher angular momentum will be suppressed by the centrifugal barrier. The information about the structure of ²⁶Mg and the decay schemes has been retrieved from National Nuclear Data Center datasets (accessed on 31 October 2024) [www.nndc.bnl.gov], except for the first transitions of the 11,319.5 keV state, whose branching ratios were derived from [17] (see

Table 1. Properties of the states of the compound nucleus ²⁶Mg used in the simulation.

${\mathbf{E}}_{\mathbf{x}}$ (keV)	${\mathit{E}}_{\mathit{r}}^{\mathbf{cm}}$ (keV)	${\mathit{J}}^{\mathit{\pi }}$	$\mathit{\omega }\mathit{\gamma }$ (eV)	Events/h	Run-Time (h)
11,319.5	$706.6\pm 2.5$	$0^{+},1^{-},2^{+}\mathrm{or}{3}^{-}$	$(4.6\pm 1.2)\times {10}^{-5}$	14,033	120
11,171	$556.33\pm 0.05$	$2^{+},1^{-}\mathrm{or}\ge 1$	$\sim {10}^{-11}\left(\mathrm{UL}\right)$1	0.034	960

¹ Calculated using ${\Gamma }_{\mathsf{\alpha }},{\Gamma }_{\mathsf{\gamma }} \mathrm{and} {\Gamma }_{\mathrm{n}}$ values from [35].

for further details). In this first feasibility study, angular correlation effects have not yet been taken into account.

3. Results and Discussion

In a low-count rate experiment, such as the one under study, the suppression of background is crucial, since its magnitude ultimately determines the minimum detectable signal level. In a $\mathsf{\gamma }$-ray spectrum, the detected background accounts several contributions arising from cosmic-ray interaction with the atmosphere (cosmic-ray background), the internal radioactivity of the detector itself and the presence of radioactive isotopes in the air and in the surrounding rocks (environmental background). To optimize the signal-to-background ratio, effective background suppression techniques must be applied. When significant shielding is used, both the cosmic flux and the ambient gamma-ray background are reduced, while radioactive contamination from structural and shielding materials near the detector becomes the most prominent source of background. Locating detectors deep underground helps minimizing cosmic background, though tens or even hundreds of meters of overlying rock are required to strongly attenuate the hardest component of muon flux [14]. For this reason, the underground Bellotti Ion Beam Facility at LNGS, with its 1400 m of rock overburden, is the perfect location for studying low count rate nuclear reactions, such as those of astrophysical relevance.

The benefit of operating in a deep-underground environment is illustrated by the comparison of the three background spectra in Figure 2.

For the underground spectrum, the natural shielding provided by the rock overburden efficiently suppresses the cosmic-ray background, specifically the component above the 2.6 MeV, by more than 4 orders of magnitude. The background contribution below 2.6 MeV mainly arises from radioactive isotopes normally present in the rocks. This component can be attenuated surrounding the detector with an additional shielding, as shown by the red line which represents the background suppression achieved enclosing the detector in a 15 cm of thick lead shielding.

Two states of the compound nucleus ²⁶Mg have been under investigation, and their properties are summarized in Table 1.

The first excited state, ${\mathrm{E}}_{\mathrm{x}}=11.32\mathrm{MeV}$, corresponds to the well-known resonance at $0.83\mathrm{MeV}$ energy in the laboratory frame and $706\mathrm{keV}$ in the center of mass. This resonance was measured for the first time by Wolke in 1989 [15] and remeasured several times, being so far the only resonance in the Gamow window accessible through direct measurements on surface [17,18]. The most recent values of energy and the resonance strength $\mathsf{\omega }\mathsf{\gamma }$ provided by Hunt et al. [17] are reported in Table 1, while the branching ratios of the two first transitions used to simulate the signal are listed in

Table 2. Properties of the two first transitions from the excited state ${\mathrm{E}}_{\mathrm{x}}=\mathrm{11,319.5} \mathrm{keV}$ of ²⁶Mg used in the simulation. Values from [17].

${\mathit{E}}_{\mathit{x}}$  (keV)	${\mathit{E}}_{\mathit{\gamma }}$  (keV)	${\mathit{J}}^{\mathit{\pi }}$	Branching Ratio
7061	4260	$1^{-}$	$46\pm 12$
1808.74	9512	$2^{+}$	$54\pm 12$

. Assuming a beam current of $300\mathsf{\mu }\mathrm{A}$, the expected event rate is approximately 14,033 counts per hour.

The second state investigated is located at ${\mathrm{E}}_{\mathrm{x}}=11.17\mathrm{MeV}$. This state is of particular interest due to the potential presence of an $\mathsf{\alpha }$-cluster at this energy with a large $\gamma$ partial width, as suggested by Talwar et al. [36]. Their findings indicates that the resonance associated with this state dominates the ²²Ne(α, γ)²⁶Mg stellar reaction rate within the He-burning temperature range $0.18\le T_9\le 0.4$, increasing the $(\mathsf{\alpha }, \mathsf{\gamma })$ rate by nearly two orders of magnitude above the values reported in the literature by Longland [37] and Bisterzo [6]. However, despite numerous indirect measurements, a definitive spin-parity assignment for this state remains inconclusive [19,36,38], and the $\mathsf{\omega }\mathsf{\gamma }$ value is only known as an upper limit [35]. Under optimal conditions with the maximum beam current delivered by LUNA MV and an extended 40-day measurement period, we estimate that we will reach a level of only 33 detectable events, allowing for the first time for an extraction of the resonance strength or a significant reduction of its upper limit.

The simulated signal has been combined with the experimental background, whose spectrum is normalized to the measurement time reported in Table 1 to match the simulation. The results are shown in the following subsections.

3.1. Simulation of the De-Excitation of the 11,319.5 keV State of ²⁶Mg

3.1.1. Scenario I: Surface Measurement

The first case under study corresponds to a measurement performed on surface and with the array unshielded. Since the experimental background spectrum that was available extends only up to 8 MeV, a linear extrapolation has been performed to cover the entire energy region up to 14 MeV. The background was extrapolated by fitting a linear model to the experimental data in the energy interval [4000, 6000] keV, and then extended to higher energies. Poissonian random fluctuations were added to this extrapolated background to mimic realistic background behavior. The experimental background is shown by the solid light-blue line in Figure 3a, while the extrapolated background is represented by the light-blue dotted line.

In Figure 3b, the two peaks corresponding to the two primary transitions $\mathrm{11,319.5} \mathrm{keV}\to 7061$ keV and $\mathrm{11,319.5} \mathrm{keV}\to 1808.74\mathrm{keV}$ are indistinguishable from the background, thus a measurement of the $\mathsf{\omega }\mathsf{\gamma }$ appears to be unfeasible.

3.1.2. Scenario II: Deep-Underground Measurement and No Shielding

To improve the signal-to-background ratio, in the second case study, the signal has been combined with the background acquired deep-underground at Bellotti IBF and with the detector still unshielded. Thanks to the natural shielding provided by the rock overburden, the component of the cosmic-ray flux is completely suppressed (Figure 4a), and the two peaks corresponding to the two primary transitions are now clearly visible, as shown in Figure 4b. However, the spectrum below 2.6 MeV is still dominated by the background due to environmental radioactivity.

3.1.3. III Scenario: Deep-Underground Measurement and Lead Shielding

The third scenario corresponds to a measurement deep underground and with the detector shielded. The lead shielding surrounding the detector reduces the background below 2.6 MeV, further improving the signal-to-background ratio in this region Figure 5a. As a result, the bump corresponding to the transition from the first excited state to the ground state emerges from the background and the statistics provided can be used to re-evaluate the resonance strength $\mathsf{\omega }\mathsf{\gamma }$.

3.2. Simulation of the De-Excitation of the ²⁶Mg 11,171 keV State

The simulation of the signal from the de-excitation of the 11,171 keV state was hampered by the lack of information on the decay scheme and the unresolved spin-parity assignment of this state. To visualize the achievable sensitivity, the signal was simulated using branching ratios from a nearby state, ${\mathrm{E}}_{\mathrm{x}}=\mathrm{10,949} \mathrm{keV}$. This assumption is justified by the de-excitation mechanism and the high level density of the compound nucleus ²⁶Mg in this energy range. Typically, after the compound nucleus ²⁶Mg is populated via ²²Ne(α, γ)²⁶Mg, the de-excitation proceeds through intermediate states. Therefore, despite its unknown decay scheme, it is reasonable to expect counts in the energy range between the first excited 1808.74 keV state and ${\mathrm{E}}_{\mathrm{x}}$.

As shown in Figure 6, counts can be observed in the high-energy region, which is completely free of background noise thanks to the shielding provided by the deep-underground location. The detected signal allows for either a new estimation of the resonance strength or, at least, the establishment of a more stringent upper limit. This result proves the effectiveness of EASγ, as this state has been so far exclusively populated by indirect measurements being inaccessible of the direct ones.

4. Conclusions

The goal of this study is to investigate the feasibility of the measurement proposed by EASγ, and to demonstrate the enhancement in sensitivity achieved with its novel approach.

The main innovation of this project consists of a direct study of ²²Ne(α, γ)²⁶Mg deep-underground to benefit from the low cosmic-ray background conditions.

For this reason, in the present work, the detection of the signal from two significant states of the compound nucleus ²⁶Mg was simulated, and the detection capability of the γ-ray spectrometer was investigated both on surface and deep underground.

The first simulated state, located at ${\mathrm{E}}_{\mathrm{x}}=\mathrm{11,319.5} \mathrm{keV}$, corresponds to the well-known resonance at 835 keV. Previous studies have shown this resonance to be dominant in the stellar reaction rate, even though its exact position remains uncertain. This is the only state within the Gamow window that is currently accessible via direct measurements.

The simulation shows that the background suppression due to the deep underground location and an additional lead shielding allow to clearly identify the two peaks corresponding to the two first primary transitions and even a secondary transition, yielding to a more accurate value for the resonance strength.

The second state investigated is the low-energy state at ${\mathrm{E}}_{\mathrm{x}}=\mathrm{11,171} \mathrm{keV}$, whose detection resulted to be elusive in all the direct and some indirect measurements. If an $\alpha$-cluster state exists at this energy, it will significantly impact the stellar reaction rate, thereby influencing current stellar models and nucleosynthesis predictions. For this reason, retrieving accurate parameter values for this state is particularly important.

We demonstrate that the signal from de-excitation of the ${\mathrm{E}}_{\mathrm{x}}=\mathrm{11,171} \mathrm{keV}$ can now be studied directly for the first time using the experimental setup provided by EASγ, thus giving crucial insight into the contribution of this state to the overall stellar reaction rate.

In conclusion, this study proves that the low-background environment of the Bellotti Ion Beam Facility, along with the use of a shielded, high-efficiency NaI array, significantly improves the detection sensitivity. These findings highlight the potential of the forthcoming ²²Ne(α, γ)²⁶Mg measurement with EASγ to yield promising results.