58Ni(3He,t)58Cu*(γ) measurements with GODDESS to constrain the astrophysical rate of 57Ni(p,γ)58Cu

The observation of γ rays from the decay of 44Ti in the remnants of core-collapse supernovae (CCSNe) provides crucial information regarding the nucleosynthesis occurring in these events, as 44Ti production is sensitive to CCSNe conditions. The final abundance of 44Ti is also sensitive to specific nuclear input parameters, one of which is the 57Ni(p,γ)58Cu reaction rate. A precise rate for 57Ni(p,γ)58Cu is thus critical if 44Ti production is to be an effective probe into CCSNe. To experimentally constrain the 57Ni(p,γ)58Cu rate, the structure properties of 58Cu were measured via the 58Ni(3He,t)58Cu*(γ) reaction using GODDESS (GRETINA ORRUBA Dual Detectors for Experimental Structure Studies) at Argonne National Laboratory’s ATLAS facility. Details of the experiment, ongoing analysis, and plans are presented.


Introduction
Validating models of core-collapse supernovae (CCSNe), and the nucleosynthesis that takes place within their explosive environments, is necessary to further understand the origin of the elements.Through the observation of characteristic γ rays emitted in CCSNe remnants, the abundance of specific radioisotopes can be inferred.These inferred abundances can then be compared to model predictions as a method of validation.
One such radioisotope, 44 Ti, is produced during explosive silicon burning in CCSNe.This burning phase is usually governed by α-rich freeze-out from quasi-static equilibrium (QSE) [1], where equilibrium clusters form amongst nuclei with similar masses due to the fast reactions occurring among them.During α-rich freeze-out, one main cluster is initially present, but as the temperature decreases, lower mass nuclei subsequently drop out of equilibrium with the main cluster, and smaller clusters form among these lower mass nuclei.The predicted abundance of 44 Ti is sensitive to hydrodynamic conditions of the CCSN, as well as nuclear reaction rates.This makes it an ideal probe for CCSNe models.However, for this probe to be meaningful, it is crucial to precisely determine the reaction rates that significantly impact 44 Ti production.  4Ti production.This was likely because the authors assumed the theoretical rate was well constrained by the Hauser-Feshbach model upon which it was based.However, this assumption is questionable since there are fewer states known than are usually assumed to ensure the validity of the model, specifically 10 levels/MeV (see Table 1).

The
At the high temperatures present in CCSNe, the rate of 57 Ni(p,γ) 58 Cu will be dominated by resonances through excited states in 58 Cu.The relevant excited states will be determined by the temperatures at which 44 Ti is sensitive to this rate.Magkotsios et al. notes this temperatures range to be ∼2-5 GK [2].This implies the level energies of relevant states are expected to be in the 3-6 MeV range.Table 1 lists the current known levels in 58 Cu between 3 and 6 MeV [4].The states with high spin (J> 6) are not expected to significantly contribute to the reaction rate due to the high angular momentum transfer required for the reaction.Without these states, the level density falls short of 10 levels/MeV.With the current knowledge of the level structure of 58 Cu, it may be more appropriate to constrain the rate through the narrow resonance formalism.In this formalism, the reaction rate per particle pair (in cm 3 mole −1 s −1 ) simplifies to [5]: The sum is over all significant resonances i, µ is the reduced mass in amu, and T 9 is the temperature in GK.E i and (ωγ) i are the energy and strength of the i-th resonance in MeV, respectively.J r , J 1 , J 2 are the spin of the compound nucleus and reaction products, respectively.Γ r , Γ a , Γ b are the resonance width, and the decay widths of the entrance and exit channel, respectively.For this indirect determination to be effective, the precise determination of the structural properties of 58 Cu is needed.Referring back to table 1, it is clear that this structure information is lacking.Due to the exponential dependence between the reaction rate and resonance energy, this is especially important for level energies.Current uncertainties on many relevant level energies are ∼10-20 keV, which could significantly affect estimations of the reaction rate.

Experimental Details
To further elucidate the structure of 58 Cu and more precisely measure level energies, the 58 Ni( 3 He,t) 58 Cu*(γ) reaction was measured at the ATLAS facility at Argonne National Laboratory using GODDESS (GRETINA ORRUBA Dual Detectors for Experimental Structure Studies) [6].A ∼ 1 enA beam of 3 He at 31.5 MeV was incident upon a ∼ 1 mg/cm 2 58 Ni target.Emitted tritons were detected by the ∼ 4π silicon array, ORRUBA (Oak Ridge Rutgers Barrel Array) [7].The coincident γ-rays emitted in the deexcitation of the residual 58 Cu nucleus were detected by the germanium array, GRETINA (Gamma-Ray Energy Tracking In-beam Nuclear Array) [8].A drawing of ORRUBA inside the GRETINA target chamber is shown in figure 1. Coupling these two arrays enables level energies to be reconstructed through measurements of γ ray energy, providing the high resolution needed to constrain the reaction rate.
ORRUBA consists of silicon detectors in a barrel configuration with further silicon detectors on the ends, allowing for both energy and position measurements of charged particles.The array is partially comprised of ∆E-E telescopes for charged particle identification [7].Particle identification is crucial to separate ( 3 He,t) events from other, more prominent, reaction channels.
GRETINA consists of 48 highly segmented coaxial germanium crystals.With this segmentation, the position of γ ray interactions is measured with ∼mm resolution.This allows for increased detection efficiency of high energy γ rays through tracking, and, when combined with the triton position measurements, provides precise Doppler corrections for γ rays [8].

Analysis
An example particle identification (PID) spectrum from the silicon telescopes is shown in figure 2. As can be seen, the particle species can be identified.By gating on the tritons, a spectrum of γ ray energy vs. 58 Cu excitation energy from triton-γ coincidences can be generated, as shown in figure 3. The excitation energy is determined from the triton energy and reaction kinematics.γ rays emitted in the deexcitation of 58 Cu will be correlated with excitation energy.γ rays due to random coincidences will instead result in a vertical line spanning the entire excitation range.In this spectrum, we do not only see known γ rays correlated with excitation energy (for example at 849 keV and 1208 keV) [4], but also γ rays not previously identified with decays in 58 Cu (for example at 2665 keV).

Conclusion and Future Plans
An experimental constraint on the 57 Ni(p,γ) 58 Cu reaction rate would reduce the uncertainty in the final abundance of 44 Ti in CCSNe nucleosynthesis calculations.To this end, further studies of the structure of 58 Cu were performed.Preliminary analysis suggests previously unknown γ rays from 58 Cu decays have been identified.Analysis of triton-γ-γ coincidences is underway to reconstruct the level structure and decay scheme of 58 Cu.Once the structure properties of 58 Cu are more completely determined, they will be used to constrain the 57 Ni(p,γ) 58 Cu reaction rate.
57Ni(p,γ)58Cu Reaction Rate According to Magkotsios et al. [2], the reaction rate of 57 Ni(p,γ) 58 Cu strongly influences the yield of 44 Ti in CCSNe.Magkotsios et al. suggest this influence is due to the reaction determining the relative abundances of 44 Ti and neighboring nuclei when they drop out of the main equilibrium cluster during α-rich freeze-out.More recent 44 Ti sensitivity studies were performed by Hermansen et al. [1] and Subedi et al. [3].In Hermansen et al., 57 Ni(p,γ) 58 Cu was verified to affect the abundance of 44 Ti, but to a lesser extent than Magkotsios et al.In Subedi et al. the rate was not identified as having an influence on