First measurement in the Gamow window of a reaction for the γ -process in inverse kinematics: 76 Se( α, γ ) 80 Kr

The p -nuclei are the few stable nuclei heavier than iron on the neutron-deﬁcient side of the valley of stability that cannot be produced through astrophysical neutron-capture reactions. The limited experimental data on reactions through which the p -nuclei might be produced leaves the origin of their production largely unknown. This work presents the ﬁrst cross section measurements of the 76 Se( α, γ ) 80 Kr reaction. The rate of the time reversed reaction, 80 Kr( γ, α ) 76 Se, is one of the most uncertain of possible reactions which can occur at the 80 Kr branching point on the γ -process photo-disintegration pathway. The reaction ﬂow through 80 Kr will directly aﬀect the ﬁnal abundance of the p nuclide 78 Kr. Experimental cross sections at two astrophysically relevant energies are reported and compared to cross sections calculated using Hauser-Feshbach codes talys , non-smoker , and smaragd . The success of these ﬁrst ( α, γ ) cross section measurements performed in inverse kinematics in the energy region of the γ -process opens the door for future studies of reactions on radioactive γ -process nuclides.


Reuse
Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item.

Takedown
If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.

Introduction
Of the elements heavier than iron, some of the most interesting isotopes also happen to be among the least abundant. The p-nuclei are a collection of stable isotopes heavier than iron, which sit along the neutron, n, deficient side of the valley of stability, and which cannot be produced by the known n-capture processes (the r-, and sprocesses). The production of these p-nuclei requires a separate astrophysical process which is 10 commonly called the p-process [1,2]. While several astrophysical sites and nucleosynthesis pathways have been proposed, it is not yet clear which (or which combination) is responsible for their production. Recent work of Travaglio et al. [3] for the 15 first time employed Galactic Chemical Evolution models with metallicity-dependent core collapse supernovae yields to investigate the contributions of those various sites to the solar abundances of the p-nuclei. 20 Previously, one of the favoured scenarios for pnuclei production was a supernova shock-front passing through the O-Ne layer of a massive star undergoing core-collapse [4,5,6,7]. The p-nuclei may be produced when pre-existing heavy seed- 25 nuclei undergo photo-disintegration reactions due to the high temperatures in this environment (1.7 to 3.3 GK [7]). To distinguish this process from the other p-process candidates, this mechanism is referred to as the γ-process. However, the exact production site, or sites, remain uncertain, with Type 1A supernovae also currently favoured.
At the start of the γ-process, (γ, n) reactions dominate, driving the reaction flow to n-deficient isotopes of the same element. However, at some 35 point the rate of the (γ, p) and/or the (γ, α) reactions exceed the rate of the (γ, n) reactions and the reaction flow is deflected to the isotopic chain of a lighter element [1,4,7,8]. These branching points and the relative rates of all their associated 40 reactions are critical nuclear inputs when studying any scenario and its resulting isotopic abundances. Currently very few of the reactions relevant to the γ-process have been studied experimentally and, among these, there are no data for radiative cap-45 ture reactions on radioactive nuclei. While predictions from Hauser-Feshbach (HF) model codes can provide some guidance where experimental reaction data are lacking, there are often large uncertainties associated as the predicted values vary significantly 50 based on the choice of model inputs. For (γ, α) reactions, the variation in the α optical model potentials (αOMP) is particularly significant (see Fig. 2 and Ref. [9,10]). With scarce α-capture data at energies relevant for the γ-process being available to-55 date, continuous experimental efforts in the mass and energy range of the γ-process are needed to better constrain the theory.
One γ-process branching point occurs at 80 Kr and the resulting reaction flow will directly affect 60 the abundance of the p-nuclide 78 Kr [6]. Of the three possible photo-disintegration reactions which can occur, 80 Kr(γ, α) 76 Se is currently the most uncertain. Therefore, the time reversed reaction, 76 Se(α, γ) 80 Kr, was identified as a priority measurement for γ-process studies [6].
This letter presents the first cross section measurements of 76 Se(α, γ) 80 Kr. These measurements were performed at energies below the (p,n) channel threshold, where the sensitivity to the level density 70 and the γ-ray strength function is less prominent, allowing for constraint of the α optical potential model directly at energies relevant to the γ-process. Moreover, these are the first measurements of a γprocess reaction performed in inverse kinematics in 75 the Gamow window. Previous work, including Glo-rius et al. [11] who recently reported on the measurement of 124 Xe(p,γ) 125 Cs, have been conducted at energies just above the Gamow window. Given that much of the γ-process reaction flow involves 80 unstable nuclei, inverse kinematic techniques will be critical for future γ-process studies (see Ref. [12] for current status of γ-process (p, γ) measurements in inverse kinematics).

85
The DRAGON [13,14,15] recoil separator used in this work is located in the ISAC facility [16] at TRIUMF. DRAGON is designed to study radiative proton and α capture reactions at sub-Coulomb barrier energies in inverse kinematics. It is com-90 prised of three main sections: (i) a windowless differentially pumped gas target; (ii) a high-supression two-stage separator; and (iii) a recoil detector system. The separator consists primarily of two sets of magnetic and electric dipoles. The recoil detector DRAGON's windowless gas target was filled with helium gas at a pressure between 10.6 − 11.1 mbar throughout the experiment. The target's effective length has previously been measured to be 105 12.3(5) cm [17]. Two silicon detectors were located inside of the target chamber to monitor the α particles elastically scattered by the incoming beam for the purposes of beam normalization. There was also an array of 30 high-efficiency Bismuth Ger-110 manate (BGO) detectors surrounding the chamber which were used for detecting γ rays coincident with recoil events. The beam current was monitored with absolute Faraday cup (FC) readings up and downstream of the target, which were taken every 115 hour at the start and end of every run.
Downstream of the separator, two MCPs measured the secondary electron emission from ions traversing the diamond-like carbon foils placed in the beamline. The foils were sufficiently thin 120 (20 µg/cm 2 ) so that the MCPs could be used in tandem with the IC located immediately downstream of them. The time difference between the prompt-γ detection from the BGO array and the recoil MCP detection allowed for the separator TOF to be cal-culated. See Refs. [18,19] for more details on this detection system.
A beam of 76 Se 12+ , produced from a 74% enriched 76 Se sample placed in the ISAC Off-line Ion Source [20], was impinged on the windowless gas target with an average intensity of 2 × 10 10 s −1 . The beam was accelerated to energies of E beam = 1.513 (3) were then separated from the unreacted beam using DRAGON's separator [13,14,21].
Given that DRAGON was specifically designed to study explosive nucleosynthesis with beams of mass A ≤ 30, this measurement of 76 Se(α, γ) 80 Kr 145 represents a significant departure in beam and recoil masses. The commissioning work to establish the feasibility of the new techniques employed here was reported in Ref. [22].

150
To determine the experimental recoil yield per incident ion (Y ) at each energy, the total number of recoil events (N tot r ) was divided by the total number of incident beam particles (N b ). In order to calculate N tot r the number of detected recoil events 155 N det r was divided by all of the separator and detector efficiencies. The yield is then as follows: where η BGO is the the BGO γ detection efficiency, η CSF is the charge state fraction for the selected re-160 coil charge state, η t is the separator transmission, η MCP is the MCP TOF detection efficiency, η det is the combined MCP foil transmission and IC detection efficiency, and η live is the live-time of the data acquisition system. The experimental yield 165 was then used to determine the experimental cross section (σ). As the level density at the measured energies was expected to be high, multiple resonances were expected to be present in the target region and thus the cross section was calculated as an effective 170 cross section, integrated across the energy range of the target: where N t /A is the target density per unit area. All N det r , N b and efficiency values are given in 175 table 1.

Beam normalization and energy
To determine N b , beam normalization was performed using the procedure laid out in Ref. [23]. This involved calculating a normalization value that 180 related the number of elastic scattering events detected in the silicon detectors to the number of incident beam ions, using Faraday cups located up and downstream of the target. The number of events detected in the silicon detectors could then subse-185 quently be used to calculate the number of incident beam ions for any given run.
Due to the low charge state of the incoming beam and the limited electric rigidity of DRAGON's electric dipoles, the beam energy could not be mea-190 sured directly as is typically done [14]. Instead, the beam energy was measured after passing through the target and stripper foil. The initial beam energy was then calculated based on energy loss data from SRIM [24]. This resulted in an uncertainty 195 in E c.m. of 12 keV due to uncertainty in the SRIM data and target thickness.

Recoil charge state distribution and transmission
The recoils transmitted to the end detector 200 were all in the 25+ charge state which was the most abundantly populated charge state that could be transmitted through the separator 6 . The charge state fractions (CSF) were measured experimentally using beams of 84 Kr 14+ . As these 205 charge state measurements also needed to encompass future 76 Se(α, γ) 80 Kr measurements, CSF were measured at five beam energies from 1.12 to 1.53 MeV/nucleon. The CSF presented in Table 1 (η CSF ) were interpolated from a second order poly-210 nomial fit to these data. The uncertainties are taken from the weighted average of the difference between the fit and the measurements. The recoil cone angle was calculated to be <3 mrad, well within DRAGON's acceptance of 215 <20 mrad [13]. The recoil separator transmission was hence very high, calculated as 98.75% for both beam energies using a GEANT 3 simulation.

Detector efficiencies and live time
The detection efficiency of the BGO array (η BGO ) 220 depended on the energy and multiplicity of the γrays produced during the reaction. As the actual γ cascades from the populated excited states in 80 Kr are not known, the maximum and minimum efficiencies were determined from GEANT4 simula- The detection efficiency of the MCP TOF system (η MCP ) and of the IC (η det ) was determined using attenuated beam data, as described in Ref. [28].
The system live time (η live ) was determined using 240 the procedure described in Ref. [29]. Table 1 contains the complete tabulated set of efficiency values.

Particle identification
With a standard tune, the unsuppressed beam rate was high enough to overwhelm the IC. Reduc-245 ing the voltage of the second electrostatic dipole by a small amount (≤ 1.4%) significantly reduced the rate of beam events at the end detectors. GEANT3 simulations [13] for these deliberate mistunes indicate no reduction in separator transmission, η t .

250
Identification of 80 Kr recoils from the unsupressed beam events was performed by applying  cuts on the total IC energy, the energy loss in each of the four IC anodes, local TOF using the MCP, and the TOF through the separator (time between 255 coincident γ-ray and MCP events). The clearest particle identification was then seen in a plot of the total IC energy vs. the separator TOF (Fig. 1). The regions of interest (ROIs) indicated in Fig. 1 represent the IC energy and separator TOF cuts. For 260 each energy N det r is the number of events in the cut, minus the calculated background (Table 1). Due to the time structure of the bunched beam, background events did not have a completely random separator TOF (as seen in Fig. 1b); they appeared 265 in packets separated by 84.8 ns. To properly determine this background, the recoil cut was displaced along the separator TOF axis in periods of this magnitude, multiple times. The number of background events within these cuts was then averaged 270 to give the expected number of background events inside the ROIs.

Results and discussion
The beam intensities, recoil counts, and efficiencies presented in Table 1  is presented in Fig. 2.
The calculated σ HF depend on both the code used and choice of input parameters. Eight sets of σ HF are calculated using the talys code version 1.9 [31] 285 (TL) for each available α-optical potential model αOMP: 1) Koning-Delaroche [32], 2) McFadden-Satchler [33], 3) Table 1 in Demetriou et al. [34], 4) Table 2 in Ref. [34], 5) a dispersive model in Ref. [34], 6) Avrigeanu [35], 7) Nolte [36], and 8) 290 Avrigeanu [37]. Within the energy range covered by this work, the α-capture cross section models do not show strong dependence on the level density and the γ-ray strength functions (γSF) implemented in the calculations. At most the resulting 295 cross sections changed by 23%, thus these parameters were kept constant through the calculations and were set to the constant temperature matched to the Fermi gas model [38] for the level density and the Kopecky-Uhl generalized Lorentzian [39] for the 300 γSF to match those of the non-smoker code for better comparison.
It can be seen in Figure 2 that the results of nonsmoker are in a good agreement with the higherenergy data point while overestimating the lower-305 energy point. Cross sections obtained from a new version of the non-smoker code, smaragd, tend to underestimate the higher-energy point, while they overlap with the lower-energy data. The results of talys calculations, span nearly two orders 310 of magnitude for various models of the αOMP available through the code. The results obtained with αOMP=2 , i.e. the McFadden-Satchler potential, which is used in the non-smoker code, are similar to those of non-smoker. Only the results for αOMP=3, i.e., that of Demetriou et al. [34] show an agreement with both experimental data points simultaneously to within their 68% confidence level. The gray-shaded area in Figure 2 indicates the uncertainty range of the HF cross section obtained by 320 scaling the cross section for αOMP=3 up and down to match the experimental uncertainties. The scaling factors were 1.3 and 1.7 for the upper and lower limits, respectively. That substantially reduced the uncertainty in the cross section predictions from 325 the HF calculations, which is typically quoted to be a factor of 10 for the α-capture reactions. The results for αOMP=2 and both non-smoker and smaragd fall within that uncertainty range as well.
From the HF input parameters used for the cross 330 sections, the reaction rates for the 76 Se(α,γ) 80 Kr were derived. The recommended rate was calculated using the αOMP=3 model. Figure 3 shows ratios of the rates calculated with talys relative to the recommended one. The shaded area corre-335 sponds to the range of uncertainty in the recommended rate that stems from the uncertainty in the calculated cross section. The color and style of the lines corresponds to that of Figure 2. Additionally, two evaluations of the reaction rate from 340 non-smoker taken from the reaclib database are shown in Figure 3: the recommended rate "th8" [40] and the rate from the parameterized fit to non-smoker calculations "thra" [41]. It should be noted, that as expected the results for αOPM=2 345 and the recommended reaclib rate fall within the uncertainty range. The parametrized fit to the non-smoker data significantly deviates from the recommended rate, however, it is unclear from [41] whether the discrepancy is due to the fit precision 350 or due to changes in the rate calculations between references [40] and [41]. The values of the recommended rate for the 76 Se(α,γ) 80 Kr reaction within the γ-process Gamow window are listed in Table 2 together with the lower and upper limits.

355
The rates of the forward reactions can be used to calculate the reverse, photodisintegration rates in order to determine at what temperatures the 80 Kr(γ,α) 76 Se rate will dominate over the 80 Kr(γ,n) 79 Kr, allowing for direct feeding of the p-360 nucleus 76 Se and bypassing 78 Kr. For that purpose, for the same input parameters used for the direct Table 2: Reaction rates for the 76 Se(α,γ) 80 Kr reaction obtained from the talys using the αOMP=3 potential. The upper and lower limits correspond to the uncertainty in the HF cross section indicated in Figure 2.
T N A < σν > (cm 3 s −1 mol −1 ) recommended lower limit upper limit 1. rates are plotted as ratios to the (γ,n) rate. From the ratio, the temperature at which the α emission becomes dominant can be estimated. If the total uncertainty of the talys rates is used, the uncertainty in the temperature spans 1.6-2.6 GK. With 380 the reduced uncertainty of this work, that range is 1.9-2.2 GK.

Conclusions
In conclusion, the first measurement of cross sections for 76 Se(α,γ) 80 Kr at γ-process energies have 385 been obtained in inverse kinematics using a recoil separator. There is just a hand-full of available (α,γ) data in the 75 ≤ A < 90 mass region, thus this measurement provides an important insight to the α-capture cross sections in the re-390 gion of the lightest p-nuclei. The measured cross sections were best matched by talys predictions using the αOMP3 from Table 1 in Demetriou et al. [34] with an uncertainty band of about 30%. The σ HF obtained with the potential of McFadden 395 and Satchler [33] with both smaragd and talys codes fell within that uncertainty range. This is   Figure 4: Ratios of (γ,α) and (γ,p) rates to (γ,n) rates obtained with Talys. Gray shaded band is the uncertainty in the (γ,α)/(γ,n) ratio obtained from Talys. The red band corresponds to the (γ,α)/(γ,n) ratio resulting from this work. The dashed regions indicate the (γ,p)/(γ,n) ratio (black) and the uncertainty in the (γ,n) rate (blue).
consistent with the results of Ref.
[9] which found that σ HF from the talys code using the αOMP from Table 1 in Demetriou et al. [34] (αOMP3) 400 resulted in the smallest average discrepancy from the data across all the stable Ni isotopes and consistently reproduces the α-capture cross sections across the γ-process nuclei [10]. Reaction rates from models with σ HF consistent with this work 405 all differed by less than a factor of 1.3 for temperatures from 1 − 3.5 GK, a significant reduction from the most commonly presumed factor of 10 for (α, γ) reactions in the p-process mass region. Additionally, this work reduces by a factor of at 410 least 3 the uncertainty in the temperature at which the 80 Kr(γ, α) 76 Se reaction becomes the dominant photo-disintegration pathway from 80 Kr in the γprocess. With the updated rates, the γ-process scenario will feed the production of 76 Se only at the 415 temperatures below 1.9-2.2 GK, at higher temperature the (γ,n) channel will feed the production of 78 Kr.
The success of this measurement is due to the unique combination of the low beam energies avail-420 able from the ISAC facility, the windowless gas target technology developed for DRAGON, and the beam suppression achieved using the DRAGON separator. This method may then provide an increased sensitivity to cross section measurements 425 at lower energies compared to in-beam and activation measurements performed in regular kinemat-ics. This is particularly applicable when, as in the present case, the isotope of interest results in chemically unstable targets. Also, due to the short 430 half-lives involved, any future studies of reactions on radioactive isotopes will need to be performed in inverse kinematics. The demonstration of this technique at γ-process masses and energies opens the door for measurements using radioactive beams 435 and will allow future studies of (α, γ) reactions on the unstable isotopes in the γ-process.

Acknowledgments
The authors thank the ISAC operations and technical staff at TRIUMF. TRIUMF's core operations