Approaching the Gamow window with stored ions: Direct measurement of $^{124}$Xe(p,$\gamma$) in the ESR storage ring

TL;DR

This paper presents the first direct measurement of low-energy proton-capture cross sections of $^{124}$Xe using a heavy ion storage ring, providing critical data for astrophysical models of explosive stellar environments.

Contribution

It introduces a novel experimental approach to measure nuclear reaction rates at energies relevant to astrophysics using stored ions in a heavy ion storage ring.

Findings

Good agreement with theoretical predictions of proton width at low energies.

Measured cross sections are on the high energy tail of the Gamow window.

Method enables investigation of nuclear reactions on rare ion beams at low energies.

Abstract

We report the first measurement of low-energy proton-capture cross sections of $^{124}$Xe in a heavy ion storage ring. $^{124}$Xe$^{54+}$ ions of five different beam energies between 5.5 AMeV and 8 AMeV were stored to collide with a windowless hydrogen target. The $^{125}$Cs reaction products were directly detected. The interaction energies are located on the high energy tail of the Gamow window for hot, explosive scenarios such as supernovae and X-ray binaries. The results serve as an important test of predicted astrophysical reaction rates in this mass range. Good agreement in the prediction of the astrophysically important proton width at low energy is found, with only a 30% difference between measurement and theory. Larger deviations are found above the neutron emission threshold, where also neutron- and ${\gamma}$-widths significantly impact the cross sections. The newly established experimental method is a very powerful tool to investigate nuclear reactions on rare ion beams at low center-of-mass energies.

Tables

Table 1. Table 1: Final results for the 124 Xe(p, γ 𝛾 \gamma ) cross section and interim results used in Eqs. ( 1 ) to ( 3 ). See text for details.

$E_{\text{CM}}$	${\sigma }_{(p,\gamma )}$		$N_{(p,\gamma )}$	$N_{\text{K}}/{ϵ}_{\text{K}}\Delta \Omega \left[{10}^6/\text{sr}\right]$			$d{\sigma }_{\text{K}}/d\Omega \left[\text{barn/sr}\right]$
[MeV]	[mbarn]			90°	60°	35°	90°	60°	35°
$5.47$	$14.0\pm {2.4}_{\text{stat}}\pm {0.9}_{\text{syst}}$		$785\pm 134$	$13.51\pm 1.06$	$10.73\pm 0.55$	$4.86\pm 0.28$	$244.5$	$190.2$	$86.4$
$5.95$	$28.0\pm {2.6}_{\text{stat}}\pm {1.9}_{\text{syst}}$		$1591\pm 149$	$12.54\pm 0.98$	$9.93\pm 0.51$	$-$	$223.8$	$174.2$	$79.1$
$6.65$	$65.8\pm {4.4}_{\text{stat}}\pm {4.2}_{\text{syst}}$		$1280\pm 85$	$3.91\pm 0.31$	$3.03\pm 0.15$	$1.35\pm 0.08$	$199.0$	$154.9$	$70.4$
$6.96$	$97.7\pm {2.7}_{\text{stat}}\pm {6.7}_{\text{syst}}$		$5500\pm 153$	$10.53\pm 0.82$	$8.36\pm 0.43$	$-$	$189.7$	$147.7$	$67.1$
$7.92$	$43.2\pm {2.2}_{\text{stat}}\pm {2.8}_{\text{syst}}$		$2774\pm 141$	$10.40\pm 0.81$	$8.35\pm 0.42$	$3.74\pm 0.22$	$165.3$	$128.8$	$58.6$

Equations

$${\sigma }_{(\mathrm{p},\gamma )}=N_{(\mathrm{p},\gamma )}\frac{{ϵ}_{\text{K}}\Delta \Omega }{N_{\text{K}}}\frac{d{\sigma }_{\text{K}}}{d\Omega }.$$

$$F_{\text{norm},i}$$

$$⟨F_{\text{norm}}⟩$$

Full text

proton capture, storage ring, nuclear astrophysics

††preprint: APS/123-QED

Charged-particle induced reactions like (p,$\gamma$) and ($\alpha$,$\gamma$) and their reverse reactions play a central role in the quantitative description of explosive scenarios like supernovae Travaglio et al. (2018) or X-ray binaries Schatz and Rehm (2006), where temperatures above 1 GK can be reached. The energy interval in which the reactions most likely occur under astrophysical conditions is called the Gamow window Rolfs and Rodney (1988); Rauscher (2010). Experimentalists usually face two major challenges when approaching the Gamow window: firstly, the relatively low center-of-mass energies of only a few MeV or less, and secondly, the rapid decrease of cross sections with energy. The high stopping power connected to low-energy beams typically limits the amount of target material, and thus the achievable luminosity. A measurement of small cross sections, on the contrary, requires high luminosities.

The description of charged-particle processes in explosive nucleosynthesis – e.g., the $\gamma$ process occurring in core-collapse and thermonuclear supernovae Rauscher et al. (2013, 2016); Nishimura et al. (2018) and the rp process on the surface of mass-accreting neutron stars Schatz et al. (1998) – requires large reaction networks including very short-lived nuclei. Experimental data are extremely scarce Szücs et al. (2014), especially in the mass region $A>70$, and the modelling relies on calculated cross sections. It is therefore essential to test the theory and its central input parameters. In this Letter we report the first study of the 124Xe(p,$\gamma$)125Cs reaction. The cross section is measured on the high energy tail of the Gamow peak, which is located between 2.74 and 5.42 MeV at 3.5 GK in the $\gamma$ process Rauscher (2010). While the 124Xe(p,$\gamma$) reaction serves as a major milestone for improving the experimental technique to reach lower center-of-mass energies, it also provides important constraints on the so far purely theoretically predicted reaction rates used to model the $\gamma$ process.

In the past, it has been demonstrated at different rare ion beam (RIB) facilities by experiments on ions of mass $A<40$ Delbar et al. (1993); D’Auria et al. (2004); Akers et al. (2013); Lotay et al. (2016) that inverse kinematics techniques can be successfully applied to study capture reactions on unstable nuclei. The experiment presented in this Letter has been performed at GSI, Darmstadt gsi ; fai . Here, the combination of the heavy-ion storage ring ESR Franzke (1987) and the FRagment Separator (FRS) Geissel et al. (1992) can address all of the aforementioned challenges for reaction measurements in the Gamow window even for the heavy ion beams of interest for the $\gamma$ process. Stored low-energy ions orbit the ring at several hundred kHz, repeatedly impinging on the thin internal target. This recycling of the beam boosts the available luminosity by at least five orders of magnitude, compensating for thin targets and limited beam intensities.

Recently, a pilot experiment at ESR investigating the reaction 96Ru(p,$\gamma$)97Rh demonstrated the feasibility of this approach for proton-capture reactions Mei et al. (2015). However, only a beam energy of 9 AMeV could be reached. For a 96Ru beam impinging on a 1H target this converts to a center-of-mass energy of 8.976 MeV, still several MeV away from the Gamow window. Going to even lower energies is a challenge for both, accelerator and experiment.

For the current experiment, the 124Xe-beam was accelerated to about 100 AMeV in the UNIversal Linear ACcelerator (UNILAC) and SchwerIonenSynchroton (SIS18), extracted to the ESR transfer beam line, completely stripped off bound electrons and finally injected into the ESR. Once the beam was stored, its momentum spread was brought down to and maintained at $\frac{\Delta p}{p}\approx 10^{-5}$ with the electron cooling system of the ring Litvinov et al. (2013). In the next step, the ions were decelerated to the desired energies of a few AMeV. About $10^{6}$ - $10^{7}$ 124Xe54+ ions at energies as low as 3 AMeV can potentially be stored in the ESR. At this point the internal ultra-pure H2 target was switched on reaching densities of about $10^{14}$ atoms/cm2 Kühnel et al. (2009). This corresponds to an energy loss of about 5-10 eV, which is compensated by the electron cooler. The beam passed through the hydrogen target with a revolution frequency of about 250 - 500 kHz, resulting in peak luminosities of about $L=10^{26}~{}\text{cm}^{-2}\text{s}^{-1}$. Measurements at 5 beam energies starting from 8 AMeV and reaching down as low as 5.5 AMeV were performed to investigate the 124Xe(p,$\gamma$) reaction in inverse kinematics. Atomic interactions with the atoms of the target and the residual gas limit the storage time of highly charged ions at low energies. With the 124Xe54+ beam stored at 7 AMeV a beam lifetime of about 2.5 s could be achieved, resulting in a reasonable measurement period of about 12 s before the ring had to be refilled. A single fill cycle of the ESR took about 50 s, implying a duty cycle of about 25%.

The 125Cs products of the (p,$\gamma$) reaction are subject to a negligible momentum recoil caused by the emission of the $\gamma$ cascade, see e.g. Ruiz et al. (2014). This allows the entire recoil cone to be covered by a single particle detector. In order to separate the reaction products from the stored beam, the detection system is implemented at the end of the first dipole magnet downstream of the target as shown in Fig. 1. The lower magnetic rigidity results in a separation from the stored beam of about 4 cm, which was also predicted by beam-optical simulations. It should be noted that for an undisturbed detection of the (p,$\gamma$) reaction products, it is essential to utilize a fully stripped primary beam. Otherwise, the stored ions which loose an electron at the target would hit the detector at approximately the same position as the (p,$\gamma$) products, due to a comparable magnetic rigidity. This would lead to a fatal background contribution, since at low energies the cross section for ionization is much larger than for proton capture.

The main challenges for this experiment were the storage and detection of ions at Gamow window energies. In order to store highly charged ions at energies below 10 AMeV ultra-high vacuum (UHV) conditions of about $10^{-11}$ mbar in the entire ring are crucial. Otherwise the atomic interactions of the revolving beam with the residual gas atoms would reduce possible storage times to the sub-second level Grieser et al. (2012); Stöhlker et al. (1998), which would render reaction studies impossible. These boundary conditions dictate a highly restrictive list of materials that can be brought into the UHV environment. Therefore, the regular particle detection systems at the ESR are operated inside detector pockets, which are separated from the ring vacuum by entrance windows made of 25-100 $\mu$m stainless steel Klepper and Kozhuharov (2003). As heavy ions of energies below 10 AMeV hardly penetrate such windows, the design and implementation of a new in-vacuum detection system was the major step towards the low energies of the Gamow window.

The new in-vacuum setup consists of a Micron Semiconductor Ltd W1-type double-sided silicon strip detector (DSSSD) dss of 500 $\mu$m thickness, which stops low-energy ions completely. To be compatible to the UHV environment, the wafer is mounted on a ceramic printed-circuit board, equipped with low-outgassing cables and designed for in-situ bakeout at about 125 °C. The DSSSD is able to detect ion energy deposits of several hundred MeV at 100% efficiency with a spatial resolution of about 3 mm and an energy resolution better than 1%. The setup has been installed at 53.5° bending angle of the 60° dipole magnet downstream of the target as indicated in Fig. 1.

To extract absolute (p,$\gamma$) cross section values in the analysis, the luminosity in the ring has to be known. It depends on the areal thickness of the target, the beam current and their mutual geometric overlap. For this purpose, the investigation of the (p,$\gamma$) cross section is carried out relative to a measurement of the radiative electron-capture process from the H2 target to the K-shell of 124Xe54+ (K-REC). High-purity germanium semiconductor detectors surrounding the target at 90°, 60° and 35° with respect to the beam axis were used to detect the X-ray signature of the K-REC. The REC process is one of the dominant processes in ion-atom (ion-electron) collisions and has been studied in details in recent decades Eichler and Stöhlker (2007). These studies have demonstrated that all experimental REC results can be well understood within the framework of the relativistic distorted-wave approach. Based on this approach the K-REC differential cross sections can be predicted with an uncertainty $\leq$ 2%. The main source of this uncertainty arises from the fact that a molecular H2 target is used instead of atomic H Artemyev et al. (2010).

For all beam energies the DSSSD was positioned about 1 cm away from the orbit of the beam to capture the (p,$\gamma$) products in the center of the active area. The hit distribution across the surface of the DSSSD at 7 AMeV is shown in Fig. 2. The narrow cluster of 125Cs ions from the (p,$\gamma$) reaction in the center of the detector is clearly visible above the broad background of 124Xe ions from Rutherford elastic scattering off the hydrogen target.

For ion detection with the DSSSD a coincidence condition between front and back side of the detector in combination with a simple energy threshold at 1/3 of the nominal ion energy has been applied. This leads to a clean ion-hit identification also taking into account inter-strip events, which result in energy sharing between adjacent strips Yorkston et al. (1987). Since no notable losses have been observed, an ion detection efficiency of 100% is assumed.

The determination of the (p,$\gamma$) cross section $\sigma_{\mathrm{(p,}\gamma\mathrm{)}}$ can be described as

[TABLE]

Here, $N_{\mathrm{(p,}\gamma\mathrm{)}}$ is the number of detected 125Cs ions, $N_{\textrm{K}}$ denotes the number of K-REC X-rays detected with the efficiency $\epsilon_{\textrm{K}}$ within the solid angle $\Delta\Omega$, and $d\sigma_{\textrm{K}}/d\Omega$ is the K-REC differential cross section.

The extraction of the number of proton-capture events from the 2-dimensional histograms was accomplished by fitting and subtracting the Rutherford background. The shape of this background component was simulated with the Monte Carlo based MOCADI code Iwasa et al. (2011). The simulation took into account the well-known Rutherford scattering kinematics and angular distribution Rutherford (1911) as well as all ion-optical elements, such as quadrupole and dipole magnets, which deform and shift the initial distribution. Additionally, background from nuclear channels such as (p,n) and $\mathrm{(p,}\alpha\mathrm{)}$ has been investigated and was found to be insignificant, either due to a clear separation in the dipole field or due to a negligible cross section as predicted by theory. This is confirmed by the Rutherford background fits, which describe the experimental data with $\chi^{2}_{\mathrm{reduced}}$ values close to 1. The residual ion hits after background subtraction are concentrated in a narrow cluster, which was integrated to obtain the number of (p,$\gamma$) reaction products $N_{\mathrm{(p,}\gamma\mathrm{)}}$.

For normalization the K-REC process is measured by means of X-ray spectroscopy. A typical spectrum taken at 8 AMeV is shown in Fig. 3. In addition to the K-REC signature at about 45 keV, the Lyman series ($K_{\alpha},K_{\beta},K_{\gamma}$) is clearly visible, as well as the REC processes involving the L- and M-shell of xenon. Unmarked peaks are due to detector response or could not be identified unambiguously. The X-ray spectra were recorded simultaneously with the (p,$\gamma$) spectra in the DSSSD. The number of K-REC counts, $N_{\textrm{K}}$, resulted from integrating the K-REC peak assuming a linear background.

The energy-dependent X-ray detection efficiency was measured using calibrated radioactive sources (133Ba,210Pb,241Am) at exactly the same distance from the detector as the hydrogen target during the experiment, which includes a measurement of the solid angle $\Delta\Omega$. The interpolation to K-REC energies was done by fitting the measured efficiency data.

The X-ray normalization procedure has been confirmed by an independent luminosity determination making use of the background distribution detected with the DSSSD based on the Rutherford formula Rutherford (1911). Due to uncertainties in detector position and beam-optical parameters, as well as from nuclear contribution to the scattering cross section Nurmela et al. (1998), the uncertainty of this method is on the order of 10-20%, but the results agree with the X-ray normalization within 10%.

The measurements at 7 AMeV and 6 AMeV were carried out with two X-ray detectors at 90° and 60°. For the runs taken at 5.5 AMeV, 6.7 AMeV and 8 AMeV an additional detector at 35° was available. For each beam energy the (p,$\gamma$) cross sections based on normalization to individual X-ray detectors agreed within the uncertainties. The final results were obtained from the weighted average of the individual normalization factors $F_{\textrm{norm},i}$:

[TABLE]

where $\sigma_{i}$ is the individual uncertainty associated with $F_{\textrm{norm},i}$ not taking into account common uncertainties, like the one connected to the K-REC cross section.

The final cross section values are listed in Tab. 1 for all center-of-mass energies. These energies are determined from the applied voltage at the electron cooler as demonstrated by Ullmann et al. (2015). The error in the voltage measurement leads to an uncertainty for $E_{\textrm{CM}}$ of about 10 keV. The cross-section uncertainties for the two lowest energies are dominated by the statistical component of $N_{\mathrm{(p,}\gamma\mathrm{)}}$, which also includes the uncertainty of the Rutherford fit. At higher beam energies the systematic component becomes equally important, which mainly originates from the X-ray normalization, including uncertainties from the K-REC cross section (2%), the calibration standards (5%) and the X-ray efficiency (5%). It has to be noted that the latter is subject to averaging according to Eq. (3). The results of intermediate analysis steps are also provided in Tab. 1. Here, the individual efficiency-corrected K-REC counts per steradian $N_{\textrm{K-REC}}/\epsilon_{\textrm{K-REC}}\Delta\Omega$ as well as the effective theoretical $d\sigma_{\textrm{K}}/d\Omega$ are listed separately for all beam energies and available detector angles. Together with the number of (p,$\gamma$) products $N_{\mathrm{(p,}\gamma\mathrm{)}}$ the full dataset for use in Eqs. (1) to (3) is available.

Theoretical nuclear cross sections for medium- and heavy-mass nuclei at astrophysical energies are usually calculated within the Hauser-Feshbach (HF) formalism based on the formation of a compound nucleus at high level density Hauser and Feshbach (1952); Rauscher (2011). Formation and decay probabilities of the compound system are quantified in so-called averaged widths. The majority of reaction rates used in large nucleosynthesis networks are based on such HF calculations. We used our new data to test the HF cross section predictions and the underlying physical parameters directly relevant for the $\gamma$ process Rauscher et al. (2013). For this purpose we use the HF code SMARAGD Rauscher (2011, ), which relies on a widely used combination of nuclear models for astrophysical rate prediction Rauscher and Thielemann (2000); Cyburt et al. (2010). In detail, the nuclear input to the HF code consists of the microscopic proton+nucleus optical model potential by Jeukenne et al. (1977) with low-energy modifications by Lejeune (1980), the nuclear level density by Rauscher et al. (1997) including a parity dependence according to Mocelj et al. (2007), and the gamma-strength as described in Rauscher and Thielemann (2000); Rauscher et al. (1997).

Of special astrophysical interest is the energy range below the neutron-emission threshold $S_{n}=6.71$ MeV Rauscher (2010); Rauscher et al. (2013); Nishimura et al. (2018). In this region the proton width is typically the most sensitive input parameter for (p,$\gamma$) cross sections Rauscher (2012), making it a key ingredient for HF rate predictions in the $\gamma$ process Rauscher et al. (2013). In Fig. 4 the experimental cross section values are compared to results of the SMARAGD code. For the unmodified SMARAGD prediction the deviation of about 30% at the lower end of the measured energy range is within the expectations, since the underlying models aim at a global description of nuclear properties. However, better agreement can be obtained by locally increasing the proton width for the compound nucleus 125Cs by 30% which increases the calculated cross section by about the same amount. This confirms that the usually adopted uncertainty of about a factor of $2$ for global HF rate predictions of (p,$\gamma$) and inverse reactions Rauscher et al. (2016) holds in this mass region.

Above the neutron-emission threshold, the cross-section predictions are additionally sensitive to the $\gamma$- and neutron widths. Therefore it is impossible to unambiguously identify the source of the strong deviation between theory and experiment at these energies. Varying all widths shows that it is impossible to simultaneously reproduce the data points at the two highest energies. Either the cross section at the highest measured energy is strongly overpredicted or the data point at the second-highest energy is underpredicted. The latter case is shown in Fig. 4, which requires a strong increase in the neutron width or alternatively a strong decrease of the $\gamma$ width in the compound nucleus to bring down the cross section to coincide with the data point at the highest energy. Such a strong variation would be typical for a single resonance structure but this would not be expected at the high level density found in the compound nucleus 125Cs at the populated excitation energies.

In Summary, with the study of 124Xe(p,$\gamma$)125Cs presented here, the in-ring method for direct (p,$\gamma$) measurement was proven to be applicable for heavy nuclides and to provide measurements in an astrophysically relevant energy range. In combination with the rare ion beam production in the FRS at GSI Geissel et al. (1992) this offers new opportunities to significantly improve weakly constrained astrophysical reaction rates used in nuclear reaction networks responsible for the synthesis of the p nuclei in explosive stellar scenarios. The present data for 124Xe(p,$\gamma$) between 5.5 and 8 MeV provide a sensitive test of cross section predictions and especially the prediction of the proton width which is important for the theoretical modelling of astrophysical proton capture and inverse reactions. Although several modifications of theoretical parameters were needed to describe the experimental dataset, we can confirm that the theory provides reliable (p,$\gamma$) predictions within the assumed accuracy of about a factor of two. This especially holds for the proton width and the lower part of the measured energy range.

In the future it is envisioned to extend the proton-capture campaign to radioactive beam studies, addressing key reactions like 59Cu(p,$\gamma$), which has high impact on the light curve and heavy element production in X-ray burst models Cyburt et al. (2016). The only strong limitation for radioactive beam experiments at the present ESR facility is the half-life of the stored ion; it should be on the order of tens of seconds at least. Moreover, with the in-ring technique it is conceivable to broaden the range of reaction channels that can be studied in inverse kinematics, e.g. ($\alpha$,$\gamma$) or (p,n) reactions would be possible, with only minor modifications to the experimental setup.

Driven by the high scientific potential, there are several initiatives for new storage-ring facilities around the world with a focus on low-energy studies. The storage ring at HIE-ISOLDE project Grieser et al. (2012), for instance, combines a low-energy ring with an ISOL-type RIB facility, while the CRYRING@ESR project Lestinsky et al. (2016) represents a low-energy extension of the ESR machine. This work delivers a proof-of-principle for one of the key physics cases connected to such ring projects.