Results of total cross-section measurements of the 87 Rb(p, γ ) 88 Sr reaction

. The existence of a set of stable proton-rich nuclei - the p nuclei - cannot be explained via neutron-capture reactions. Therefore, another mechanism has to exist in order to explain their origin, the most probable, especially at high masses, being photodisintegration reactions. This gives rise to the γ process. Since most photodisintegration reactions involved in the process are not experimentally accessible, reliable statistical model calculations are needed to predict cross sections and reaction rates. To improve these calculations nuclear input parameters need to be constrained and a large experimental database is needed. Via comparison of experimental data to theoretical predictions di ff erent models can be tested and constrained. In order to study the 87 Rb(p, γ ) 88 Sr reaction, for which previously no experimental data have been available, an in-beam experiment at at the University of Cologne’s high-e ffi ciency HPGe γ - ray spectrometer HORUS was performed. Proton beams with energies between E p = 2000 to 5000 keV reaching deep into the Gamow window of the reaction were provided by the 10 MV FN Tandem accelerator. Cross-section values at six proton beam energies were determined. The experimental results are in good agreement with statistical model calculations. The obtained results are the first experimental cross-section values for the 87 Rb(p, γ ) 88 Sr reaction and help to constrain the nuclear physics input for statistical model calculations.


Introduction
Neutron-capture processes are responsible for the production of most elements heavier than iron. About 30 -35 stable, proton-rich nuclei -the so called p nuclei [1] -are bypassed by these processes. These nuclei are predominantly produced in the γ process, which consists of different combinations of photodisintegration reactions, e.g. (γ,p) or (γ,α), on mainly unstable neutron capture seed nuclei.
For statistical model calculations, nuclear physics input parameters -e.g. particle and nucleus optical model potentials, nuclear level densities, and γ-ray strength functions -are needed and measurements in the Gamow window are of utmost importance.
Systematic studies of the N = 50 isotonic chain are of interest since the p nuclide 92 Mo shields the extinct radionuclide 92 Nb from being produced by the rp-and νp-processes [2]. 92 Nb can be produced by the γ process [2]. By studying the inverse radiative-capture reactions, that is (p,γ) instead of (γ,p), thermal population of excited states are accounted for.
The 87 Rb(p,γ) 88 Sr reaction has not been measured before and its results hopefully helps to understand the production of 92 Mo and 92 Nb and improve statistical model calculations.

Experimental Details and Method
The 87 Rb(p,γ) 88 Sr reaction has been measured in the Astrochamber installed within the HO-RUS γ-ray spectrometer at the 10 MV FN Tandem accelerator at the Institute for Nuclear Physics at the University of Cologne.
The in-beam technique allows to measure transitions to the ground state to determine the total cross section by detecting the γ rays stemming from a highly excited compound nucleus with an excitation energy of E x = E c.m. + Q due to the impinging protons, where Q denotes the Q value and E c.m. denotes the center-of-mass energy. γγ-coincidence measurements are sometimes necessary to find possible contaminants in the γ-ray spectra and to identify the transitions to the ground state of the reaction of interest. The prompt γ-ray decays into the ground state which were observed in the experiment are illustrated in Fig. 1 and two γ-spectra can be seen in Fig. 2.
The HORUS γ-ray spectrometer consists of up to 14 HPGe detectors where six of them are equipped with bismuth germanate (BGO) shields for Compton background suppression. These detectors cover five different angles with respect to the beam axis which allows to measure angular correlations and to perform γγ-coincidence measurements. Details on the setup can be found in Ref. [4].
Proton beam energies of E p = 2000 to 5000 keV were provided by the 10 MV Tandem accelerator. Irradiation times between 8 h to 20 h and beam currents of 130 to 630 nA were used.
Since 87 Rb has a melting point of T m ≈ 40 • C, a pure 87 Rb target would melt during the irradiation. Therefore, Rb 2 CO 3 (rubidiumcarbonate) with a melting point of T m ≈ 840 • C was used with an isotopic enrichment in 87 Rb of 99.2(1) %. The Rb 2 CO 3 target was produced in-house by evaporating Rb 2 CO 3 with a thickness of 0.65(15) mg cm 2 onto a gold backing . The thickness was determined via Rutherford backscattering spectrometry (RBS) at the RUBION facility in Bochum, Germany, after the in-beam experiment took place. This showed that the target layer and the backing layer are not clearly distinguishable after irradiation. Therefore, the determination of target thickness is ongoing and the uncertainty is not finalized. The energy loss in the target is obtained from SRIM [3] simulations and is about 25 to 46 keV depending on the proton beam's energy.
The total cross section is given by where N p and N t denote the number of projectiles and target nuclei per area, respectively, and N R denotes the number of proton-capture reactions. The emitted γ rays follow an angular distribution W(Θ) with respect to the beam axis. The number of γ-rays N γ (E γ ) is corrected for the dead time of the data acquisition τ as well as for the full-energy peak efficiency ϵ (E γ ) leading to the following expression: The fitting of a sum of Legendre polynomials to the experimental data for each γ-ray transition at each beam energy leads to the angular distribution The sum of all A 0 coefficients represent the total number of proton-capture reactions N R .  Figure 1. Schematic level scheme of the 87 Rb(p,γ) reaction [5]. The observed γ-ray transitions to the ground state are shown in orange. The transition in light blue was not investigated directly but indirectly via the branching ratio [5] of the transition in darker blue.

γ-ray Spectra
In Fig. 2 the comparison of typical γ-ray spectra at proton beam energies of E p = 2000 keV and 5000 keV are shown. A higher beam-induced background and more transitions of the (p,n)-product 87 Sr are visible for a proton beam energy of E p = 5000 keV. For E p = 2000 keV small contributions of contaminants in the target material and the target chamber are visible due to the low beam-induced background. At the higher measured beam energies the γray spectra become increasingly complicated to analyse and a precise reconstruction of peak origins is necessary.

Total cross-section results
The obtained values of the total cross sections are listed in Table 1. The energies are given as center-of-mass energies corrected for the energy loss in the target. Note, that the uncertainty for the energy loss in the target obtained from SRIM [3] is much smaller than the accuracy of the accelerator. Therefore, the absolute values of this uncertainty do not differ. The uncertainties for the cross section values stem from the uncertainties of the number of projectiles (≈ 5 %), the target thickness (≈ 25 %), full-energy peak efficiency (≈ 4 %), and the statistical error after fitting the Legendre polynomials (≈ 10 %).  Figure 3 shows preliminary cross-section values obtained in this work in comparison to theoretical statistical model calculations using the TALYS 1.95 code [6]. The microscopic level density (Skyrme force) from Hilaire's combinatorial tables [7] (micr. LD5, cf. Fig. 3) Figure 3. Experimental cross sections for the 87 Rb(p,γ) 88 Sr reaction obtained in this work (black points). Statistical model calculations using the TALYS 1.95 code [6] are shown. The microscopic level density from Hilaire's combinatorial tables [7] has been used in combination with the γ-ray strength function models Goriely T-dependent HFB [10] and Gogny D1M HFB+QPRA [11].