EExperimental techniques to study the γ process for nuclear astrophysics atthe Cologne accelerator laboratory F. Heim a, ∗ , J. Mayer a , M. M¨uller a , P. Scholz b , M. Weinert a , A. Zilges a a University of Cologne, Institute for Nuclear Physics, Z¨ulpicher Straße 77, D-50937 Cologne, Germany b University of Notre Dame, Department of Physics, Indiana 46556-5670, USA
Abstract
The nuclear astrophysics setup at the Institute for Nuclear Physics, University of Cologne, Germany isdedicated to measurements of total and partial cross sections of charged-particle induced reactions at as-trophysically relevant energies. These observables are key ingredients for reaction network calculations ofvarious stellar scenarios, and crucial for the understanding of the nucleosynthesis of elements. The experi-ments utilize the high-efficiency γ -ray spectrometer HORUS, and the 10 MV FN-Tandem accelerator. Anupdated target chamber as well as further experimental methods established in the last years will be pre-sented which allow to measure cross sections down to the nb region. The reliability of the measured crosssections is proven by a Y(p, γ ) Zr commissioning experiment. Additionally, an application for nuclearastrophysics will be presented. The results of a Nb(p, γ ) Mo experiment will be discussed as well as theirdeviations compared to formerly reported results.Published in Nuclear Instruments and Methods in Physics Research Section A 966, 163854 (2020).DOI: 10.1016/j.nima.2020.163854 c (cid:13) http://creativecommons.org/licenses/by-nc-nd/4.0/ . Keywords: nuclear astrophyiscs, total cross sections, partial cross sections, γ -ray spectroscopy, in-beammethod, HPGe detectors
1. Introduction
The longstanding question why, and in particularhow different elements are formed inspired the cre-ation of the interdisciplinary field of nuclear astro-physics [1]. The correct description of the complexprocesses found in various astrophysical scenariostypically requires a detailed understanding of theunderlying nuclear physics. In particular, the nucle-osynthesis of neutron deficient p nuclei remains oneof the unsolved puzzles [2, 3]. The γ process, whichis assumed to be responsible for the largest contri-bution to the abundance of the p nuclei, builds ahuge network of photodisintegration reactions andincludes thousands of different reactions on mainlyunstable and exotic nuclei. Thus, one often needsto rely on theoretical calculations for estimates of ∗ Corresponding author
Email address: [email protected] (F. Heim) cross-sections of reactions away from the experi-mentally known regions. The extension of the avail-able experimental database is therefore one of themain tasks of experimental nuclear astrophysics.Since cross sections at astrophysically relevant en-ergies, i.e. , inside the Gamow window, are typicallyin the lower µ b range, sensitive measurement tech-niques are mandatory.Various direct methods are available for the de-termination of absolute cross sections. A well-established technique for cross-section measure-ments is the activation method . This is a two-step method, during the first step unstable reac-tion products are produced and during the secondstep the radioactive decay is analyzed in a countingsetup. In most cases the γ -ray transitions in thedaughter nucleus are observed but α - or β -particlesmight also be counted. This method requires unsta-ble reaction products with appropriate decay half-lives and decay schemes. A review article on the Preprint submitted to Nuclear Instruments and Methods in Physics Research A July 28, 2020 a r X i v : . [ nu c l - e x ] J u l ctivation method can be found in Ref. [4] and re-cent experimental data are provided, e.g., in Refs.[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16].The in-beam 4 π -summing technique overcomessome limitations of the activation technique andutilizes a large scintillator crystal which covers asolid angle of almost 4 π around the target positionand summarizes the energies of all γ -rays emittedin a certain time window [17, 18, 19, 20, 21].Measuring radiative-capture reaction cross sec-tions with both stable and unstable reaction prod-ucts is also feasible with the in-beam high resolution γ -ray spectroscopy technique . The basic idea of thismethod is the observation of the prompt decay via γ -ray transitions from a highly excited compoundnucleus with an excitation energy of E x = Q + E cm into different states of the reaction product (seeFig. 1), where E cm denotes the center-of-mass en-ergy. Note that other than radiation emitted from asource, the photons stemming from the decay of theexcited compound nucleus are not emitted isotrop-ically but with an angular distribution with respectto the beam axis. Utilizing a multi detector γ -rayspectrometer in combination with a dedicated tar-get chamber allows to measure these angular dis-tributions, and hence to extract absolute cross sec-tions.This method and the dedicated setup for the in-beam measurement of absolute cross sections at theTandem accelerator lab of the University of Cologneis addressed in this paper. In Section 2 experi-mental details of the in-beam γ -ray spectroscopymethod will be presented. In particular, emphasiswill be given to recent developments which secure amore efficient and reliable analysis of cross-sectionexperiments. In Section 3 details of the revisedtarget chamber dedicated for the experiments willbe presented as well as results of the Y(p, γ ) Zrcommissioning experiment. The results of the as-trophysical relevant experiment Nb(p, γ ) Mo willbe discussed in Section 4. γ -ray spectroscopy at HORUS in Cologne The γ -ray spectrometer HORUS ( H igh efficiency O bservatory for γ - R ay U nique S pectroscopy) is amulti-purpose setup which is used for γ -ray spec-troscopy experiments addressing very different pur-poses. Various target chambers dedicated to specialtypes of experiments can be installed inside HO-RUS, see e.g., Refs. [15, 23, 24, 25, 26]. E cm + Q Nb + p Mo γ γ γ Figure 1: Illustration of the reaction mechanism that leadsto the highly excited compound nucleus after a radiative-capture reaction. The intensity for the prompt de-excitationinto the ground state of the reaction product directly ( γ ) orinto various levels ( γ , γ and so on) is called a partial crosssection (red arrows). The sum of all ground-state transitionsis used to determine the total cross section (blue arrows). HORUS can hold up to 14 High Purity Ger-manium (HPGe) detectors of which six can beequipped with Bismuth germanate (BGO) shieldsfor an active suppression of background fromCompton scattering. Its geometry is based on acube with 14 HPGe detectors placed on its six facesand eight corners. This leads to a coverage of fivedifferent angles of 35 ◦ , 45 ◦ , 90 ◦ , 135 ◦ and 145 ◦ withrespect to the beam axis, which allows the determi-nation of angular distributions. One hemisphere ofthe HORUS spectrometer is shown in Fig. 2. Alldetector end caps can be shielded with copper andlead plates of thicknesses of up to a few millimetersto suppress low energy γ - and X-rays and the detec-tors are positioned as close to the target chamberas possible, typically at distances of 9 cm up to 17cm.The preamplified signals from the HPGe detec-tors are processed using the Digital Gamma Finder(DGF-4C Rev. F) modules by XIA [27, 28]. Eachmodule provides four input channels as well as ded-icated VETO inputs for each channel, which areused for the active background suppression of theBGO shields. The incoming signals are digitizedat a rate of 80 MHz by flash ADCs with a depthof 14 bit. Detector, energy and timing informationare stored in a listmode format, allowing an offline2 igure 2: One hemisphere of the HORUS γ -ray spectrome-ter. The target chamber is installed in the center at the pointof intersections of all 14 HPGe detectors. Six detectors canbe equipped with BGO shields for an active Compton back-ground suppression. analysis of the data including γγ coincidences [29].The dynamic energy range is adjustable. For cross-section studies the upper energy limit is usually setto 12-18 MeV. The γ -process nucleosynthesis is assumed to ap-pear in explosive stellar scenarios at temperaturesof about 2.0 to 3.0 GK [3]. The Maxwell-Boltzmanndistribution provides a velocity distribution for theinteracting particles in the plasma. Since the tun-neling probability and hence the cross section in-creases exponentially with increasing particle en-ergy, the astrophysically relevant energy region –the Gamow window – is given by a convolution ofthose two probability functions, see e.g. Ref. [30].For this reason, a precise determination of the beamenergy in astrophysically motivated experiments isinevitable.While passing through the target material thebeam particles will loose energy ∆ E before leavingthe target layer and reaching the gold backing foil.This loss is estimated using the SRIM simulationcode [32]. The effective beam energy is determinedby: E p = E NMR + E OS − ∆ E , (1)where E p denotes the effective proton beam energy, E NMR the beam energy expected from the settingsof the Nuclear Magnetic Resonance (NMR) probeinside the 90 ◦ deflecting magnet of the Tandem ac-celerator and E OS the observed offset of the NMR C oun t s p e r c h a r g e [ a . u . ] E NMR [keV]FitExperiment
Figure 3: Resonance curve of the Al(p, γ ) Si reaction ona 100 µ g/cm thick Al target. The results show that theactual beam energy is about 17 keV higher than expectedfrom the settings of the NMR probe inside the 90 ◦ deflectingmagnet of the Tandem accelerator. This resonance scan isan appropriate method to determine the beam energy, butis time-consuming since it requires at minimum one day ofbeam-time. probe. In the following two different approachesto determine the energy offset will be presented, aswell as their specific advantages and disadvantages. a. The Al(p, γ ) Si resonance
The resonance of the Al( p, γ ) Si reaction at E p = 3674.4 keV [31] was scanned in small energy steps(up to a few keV). The peak volume of the 2838keV peak, i.e. , the transition 4 +1 → +1 in Si, wasnormalized to the accumulated charge deposited onthe target. The result is a resonance curve, whichis shown in Fig 3. The width of the rising edgeof the resonance curve is determined by the energyspread of the proton beam provided by the Tan-dem accelerator and amounts to about 8 keV. Thewidth of the plateau is caused by the energy lossof the protons in the Al target. From the positionof the rising edge the offset, and hence the effectiveparticle beam energy can be determined. b. Beam calibration from prompt γ -rays In most of the radiative-capture experiments weare interested in the prompt γ -ray de-excitation ofthe compound state as indicated by red arrows inFig. 1. From the position of the respective primary γ -ray transitions the center-of-mass energy can bededuced via: E c.m. = E γ − Q + E state , (2)where E γ is the γ -ray energy of the prompt transi-tion, E state is the respective energy of the state that3
100 150 200 250 300 350 400 450 500 10150 10200 10250 10300 10350 10400 10450 10500 10550
Peak position 10366 keV E p = 3500keV C oun t s p e r k e V E γ [keV] Peak Nb(p, γ )Background Figure 4: The shown peak contains primary γ -ray transitionsthat directly populate the 2 nd excited state in Mo at 1574keV. The Q value of the Nb( p, γ ) Mo reaction is Q =8490keV. The energy loss ∆E of the protons amounts to about49 keV and causes a broad peak, however this method allowsan energy calibration of the accelerator with in-beam γ -rayspectra taken from the experiment. is populated by the primary γ -ray and Q is the Q value of the reaction. For detectors with an an-gle of 90 degrees with respect to the beam axis thecombination of Eq. 1 and 2 directly yields the en-ergy offset of the accelerator from the in-beam γ -rayspectra. For angles different from 90 ◦ , Doppler cor-rections need to be taken into account. As shownin Fig. 4 the corresponding peaks are broadeneddue to the energy loss in the target, but with anappropriate amount of statistics the peak positionscan be extracted very accurately. The main advan-tage of this method is that no modification of theexperimental setup, i.e. , variation of beam energyand/or target, is required. The uncertainty of theenergy determination using this method is mainlydefined by the uncertainty of the energy loss in thetarget as well as by the precision of the peak po-sition. The width of the prompt peak in Fig. 4 isabout 23 keV. The uncertainty of the energy loss isalmost negligible, since the target thickness can bedetermined quite accurately (see Sec. 3.1). Finally,as an total uncertainty for the determination of thebeam energy we approximate 25 keV for the datashown in Fig. 4. Although compound reactions are the dominantreaction mechanism for particle energies of as-trophysical interest, a contribution of memory-preserving, direct-like reaction processes is exhib-ited by the measured angular distributions. Notethat the measured angular distribution is a super- p = 3.5 MeV, E Level = 871 keV W ( θ ) [ ] Angle θ [°] Legendre FitExperiment
Figure 5: The radiation emitted from the excited compoundnucleus follows an angular distribution. The experimentallydetermined values for the individual angles can be fitted bya series of Legendre polynomials. Here shown as an exampleis the 2 +1 → g.s. in Mo ( E γ = 871 keV) for an incidentproton energy of 3.5 MeV. position of contributions from several γ -ray cas-cades. The experimental yield Y ( E γ ) is first cor-rected for the full-energy peak efficiency (cid:15) ( E γ ) andthe dead time correction of the data acquisition τ : W (Θ) = Y ( E γ , Θ) (cid:15) ( E γ ) · τ (3)At the HORUS γ -ray spectrometer Y ( E γ ) is mea-sured at five angles and the angular distribution isobtained by fitting a sum of Legendre polynomialsto the five experimental values: W (Θ) = A X k =2 , α k P k ( cos Θ) (4)In this equation A and α k denote energy depen-dent coefficients and P k the Legendre polynomialsP and P . Taking only Legendre polynomials upto the order of k = 4 into account is justified by theassumption that dipole and quadrupole transitionsdominate the electromagnetic de-excitations. Re-cent experiments have shown that α k varies slightlywith beam energy [39, 40, 44]. Hence, the angu-lar distributions need to be obtained for each γ -raytransition at each beam energy. Figure 5 shows anexample of the angular distribution for the decay2 +1 → g.s. in Mo ( E γ = 871 keV) for an incidentproton energy of 3.5 MeV. Full-energy peak efficiencies are required for thedetermination of absolute cross sections and aretypically obtained using the standard calibration4 E ffi c i e n c y [ % ] E γ [keV] Experiment (2019)SimulationOld Setup (2014)
Figure 6: The shown full-energy peak efficiencies were ex-tracted using a standard calibration
Ra source as well asin-house produced Co (T / =77 d) and Ga (T / =9.5 h)sources for one HPGe detector at a distance of 11 cm. Thein-house produced sources allow to determine experimentalefficiencies up to γ -ray energies of 4.8 MeV. The simulatedefficiencies using Geant4 [33] agree very well with the ex-perimental results. For comparison, the efficiency using theold target chamber are shown in dash-dotted (see. Sec. 3for details). Efficiencies for the same detector at the samedistance are shown. sources
Eu and
Ra. They provide absolute ef-ficiencies up to γ -ray energies of about 2.5 MeV. Anin-house produced Co source (T / =77 d) emitsphotons of energies up to 3.5 MeV. The relativeefficiencies can be normalized to data from the cal-ibrated sources. However, for many experimentsthe energy range needs to be extended further upto about 10 MeV.In the past, the Al(p, γ ) Si resonance at E p = 3674.4 keV (see Sec. 2.1 a) has been used fre-quently. The absolute γ -decay branching ratios forthe depopulaton of the excited state at E x = 15 127keV are known from Ref. [31]. However, all γ -raysstemming from this resonance follow an angular dis-tribution. The coefficients α and α are also de-termined in Ref. [31] but have large uncertainties.This large error makes the results less useful. Thetransitions into higher-lying states with γ -ray en-ergies of about 4-6 MeV, which are used to scalethe efficiencies, exhibit lower uncertainties for α and α but their statistical uncertainties amountto up to 25 %. Therefore, the absolute efficienciesdetermined from the Al(p, γ ) Si resonance maybe doubtful.A new approach to extend the efficiency cali-brated energy range is the use of an in-house pro-duced Ga source. The rather short half-life of9.5 h demands to perform the Zn(p,n) activa-tion immediately before the calibration experiment.
Table 1: Fit parameter for the efficiency function given inEq. 5. The total detection efficiency at E γ = 1300 keVamounts to about 3.3 %. a b [keV − ] c d [keV − ]4.8(3) × − × − × − × − This activation demands for proton beam energiesof about 10 MeV, beam intensities of a few nA andirradiation times of only 1-2 hours. Ga emits sev-eral high-intensity γ -rays of energies between 3.5and 4.8 MeV [34] and it can be normalized accu-rately to data from, e.g. , a Ra source at lower en-ergies. Note, that the two highest γ -ray transitionsat 4806 keV and 4295 keV are exactly 511 keV apart,and hence single-escape contributions are buried inthe full-energy peak at 4295 keV. There are two dif-ferent ways to compensate for this:First, if the experimental setup is sufficiently wellsimulated, e.g , with Geant4 [36], not only full-energy peak efficiencies (see Fig. 6) but also single-escape efficiencies can be obtained. Hence, thesingle-escape contribution can be estimated.Secondly, the γ -ray at 4295 keV describes aground-state transition in Zn. The correspond-ing level also de-excites via other γ -ray transitionswith very precisely known branching ratios. In par-ticular, the 1190 keV transition into the 0 +4 state iswell-suited to estimate the intensity of the 4295 keV γ -ray transition. In our experiments both of theseapproaches delivered very similar results with rela-tive uncertainties of about 10 %. The full-energypeak efficiencies obtained from Ra, Co and Ga sources are fitted by a function of the form (cid:15) ( E γ ) = a · exp ( − b · E γ ) + c · exp ( − d · E γ ) . (5)The fit parameters are given in Tab. 1. γ - γ coincidence measurements The use of γγ -coincidences is a well-establishedand powerful tool to suppress beam-induced back-ground in γ -ray spectroscopy experiments. Due tothe high granularity of HORUS and the event-by-event data format, symmetric γγ -matrices can beconstructed which contain all coincidences betweensignals of any pair of detectors. This is done us-ing the SOCOv2 (Sorting Code Cologne) [35] un-der consideration of subtracting the time-correlatedbackground. Using this technique, the backgroundin the γ -ray spectra can be reduced by many or-ders of magnitude. Many prompt γ -rays from the5
800 820 840 860 880 900 920 940 C oun t s p e r k e V Energy E γ [keV] Gate on 871 keV10 Mo + + +
871 keV871 keV C oun t s p e r k e V E p = 3500 keV Figure 7: The γγ coincidence method applied on the Nb(p, γ ) Mo reaction for a proton energy of 3500 keV.Gating on 871 keV in the original spectrum (top panel) re-veals that the 0 +2 state at 1742 keV is not populated sinceno coincidences between 871 keV γ -rays are observed. excited compound nucleus have very low intensitiesand vanish in the background. To determine ab-solute gamma-ray intensities from γγ -coincidencespectra the absolute coincidence efficiencies are re-quired. In particular for γ -ray cascades that con-tain a prompt γ -ray from the excited compoundstate to a low-lying state (in general with γ -ray en-ergies of up to 10 MeV and more) these cannot bedetermined experimentally. Since there are no cal-ibration sources which emit γ -ray cascades includ-ing such high γ -rays and precise information aboutbranching ratios and dead-time of the data acquisi-tion is needed, we can only estimate the coincidenceefficiencies from Geant4 simulations.Applying the γγ -coincidence method helps toidentify unambiguously γ -ray transitions fromthe reaction of interest. In the case of the Nb(p, γ ) Mo reaction the γγ -coincidence tech-nique is very valuable since the 0 +2 state at 1742 keVdecays via a 871 keV γ -ray into the 2 +1 state whichthen de-excites via γ -ray emission with an energyof 871 keV as well. The gate on E γ = 871 keV (seeFig. 7) revealed that the 0 +2 state at 1742 keV isnot populated in this reaction and the 871 keV peakonly contains events from the 2 +1 → g.s. transition. Primary γ -ray transitions are of high interest inmost experiments since their intensities are mainlyaffected by the γ -ray strength function in the com-pound nucleus [37]. The observation of the corre- E cm + Q Nb Mo Figure 8: Schematic illustration of two step γ -ray cascadesthat lead to the population of a specific state. The absoluteintensity of high energetic prompt γ -rays (solid arrows) canbe estimated via the intensity of low-energetic second genera-tion γ -rays (dotted arrows). The blue (red) arrows representthe sum peak that contains two γ -rays which populate thefirst (second) excited state in the reaction product. sponding peaks belonging to the prompt γ -ray tran-sition was already introduced in Sec. 2.1.b and veryvaluable results have been extracted utilizing thismethod for (p, γ ) reactions on Y, Mo and
Ag[38, 39, 40].At those high γ -ray energies, pair productionis a major problem since the resulting single anddouble-escape peaks in the γ -ray detectors mightoverlap with other γ -ray transitions of interest.In particular, prompt γ -ray transitions into levelsabove 2 MeV often cannot be identified unambigu-ously. This issue can be overcome applying the γγ coincidence technique presented in Sec. 2.4.Another way of extracting primary γ -ray tran-sitions is the method of discrete two-step cascadespectra. The TSC method was originally developedto study γ -ray strength functions and nuclear leveldensities in (n, γ ) reactions [41, 42, 43]. TSC ma-trices can be constructed from the event-by-eventlistmode format and contain all γ -ray events thatpopulate a certain level via a two-step γ -ray cas-cade from the excited compound state (see Fig.8). Hence, the sum of these γ -rays can be de-scribed in analogy with Eq. 2 with the substitution E γ = E ( γ )+ E ( γ ). The so-called sum peaks – theprojection of the TSC matrix on the axis of sumenergies – contain events from single γ -rays whichcontribute to the population of a certain state. Therespective γ -ray peaks benefit from the high energy6esolution of the HPGe detectors since the peaks arenot broadened due to energy loss. This method hasbeen succesfully applied to the , Cu(p, γ ) , Znreaction [44] and will be applied to future experi-ments.
3. Details of the re-designed target chamber
The target chamber used for nuclear astrophysicsexperiments at the University of Cologne has beencompletely revised in 2019 by the in-house mechan-ical workshop and is shown in Fig. 9. The de-sign of the chamber has changed from a sphericalto an asymmetric geometry which is on one sideflat and on the other side half of a polyhedron.The new chamber features a significantly thinnerwall of 2 mm Al and is much more compact in itsdimensions compared to the old chamber which isdescribed in Ref. [22]. The tube that houses thein-beam Rutherford Backscattering Spectrometry(RBS) detector has a length of 9 cm and a diam-eter of 2 cm and its position has been relocated atan azimuthal angle of 45 ◦ . In combination witha reduced volume of the chamber, this allows tomount an additional HPGe detector in HORUS andto move all detectors around 20 % closer to the tar-get position at distances of around 6 to 13 cm. Ad-ditionally, read-outs for the current on the apertureand the chamber as well as the power supply for thesuppression voltage were moved to the stand of thechamber. In total, these changes result in a signifi-cant increase of the full-energy peak efficiency by afactor of about 2 over the whole energy range (seeFig. 6).The new chamber can be connected to the beampipe on both sides. This allows to stop the beamin a carbon or tantalum cup a few meters down-stream in experiments in which the beam is notstopped inside the target or its backing and duringbeam focusing procedures. Compared to the oldsetup, which required to stop the beam inside orclosely behind the chamber, this prevents from ac-tivating contaminants close to the target position.The chamber as well as the beam entrance pipeis coated with 0.1 mm tantalum to reduce beam-induced background further. The built-in silicon detector for RutherfordBackscattering Spectrometry (RBS) measurementsis used to monitor the target stability during the
Figure 9: The chamber for nuclear astrophysics mountedinside the γ -ray spectrometer HORUS. The beam (comingfrom the left side) impinges on the target which is surroundedby a liquid-nitrogen cooled copper finger. The chamber fea-tures a much thinner wall and all connectors moved to thestand of the chamber compared to the previous chamber.By this, the overall full-energy peak efficiency increased bya factor of about 2. Furthermore, the chamber is connectedto the beam dump and allows to stop the beam at a car-bon/tantalum cup a few meters downstream. experiment and to determine the target thickness.The detector is placed under a backward angleof 135 ◦ , features an in-beam energy resolution ofabout 15 keV for protons and covers a solid an-gle of 0.2 to 20 msr, depending on the diameter ofthe aperture that is used. A typical RBS spectrumof a Nb target irradiated with protons at an en-ergy of E p = 3.5 MeV is shown in Fig. 10. Thetarget was manufactured as a self-supporting foilby rolling from metallic niobium. Since niobium ismonoisotopic, no other constituents are expected.The targets were very thin – about 1 mg/cm –in order to minimize the energy loss and thus thewidth of the prompt γ -ray peaks (see Fig. 4). Thebeam is stopped in a gold backing with thicknessof around 300 mg/cm attached to the backside ofthe niobium.The effective target thickness can be extractedfrom simulations using the SIMNRA code [45]. Theagreement between the measured RBS spectrumand the simulation is excellent (see. Fig. 10).Typically, the target thickness is additionally de-termined prior to the experiment using the ded-icated RBS setup at the RUBION dynamitron-tandem accelerator at the Ruhr-University Bochum[46, 47]. Hence, the in-beam RBS setup inthe target chamber can be used in two ways.First, as explained, the in-beam RBS detec-7 C oun t s p e r k e V E p [keV] ExperimentSimulation
Figure 10: RBS spectrum measured with the in-beam silicondetector. Protons with an energy of 2.0 MeV impinged on Nb and a thick gold backing. The edge on the far right sideindicates the Nb layer and the next edge the beginning ofthe
Au backing. The falling edge of the peak on top ofthe plateau determines the thickness of the Nb layer. tor can be used to determine the target thick-ness. The resulting target thickness for Nb(1.3 ± ) agrees with the values obtainedin Bochum (1.1 ± ) within the error bars.Second, if the target thickness has been determinedprior to an experiment, the number of beam parti-cles can be extracted from the in-beam RBS spectra(see Section 3.2). To ensure the correct determination of the totalnumber of impinging particles on the target, thebeam current is read out at three different posi-tions. The current measurement at the target itselfis straightforward, since it is electrically connectedto a target ladder. The impinging ion beam on thetarget leads to scattered beam particles and the re-lease of δ -electrons and therefore the current hasto be corrected via measuring the (negative) cur-rent on the chamber. Two current integrators de-termine the accumulated charge individually withan overall uncertainty of about 5 %. To prevent the δ -electrons from escaping from the chamber intothe upstream beampipe, a suppression voltage of-400 V is applied. The current on the Faraday cupbehind the chamber is also recorded.Additionally, the measured in-beam RBS spectracan be used to obtain the total number of beamparticles. Given the case that all other relevant in-put parameters (energy calibration, solid angle ofthe detector, target thickness) for the RBS simula-tion explained in Sec. 3.1 are sufficiently well deter-mined, the number of beam particles remains the Table 2: Relevant parameters that affect the sensitivity limitof in-beam cross-section measurements. During the lastyears, the experimental performance has significantly im-proved and has pushed the limit to less than 0.1 µ b. The ef-ficiency at a γ -ray energy of E γ =10 000 keV is taken into ac-count as well as a typical target thickness of 7 × at/cm .The experimental values for the irradiation time t beam andbeam current I beam are taken from a typical experiment(2014) and using the new setup (2019) respectively. See textfor details. Status (cid:15) eff [%] t beam [h] I proton [nA] σ lim [ µ b]2014 0.13 70 250 0.42019 0.25 87 685 0.05Optimal 0.30 144 1000 0.02 only free parameter. This allows to estimate thebeam current with an uncertainty of less than 10 %and was successfully tested for the Nb(p, γ ) Moreaction. The simulation shown in Fig. 10 yields N p = (3 . ± . × particles and is in excellentagreement with the value obtained from the currentread-out which yielded N p = (3 . ± . × . The direct measurement of cross sections in the µ b range is very challenging and sets high techni-cal requirements. The sensitivity limit for directcross-section measurements is affected by the de-tector efficiency, the maximum available beam cur-rent and time. The target thickness is limited bythe acceptable energy loss which should not exceedabout 30-40 keV and is typically in the order of 10 at/cm . In the last years, intensive effort has beenput into the improvement of the aforementioned pa-rameters and significantly improved the sensitivitylimit for cross-section measurements. The limit hasbeen defined here as the minimum cross section,that yields γ -ray peaks with at least 1000 counts.Hence, the statistical uncertainty amounts to about3 %. The improvement of different parameters dur-ing the last five years as well as the the presentcross-section limit are given in Table 2. Note, thatthe current lower limit of σ min = 0 . µ b is verylow for an in-beam measurement and has been im-proved by a factor of 8 during the last five years.The optimal performance in Table 2 considers a sta-ble beam with an intensity of 1000 nA continuouslyimpinging on the target for 1 week. In order to show that cross section measurementson heavy nuclei using the new setup are reliable,we have measured the Y(p, γ ) Zr reaction as a8est case at six different beam energies between E p = 2 to 3 MeV. We have chosen to use thisreaction as commissioning experiment because to-tal cross-section data obtained from three indepen-dent experiments exist, see Ref. [22, 54, 55]. Weused a natural Y target with an Y enrichment of99.9 % which was prepared as a self-supporting foilvia rolling. The target thickness was determinedfrom a RBS measurement performed at the Ruhr-University in Bochum (as described in Sec. 3.1)and amounts to 0.85(2) mg/cm . A 230 mg/cm thick gold foil was attached to the backside to en-sure that the beam is completely stopped withinthe target. The irradiation times varied between30 to 100 minutes (depending on the beam energy)at beam intensities of about 600 nA.The total (p, γ ) cross section is given by: σ ( p,γ ) = N ( p,γ ) N p · N t , (6)where N p is the number of projectiles and N t thenumber of target nuclei. The total number of re-actions N ( p,γ ) is obtained by measuring the angu-lar distribution of all γ -rays populating the groundstate as described in Sec. 2.2. The combination ofEq. 4 and 6 yields the final expression for the total(p, γ ) cross section: σ ( p,γ ) = Σ Ni =1 A i N p · N t , (7)assuming N ground state transitions and N ( p,γ ) asthe sum of all A . For the Y(p, γ ) Zr experimentthe intensities of six ground state transitions havebeen determined. In the compound nucleus Zr,there is a 0 +2 state at 1761 keV that decays solelyinto the ground state via E0 transition. Since thistransition is not observable in the γ -ray spectra,the population of the 0 +2 state at 1761 keV wasdetermined as well. However, for the three low-est beam energies no significant population of the0 +2 state has been observed. Upper values for thecontribution of the corresponding transitions weredetermined and are included in the error of the to-tal cross sections. In addition, there is an isomeric5 − state at 2319 keV which has a half-life of about800 ms. In order to detect all γ -rays from the corre-sponding decay, the data acquisition has been con-tinued for several seconds after stopping the irradi-ation.The total cross-section results for the Y(p, γ ) Zr test experiment with our new setup are compared to the existing data in Fig.12. A good agreement is observed, as well as verysmall uncertainties. In summary, we conclude thatthe new setup provides robust and reliable data.
4. Application: Cross-section measurementof the Nb(p, γ ) Mo reaction
Systematic cross-section measurements are themain task of the setup presented in this article. Viathe comparison of experimental results to statisti-cal model calculations different nuclear physics in-put models can either be constrained or excluded.However, the Nb(p, γ ) Mo reaction is of specialinterest for nuclear astrophysics. The compoundnucleus Mo is – together with a few other p nu-clei – systematically underproduced in various the-oretical network calculations [48, 49]. Therefore,a deeper understanding of the underlying nuclearphysics in this nucleus is of paramount importance.The cross section of the Nb(p, γ ) Mo reactionwas determined at three proton energies: E p = 3.0,3.5 and 4.5 MeV. The Gamow window for this reac-tion is between 1.71 MeV and 3.39 MeV at a Tem-perature of 3 GK [30]. Further experimental de-tails were presented in Sec. 3.1 and 3.2. Figure 11shows a typical γ -ray spectrum for a beam energy of E p =3.5 MeV. The spectrum was obtained by sum-ming up all detectors mounted under an angle of90 ◦ with respect to the beam axis. Although con-siderable beam-induced background, mainly fromthe ( p, n ) reaction channel, was observed, all peaksin the spectrum can be clearly identified. For Nb(p, γ ) Mo reaction six ground statetransitions were observed in total. The largest con-tribution stems from the 2 +1 → g.s. transition atE γ =871 keV which accounted for about 95 % of thepopulation of the ground state. Systematic stud-ies have revealed that the relative contributions ofvarious ground-state transitions to the ground-statepopulation remain almost constant with beam en-ergy [40].The cross section results are given in Table 3 andshown in Fig. 13. The uncertainties in the crosssection values are composed of the uncertainties inthe number of projectiles ( ≈ ≈
10 %), full-energy peak efficiency ( ≈ ≈
200 400 600 800 1000 Nb(p, γ ) Mo E p = 3500 keV
548 685 769 C oun t s p e r . k e V Energy in keV Mo Mo Au Figure 11: Typical γ -ray spectrum of the Nb(p, γ ) Mo re-action for E p =3.5 MeV. The spectrum was obtained by sum-ming up all detectors mounted under an angle of 90 ◦ withrespect to the beam axis. The γ -rays that are not producedby the (p, γ ) reaction stem either from elastic scattering onthe backing Au or from the Nb(p,n) Mo reaction. The871 keV transition in Mo is a ground state transition andmarked with an asterisk. work are compared to experimental results reportedin Ref. [50]. The new results are slightly higherby a factor of about 1.4, which might be explainedby the experimental procedure used to derive theresults in Ref. [50]. First, the results from Ref.[50] were obtained by taking only the 2 +1 → g.s. transition at E γ =871 keV into account. In com-parison, we have included six ground-state transi-tions. Secondly, in Ref. [50] no suppression volt-age is mentioned. Hence, we assume that the mea-sured current could not be corrected for δ -electronsand therefore the cross section is underestimated.Third, the angular distributions in Ref. [50] weredetermined for beam energies between E p =2.0 and3.0 MeV only and taken as constant over the wholeenergy range. Additionally, the values above beamenergies of E p =3.0 MeV reported in Ref. [50] arescaled to absolute data from a measurement usingniobium oxide as a target. For this scaling pro-cedure an additional uncertainty of about 5 % isreported.We estimated the possible impact of each of these Table 3: Total (p, γ ) cross section results for the Nb(p, γ ) Mo reaction. Energies are given as effectivecenter-of-mass energies. E c.m [keV] σ tot [ µ b]2988 ±
10 116 ± ±
10 227 ± ±
10 177 ± Y(p, γ ) Zr σ t o t [ m b ] E c.m. [MeV] Scholz 2020 (This work)Harissopulos 2013Netterdon 2014Tsagari 2004
Figure 12: Results for the total cross sections of the Y(p, γ ) Zr reaction (red circles) measured with the newsetup in Cologne compared to formerly published results[22, 54, 55]. Since the results are in good agreement witheach other, we can conclude that our setup provides reliabledata.
10 100 2 2.5 3 3.5 4 4.5 5 Nb(p, γ ) Mo σ t o t [ µb ] E c.m. [MeV] This workHarissopulos 2001
Figure 13: Experimental totals cross sections of the Nb(p, γ ) Mo reaction. The results obtained in this workare compared to data from Ref. [50]. contributions. Taking correction factor for missingg.s. transitions ( ≈ δ -electrons ( ≈
10 %), wrong angular correlations ( ≈
18 %) anduncertainties from the scaling procedure ( ≈
5. Summary
In this article the experimental setup for exper-iments to study cross sections relevant for nuclearastrophysics at the University of Cologne was pre-sented. The HORUS γ -ray spectrometer combinedwith the revised target chamber is an excellent toolto measure even very small cross sections down tothe nb range at astrophysically relevant energies.Additionally, it enables the measurement of γγ -coincidences and discrete two-step cascade spectrawhich allow to perform an even more sophisticated10nalysis and study important nuclear physics con-cepts as the γ -ray strength function or nuclear leveldensities.The astrophysical relevant Nb(p, γ ) Mo reac-tion was successfully measured and total (p, γ ) crosssections for proton energies between E p = 3 . − .
6. Outlook
In addition to the 10 MV FN-Tandem acceler-ator, the University of Cologne operates a 6 MVTandetron accelerator which is primarily used forAccelerator Mass Spectrometry (AMS) [53]. Theaccelerator can provide stable proton beam intensi-ties of several µ A with very low ripple. At present,construction of a HPGe array which is solely ded-icated for nuclear astrophysics experiments is be-ing planned for this machine. Seven HPGe de-tectors with relative efficiencies of 80 % and twoclover detectors with relative efficiencies of 120 %will be mounted. The Tandetron accelerator canbe operated independently from the 10 MV FN-Tandem accelerator. Commissioning of this setupis expected to begin in the near future.
Acknowledgments
We gratefully thank K. O. Zell and A. Blazhevfor the target preparation, and H.W. Becker andV. Foteinou of the Ruhr-Universit¨at Bochum forthe assistance during the RBS measurements.This project has been supported by the DeutscheForschungsgemeinschaft under the contracts ZI510/8-1.
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