# Proton inelastic scattering on 56Fe: Insights from the 9-MV Tandem Accelerator measurements @ IFIN-HH

A. Coman, C. Borcea, R. Borcea, M. Boromiza, S. Calinescu, D. Chiriac, C.

Costache, P. Dessagne, I. Dinescu, A. Farzanehpoor Alwars, et al.

► To cite this version:

A. Coman, C. Borcea, R. Borcea, M. Boromiza, S. Calinescu, et al., Proton inelastic scattering on 56Fe: Insights from the 9-MV Tandem Accelerator measurements @ IFIN-HH. Nuclear Physics A, 2025, pp.123080. 10.1016/j.nuclphysa.2025.123080. hal-05021867

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# Proton inelastic scattering on $^{56}$Fe: Insights from the 9-MV Tandem Accelerator measurements @ IFIN-HH

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A. Coman<sup>a, ID</sup>, C. Borcea<sup>a</sup>, R. Borcea<sup>a</sup>, M. Boromiza<sup>a</sup>, S. Calinescu<sup>a</sup>, D. Chiriac<sup>a</sup>, C. Costache<sup>a</sup>, P. Dessagne<sup>b</sup>, I. Dinescu<sup>a</sup>, A. Farzanehpoor Alwars<sup>c</sup>, N. Florea<sup>a</sup>, A. Gandhi<sup>a</sup>, G. Henning<sup>b</sup>, M. Kavatsyuk<sup>c</sup>, M. Kerveno<sup>b</sup>, C. Mihai<sup>a</sup>, A. Negret<sup>a, ID, *,</sup>, A. Oprea<sup>d</sup>, C. Petrone<sup>a</sup>, A. Plompen<sup>d</sup>, A. Scafes<sup>a</sup>, D. Tofan<sup>a</sup>, A. Turturica<sup>a</sup>, G. Turturica<sup>a</sup>

## ARTICLE INFO

### Keywords:

Inelastic scattering cross section
Gamma spectroscopy

## ABSTRACT

Investigations into the inelastic scattering of neutrons and protons off $^{56}$Fe are relevant both for the development of new nuclear facilities and also for obtaining a better understanding of nuclear reaction mechanisms. While a new experiment measuring the neutron inelastic cross section on $^{56}$Fe at the Geel Electron Linear Accelerator (GELINA) neutron source of the EC-JRC, Geel (Belgium) is scheduled in the near future, a complementary proton-induced measurement was already performed at the 9-MV Tandem accelerator of IFIN-HH (Romania). The setup consisted of two HPGe detectors for γ-ray detection, and of a Faraday Cup coupled to a high-precision charge integrator for proton beam integration. This paper focuses on the IFIN-HH measurements presenting the experimental setup and particularities and the extracted results following proton inelastic scattering off three iron targets: 3.0 mg/cm$^2$ of $^{nat}$Fe and 0.6 and 3.3 mg/cm$^2$ of $^{56}$Fe (enriched to 99.77%). We were able to measure the cross section for the first three most intense transitions arising from the inelastic channel on $^{56}$Fe. We will also present a comparative analysis of our results with previously reported cross section data and TALYS 2.0 theoretical predictions - using both standard and tuned parameters for the nucleon-$^{56}$Fe optical model potential.

## 1. Introduction

In the second part of the 20th century the energy production based on nuclear fission became important in many developed economies. It yielded many advantages compared to fossil fuel-based energy production like low carbon footprint, fuel efficiency, improved sustainability, and so on. However, nuclear energy has its own specific difficulties: more complex and more expensive power plants, fuel availability (just 0.7% of natural uranium consists of $^{235}$U), important safety and proliferation concerns or the very

<footnote><sup>a</sup> Horia Hulubei National Institute for Physics and Nuclear Engineering, Magurele, Romania</footnote>

<footnote><sup>b</sup> CNRS, Université de Strasbourg, Strasbourg, France</footnote>

<footnote><sup>c</sup> Energy and Sustainability Research Institute Groningen, University of Groningen, Groningen, the Netherlands</footnote>

<footnote><sup>d</sup> European Commission – Joint Research Centre, Geel, Belgium</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: negret@nipne.ro (A. Negret).</footnote>

<footnote>https://doi.org/10.1016/j.nuclphysa.2025.123080</footnote>

<footnote>Received 13 September 2024; Received in revised form 7 February 2025; Accepted 31 March 2025</footnote>
pressing issue of nuclear waste. To improve on these issues specialists on all fields connected to nuclear energy are currently exploring new types of nuclear reactors called generically Generation IV fast reactors. Among many other crucial improvements, such nuclear facilities should use much more abundant fuels (like $^{238}$U) and also recycle part of the nuclear waste they generate while transmuting the initial longer-lived fission products to shorter-lived nuclides. These updates of current nuclear reactors however require substantial improvements of nuclear data relevant for this type of applications, in particular of the neutron inelastic channel on structural materials. As such, iron isotopes are crucial nuclei for which the uncertainty associated to neutron cross section measurements should be lowered considerably (over the last 10-15 years several evaluation working groups took on this issue [1,2]). Unfortunately, there are still open questions regarding the $^{56}$Fe neutron inelastic cross section (see Refs. [3,4]). To aid these efforts, our group plans to re-measure the neutron-induced inelastic channel at GELINA. As neutron beam experiments are particularly demanding, we explore in parallel a different approach to this problem: we aim to infer neutron cross sections from proton-induced ones on the same target. This approach makes use of isospin symmetry in nuclei which generates, up to the Coulomb term for incident protons, formally identical neutron- and proton-$^{56}$Fe optical model potentials (OMPs) and fairly similar nuclear structure of the two compound nuclei ($^{57}$Fe versus $^{57}$Co) through which the neutron and proton inelastic reactions proceed. This makes the two compared reactions behave in a similar manner and may aid in relating the two reaction channels through a procedure which combines experimental work (measuring the inelastic cross sections by $\gamma$ spectroscopy) with reaction calculations. Obviously, such an attempt requires a consistent theoretical input. The detailed steps of this approach as currently implemented, and its main drawbacks, are described extensively in our previous work dedicated to other physics cases [5,6]. The present paper describes therefore the first essential step towards this important end goal, that is, the experiment providing the initial proton-induced data on which, after tuning, a better quality proton OMP for this target nucleus can be extracted (see Section 3).

Natural iron consists of four stable isotopes with the following natural abundances: $^{56}$Fe [91.75(11)%], $^{54}$Fe [5.85(11)%], $^{57}$Fe [2.12(3)%] and $^{58}$Fe [0.28(1)%] [7]. Among them, $^{54}$Fe has a magic number of neutrons whereas the even-even $^{56}$Fe is two neutrons and two protons off from closing the $1f_{7/2}$ major shell at 28. This generates a very interesting nuclear structure with $^{56}$Fe displaying, like almost all even-even nuclei, a $0^+$ ground state (g.s.) followed by a $2^+$ and a $4^+$ first and second excited states, respectively. But, in the case of $^{56}$Fe these two states are not interpreted as part of the rotational band (like it was the case, for instance, in $^{58}$Ni, a previously-studied physics case by our group [6]) but as vibrational excitations build on the $0^+$ g.s. This vibrational band also includes the $2_2^+$ state at 2657.5 keV. For $^{58}$Ni, the lower-lying collective states collected most of the inelastic strength. This was the case especially for the first $2^+$ state, which translated into fairly large $\gamma$-production cross sections for the transitions decaying from these states. We observe the same behavior also for $^{56}$Fe, albeit to a lesser degree likely due to a smaller collectivity of vibrational states compared with purely rotational ones. Following the experiment, we successfully extracted the inelastic $\gamma$-production cross sections for the most prominent 3 transitions in $^{56}$Fe and compared them with previously published experimental data and TALYS [8] theoretical predictions.

## 2. Experimental setup and particularities

For the measurement of the inelastic channel on $^{56}$Fe, we made use of a proton beam provided by the 9-MV Tandem Accelerator of IFIN-HH [9,10] and of an experimental setup routinely used by our group in several past measurements (see Refs. [5,6]). To measure the radiation of interest arising from the inelastic channel we employed $\gamma$ spectroscopy with two high-purity germanium (HPGe) detectors (50% relative efficiency) positioned at 110° and 150° relative to the direction of the incident proton beam. Information about the incident beam was provided by a Faraday cup made of tantalum and placed 1-2 cm after the $^{56}$Fe target. The current from the cup was collected by a high-sensitivity electric charge integrator. The signals from the charge integrator, as well as those from the detectors, were sent to a fully digital DAQ. The module digitizes the raw waveforms at a frequency of 500 MHz and has a very good resolution in terms of amplitude determination (14 bits) [11]. Probably the most relevant feature of this digitizer is that it processes the collected data in real time without needing to transfer the digitized signals to a PC for applying digital algorithms for event amplitude and time extraction. This feature allows for good working conditions even at relatively high counting rates, typical for this type of experiments. The time and amplitude of each detected event were ultimately written on a PC in time-amplitude list files (very helpful for subsequent data analysis).

The measurement had several experimental particularities and difficulties. Because the proton energy loss inside the target is not negligible, we quantified this effect by employing the SRIM [12] code and the uniform probability distribution (i.e., we basically assume a linear energy loss over the target thickness as we are very far from the Bragg total absorption peak even for the slowest incident protons). Using this distribution, the average proton energy and its uncertainty were then easily calculated. During this experiment, we measured two (isotopically enriched to 99.77%) $^{56}$Fe targets and a $^{nat}$Fe target of different thickness: one very thin (0.6 mg/cm$^2$) and two relatively thick (3.0 and 3.3 mg/cm$^2$). The thin target allowed us to measure with very small incident energy steps (50 keV), aiming to probe cross section resonances, while the thick $^{56}$Fe one yielded very good statistics in a reasonable beam time. It also provided the possibility of additional cross-cheks of the data: the cross section points measured with the thick target should average-out the resonances measured with the thin one. As we measure absolute cross sections, we also needed to calibrate in efficiency our HPGe detectors. This was done using a point-like $^{152}$Eu calibration source placed in the same position as the one of the $^{56}$Fe target. Finally, to extract the absolute efficiency at the $\gamma$ energies specific to $^{56}$Fe, we interpolated and/or extrapolated the experimental efficiency points associated to $^{152}$Eu.

The Coulomb barrier of protons on $^{56}$Fe is approximately 4 MeV and the cross section of the inelastic channel reaches relevant values only above 4.5-5 MeV. Consequently, the incident energy with which we started the measurements was set to 4.2 MeV. Throughout the experiment, we were required to work at relatively high counting rates (2000-12000 events/s), to keep the beam
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** The γ-ray spectra associated to three specific situations: the $^{56}$Fe(p,p')$^{56}$Fe reaction, the $^{56}$Fe production via the decay of $^{56}$Co following the $^{56}$Fe(p,n) reaction and the $^{58}$Ni(p,p')$^{58}$Ni reaction respectively. The measurement time was 600 s for all the displayed runs. For beam ON, the incident protons had $E_p$ = 9.7 MeV and similar intensity. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)</figcaption></figure>

time low, which led to losses due to the dead time of the detectors. Corrections for this were applied to all data shown in the present paper. The detailed dead time correction procedure associated to our group's in-beam γ spectroscopy experiments can be found in our article dedicated to this subject (see Ref. [13]).

Another difficulty of this measurement was generated by the fact that the cross section of the $^{56}$Fe(p,n)$^{56}$Co reaction channel, which competes with the inelastic one, is fairly large. This, coupled with the mean lifetime of only 77 days of the residual $^{56}$Co, opened the possibility of target activation and thus, following $\beta^+$ decay, generated a polluting contribution in the γ peaks of interest from $^{56}$Fe because $^{56}$Co has significant $\beta$ branching to several excited levels in $^{56}$Fe. Perhaps an even greater difficulty was the presence of a fairly strong background line at 843.76-keV from $^{27}$Al, very close to the 846.76-keV transition in $^{56}$Fe. The γ line from $^{27}$Al is generated by the inelastic scattering of those protons deviated from the beam (after interaction, most likely elastic, with the $^{56}$Fe target and the collimators) ending up on the aluminum-based walls of the reaction chamber. Further, both peaks rest on a “germanium triangle” generated by the neutrons reaching the detector crystal and producing inelastic reactions. This issue was generated by the fact that the (p,n) channel on $^{56}$Fe is quite intense, producing a relatively large number of neutrons. In order to subtract all the unwanted contributions, two additional measurements were conducted. A “beam OFF” decay measurement was performed after each irradiation of the $^{56}$Fe target to quantify the contribution from $^{56}$Co decay. Additionally, a “beam ON” measurement using a $^{58}$Ni target was used as a reference, since $^{58}$Ni does not exhibit γ-ray lines close to those of $^{56}$Fe, allowing for an estimation of the contamination caused by $^{27}$Al and by germanium. The contribution from $^{56}$Co was determined for each proton energy by integrating the peak area of interest in the decay spectra “beam OFF” normalized to the corresponding $^{56}$Fe target measurement duration. The contribution linked to the 843.76-keV transition of $^{27}$Al was estimated also for each proton energy using the ratio between the peak areas of the first and second transitions in $^{27}$Al ($E_γ$ = 843.76 keV and $E_γ$ = 1014.52 keV, respectively) determined from the $^{58}$Ni spectra. The ratio was used together with the 1014.52-keV peak area from the $^{56}$Fe measurement to estimate for each run the contribution coming from the 843.76-keV transition. The corrections from $^{56}$Co-decay were found to range between 0.2% and 2% while the one from the $^{27}$Al-peak was calculated to be around 3%. Fig. 1 illustrates spectra corresponding to the $^{56}$Fe(p,p')$^{56}$Fe reaction, the production of $^{56}$Fe coming from the decay of $^{56}$Co following the $^{56}$Fe(p,n) reaction and the $^{58}$Ni(p,p')$^{58}$Ni reaction, respectively.

We refer the interested reader to Refs. [13,14]) for an extensive description of our data analysis procedure leading to angle-integrated γ-production cross sections for all observed transitions arising from the proton inelastic channel.

### 3. Results and discussions

Following the experiment, we were able to extract the inelastic γ-production cross sections for the most intense transitions in $^{56}$Fe. The experimental values were compared with previous reported experimental results and with theoretical calculations performed using the TALYS default calculations. We note that in the present work, following “TALYS 2.0 default [8]”, we assume a (near) spherical g.s. and very small deformation parameters ($\beta_L$) for several excited levels (only the first $2^+$ state at 846.76 keV has a relevant deformation: $\beta_L$ = 0.239). Hence, we assume weakly coupled channels and we include 10 levels in the coupling scheme (the list includes the levels from which we observed transitions in our experiment). Following TALYS 2.0 [8], we only perform a Distorted Wave Born Approximation (DWBA) calculation for describing the inelastic scattering to these discrete states in $^{56}$Fe. Below we show the impact of changing the deformation parameters for the first three excited levels. However, no attempts were made to change the coupling scheme by either including more levels or by modifying the type of collectivity of these excited states.
<figure><img src="image_5.png" /><figcaption>Fig. 2. The experimental γ-production cross section for the first three transitions in $^{56}$Fe extracted in the present work compared with Dyer et al. [15] and with TALYS 2.0 [8] theoretical predictions made using default and tuned input parameters.</figcaption></figure>

The first excited level in $^{56}$Fe with $E_L$ = 846.76 keV and $J^π$ = 2$^+$, decays to the g.s. through an intense E2 γ ray with $E_γ$ = 846.76 keV. Fig. 2(a), plots the excitation function for this transition extracted in the present work together with previously reported data. There is excellent agreement with the data measured by Dyer et al. [15] in the entire incident energy range, except a small difference at very high energies: the points at 15.5 and 16.5 MeV. These may be real compound nucleus resonances as they are confirmed by both the 3.0 and 3.3-mg/cm$^2$ targets (see Fig. 2, panel a). These thicknesses are small enough to actually probe (a bulk of) resonances especially considering that the Dyer et al. [15] display much larger incident energy uncertainty. In the same figure our results are compared with TALYS 2.0 [8] theoretical calculations using the settings described above. The reaction code models very well the measured data for this transition, especially the threshold region, with perhaps a slight underestimation in the 6-10 MeV range (see Fig. 2, panel a). Among others, this seems to confirm to a large extent the assumed coupling scheme, mentioned in the previous paragraph, for the first excited level. We emphasize the very good agreement between our results obtained with the thick versus thin targets. This validates to some extent our experimental technique and data analysis procedure, especially the dead time corrections (the thick target runs were measured at very high counting rates compared to the thin target case).

The next two excited levels in $^{56}$Fe decay emitting two γ rays with $E_γ$ = 1238.2 and 1810.7 keV (we did not observe the much weaker 2657.5-keV transition de-exiting the third level). Our results for these transitions are shown in Fig. 2, panels b and c. We do not however report here the cross section for the 1238.2 and 1810.7-keV lines associated to the $^{nat}$Fe measurement as this was a test run for cross checks only which therefore translated into very reduced statistics for these γ rays. Moreover, the thin target measurement did not allow us to observe secondary transitions in $^{56}$Fe as in this case the focus was on mapping out the $^{57}$Co resonances with very small incident energy steps and therefore the data taking time per cross section point was very small (typically 10-15 minutes). Again, we emphasize the very good agreement between our results and the data of Dyer et al. [15] also for these secondary transitions. Quite surprisingly, even though TALYS [8] describes very well the main transition in $^{56}$Fe, it consistently underestimates our results for the 1238.2-keV γ line even though the predicted shape of the excitation function is correct. Even worse, for the 1810.7-keV γ ray, the reaction code completely under-predicts the cross section above 8 MeV. This difference is too big to be explained by higher-lying feeding not taken into account during the calculations and therefore indicates more serious issues with other reaction ingredients (perhaps even at the level of the optical model which directly impacts the transmission coefficients to the 2657.5 keV state). Other causes may be an underestimation of the collectivity of the states decaying through these two γ rays when constructing the coupling scheme. To check this, we modified the coupling strength of the first three excited levels in $^{56}$Fe - assumed by TALYS 2.0 [8]-default to be only 0.239, 0.022 and 0.045, respectively - to the next values: $β_L$ = 0.189 ($E_L$ = 846.76 keV), $β_L$ = 0.352 ($E_L$ = 2085.1 keV) and $β_L$ = 0.205 ($E_L$ = 2657.5 keV). The results of these modifications are displayed in Fig. 2 as “TALYS 2.0 [8]-tuned” curves. These changes improved considerably the agreement with experiment, even for the first transition, indicating that likely one of the causes for the poor theoretical description provided by the default calculation relates to the improper description of the collectivity associated to these excited states. Unfortunately we did not detect higher-lying transitions to check if the observed improvement corresponding to the tuned calculations applies across transitions. We note that, even with these changes, the plateau region between 8 and 14 MeV associated to the third transition in $^{56}$Fe is still underestimated while both our data and Dyer et al. [15] are consistent in that region (see Fig. 2(c)). This small under-prediction may be generated by missing feeding not taken into account by TALYS [8].

Next step is to use what we have learned in the proton case to model the neutron inelastic reaction, that is, to use the same deformation parameters also in the neutron calculation and see if this proton-inferred neutron inelastic cross section describes better than the default TALYS [8] the results of the measurement planned at GELINA.
## 4. Conclusions

This paper reports on the proton-induced inelastic γ-production cross sections for three transitions in $^{56}$Fe measured with HPGe detectors at the 9-MV Tandem Accelerator of IFIN-HH (Romania). Our results are compared with previously reported data for the inelastic channel and yield a very good agreement across transitions. However, when comparing with the theoretical predictions provided by TALYS 2.0 [8] default for these reaction observables, we see large under-predictions except the main transition at 846.76 keV that is modeled very well by the code. We show that, by modifying the deformation parameters of the excited levels associated to the observed transitions in $^{56}$Fe, the agreement with experiment is greatly improved especially for the third transition.

### CRediT authorship contribution statement

A. Coman: Writing – original draft, Supervision, Methodology, Formal analysis, Conceptualization. C. Borcea: Writing – review & editing, Supervision. R. Borcea: Resources. M. Boromiza: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. S. Calinescu: Resources. D. Chiriac: Resources. C. Costache: Resources. P. Dessagne: Resources. I. Dinescu: Resources. A. Farzanehpoor Alwars: Resources. N. Florea: Resources. A. Gandhi: Resources. G. Henning: Writing – review & editing, Resources, Conceptualization. M. Kavatsyuk: Resources. M. Kerveno: Writing – review & editing, Resources. C. Mihai: Supervision, Resources. A. Negret: Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. A. Oprea: Resources. C. Petrone: Resources. A. Plompen: Writing – review & editing. A. Scafes: Resources. D. Tofan: Resources. A. Turturica: Software, Resources. G. Turturica: Software.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alexandru Negret reports financial support was provided by European Commission Seventh Framework Programme for Research and Technological Development Euratom. Greg Henning reports financial support was provided by European Commission Seventh Framework Programme for Research and Technological Development Euratom. Alexandru Negret reports financial support was provided by Executive Unit for Financing Higher Education Research Development and Innovation. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was supported by a grant of the Ministry of Research, Innovation and Digitalization, CNCS-UEFISCDI, project number PN-III-P4-PCE-2021-0490, within PNCDI III, and by the Euratom Research and Training Programme under grant agreements No 847594 (ARIEL), No 847552 (SANDA) and No 101164596 (APRENDE).

### Data availability

Data will be made available on request.

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