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A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated., Comment: Prepared for submission to JINST

HoNiSi$_{3}$ is an intermetallic compound characterized by two successive antiferromagnetic transitions at $T_{N1} = 6.3$ K and $T_{N2} = 10.4$ K. Here, its zero-field microscopic magnetic structure is inferred from resonant x-ray magnetic diffraction experiments on a single crystalline sample that complement previous bulk magnetic susceptibility data. For $T < T_{N2}$, the primitive magnetic unit cell matches the chemical cell. The magnetic structure features ferromagnetic {\it ac} planes stacked in an antiferromagnetic $\uparrow \downarrow \uparrow \downarrow$ pattern. For $T_{N1} < T < T_{N2}$, the ordered magnetic moment points along $\vec{a}$, and for $T < T_{N1}$ a component along $\vec{c}$ also orders. A symmetry analysis indicates that the magnetic structure for $T

About half of the heavy elements beyond iron are known to be produced by the rapid neutron capture process, known as r-process. However, the astrophysical site producing the r-process is still uncertain. Chemical abundances observed in several cosmic sites indicate that different mechanisms should be at play. For instance, the abundances around silver measured in a subset of metal-poor stars indicate the presence of a weak r-process. This process may be active in neutrino-driven winds of core collapse supernovae where (${\alpha}$,n) reactions dominate the synthesis of Z ~ 40 elements in the expelled materials. Scarcely measured, the rates of (${\alpha}$,n) reactions are determined from statistical Hauser-Feshbach calculations with ${\alpha}$-optical-model potentials, which are still poorly constrained. The uncertainties of the (${\alpha}$,n) reaction rates therefore make a significant contribution to the uncertainties of the abundances determined from stellar modeling. In this work, the $^{88}$Sr(${\alpha}$,n)$^{91}$Zr reaction which impacts the weak r-process abundances has been probed at astrophysics energy for the first time; directly measuring the total cross sections at astrophysical energies of 8.37 - 13.09 MeV in the center of mass (3.8 - 7.5 GK). Two measurements were performed at ATLAS with the electrically-segmented ionization chamber MUSIC, in inverse kinematics, while following the active target technique. The cross sections of this ${\alpha}$-induced reaction on $^{88}$Sr, located at the shell closure N = 50, have been found to be lower than expected, by a factor of 3, despite recent statistical calculations validated by measurements on neighboring nuclei. This result encourages more experimental investigations of (${\alpha}$,n) reactions, at N = 50 and towards the neutron-rich side, to further test the predictive power and reliability of such calculations., Comment: 9 pages, 6 conference

Recently it has been pointed out that an outstanding application of an IBM quantum computer is to reverse the arrow of time [Lesovik et al. Sci. Rep. 9, 1 (2019)]. The issue of the consequences of the reversal of the arrow of time on the execution of a CNOT gate by a quantum device is addressed. It is predicted that if the CNOT gate is executed towards the future then this was previously executed in the past. The above might confirm the paradigm that an event in the present time influences another event in the past time [2]. Such a physical phenomena is called retrocausality., Comment: 8 pages, 5 figures

We report the observation of an unexpected quadratic temperature dependence of the heat capacity in the vanadium sulphide metal V5S8 at low temperatures which is independent of applied magnetic field. We find that the behaviour of the heat capacity is consistent with an unconventional phonon spectrum which is linear in wavevector in the c direction but quadratic in the a-b plane, indicating a form of geometrical elastic criticality. In the case of V5S8 we also observe an unusual intermediate transition at high magnetic fields between the expected spin-flop and spin-flip transitions. We demonstrate that the intermediate field-induced transition is in agreement with a model of two sublattices with frustrated inter- and intra-sublattice spin couplings.

The $^{22}$Mg($\alpha$,$p$)$^{25}$Al reaction rate has been identified as a major source of uncertainty for understanding the nucleosynthesis flow in Type-I x-ray bursts (XRBs). We report a direct measurement of the energy- and angle-integrated cross sections of this reaction in a 3.3-6.9 MeV center-of-mass energy range using the MUlti-Sampling Ionization Chamber (MUSIC). The new $^{22}$Mg($\alpha$,$p$)$^{25}$Al reaction rate is a factor of $\sim$4 higher than the previous direct measurement of this reaction within temperatures relevant for XRBs, resulting in the $^{22}$Mg waiting point of x-ray burst nucleosynthesis flow to be significantly bypassed via the ($\alpha,p$) reaction, Comment: 6 pages, 3 figures, 1 table

Deuteron elastic scattering from 15C and inelastic scattering reactions to the first excited state of 15C were studied using a radioactive beam of 15C in inverse kinematics. The scattered deuterons were measured using HELIOS. The elastic scattering differential cross sections were analyzed using the optical model. A matter deformation length {\delta}d = 1.04(11) fm has been extracted from the differential cross sections of inelastic scattering to the first excited state. The ratio of neutron and proton matrix elements Mn/Mp = 3.6(4) has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of 15C were determined and discussed. Results from ab-initio no-core configuration interaction calculations were also compared with the experimental observations. This result supports a moderate core decoupling effect of the valence neutron in 15C similarly to its isotone 17O, in line with the interpretation of other neutron-rich carbon isotopes.

An in-flight beam of $^{16}$N was produced via the single-neutron adding ($d$,$p$) reaction in inverse kinematics at the recently upgraded Argonne Tandem Linear Accelerator System (ATLAS) in-flight system. The amount of the $^{16}$N beam which resided in its excited 0.120-MeV $J^{\pi}=0^-$ isomeric state (T$_{1/2}\approx5$ $\mu$s) was determined to be 40(5)% at a reaction energy of 7.9(3) MeV/$u$, and 24(2)% at a reaction energy of 13.2(2) MeV/$u$. The isomer measurements took place at an experimental station $\approx30$ m downstream of the production target and utilized an Al beam-stopping foil and a HPGe Clover detector. Composite $^{16}$N beam rate determinations were made at the experimental station and the focal plane of the Argonne in-flight radioactive ion-beam separator (RAISOR) with Si $\Delta$E-E telescopes. A Distorted Wave Born Approximation (DWBA) approach was coupled with the known spectroscopic information on $^{16}$N in order to estimate the relative $^{16}$N isomer yields and composite $^{16}$N beam rates. In addition to the observed reaction-energy dependence of the isomer fraction, a large sensitivity to angular acceptance of the recoils was also observed., Comment: 21 pages, 7 figures

Understanding the explosion mechanism of a core-collapse supernova (CCSN) is important to accurately model CCSN scenarios for different progenitor stars using model-observation comparisons. The uncertainties of various nuclear reaction rates relevant for CCSN scenarios strongly affect the accuracy of these stellar models. Out of these reactions, the $^{13}$N($\alpha$,$p$)$^{16}$O reaction has been found to affect various stages of a CCSN at varying temperatures. This work presents the first direct measurement of the $^{13}$N($\alpha$,$p$)$^{16}$O reaction performed using a 34.6 MeV beam of radioactive $^{13}$N ions and the active-target detector MUSIC (MUlti-Sampling Ionization Chamber) at Argonne National Laboratory. The resulting total $^{13}$N($\alpha$,$p$)$^{16}$O reaction cross sections from this measurement in the center-of-mass energy range of 3.26 - 6.02 MeV are presented and compared with calculations using the Hauser-Feshbach formalism. Uncertainties in the reaction rate have been dramatically reduced at CCSN temperatures., Comment: References 27 and 31 has been changed

The isomeric state of $^{16}$N was studied using the $^{16}$N$^{g,m}$($d$,$^3$He)~proton-removal reactions at \mbox{11.8~MeV/$u$} in inverse kinematics. The $^{16}$N beam, of which 24% was in the isomeric state, was produced using the ATLAS in-fight facility and delivered to the HELIOS spectrometer, which was used to analyze the $^{3}$He ions from the ($d$,$^{3}$He) reactions. The simultaneous measurement of reactions on both the ground and isomeric states, reduced the systematic uncertainties from the experiment and in the analysis. A direct and reliable comparison of the relative spectroscopic factors was made based on a Distorted-Wave Born Approximation approach. The experimental results suggest that the isomeric state of $^{16}$N is an excited neutron-halo state. The results can be understood through calculations using a Woods-Saxon potential model, which captures the effects of weak-binding., Comment: 8 pages, 7 figurs

The authors reply to the Comment arXiv:2104.03770 by P. Canfield et. al.

The partial (up to 7 %) substitution of Cd for Zn in the Yb-based heavy-fermion material YbFe$_2$Zn$_{20}$ is known to induce a slight ($\sim 20$ %) reduction of the Sommerfeld specific heat coefficient $\gamma$ and a huge (up to two orders of magnitude) reduction of the $T^2$ resistivity coefficient $A$, corresponding to a drastic and unexpected reduction of the Kadowaki-Woods ratio $A/\gamma ^2$. Here, Yb $L_{3}$-edge X-ray absorption spectroscopy shows that the Yb valence state is close to $3+$ for all $x$, whereas X-ray diffraction reveals that Cd replace the Zn ions only at the $16c$ site of the $Fd\bar{3}m$ cubic structure, leaving the $48f$ and $96g$ sites with full Zn occupation. Ab-initio electronic structure calculations in pure and Cd-doped materials, carried out without considering correlations, show multiple conduction bands with only minor modifications of the band dispersions near the Fermi level and therefore do not explain the resistivity drop introduced by Cd substitution. We propose that the site-selective Cd substitution introduces light conduction bands with substantial contribution of Cd($16c$) $5p$ levels that have weak coupling to the Yb$^{3+}$ $4f$ moments. These light fermions coexist with heavy fermions originated from other conduction bands with larger participation of Zn($48f$ and $96g$) $4p$ levels that remain strongly coupled with the Yb$^{3+}$ local moments., Comment: 9 pages, 4 figures, to appear in Phys. Rev. B

Nanofluids are suspensions of nanoparticles in a base heat-transfer liquid. They have been widely investigated to boost heat transfer since they were proposed in the 1990's. We present a statistical correlation analysis of experimentally measured thermal conductivity of water-based nanofluids available in the literature. The influences of particle concentration, particle size, temperature and surfactants are investigated. For specific materials (alumina, titania, copper oxide, copper, silica and silicon carbide), separate analyses are performed. The conductivity increases with the concentration in qualitative agreement with Maxwell's theory of homogeneous media. The conductivity also increases with the temperature (in addition to the improvement due to the increased conductivity with water). Surprisingly, only silica nanofluids exhibit a statistically significant effect of particle size, whereby smaller particles lead to faster heat transfer. Overall, the large scatter in the experimental data prevents a compelling, unambiguous assessment of these effects. Taken together, the results of our analysis suggest that more comprehensive experimental characterizations of nanofluids are necessary to estimate their practical potential.

The mixing process of multiple jets of liquefied petroleum gas and air in a diffusion flame is numerically analysed. The case study considers a four-port array burner where the fuel is injected by four peripheral nozzles and mixed with the surrounding air. Simulations are conducted with the Reynolds-Averaged Navier-Stokes technique, and the turbulence effect is modelled with the realizable k-e model. In addition, the eddy dissipation model is implemented to calculate the effect of the turbulent chemical reaction rate. Results show that the essential mixture mechanism occurs within a flame cone derived from the fuel jets interaction. However, the mixing process is driven by jets drag allowing an air/fuel smooth mixture to reach the flammability limits at two zones: one at a lower location or close to the burner surface and a second before the flame front development. The entire mixing mechanism culminates with the development of the flame necking cone. Any air concentration that falls into the cone radius will be entrained, contributing to the overall flame structure. Since the cone radius reach is limited only by radial distance of the jet array and the nozzles distance, the flame heights, consequently, depend solely on fuel mass flow.

This paper presents an experimental methodology to measure the height of the flame using convolution image processing and statistical analysis. The experimental setup employs a burner with four circularly arranged nozzles. Six different volumetric fuel flows were employed, and flame images were captured from three different visualization planes utilizing a three high-definition camera array, a thermal imaging camera and an image-processing algorithm. The flame height was indirectly measured using pixel quantification and conversion through a reference length. Although the fuel flow was the most significant factor, the visualization plane and the image source were also found to be particularly relevant, since certain flame features were only perceivable depending on the approach. The measurements were compared to different existing theoretical correlations, yielding an overall adjustment ranging from 3.25 to 3.97cm. The present methodology yields an overall statistical tolerance of 1.27 cm and an expanded uncertainty of 0.599 cm. Furthermore, the thermal imaging has revealed a consistent difference in the overall luminous observable flame of 2.54 cm. For this particular burner configuration, correlations were derived by statistical modelling, which explain the flame height fluctuations with an average setting of 97.23%.

This paper presents a flame-height correlation for laminar to transition-to-turbulent regime diffusion flames. Flame-height measurements are obtained by means of numerical and experimental studies in which three high definition cameras were employed to take frontal, lateral and 45{\deg} angled images simultaneously. The images were analysed using an image-processing algorithm to determine the flame-height through indirect measurement. To locate an overall chemical-flame-length, numerical simulations were conducted with the unsteady Reynolds-Averaged Navier-Stokes technique. The eddy-dissipation model was also implemented to calculate chemical reaction rate. The experiments show that this proposed correlation has an adjustment variation of luminous flame-height for the laminar regime of 16.9%, which indicates that, without the use of the intermittent buoyant flame-height correlation, it globally best represents the flame-height in this regime. For the laminar and transition-to-turbulence regime the adjustment variations are 5.54% compared to the most accepted flame-height correlations, thus providing an acceptably good fitting. The numerical results show that the proposed range for the chemical-flame-length is located between the luminous and flickering flame zone compared to the experimental flame images. These results agree with the chemical length zone reported in the literature. Therefore, the correlation can be used for laminar and transition-to-turbulent combustion regimes.

Background: Resonance scattering has been extensively used to study the structure of exotic, neutron-deficient nuclei. Extension of the resonance scattering technique to neutron-rich nuclei was suggested more than 20 years ago. This development is based on the isospin conservation law. In spite of broad field of the application, it has never gained a wide-spread acceptance. Purpose: To benchmark the experimental approach to study the structure of exotic neutron-rich nuclei through resonance scattering on a proton target. Method: The excitation function for p+8Li resonance scattering is measured using a thick target by recording coincidence between light and heavy recoils, populating T=3/2 isobaric analog states (IAS) in 9Be. Results: A good fit of the 8Li(p,p)8Li resonance elastic scattering excitation function was obtained using previously tentatively known 5/2- T=3/2 state at 18.65 MeV in 9Be and a new broad T=3/2 s-wave state - the 5/2+ at 18.5 MeV. These results fit the expected iso-mirror properties for the T=3/2 A=9 iso-quartet. Conclusions: Our analysis confirmed isospin as a good quantum number for the investigated highly excited T=3/2 states and demonstrated that studying the structure of neutron-rich exotic nuclei through IAS is a promising approach., Comment: 7 pages, 4 figures, 1 table, submitted to Physical Review C

The crystal growth and the structural, transport and magnetic properties of the magnetically frustrated YbMn$_2$Sb$_2$ single crystals are reported. The crystals show a trigonal symmetry (space group $P\bar{3}m1$), where corrugated honeycomb layers of MnSb are separated by Yb atoms. No structural phase transition was observed down to 22~K. The resistivity measurements show a predominantly insulating behavior. The combined resistivity, dc susceptibility and heat capacity measurements confirm successive transitions at 230~K, 116~K and 27~K, being the transition at $T_N$=116~K due to the Mn$^{+2}$ lattice antiferromagnetic ordering. Muon spin rotation experiments ($\mu$SR) reveal a more complicated scenario, with temperature dependence of the magnetic volume fraction reflecting short range and long range magnetic order, and a strongly disordered magnetic ground state. The role of spin-lattice coupling and its relationship with exchange interactions between Mn moments are discussed as possible cause of the complex magnetic behavior observed.

The series of intermetallic compounds $R$NiSi$_3$ ($R$ = rare earth) shows interesting magnetic properties evolving with $R$ and metamagnetic transitions under applied magnetic field for some of the compounds. The microscopic magnetic structures must be determined to rationalize such rich behavior. Here, resonant x-ray magnetic diffraction experiments are performed on single crystals of GdNiSi$_{3}$ and TbNiSi$_{3}$ at zero field. The primitive magnetic unit cell matches the chemical cell below the N\'eel temperatures $T_{N}$ = 22.2 and 33.2 K, respectively. The magnetic structure is determined to be the same for both compounds (magnetic space group $Cmmm'$). It features ferromagnetic {\it ac} planes that are stacked in an antiferromagnetic $+-+-$ pattern, with the rare-earth magnetic moments pointing along the $\vec{a}$ direction, which contrasts with the $+--+$ stacking and moment direction along the $\vec{b}$ axis previously reported for YbNiSi$_3$. This indicates a sign reversal of the coupling constant between second-neighbor $R$ planes as $R$ is varied from Gd and Tb to Yb. The long {\it b} lattice parameter of GdNiSi$_{3}$ and TbNiSi$_{3}$ shows a magnetoelastic expansion upon cooling below $T_N$, pointing to the conclusion that the $+-+-$ stacking is stabilized under lattice expansion. A competition between distinct magnetic stacking patterns with similar exchange energies tuned by the size of $R$ sets the stage for the magnetic ground state instability observed along this series.

New experimental data for the $^{38}$Ar($\alpha$,n)$^{41}$Ca and $^{38}$Ar($\alpha$,p)$^{41}$K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly-magic $^{40}$Ca despite of their relatively low level densities. The present study investigates the sensitivities and finds that the $\alpha$-nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of ($\alpha$,n) and ($\alpha$,p) reactions in the statistical model. Furthermore, the width fluctuation correction plays an essential role in the peculiar case of $^{38}$Ar. The best-fit parameters from $^{38}$Ar are applied to the mirror nucleus $^{38}$Ca and the neighboring $^{36}$Ar and $^{40}$Ar nuclei. For $^{38}$Ca this results in an astrophysical reaction rate of the $^{38}$Ca($\alpha$,p)$^{41}$Sc reaction which has a flatter temperature dependence compared to all previous calculations. For $^{40}$Ar a better reproduction of $^{40}$Ar($\alpha$,p)$^{43}$K data from literature is obtained. The disagreement between calculation and an early experimental data point for the $^{36}$Ar($\alpha$,p)$^{39}$K reaction persists., Comment: 14 pages, 10 figures; Phys. Rev. C, accepted for publication

The $^{36}$Ar$(n,\gamma)^{37}$Ar ($t_{1/2}$ = 35 d) and $^{38}$Ar$(n,\gamma)^{39}$Ar (269 y) reactions were studied for the first time with a quasi-Maxwellian ($kT \sim 47$ keV) neutron flux for Maxwellian Average Cross Section (MACS) measurements at stellar energies. Gas samples were irradiated at the high-intensity Soreq applied research accelerator facility-liquid-lithium target neutron source and the $^{37}$Ar/$^{36}$Ar and $^{39}$Ar/$^{38}$Ar ratios in the activated samples were determined by accelerator mass spectrometry at the ATLAS facility (Argonne National Laboratory). The $^{37}$Ar activity was also measured by low-level counting at the University of Bern. Experimental MACS of $^{36}$Ar and $^{38}$Ar, corrected to the standard 30 keV thermal energy, are 1.9(3) mb and 1.3(2) mb, respectively, differing from the theoretical and evaluated values published to date by up to an order of magnitude. The neutron capture cross sections of $^{36,38}$Ar are relevant to the stellar nucleosynthesis of light neutron-rich nuclides; the two experimental values are shown to affect the calculated mass fraction of nuclides in the region A=36-48 during the weak $s$-process. The new production cross sections have implications also for the use of $^{37}$Ar and $^{39}$Ar as environmental tracers in the atmosphere and hydrosphere., Comment: 18 pages + Supp. Mat. (13 pages) Accepted for publication in Phys. Rev. Lett

A beam containing a substantial component of both the $J^{\pi}=5^+$, $T_{1/2}=162$ ns isomeric state of $^{18}$F and its $1^+$, 109.77-min ground state has been utilized to study members of the ground-state rotational band in $^{19}$F through the neutron transfer reaction $(d$,$p)$ in inverse kinematics. The resulting spectroscopic strengths confirm the single-particle nature of the 13/2$^+$ band-terminating state. The agreement between shell-model calculations, using an interaction constructed within the $sd$ shell, and our experimental results reinforces the idea of a single-particle/collective duality in the descriptions of the structure of atomic nuclei.

Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities, so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 95%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. The usual measures of turbulence levels, such as the Reynolds number (Re) or shear stresses, do not account for the subsequent relaminarization. Instead an amplification mechanism measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI) -- a relative of the standard MRI -- in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones., Comment: 26 pages, 9 figures, accepted for publication in New Journal of Physics

Temperature dependent magnetization, muon spin rotation and $^{57}$Fe M\"ossbauer spectroscopy experiments performed on crystals of intermetallic FeGa$_{3-y}$Ge$_{y}$ ($y=0.11,0.14,0.17,0.22,0.27$, $0.29,0.32$) are reported. Whereas at $y=0.11$ even a sensitive magnetic microprobe such as $\mu$SR does not detect magnetism, all other samples display weak ferromagnetism with a magnetic moment of up to 0.22 $\mu_B$ per Fe atom. As a function of doping and of temperature a crossover from short range to long range magnetic order is observed, characterized by a broadly distributed spontaneous internal field. However, the $y=0.14$ and $y=0.17$ remain in the short range ordered state down to the lowest investigated temperature. The transition from short range to long range order appears to be accompanied by a change of the character of the spin fluctuations, which exhibit spin wave excitations signature in the LRO part of the phase diagram. M\"ossbauer spectroscopy for $y=0.27$ and 0.32 indicates that the internal field lies in the plane perpendicular to the crystallographic $c$ axis. The field distribution and its evolution with doping suggest that the details of the Fe magnetic moment formation and the consequent magnetic state are determined not only by the dopant concentration but also by the way the replacement of the Ga atoms surrounding the Fe is accomplished.