Measurement and analysis of nuclear γ -ray production cross sections in proton interactions with Mg, Si and Fe nuclei abundant in astrophysical sites over the incident energy range E=30−66 MeV
W. Yahia-Cherif, S. Ouichaoui, J. Kiener, E.A. Lawrie, J.J. Lawrie, V. Tatischeff, A. Belhout, D. Moussa, P. Papka, H. Benhabiles, T.D. Bucher, A. Chafa, J.L. Conradie, S. Damache, M. Debabi, I. Deloncle, J.L. Easton, C. Hamadache, F. Hammache, P. Jones, B.V. Kheswa, N.A. Khumalo, T. Lamula, S.N.T. Majola, J. Ndayishimye, D. Negi, S.P. Noncolela, N. de Séréville, J.F. Sharpey-Schafer, O. Shirinda, M. Wiedeking, S. Wyngaardt
aa r X i v : . [ nu c l - e x ] J a n Measurement and analysis of nuclear γ -ray production cross sections in protoninteractions with Mg, Si and Fe nuclei abundant in astrophysical sites over theincident energy range E = 30 − MeV.
W. Yahia-Cherif, ∗ S. Ouichaoui, † J. Kiener, E.A. Lawrie,
3, 4
J.J. Lawrie, V. Tatischeff, A.Belhout, D. Moussa, P. Papka,
3, 5
H. Benhabiles, T.D. Bucher,
3, 5
A. Chafa, J.L. Conradie, S.Damache, M. Debabi, I. Deloncle, J.L. Easton,
3, 4
C. Hamadache, F. Hammache, P. Jones, B.V.Kheswa,
3, 5
N.A. Khumalo, T. Lamula, S.N.T. Majola,
3, 9, 10
J. Ndayishimye,
3, 5
D. Negi,
3, 11
S.P.Noncolela,
3, 4
N. de S´er´eville, J.F. Sharpey-Schafer, O. Shirinda,
3, 5
M. Wiedeking, and S. Wyngaardt University of Sciences and Technology Houari Boumedienne (USTHB),Faculty of Physics, P.O. Box 32, EL Alia, 16111 Bab Ezzouar, Algiers, Algeria Centre de Sciences Nucl´eaires et de Sciences de la Mati`ere (CSNSM),CNRS-IN2P3 et Universit´e de Paris-Sud, 91405 Orsay Campus, France iThemba LABS, National Research Foundation, P.O. Box 722, Somerset West 7129, South Africa Department of Physics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa Department of Physics, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa Universit´e M’Hamed Bougara, Institut de G´enie Electrique et Electronique, 35 000 Boumerd´es, Algeria CRNA, 02 Bd. Frantz Fanon, B.P. 399 Alger-gare, Algiers, Algeria Institut de Physique Nucl´eaire (IPN), CNRS-IN2P3 et Universit´e Paris-Sud, 91405 Orsay Campus, France Department of Physics, University of Cape Town,Private Bag X3, 7701 Rondebosch, South Africa Department of Physics, University of Johannesburg,P.O. Box 524, Auckland Park 2006, South Africa Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai 400005, India University of Stellenbosch, Private Bag X1, 7602 Matieland, South Africa
Gamma-ray production cross section excitation functions have been measured for 30, 42, 54 and66 MeV proton beams accelerated onto targets of astrophysical interest, nat
C, C + O (Mylar), nat
Mg, nat
Si and Fe, at the Sector Separated Cyclotron (SSC) of iThemba LABS (near Cape Town, SouthAfrica). The AFRODITE array equipped with 8 Compton suppressed HPGe clover detectors wasused to record γ -ray data. For known, intense γ -ray lines the previously reported experimental datameasured up to E p ≃
25 MeV at the Washington and Orsay tandem accelerators were extendedto higher proton energies. Our experimental data for the last 3 targets are reported here anddiscussed with respect to previous data and the Murphy et al. compilation [ApJS 183, 142 (2009)],as well as to predictions of the nuclear reaction code TALYS. The overall agreement between theoryand experiment obtained in first-approach calculations using default input parameters of TALYShas been appreciably improved by using modified optical model potential (OMP), deformation,and level density parameters. The OMP parameters have been extracted from theoretical fits toavailable experimental elastic/inelastic nucleon scattering angular distribution data by means of thecoupled-channels reaction code OPTMAN. Experimental data for several new γ -ray lines are alsoreported and discussed. The astrophysical implications of our results are emphasised. PACS numbers: 23.20.Lv γ ;24.10.-i ; 24.10.Eq ; 25.40.Ep; 96.60.qe ; 96.50.XyKeywords: Nuclear reactions, clover detectors, γ -ray production cross sections, TALYS code calculations,optical model potential, astrophysical implications. I. INTRODUCTION
Gamma astronomy uses γ − ray lines produced in inter-actions of highly accelerated charged particles in astro-physical sites as a tool for probing non-thermal processesin the Universe [1, 2]. For example, in strong solar flares(SFs), electrons and ions (protons, He, He and heavierions) are accelerated to energies of several hundreds MeV.Their interactions with abundant nuclei in the solar at-mosphere result in complex γ − ray emission spectra con- ∗ escafl[email protected] † [email protected], [email protected] sisting of several components [3] including narrow, broad,and non-resolved weak lines.The broad component of γ − ray emission spectra fromSFs results from the interactions of accelerated heavyions on hydrogen and helium nuclei and is subject tolarge Doppler effects making its analysis rather compli-cated. In contrast, the narrow γ − ray line component,primarily generated in nuclear reactions induced by ac-celerated protons and α − particles on abundant heaviernuclei ( C, N, O, Ne, Mg, Si and Fe), isless affected by Doppler line shifts and broadenings. Athorough analysis of the intensities and shapes of γ − raylines [4] might reveal the properties of particle distribu-tions that are related to the particle acceleration mecha-nism and to the magneto-hydrodynamic structure of theastrophysical, ambient medium [5, 6]. It might also pro-vide valuable information on the properties (density, tem-perature, ambient chemical elemental composition, etc.)of the emitting astrophysical sites (Sun, stars).On the other hand, similar complex γ − ray spectra in-volving a large component of both narrow and broad γ − ray lines are generated in the interactions of low-energy cosmic rays (LECRs, of kinetic energies, E c . − ) with abundant nuclei in the interstellarmedium (ISM) [7]. Strong γ − ray lines produced in theISM are emitted directly by the excited nuclei and/or bynuclear reaction products following fusion-evaporation,direct, charge-exchange or pre-equilibrium processes in-duced by energetic protons and α − particles on these nu-clei.Among the strongest γ − ray lines are the line at4439 keV from the decay of the 2 + first excited stateof C, the line at E γ = 6129 keV emitted by the 3 − second excited state of O, and the lines of N, Ne, Mg, Si and Fe at energies of E γ = 1635, 1634, 1369,1779 and 847 keV, respectively. All these strong, main γ − ray lines are emitted in transitions from the first ex-cited states of abundant nuclei while weaker lines, resultfrom the deexcitation of higher-lying nuclear states.To understand the observed γ − ray spectra from astro-physical sites, the interaction processes at work in theseenvironments requires the knowledge of γ − ray line pro-duction cross sections over a wide energy range of theaccelerated particles, extending from reaction thresholdsup to several hundreds of MeV. Gamma-ray line produc-tion cross sections for the strong lines at E γ = 4 .
438 MeVand 6 .
129 MeV of C and O are available [7] up to E p = 85 MeV. Systematic γ − ray cross section measure-ments for the strongest lines have been carried out [8–10]at the Washington university tandem accelerator. Theyhave later been extended ([11, 12] and Refs therein) tomoderately strong lines at the 14-MV tandem accelera-tor of Orsay. However, the particle energy range exploredin those experiments was limited to E p <
25 MeV and E α <
40 MeV, respectively. Production cross sectionsfor some lines have also been measured ([13] and Refstherein) at cyclotron facilities for higher particle energies(up to E p = 50 MeV and E α = 40 MeV). In contrast, ex-perimental data for a large number of other, less intenselines covering the lowest proton energy range of astro-physical interest are scarce or even lacking. A databaseof γ − ray line cross section excitation functions has beenestablished four decades ago by Ramaty et al. [14] andwas later successively updated by Kozlovsky et al. [15](in 2002) and by Murphy et al. [16] (2009). This compi-lation reports cross section data for γ − ray lines producedin proton and α − particle induced reactions on target nu-clei from He to Fe for particle incident energies rang-ing from reaction thresholds up to several hundred MeV,and also in He + ion induced reactions. Predicted trendsfor numerous weak lines over the high energy region notcovered by experiment are exclusively based on TALYS code [17] extrapolations. Conversely, existing experimen-tal cross section data can be used to check and improvethe predictions of nuclear reaction theoretical models.More recently, measurements of γ − ray line cross sec-tions have been carried out [18, 19] at the Orsay tan-dem accelerator for reactions induced by swift protonsand α − particles on N, O, Ne, and Si targets over theincident energy range extending up to 26 and 39 MeV,respectively. The measured cross section data completedearlier data sets taken at the same facility [11, 12, 20, 21]for lower particle energies. However, the experimental γ − ray production cross sections remain absent for higherenergies.During particle-nucleus collisions various reactionmechanisms (compound nucleus formation, direct reac-tions, pre-equilibrium emission, etc.) occur with differ-ent probabilities depending on the projectile energy, theinteraction time and the structure of the nuclear reac-tion partners. They should be quantitatively taken intoaccount in calculations by nuclear reaction codes likeTALYS [17] or EMPIRE II [22]. Calculations performedby members of our group using these codes assumingbuilt-in default OMP and nuclear level structure param-eters have led to γ − ray line production cross sections sig-nificantly lower than the experimental values for particleenergies above 20 −
30 MeV. However, the agreements be-tween the calculated γ − ray line production cross sectionsand corresponding experimental data can be appreciablyimproved by using in TALYS modified nuclear level de-formation parameters instead of the built-in default onesas shown in Ref. [18, 19], e.g., for the N, Ne or Sinuclei. Furthermore, these calculations revealed the pres-ence of large structures at higher particle energies whereno experimental data are available.Consequently, measurements of γ − ray line productioncross sections for projectile energies of E >
30 MeV arenecessary. Such experimental data are of crucial impor-tance for understanding the nuclear interaction processestaking place in astrophysical sites and for reliably adjust-ing theoretical model parameters. Furthermore, thesedata are of great interest for various applications suchas proton radiotherapy [23], non-destructive analysis ofarcheaological materials [24], etc. We aim to expand theexisting cross section database [16], to check and improvethe predictions of modern nuclear reaction codes [17, 22],and to simulate the nuclear collisions at work in SFsand the ISM in by modelling γ − ray emission fluxes fromthese sites [25–27]. In this context, we have undertaken acomprehensive experimental program for measuring nu-clear γ − ray line production cross sections for protonsand alpha-particles at energies E lab = 30 −
200 MeV, onvarious target nuclei known to be abundant in the solaratmosphere and in the ISM.In the present paper, we report and discuss our re-sults obtained in an experiment carried out at the SSCfacility of iThemba LABS for 30 −
66 MeV proton beamsinteracting with Mg, Si, and Fe target nuclei.In Sections II and III we describe the experiment andthe data analysis, respectively. The experimental resultsare reported and discussed in Section IV, where thecross section excitation functions for known, main γ − raylines are compared to previous counterparts measured atproton energies, E p <
30 MeV [8, 11–13, 18, 19]. Resultsfor new lines, measured for the first time in this work, arealso reported in this section, where present and previousexperimental cross section data are compared to theMurphy et al. database [16] and to TALYS calculationsin Section V. An astrophysical application of γ − rayline cross sections is presented in Section VI. Finally, asummary and conclusion is provided in Section VII.We supply in the Appendix the procedure used for ex-tracting, within the framework of the coupled-channelsnuclear reaction approach, improved OMP and nuclearlevel deformation parameters that prove to be more ap-propriate for γ -ray line production cross section calcula-tions than the default input data of TALYS. In addition,we provide information on the experimental angular dis-tribution data for nucleon scattering off the studied Mg,Si and Fe target nuclei, taken from the literature, thatwas used to derive new OMP and nuclear level structureparameters. II. EXPERIMENTAL SET UP AND METHODA. Beam, targets, and detection system
The experiment was carried out at the SSC facility ofiThemba LABS.Proton beams of incident energies E p = 30, 42, 54 and66 MeV and current intensity, I = 3 − . ∼ ∼ µ C.Only solid targets (natural or isotopically enriched)of C, Mylar ( C + O), Mg, Al, Si, Ca and Fe ele-ments prepared mainly at iThemba LABS (some of themwere imported from Orsay) were used in the experiment.The Mylar foils were 5 µ m thick while the thicknesses ofthe other explored targets varied in the range, 6 − . − ; the isotopic compositions and thicknesses ofthe nat Mg, Mg, nat
Si, nat
Fe and Fe targets for whichresults are presented in this paper are reported in Ta-ble I. The thickness of each target was then converted inunits of nuclei · cm − The targets were mounted onto small rectangular Alframes and placed on a ladder allowing for 4 target po-sitions: one for a beam viewer, one for an empty frameand two for frames with targets. The viewer consistedof a rectangular-shaped, 3 mm thick fluorescent Al O layer with a 3 mm diameter hole in its centre. During the experiment the proton beam spot was reduced downto less than 3 mm diameter by focusing it through thehole in the Al O viewer and was frequently checked andfocused after target changes. Improved beam tuning wasachieved by minimizing the γ count rate from an emptytarget frame.The detection of γ rays was made by means of theAFRODITE array [28–30] that consisted of 8 Comptonsuppressed clover detectors [31] of the EUROGAM phaseII type. The clovers were placed in a fixed geometry with4 detectors at 90 ◦ and 4 at 135 ◦ relative to the incidentbeam direction.With a distance between the target and the front faceof each clover of 17 . ± ◦ relative to the clover centre. Hence,a total of 32 HPGe crystals were used, which enabled usto measure γ − ray line energy spectra at four detectionangles, i.e., θ lab = 85 ◦ , 95 ◦ , 130 ◦ and 140 ◦ . The wholedetection system subtended a solid angle of ∼
11% of 4 π . B. Measurement of γ − ray energy spectra The γ − ray energy spectra from the individual HPGecrystals were recorded using a digital data acquisitionsystem based on XIA modules of DGF Pixie −
16 type.At each energy and for each target, data were acquireduntil a statistical error of better than 5% in the less in-tense peaks of the γ − ray spectrum in a single clovercrystal was reached. Irradiation times with the targetexposed to the proton beam were typically 1 hour. Aftereach target irradiation spectra from activation of the tar-get and the surrounding material were recorded for halfan hour without beam but with the irradiated target inplace. Thereafter beam-induced γ − ray background, withan empty target frame in place, was measured for half anhour. Finally, room background runs without beam andwithout a target in place were frequently measured forlonger times of ∼ . γ − ray lines with energies of at least upto E γ = 8 MeV was expected in the measured energyspectra. The energy calibration of the individual HPGecrystals was performed by means of standard radioactivesources of Cs, Co and
Eu covering the low γ − rayrange up to 1408 keV, while the prominent line of Oat E γ = 6129 keV (and associated escape lines at 5618and 5107 keV) produced in the O(p, p ′ γ ) reaction froma Mylar target was used at high energies. The relativeenergy resolution ∆ E γ /E γ , determined at E γ = 1332 keVwas less than 0 . γ − ray energies of up to E γ ∼
10 MeV, by means ofMonte-Carlo simulations of the detection system includ-ing a detailed description of the target chamber and allthe clover detectors using GEANT4 [32] (see section III).
Target Thickness Composition(mg cm − ) (This Work) Ref. [8] Ref. [13] Ref. [11] Ref. [18, 19]Mg 9.80 ± Mg ( > Mg ( > ± ± ± Fe ( > Fe ( > ± nat Mg = Mg(78.99%)+ Mg(10%) + Mg(11.01%), nat
Si = Si(92.22%) + Si(4.68%) + Si(3.09%), nat
Fe = Fe(5.85%) + Fe(91.75%) + Fe(2.12%) + Fe(0.28%). p + nat
Mg for E protons = 42 MeV, θ lab = 85 ◦
100 200 300 400 500 600 700 800 900 1000 C oun t s pe r c hanne l ( e + e -) M g N a N a N a N e M g A l N a M g + M g N a G e * G e * F e * M g * A l * + G e * C oun t s pe r c hanne l M g N e N e M g K * C oun t s pe r c hanne l N a M g + M g M g N e C oun t s pe r c hanne l O O * O * -ray energy (keV) γ FIG. 1. Calibrated γ -ray spectra produced by the scattering of 42 MeV protons off the nat Mg target. The blue histogramscorrespond to the raw spectrum of one clover crystal without background suppressions, while the red one is backgroundsubtracted.
Throughout the experiment, care was taken to mini-mize the neutron and γ − ray backgrounds. All the exper-imental runs were performed with relatively low protonbeam intensities, I ≤ − ± ∼ γ − rayspectra from a single HPGe crystal located at θ lab =85 ◦ , obtained in the irradiation of the nat Mg target with42 MeV protons. The total spectrum is shown in blue,while the spectrum after subtraction of the normalisedbeam-related background is depicted in red.
III. DATA ANALYSIS, DETERMINATION OF γ − RAY CROSS SECTIONS
Since only relatively thick solid targets were used inthe experiment (see Table I), the γ − ray lines from sometargets, for instance the Fe targets, were not found to bedramatically affected by Doppler shifts and broadenings,although for other targets, for instance Mg and Si targets,the measured γ − ray spectra were rather complex.In the data analysis the clover crystals were treatedas individual detectors and, in addition to the normalCompton suppression from the BGO suppression shield,coincident events between elements in the same cloverwere rejected. The background-corrected spectra wereobtained by subtracting the beam related background,recorded with beam on an empty target frame, after nor-malising to the same accumulated charge. The numbersof counts in the observed γ − ray peaks were extractedusing the ROOT program [33] and/or the GF3 programincluded in the RADWARE package [34]. In our analy-sis we fitted the observed γ − ray peaks with symmetricGaussian shapes on a linear background. For most of theclover detectors the resulting uncertainties in the identi-fied γ − ray energies were less than 0 . γ rays of interest was performed similarly to thatin Ref. [11, 12]. For well-defined, symmetric peaks thecorresponding areas were first extracted from Gaussiandistribution fits. For each peak, a second estimation ofits area was performed by summation over a region ofinterest after subtraction of a linear background. Thefinal peak area was determined as the average of thetwo estimations and the systematic error as the differ-ence. The total uncertainty in the peak area consistedof the systematic error, the statistical error in the peakarea and the error from the fitting procedure. For mostanalysed γ − ray lines, the statistical error was lower than2%, while the systematic error varied from 1% for intensepeaks (such as, e.g., the 1408 keV peak) to 9% (e.g., the1303 keV peak).The experimental differential cross sections for theanalysed γ − ray lines were determined from values ofthe target thickness, the total beam charge deposited inthe Faraday-cup, the extracted peak area and the ab-solute detection efficiency, ǫ ( E γ , θ ). We assumed that θ lab ≈ θ c.m. since one deals with reactions induced bylight projectiles on appreciably heavier target nuclei. Theefficiency as function of energy was derived from a fit tothe experimental data from the radioactive sources, andthe normalised data from a GEANT4 simulation usingthe following expression [34] ǫ ( E γ , θ ) = e [( A + BX ) − H +( D + EY + F Y + GY ) − H ] − /H , (1)where X = log ( E γ / Y = log ( E γ / W ( θ ) = l max X l =0 a l Q l P l ( cos ( θ )) , (2)were fitted to the experimental angular distribution data.In this expression, the summation extends only over in-teger l- values with l max taking on twice the γ − ray mul-tipolarity and the Q l are energy-dependent geometricalattenuation coefficients, as described by Rose [35] (seealso Ref. [36]). Except for the 6 .
129 MeV line of O, themultipolarity of the γ − ray lines of interest in this workis at most 2, which then fixes, l max ≤
4, in the aboveexpansion. The Q l -values were specifically calculated forthe AFRODITE detection array via our GEANT4 [32]simulations; they were found to remain almost constantover the photon energy range, E γ = 0 . −
10 MeV, i.e., Q l ∼ . − − γ − ray lines were directly derived from the a coefficients of eq. (2), using the relation, σ int = 4 πa .The corresponding results are reported and discussedin the following section, where additional information onthe analysis of the γ − ray energy spectra is provided. IV. EXPERIMENTAL RESULTS ANDDISCUSSIONA. γ − ray energy spectra and transition properties As can be seen in Figure 1, various more or less promi-nent γ − ray lines, whose origin is indicated in this figure,are observed below and above the intense line at 511 keVfrom the ( e + , e − ) pair annihilation. One notes, e.g., thepresence of asymmetric peaks for lines resulting from theinelasting scattering of secondary neutrons off the iso-topic constituents of the HPGe crystals [37, 38], i.e., offthe Ge isotope (line peak at E γ = 595 .
85 keV) and off Ge (peaks at E γ = 689 . . E γ = 198 .
39 keVemitted in the Ge(n, γ ) m Ge radiative neutron cap-ture reaction [37]. These neutron peaks affected the mea-sured γ − ray energy spectra from all the explored targets.One can also observe the line at E γ = 846 .
76 keV from the Fe(p,p ′ γ ) inelastic proton scattering and the 843 .
76 keVline of Al, produced both in the Al(p, p ′ γ ) inelasticproton scattering and the β -decay of Mg following the Al(n, p) Mg ∗ charge exchange reaction. These twolines result from reactions induced by scattered protonsand secondary neutrons on the aluminium of the targetchamber and the beam pipes. In the high energy part ofthe energy spectrum the characteristic peak associatedwith the 6 .
129 MeV line of O appears (see Figure 1),likely resulting from the energetically possible Mg(p,p2 αγ ) O reaction. The properties (transition energy,emitting isotope, corresponding nuclear levels with theirspin-parity assignements, branching ratio) of the γ − raylines of interest identified in the collected energy spectrain the proton irradiations of the Mg, Si and Fe targetsare listed in Table II. B. Absolute γ − ray efficiencies Figure 2 reports an example of the experiment abso-lute efficiency data measured with the standard radioac-tive sources and GEANT4-simulated values, normalisedto the former ones, for a single HPGe crystal. The fittedcurve to these two data sets using eq. (1) is also shown.The efficiency of the whole array in the addback modeamounts to 1 .
6% at E γ = 1 .
33 MeV , but one expectsit to be substantially lower in single-crystal mode. In-deed, the γ − ray full absorption peak efficiency for asingle Ge crystal was found to amount to ∼ .
03% at E γ = 1 .
33 MeV and to ∼ . E γ = 8 MeV onaverage (see Figure 2) which suggests a total efficiency of0 .
96% at E γ = 1 .
33 MeV for the full array. The relativeuncertainty in the detection efficiency was estimated tobe lower than 5% over the whole γ − ray energy domainexplored. C. γ − ray angular distributions The measured angular distributions of the observed γ rays, produced mainly in (p, p ′ γ ) inelastic proton scat-tering off the Mg, Si and Fe targets, are dominated by E M E
2) transitions (see Table II). Illustrativeexamples of experimental angular distributions for somelines induced by 30 and 42 MeV protons are shown inFigure 3, together with the associated least-squares Leg-endre polynomial best-fit curves generated according toequation (2).
Gamma ray energy (keV) × E ff i c i en cy FIG. 2. Absolute γ − ray efficiencies for a single HPGe crys-tal. The green data points correspond to experimental valuesmeasured using standard radioactive sources of Co,
Csand
Eu. The black data points represent the results ob-tained via GEANT4 simulations at various γ − ray energiesthat were normalised to experimental data. The red solidline is the result of the fit of the efficiency function of equa-tion (1) [34] to the experimental data and to the normalisedGEANT4-simulated values. D. Integrated γ − ray production cross sectionresults The results obtained in this work are reported in Fig-ures 4, 5 and 6 where they are compared to previous ex-perimental data from Refs. [8, 11–13, 18, 19] and to thesemi-empirical compilation of Murphy et al. [16] when σ ( E p ) extrapolations from the latter database are pro-posed. We have thus determined production cross sec-tions for a total number of 41 γ − ray lines produced inproton induced reactions on the nat Mg, nat
Si and Fetargets with 30, 42, 54 and 66 MeV proton beams, andon the Mg target for 30 and 66 MeV protons.As pointed out in Ref. [11, 12], previous γ − ray pro-duction cross section measurements have been performedfor at most three excited states in inelastic particle scat-tering or in residual nuclei following the removal of oneor more nucleons from the target nucleus. The Orsaynuclear astrophysics group in [11, 12] and [18, 19] hasextracted a large number of production cross sections for γ rays generated in proton and α − particle induced reac-tions on C, O, Mg, nat
Si and nat
Fe targets. Theirresults for incident protons accelerated up to 25 MeV onthe last three targets are plotted together with our exper-imental data in Figures 4, 5 and 6. To allow a comparisonof the cross section data sets from various experiments,data obtained with targets of different isotopic compo-sitions (see Table I) were normalised: for Fe nucleus,data from this work and Refs. [8] were normalised to thenatural isotopic composition of Fe, and results for Mgfrom this work as well as Refs. [8, 11, 12] were normalisedto the natural abundance of this isotope.
Main γ ray Intruder emitting nucleus E i E f J πi J πf Mλ Branching ratiokeV keV keV keV %Magnesium425.8 Al 425.8 g.s. +1 +1 M3 Mg 1808.74 g.s. +1 +1 E2 Mg 585.05 g.s.
12 +1 52 +1 E2 Na 583.05 g.s. +1 +1 E2 Mg 974.76 585.05
32 +1 12 +1
M1+E2 (81) Mg 974.76 g.s.
32 +1 52 +1
M1+E2 (81) Mg 1368.67 g.s. +1 +1 E2 Na 1951.8 583.05 2 +1 +1 Mg 4122.89 1368.67 4 +1 +1 E2 Mg 4238.24 g.s. +2 +1 E2 (47) Mg 450.71 g.s.
52 +1 32 +1
M1+E2 Na 472.21 g.s. +1 +1 M3 Na 439.99 g.s.
52 +1 32 +1
M1+E2 Na 331.90 g.s.
52 +1 32 +1
M1+E2 Ne 350.73 g.s.
52 +1 32 +1
M1+E2 Si 1273.39 g.s.
32 +1 12 +1
M1+E2 Si 1779.03 g.s. +1 +1 E2 Si 4617.86 1778.97 4 +1 +1 E2 Si 780.9 g.s.
12 +1 52 +1 E2 Si 957.3 g.s.
32 +1 52 +1
M1+E2 (21) Al 843.76 g.s.
12 +1 52 +1 E2 Al 416.85 g.s. +1 +1 [E2] Mg 585.05 g.s.
12 +1 52 +1 E2 Na 583.05 g.s. +1 +1 E2 Mg 974.76 585.05
32 +1 12 +1
M1+E2 (81) Mg 1368.67 g.s. +1 +1 E2 Na 1951.8 583.05 2 +1 +1 Mg 450.71 g.s.
52 +1 32 +1
M1+E2 Na 439.99 g.s.
52 +1 32 +1
M1+E2 Na 331.90 g.s.
52 +1 32 +1
M1+E2 Ne 350.73 g.s.
52 +1 32 +1
M1+E2 Fe 846.76 g.s. +1 +1 E2 Fe 2255.5 1408.45 1001238.27 Fe 2085.11 846.76 4 +1 +1 E2 (2) Fe 2657.59 846.76 2 +2 +1 M1+E2 (29) Fe 3388.55 2085.11 6 +1 +1 E2 (40) Fe 411.42 g.s. − − M1(+E2) (6) Fe 2949.2 2538.1 6 +1 +1 E2 Fe 1316.54 g.s. − − E2 (13) Fe 4683.04 3369.95 (2 + ) , + + < Fe 1408.45 g.s. − − E2 (21) Fe 1408.19 g.s. +1 +1 E2 Fe 2813.8 2539.11 − − E2 Fe 6380.9 2949.2 8 +1 +1 E2 Mn 156.29 g.s. +1 +1 M1+E2 Mn 368.22 156.29 5 +1 +1 M1 Mn 377.89 g.s. − − M1+E2 Mn 1441.15 g.s. − − E2 Cr 1434.09 g.s. +1 +1 E2 γ -ray multipolarities and branching ratios are presentedin the eighth and ninth columns respectively. D i ff e r en t i a l c r o ss - s e c t i on ( m b ) Fe (x3) nat nat
440 keV =42 MeV p E ) ° Laboratory detection angle ( D i ff e r en t i a l c r o ss - s e c t i on ( m b ) Mg (x1) =30 MeV p E FIG. 3. γ − ray angular distributions: (Top) for main linesproduced in interactions of 42 MeV protons with the nat Mg, nat
Si and Fe targets, (Bottom) for the line at E γ = 1368 keVemitted by the Mg isotope upon inelastic scattering of30 MeV protons.
One expects, in general, that the γ − ray productioncross sections should decrease smoothly as the incidentparticle energy increases beyond the low-energy regionof compound nucleus resonances since several low-energyreaction channels are then successively opened. However,this does not seem to be the case for all observed γ − raylines, as can be seen in Figures 4, 5 and 6. Below, wediscuss the obtained γ − ray production cross section re-sults with concentrating on the main γ rays following thedecay of the ground-state bands of Fe, Si and Mgisotopes. γ rays in proton reactions with Mg Production cross sections have been determined forthirteen γ -ray lines observed in proton induced reactionson the nat Mg and Mg targets, i.e., in (p, p ′ γ ) inelastic proton scattering and other binary reactions.In the nat Mg target, Mg is the most abundant isotopein comparison to Mg and Mg (see Table I). The mea-sured production cross sections in the irradiation of theMg targets are reported in Figure 4. One observes thatthe cross section values determined for 30 and 66 MeVincident protons on the isotopically enriched Mg tar-get lie slightly below those obtained from the natural Mgtarget, which is an indication of weak contributions fromreactions on the Mg and Mg isotopes leading to theproduction of Mg. Three γ − ray lines emitted by Mgwere analysed, namely the lines at E γ = 1368 . E γ = 1368 . Na), E γ = 2754 .
01 keV and E γ = 4237 .
96 keV (seeTable II for the caracteristics of the transitions). It wasnot practically possible to extract the peak area for theline at E γ = 4237 .
96 keV from the isotopically enriched Mg target due to low statistics and a very broad peakshape (see Figure 1). Particular care was given to theanalysis of these three lines due to their Doppler broad-ening and, in the case of the line at 4237 .
96 keV, to peaksplitting. A corresponding line shape calculation showedthat, due to the very short lifetime of the decaying nu-clear level and the recoil of the emitting nucleus, almostall γ rays were emitted in flight. Comparing our γ − rayproduction cross section data to previous results fromthe literature, one observes a smooth extension to higherproton energies the data of Refs. [8] and Ref. [11, 12] at E p <
30 MeV. In contrast, the cross section data reportedby Ref. [13] is significantly higher than our values.We provide in this work cross section data for the γ rays produced in the de-excitation of the first excitedstate of Mg (see Figure 4) at E γ = 585 .
03 keV, along-side two γ rays at E γ = 389 .
71 keV and 974 .
74 keV, re-sulting from the deexcitation of the second excited stateof Mg (see Table II). For the latter two lines cross sec-tions are measured for the first time. The 585 .
03 keVline overlaps with another line of very close energy at E γ = 585 .
04 keV, emitted in the de-excitation process of Na. Considering the fact that the Al compound nu-cleus decays to the ground state of Mg (with branchingratio > E γ =585 .
04 line from the Mg target to Na. In addition,the absence of lines emitted by the second excited stateof Mg from the Mg enriched target corroborates thisstatement. Previous (unpublished) experimental data forthe line at E γ = 585 .
03 keV from Ref. [11, 12] for E p <
30 MeV are reported in Figure 4, and are consistent withour cross section values measured at E p = 30 −
66 MeV.Production cross sections for the line of Mg at E γ = 1808 . E p <
27 MeV, that were obtained with aMgO target of natural isotopic composition on a thin Alfoil. But the 1808 . − − − − − − − − − ( m b ) σ C r o ss sec t i on (MeV) p Incident proton energy E
FIG. 4. Total production cross sections for γ − ray lines produced in proton reactions with the Mg (open circles) and nat
Mg(filled circles) targets (see Table II for more details and Table I for the properties of targets used in this and previous works).The experimental data are shown with full circles: in blue colour (this work), in red (Dyer et al. [8]), in green (Belhout etal. [11, 12]) and in orange (Lesko et al. [13]). The dashed-dotted curves correspond to predictions of the Murpy et al. semi-empirical compilation [16]. The results of TALYS calculations performed with default parameters are shown by grey curves;those performed with our modified OMP and level structure parameters are depicted by black curves for γ − ray lines emittedby the most abundant isotope, and by red curves for γ − ray lines from the target of natural composition. Three lines at E γ = 331 .
91, 439 .
99 and 450 .
71 keV,emitted respectively by the Na, Na and Mg isotopes(see Table II) and for which previous measurements havebeen reported in Ref. [11, 12], were analysed as well. Ascan be seen in Figure 4, our cross section data for theselines are in overall agreement with the data from Ref. [11,12] over the right hand side of the apparent bump (broadcompound resonance) at E p ∼
20 MeV, although the trend of our data goes slightly higher than theirs.Three other lines at E γ = 425 .
8, 472 .
20 and 350 .
73 keVfor which no experimental cross section data are avail-able in the literature, were observed and analysed (seeFigures 1 and 4), for which no experimental cross sec-tion data are avaible in the previous literature. Theycan be attributed to the de-excitations of the first ex-cited states of Al, Na and Ne, respectively. Con-0 − − − − − − − − − − − − − ( m b ) σ C r o ss sec t i on (MeV) p Incident proton energy E
FIG. 5. Same as in Figure 4 but for γ − ray lines produced in proton reactions with the Si targets. The same symbols are used,except that here the green circles represent the experimental data of Benhabiles et al. [18, 19]. cerning the 472 .
20 keV line, no cross section measure-ment was performed with the Mg enriched target sincethe production of Na from this target is not energeti-cally possible. The measured cross section data from the nat
Mg target come from the reactions induced by pro-tons on the Mg and Mg isotopes. The 425 . Al shows a small contribution from reactions in-duced on the less abundant isotopes of Mg. Finally, onecan easily see that the production cross section for the350 .
73 keV line of Ne is dominated (to an order of mag-nitude) at E p = 30 MeV by contributions from reactionson Mg isotopes, while for 66 MeV incident protonsthe contribution from the Mg isotope dominates. γ rays in proton reactions with Si A total of fourteen γ − ray lines have been observed inthe irradiations of the nat Si target for which we have mea-sured the production cross sections reported in Figure 5.Most of these lines were produced in binary reactions onthe , , Si isotopes (see Table II).The two main lines emitted in the deexcitation of Siare at 1778 .
97 and 2838 .
29 keV. Experimental cross sec-tion data have been reported for the 1778 .
97 keV lineby Refs. [8], [18, 19] and [13]. As can be seen in Fig-ure 5, our data are consistent with lower proton energydata from Refs. [8, 18, 19] but their values are slightly1 −
10 110 −
10 110 ( m b ) σ C r o ss sec t i on (MeV) p Incident proton energy E
FIG. 6. Same as in Figure 4 but for γ − ray lines produced in proton reactions with the Fe target. higher than the data of Ref. [13] in proportions of 23%at E p = 30 MeV and 36% at E p = 54 MeV. For the2838 .
29 keV line, the only available previous data arethose reported by Ref. [18, 19] that seem to be consis-tently extended to higher proton energies by our data.Production cross sections were also measured for the lineat E γ = 1273 . Si.We have also performed production cross section mea-surements for γ − ray lines emitted in the deexcitation ofthe Si, Al and Mg nuclei (see Table II), for whichonly Ref. [13] have reported cross section data. As canbe seen in Figure 5, an overall agreement between thetwo cross section data sets for these lines is observed. Indeed, our cross section values for the two lines of Siat E γ = 780 . . Al at843 .
76 keV, one observes a very good agreement betweenour values and the data of Ref. [13] around E p = 30 MeV,while at higher proton energies the cross sections mea-sured by these authors seem to be higher, evolving withdifferent energy dependence than our data. A γ − ray lineat E γ = 1368 .
62 keV corresponding to Mg was ob-served. As already mentioned in the case of the Mg tar-get, another line of very close energy, E γ = 1368 . Na very likely overlaps withthis line. Our experimental cross section data for thisdoublet is consistent with those reported by Ref. [13],2with moderate differences of ∼
30% and ∼
40% for pro-ton energies E p = 30 and 50 MeV, respectively.Finally, six γ − ray lines for which no previous cross sec-tion data are available in the literature, to our knowledge,were analysed. These are the lines at E γ = 416 .
85 keV of Al, 389 .
71 keV of Mg, 450 .
70 keV of Mg, 439 .
99 keVof Na and the two lines at 331 .
91 keV and 350 .
73 keVboth coming from the deexcitation of Na and Ne, re-spectively (see Table II). The measured cross sections areshown in Figure 5. γ rays in proton reactions with Fe The iron target used in the experiment was highly en-riched in Fe, to better than 99%. Production crosssections have been determined for fourteen γ − ray linesemitted from this target. The obtained experimental re-sults are reported in Figure 6. Previous cross section ex-perimental data, for the known seven lines at E γ = 411 . .
78, 1238 .
27, 1316 .
4, 1408 .
4, 1434 .
07 and 1810 .
76 keV,have been reported in Refs. [8, 11–13] and are also plottedin Figure 6 for comparison. In contrast, cross sections forthe remaining seven lines at E γ = 156 .
27, 211 .
98, 274 . .
88, 1303 .
4, 1441 . . γ − ray lines with the exception of thelines at E γ = 411 .
9, 1408 . .
07 keV for which asecond bump appears at around E p = 42 MeV.Among the first group of known lines, the three mainintense lines at E γ = 846 .
78 (2 +1 to 0 +1 ), 1238 .
27 (4 +1 to 2 +1 ) and 1810 .
76 keV (2 +2 to 2 +1 ) are produced in the Fe(p, p ′ γ ) reaction following the deexcitation of thefirst three excited states of Fe. For the first time,cross sections are measured for the line at 1303 . +1 to 4 +1 , see Table II) which sheds light on the γ -ray production cross section for the three first levelsof the g.s. band of Fe. The 846 .
78 keV line neededa careful analysis because it lies on a neutron back-ground (see Section II). In addition, the presence of twosmall peaks at E γ = 843 .
76 keV (Al background) and E γ ∼
848 keV (possibly due to the deexcitation of the5 +1 excited state of Cr to its 4 +2 excited state) had tobe considered assuming Gaussian shapes. Similarly, forthe fit of the 1238 .
27 keV γ -ray line, a small peak at E γ = 1241 . Mn isotope lo-cated at E x = 1620 .
12 keV) was added. The areas of thepeaks were extracted by considering the aforementionedfits with the RADWARE package [34]. As can be seenin Figure 6, our cross section data for these lines appearto be consistent with data measured at lower energy inRefs. [8, 11, 12]. In the case of the E γ = 846 .
78 keV and1238 .
27 keV lines there are marked differences betweenour experimental data and those of Ref. [13], the latterones being higher, by ∼
50% to ∼ ∼
30% up to ∼
70% at E p = 30 MeV and 54 MeV, respectively. Forthe E γ = 1810 .
76 keV line, our data are fairly consistentwith the previous measurements of Refs. [8, 11].Lines from the , Fe and , Mn isotopes have alsobeen observed in γ − ray energy spectra with the iron tar-get, and the production cross sections have been estab-lished.Gamma-ray production cross sections have been deter-mined for lines in , Fe produced in binary reactions onthe Fe target, namely for the E γ = 1316 . . Fe (seeTable II), and for the E γ = 3432 . +1 to 6 +1 ) linefrom Fe (see Table II). In addition, cross sections weremeasured for two doublet lines at E γ = 1408 . . Fe (see Table II). The γ rayat 1316 . E γ = 1312 . Fe(see Table II). Since no shape separation was possible dueto the Doppler broadening of both lines, their areas wereconsidered as one. Finally, our cross section data seemto describe a resonance structure which has a maximumat E p ∼
40 MeV for the doublet at E γ = 411 . E γ = 1408 keV prominent at E p = 54 MeV ( ∼ , Mn isotopes,for which no cross section measurements have been car-ried out previously to our knowledge, are presented (seeTable II). These are E γ = 156 .
27 keV and 211 .
98 keVfrom Mn, and E γ = 377 .
88 keV and 1441 . Mn.Finally, a line at E γ = 1434 .
07 keV produced in thedeexcitation of the first excited state of Cr has beenobserved and analysed. Our experimental cross section-data for this line seem to be consistent with the data ofRefs. [11–13].
E. Comparison to the Murphy et al. compilation
In this subsection our measured γ − ray line cross sec-tions are compared to the Murphy et al. database [16],which includes cross section data on about 140 intense γ − ray lines, produced in the interaction of protons and α − particles with abundant nuclei in astrophysical sites.The nuclear reaction codes TALYS [17] and EM-PIRE [22] have been used previously to calculate promptand delayed γ − ray production cross sections. These re-sults were compared to experimental data [11, 12, 18, 19]for several strong lines, emitted in proton and α − particleinduced reactions on various stable and radioactive nucleisynthesised in SFs [39].Murphy et al. [16] updated earlier databases for (p, p ′ ),( α , α ′ ), (p, x) and ( α , x) reactions and extended the exist-3ing low-energy data up to several hundred MeV/nucleonby using energy dependences obtained in TALYS calcu-lations. When available, the excitation function curvesderived by Ref. [16] are also reported in Figures 4, 5,and 6 (dashed-dotted lines).These figures show that for the majority of lines theexcitation curves from Ref. [16] have similar qualitativetrends as our experimental data. However, they over-estimate our cross sections when data from Ref. [13]are available, i.e. for E γ = 1368 .
62 keV (Mg) and E γ = 846 .
78, 1238 .
27 and 1316 . E γ = 4237 .
96, 439 .
99 and 450 .
70 keV (Mg), E γ = 2838 .
29, 843 .
76, 780 . . E γ = 411 . . V. COMPARISON TO TALYS CODEPREDICTIONS
The comparison of experimental cross sections to thosepredicted by nuclear reaction models using modern com-puter codes is crucial. The TALYS code [17] allows thecalculation of theoretical cross sections for nuclear reac-tions induced by a variety of projectiles ( γ , n, p, d, t, Heand α ) on atomic nuclei over the energy range of E lab = 1 keV up to 250 MeV, with contributions from themain nuclear reaction mechanisms (compound nucleus,direct reactions, pre-equilibrium, etc.) using built-in pa-rameter values from either phenomenological or micro-scopic models. It comprises libraries of nuclear data likemasses, level densities, discrete states, OMP, level defor-mation parameters, etc. Alternatively, one is allowed tointroduce modified nuclear data derived from an analysisof experimental data.Gamma-ray production cross sections were initiallycalculated using default parameters in TALYS [17].While the calculations reproduced the energy dependenceof the measured cross sections reasonably well for mostof the γ − ray lines, they deviated significantly in somecases. In this section, we will discuss the modificationsbrought to the TALYS source code, as well as the ad-justement of OMP and nuclear level deformation param-eters (from nucleon angular distribution analyses, see theAppendix) utilising the coupled-channels reactions codeOPTMAN [40]. The optimised OMP parameters usedin the TALYS calculations are presented in Table IIIwhile the procedure for obtaining these is described inthe Appendix. Additional adjustments of nuclear leveldensity (LD) parameters and the Fe coupling schemeare also presented and described below. The results ofthe calculations were compared with the experimentaldata from this work and Refs. [8, 11, 13, 18, 19].Over two hundred elastic and inelastic scattering angu-lar distributions of protons and neutrons on , , Mg, , , Si and , Fe have been analysed in order toextract OMP and deformation parameters. A nucleon OMP allows to better adjust the values for the Coulombcorrection, radius, and diffusivity. Theoretical fits tothe experimental data sets have been systematically per-formed using the coupled-channels reactions code OPT-MAN. Examples of elastic and inelastic proton scatteringangular distribution adjustments for Mg, Si and Feare presented in Figures 7, 8, and 9. Analysing powerstudies are out of the scope of this paper.
Nuclei , Mg Mg , Si Si , FeModels DF ASR DF ASR DFParameters V R (MeV) 50.29 50.29 51.17 51.17 50.84 λ R (MeV − ) 0.00530 0.00530 0.00557 0.00557 0.00517 W S (MeV) 7.38 7.38 8.00 8.00 7.32 WID S λ S (MeV − ) 0.00335 0.00335 0.00334 0.00334 0.00203 W V (MeV) 3.08 3.08 2.14 2.14 7.01 WID D V SO (MeV) 7.69 7.69 7.96 7.96 7.04 λ SO (MeV − ) 0.00235 0.00235 0.00350 0.00350 0.00119 W SO (MeV) -4.19 -4.19 -4.54 -4.54 -3.57 WID SO n r R /r V (fm) 1.184 1.201 1.187 1.160 1.183 r S (fm) 1.070 1.097 1.206 1.007 1.077 r SO (fm) 1.078 1.078 1.123 1.123 1.194 r C (fm) 1.294 1.294 1.234 1.234 1.375 a R /a V (fm) 0.562 0.675 0.522 0.666 0.543 a S (fm) 0.764 0.641 0.592 0.746 0.758 a SO (fm) 0.815 0.815 0.757 0.757 0.686 a C (fm) 0.257 0.257 0.179 0.179 0.241 C Coul C viso C wiso Mg Mg Mg Si Si Si Fe Fe β β -0.037 0.182 0.108 -0.056 0.001 γ (deg) 21.89 27 35.69 20.85 26.10 21.75 Table IV. Quadrupole and hexadecapole deformations, and γ -asymmetry obtained from the coupled-channels analysis ofthe inelastically scattered neutrons and protons off the nucleilisted in Table II. The value between parentheses for Mgcorresponds to the quadrupole deformation of the K π =
12 + side band with a band head at E = 585 .
045 keV.
As mentioned above, much better agreements betweenour experimental γ − ray line production cross section4 Nucleus a E sh ˜ a P shift Reference Nucleus a E sh ˜ a P shift Reference Ne 1.7866 [41] Na 1.8449 [41] Ne 2.3886 [41] Na 1.7003 0.4180 [41] Na 1.9302 [41] Mg 1.9922 [41] Mg 2.5089 [41] Mg 1.8731 0.4160 [41] Mg 1.9659 -8.500 [42] Mg 2.3630 0.671 [42] Al 2.1026 0.3902 [41] Al 2.1472 [41] Si 2.2116 0.1300 [41] Si 2.2116 -2.4670 [42] Si 1.7383 -0.930 [42] P 2.4756 [41] P 2.4079 0.3564 [41] P 2.5719 [41]
Table V. List of parameters used in the GSM. ) ° Centre-of-Masse detection angle ( D i ff e r en t i a l c r o ss s e c t i on ( b / s r) − − − − − − − − − − Mg = 49.5 MeV p E ) g.s. (x10 (x1)
2 (x0.001)
2 (x0.01) FIG. 7. Illustrative examples of results from our theoreticalanalyses of experimental angular distribution cross section-data for elastically scattered protons off Mg taken from theliterature and considered in the OPTMAN code [40] for ex-tracting new OMP and nuclear level deformation parametersused in our TALYS code calculations of γ − ray line productioncross sections. ) ° Centre-of-Masse detection angle ( D i ff e r en t i a l c r o ss s e c t i on ( b / s r) − − − − − − − − − Si = 65 MeV p E g.s. (x1) (x0.1)
2 (x0.015) FIG. 8. Same as in Figure 7 but for scattered protons off the Si target ) ° Centre-of-Masse detection angle ( D i ff e r en t i a l c r o ss s e c t i on ( b / s r) − − − − − − − − − − − Fe = 30 MeV p E = 65 MeV p E g.s. (x100)g.s. (x1) (x0.1)
2 (x0.015)
4 (x0.0001) FIG. 9. Same as in Figure 7 for scattered protons off the Fetarget. data and theoretical values calculated by means of theTALYS code were obtained when using the built-in gen-eralised superfluid model (GSM) together with experi-mental level density parameters, instead of the defaultconstant temperature + Fermi gas model (CT+FGM).For the nuclei appearing in the outgoing reaction chan-nels, available experimental data of the level density, a ,and values of the shell correction, E sh , were taken fromthe RIPL-3 database [42]. In the case of nuclei for whichno experimental data are available, values of the asymp-totic level density, ˜ a , and the pairing energy shift, P shift ,were derived from the systematics given in Ref. [41]. Allthe parameters used in the GSM model are reported inTable V below.Since the spin-orbit potential is treated as spherical inOPTMAN but deformed in TALYS, the TALYS sourcecode was modified accordingly. Furthermore, TALYSconsiders the Coulomb potential to be non-diffuse, con-trary to that in OPTMAN. Consequently, Coulomb dif-fusivity had to be included in the TALYS source code.A final modification, for full compatibility, involves theFermi energy. Values derived from neutron and protonseparation energies for each studied nucleus were adoptedinstead of using the values calculated by TALYS (seeTALYS manual).5Finally, for Fe we did not use the coupling schemegiven in the RIPL-3 library [42], where the first mem-ber of the K π = 2 + γ − band is considered to be thelevel at E x = 2959 . +2 ), while the levels at E x = 2561 . +2 ) and 3166 . +3 ) are regardedas the first two members of a β -band. The OPTMANfit of the inelastic scattering data following this levelscheme was not successful. A much better fit was ob-tained by considering the levels at E x = 3166 . . γ − band, while thelevel at 2959 . . . +1 ) are not resolved in the experimen-tal data.The total γ − ray production cross sections obtained inour calculations, using our modified OMP and level den-sity parameters in GSM, are plotted as solid curves inFigures 4, 5 and 6 together with the experimental datafrom the present and previous works [8, 11–13, 18, 19].Apart from some Mg and Si lines, a good agreement be-tween experiment and theory is achieved, with a devia-tion of at most ∼ A. Reactions with magnesium
In Figure 4, the solid black curves represent the cal-culated cross sections for the γ − ray lines produced on Mg, while the solid red curves depict the sum of thecontributions from all the isotopes in the nat
Mg target.For the lines from , Mg, the curves represent the cal-culated cross sections from reactions on these isotopes inthe nat
Mg target.As can be seen in Figure 4, the calculated cross sec-tions employing our modified OMP and deformation pa-rameters exhibit remarkably good agreement with ourexperimental data, both in absolute value and in en-ergy dependence, over the whole explored energy range.This is particularly the case for the lines of Mg ( E γ =1368 .
6, 2754 .
01 and especially 4237 .
96 keV), Na ( E γ =331 .
91 keV), Na ( E γ = 439 .
99 keV) and Mg isotope( E γ = 450 .
71 keV). However, both the default and ouradjusted OMP fail to reproduce the cross sections of theline at E γ = 1808 . Mg).Furthermore, for the lines from the deexcitation of Mg ( E γ = 585 .
03 keV, and the two new lines at 389 . .
74 keV), the calculated cross sections using theTALYS default parameters lie significantly below thosecalculated with our modified parameters and below ourexperimental data. One can note the important contri-bution from Mg to the Mg lines at E γ = 389 .
71 and974 .
74 keV, as well as the noteworthy contribution of the Mg(p,x) Na reaction to the line at E γ = 585 .
03 keV.Regarding the new lines observed at E γ = 350 .
73 keV( Ne), 425 . Al) and 472 .
20 keV ( Na) (see Ta-ble II), there is a very good agreement between the exper-imental data and the calculations done with our modifiedparameters while for the 425 . B. Reactions with silicon
The excitation functions for the two main lines of Siat E γ = 1778 .
97 and 2838 .
29 keV calculated using ourmodified input parameters and the TALYS default onesare in excellent agreement, as shown in Figure 5, bothfitting the experimental data sets very well.For the line of Si at E γ = 1273 . γ − ray lines of Si at E γ = 780 . . Al and Mg at E γ =843 .
76 and 1368 .
62 keV, respectively, the calculated exci-tation functions using our modified input parameters arein overall agreement with those derived using the TALYScode default parameters, and account well in absolutevalues for all the experimental data sets.In the case of the six new lines from the Si target, at E γ = 331 .
91 and 350 .
73 keV ( Na), 389 .
71 keV ( Mg),416 .
85 keV ( Al), 439 .
99 keV ( Na) and 450 .
70 keV( Mg) the calculated excitation functions using ourmodified parameters appear to account reasonably wellfor our experimental cross section data, both regard-ing the absolute values and the energy dependence overthe explored proton energy range. The calculations per-formed with the TALYS default parameters show some-what worse agreement with the experimental data sets.Notice also that the bumps associated with compoundresonances are predicted well by our calculations usingmodified parameters, see for instance the lines at E γ =450 .
7, 1368 .
62 and 331 .
91 keV.
C. Reactions with iron
As can be seen in Figure 6, the calculations using ourmodified OMP and nuclear level deformation parametersyield theoretical excitation functions that describe verywell the experimental data sets for the majority of γ − raylines generated in proton reactions with the Fe target.Excellent agreements between theoretical values andexperimental data are in particular observed over thewhole proton energy range, E p = 5 −
66 MeV, in thecases of the two main lines of Fe at E γ = 846 .
78 and1238 .
27 keV produced in the Fe(p, p ′ γ ) reaction. Thecalculated γ − ray production cross sections for these twolines agree very well both at high energy (our data) andat low-energy (data from [8, 11, 12]). Note the discrep-ancy between our experimental data and those reportedby Ref. [13]. Our experimental cross sectiondata for theline at E γ = 1810 .
76 keV, produced in the deexcitationof the band head of the K π = 2 + γ -band, are slightlyoverestimated by the calculated values using our modi-fied input parameters, see Figure 6, while the calculations6performed with default parameters, considerably under-estimate the data. An excellent agreement between nu-clear reaction theory and experiment is also observed inthe case of the lines at energies, E γ = 411 .
9, 1408 . .
4, 156 .
27, 377 .
88 and 1441 . E γ = 411 . Fe dominates below the proton en-ergy of 30 MeV, while the contribution from Fe is no-ticeable only above it. For the line at 1408 . E p &
15 MeV,reactions of the types Fe(p, n) and Fe(p, pn) mostlydominate. In the case of the nat
Fe target, a small con-tribution from the Fe(p, p ′ ) reaction is predicted forproton energies E p ≤
15 MeV, which explains the ob-served experimental cross sections of Ref. [11, 12] in thisenergy range. This contribution is also observed in thecase of the line at E γ = 1316 . .
8, 1303 . . γ − ray lines, as canbe seen in Figure 6. In contrast, for proton induced re-actions on the Mg and Si targets, substantially improvedagreement between TALYS calculated cross sections andexperimental data can only be obtained by using modi-fied OMP and nuclear level structure parameters. VI. CALCULATION OF THE TOTALNUCLEAR γ − RAY FLUXES IN INTERACTIONSOF LECRS IN THE INNER GALAXY
The understanding of nuclear processes at work in as-trophysical sites requires a good knowledge of γ − ray lineproduction cross sections over a wide energy range ofthe accelerated particles, extending from nuclear reac-tion thresholds up to several hundreds MeV per nucleon.However, only a limited number of experimental crosssection data sets generated in proton and α − particle in-teractions with abundant heavier nuclei in SFs and theISM was available in the literature about two decadesago. They concerned the strongest lines produced inthese reactions, but many of the data sets were limited toenergies below ∼
25 MeV for proton and α -particle inter-actions (see e.g. [15]). Therefore, nuclear reaction codecalculations were needed for estimating their values athigher particle energies, to model the γ − ray line emis-sions from these astophysical sites. In the latest crosssection compilation, Murphy et al. [16] used the nuclear reaction code TALYS for this purpose.Murphy et al. [16] also made for the first time ex-tensive nuclear reaction calculations to assess the quasi-continuum γ − ray line emission with photon energies, E γ ∼ . −
10 MeV, composed of a large number ofweaker lines, in the complete absence of correspondingexperimental cross section data. This weak-line compo-nent is dominated by interactions with abundant nuclei,where the reaction products have an important number ofexcited states below the particle emission thresholds. InSFs and ISM the most important interactions are protonand α -particle reactions with Ne, Mg, Si and Fe.This quasi-continuum component is in both astrophysi-cal sites merged with another important quasi-continuumcomponent of overlapping broad lines from interactionsof accelerated heavier ions with ambient H and He.An important, still unresolved and presently debatedquestion concerns the energy spectrum of galactic LECRs(of energies below about 1 GeV per nucleon) that wereearly assumed to be responsible for the nucleosynthesisof light elements in our Galaxy (the LiBeB problem) [43,44]. This component of cosmic rays of energy densitysimilar to that of the interstellar photon and magneticfields is assumed to play a crucial role in the dynamicsand the chemical evolution of the Galaxy, including theprocesses of cosmic ray transport and star formation [45,46].Evidence of their existence rely only on indirect obser-vations of marked ionisation rates in diffuse interstellarmolecular clouds [47, 48], such as those inferred from theabundances of the H +3 molecular ion, and on the approxi-mately linear increase of the Be abundance with metallic-ity [26]. It is expected that the interactions of the LECRswith the ISM matter in the inner Galaxy give rise to animportant nuclear γ -ray line emission, whose intensityexceeds considerably the emission due to standard CRs(see e.g. [27]). In particular, the prominent nuclear linesemitted in the deexcitation of the first few excited statesof most abundant nuclei, ( C, N, O, Ne, Mg, Si and Fe [14]) have cross section maxima at LECRenergies and are therefore strongly produced.In this context, we have performed calculations of nu-clear γ − ray line emission spectra ( γ − ray emission fluxesversus the photon energy, E γ ) based on the present γ − ray production experimental cross sectiondata, thathave been satisfactorily accounted for by nuclear reac-tion models with introducing in TALYS our own OMP,nuclear level structure and level density parameters re-ported in the previous section. We have also calculated γ − ray line emission spectra from the inner Galaxy as-suming different values for the unknown metallicity ofthis medium, taken to be about twice the metallicity ofthe Sun.For the energy spectra and the composition of the low-energy component of cosmic rays, we use source spectrafrom shock acceleration with an energy cutoff E c thatare propagated with a simple leaky-box model, the so-called SA-LECR in Benhabiles et al. [27]. The obtained7 ) - M e V - s - s r - I n t en s i t y ( c m +
583 847331351 440 + ) - M e V - s - s r - I n t en s i t y ( c m + Cosmic-ray energy (MeV) ) - M e V - s - s r - I n t en s i t y ( c m FIG. 10. Calculated nuclear γ -ray line emission spectra for LECRs produced by shock acceleration with the parameter E c =60 MeV [26] interacting with interstellar matter in the inner Galaxy. The energies of γ -ray lines analysed in this work areindicated by vertical labels in units of keV. The four spectra are calculated for various assumptions for the cross section dataand the metallicity of the ambient medium. Black: cross section data derived with our modified parameters in the TALYScode and M = 3, i.e. three-times solar metallicity; red: same, but M = 1; green: cross section data derived with the defaultparameters of TALYS and M = 3; blue: cross section data from the compilation of Murphy et al. [16] and M = 3. results for SA-LECR with energy cutoff E c = 60 MeVare reported in Figure 10 showing, in particular, domi-nating contributions of main γ − ray lines emitted in thedeexcitation of first low-lying states of the studied Mg,Si and Fe nuclei (see table II and Figures 4, 5 and 6),and of the strong lines at E γ = 4439 keV (from C) and E γ = 6129 keV (from O).Differences between calculations based on the presentcross sections and those from the TALYS calculations with default parameters (black and green curves in Fig-ure 10) can be seen for some of the moderately stronglines and in the quasi-continuum at higher energies,reaching or exceeding 30%. The nuclear γ -ray line emis-sion for lower metallicity (red line) shows, as expected,a decrease in the prominent narrow line fluxes, while theunderlying quasi-continuum component is less affected,the broad-line component not being dependent on themetallicity. Finally, the blue line shows the component8from the strong lines of the compilation of Murphy etal. [16], without the weak-line component. Strong differ-ences in some energy ranges illustrate the importance ofthis latter emission component.Space telescopes of improved technology with higherenergy resolution and better sensitivity are now projectedfor near future satellite missions, like e-ASTROGAM(and All-Sky ASTROGAM) or COSI [49]. The possibleobservation of the predicted low-energy nuclear γ − rayline emission spectrum with E γ ∼ . −
10 MeV shouldprovide the most compelling signature of the LECRs in-teractions within the inner Galaxy and may help to elu-cidate the puzzling composition and energy spectrum ofthe latter component of cosmic rays. With the presentnew data and the improvements obtained in TALYScalculations, more reliable and accurate predictions areavailable for comparison with eventual future observa-tions.
VII. SUMMARY AND CONCLUSION
In the present work, we report experimental cross sec-tion excitation functions for 41 γ -ray lines produced ininteractions of 30, 42, 54 and 66 MeV proton beams de-livered by the SSC facility of iThemba LABS with Mg,Si and Fe, that are abundant nuclei in the SFs and ISMastrophysical sites. While cross section data for half ofthese lines are reported for the first time, the other halfconsists of lines resulting from the deexcitation of low-lying excited nuclear states for which data at lower ener-gies already exist. Our experimental cross section datafor these lines are found to be fairly consistent with pre-vious data sets measured at the Washington [8] and Or-say [11, 12, 18, 19] tandem accelerators for E p <
27 MeV,that are thus extended to higher proton energies. Theobserved small differences are likely due to variations inthe experimental conditions, such as the properties of thetargets used (see Table I). In two cases, however, our ex-perimental cross sections for known lines are significantlylower than previous data measured at the LBL cyclotronfacility for proton energies up to 50 MeV [13].We have also compared our experimental data to thesemi-empirical compilation of Murphy et al. [16] in thecase of lines for which previously measured values havebeen extrapolated to higher proton energies on the basisof TALYS code calculations. The current experimentalresults thus improve this existing unique database fornuclear γ -ray production cross sections and allow for amore reliable extrapolation to higher energies.Our experimental cross section data have also beencompared with the predictions of nuclear reaction mod-els via TALYS code calculations. First, the integral crosssections calculated using the built-in default OMP andnuclear level structure parameters of TALYS showed tobe in overall agreement in terms of energy dependence,but exhibited noticeable differences in absolute valueswith experimental data for most observed γ -ray lines. Appreciable improvements have been obtained by intro-ducing modified OMP parameters, as well as our couplingscheme and level density parameters of nuclear collec-tive levels as input data in the TALYS code. These pa-rameters were determined via our theoretical analysis ofa large number of experimental nucleon elastic/inelasticscattering differential cross section data sets available inthe literature using the coupled- channels code OPT-MAN (see the Appendix). We have obtained substan-tially improved agreements between the calculated inte-gral cross sections and the corresponding experimentaldata mainly for the Mg and Si targets, while the exper-imental results for the Fe targets appeared to be alsosatisfactorily accounted for by TALYS calculation usingthe default input parameters.Experimental nuclear γ -ray line production cross sec-tions are of great importance in various scientific re-search fields and practical applications, notably in nu-clear physics and nuclear astrophysics where they arecrucially needed for diverse purposes, e.g. :(i) Testing/improving the ability of reaction codes [17,22] to predict [16] the cross sections for nuclear reactionswhere experimental data are lacking.(ii) Modeling, analysing and interpreting nuclear pro-cesses, such as the γ -ray line emissions from astrophysicalsites like solar flares and the interactions of cosmic raysin the ISM, and in particular the low-energy cosmic-raycomponent thought to be responsible for high ionisationrates in diffuse clouds towards the inner Galaxy.On the basis of the present and previ-ous [8, 11, 12, 18, 19] experimental γ -ray line productioncross section data and results of the TALYS code, wehave performed calculations of γ -ray line emission spec-tra over the photon energy range, E γ = 0 . −
10 MeV,expected to be generated in the interactions of theLECRs in the inner Galaxy. The accuracy of predictionsfor the γ -ray line emission in solar flares will likewiseprofit from the present extension of the reaction crosssection data to higher energies. The obtained resultsshould allow reliable comparisons (see Ref. [27]) withobservational data from new generation space telescopesof higher energy resolution and better sensitivity. Thecombined progress may lead to accurate determinationsof the accelerated particle populations and the interac-tion medium in solar flares and the presently unknownproperties of the LECRs within the galactic Centercould then be considerably constrained. ACKNOWLEDGMENTS
The authors are indebted to the technical staff of theiThemba LABS SSC accelerator for their kind help andfriendly cooperation. This work has been carried out inthe framework of a joint scientific cooperation agreementbetween the USTHB university of Algiers and iThembaLABS of Cape Town. The work was partially supported9by the General Direction of Scientific Research and Tech-nological Development of Algeria (project code A/AS-2013-003), and by the National Research Foundation ofSouth Africa under grants GUN: 109134 and UID87454.Besides, travel support was granted to the collaboratingFrench researchers by the CSNSM and the IPN of Orsay(CNRS/IN2P3 and University of Paris-Sud). Thanks aredue to all persons from these institutions who helped inthe realisation of this project. W. Yahia-Cherif would liketo adress particular thanks to Dr. P. Adsley (iThembaLABS), Dr. B. M. Rebeiro (IPN Lyon) and Mr. K. C. W.Li (Stellenbosch University) for all their help and supportin this work.
APPENDIX: DETERMINATION OF THE OMPAND COLLECTIVE LEVEL DEFORMATIONPARAMETERS
The potential as used in the OPTMAN code [40] isexpressed by: V ( E, r ) = − V R ( E ) f R ( r, r R ) − [∆ V V ( E ) + iW V ( E )] f V ( r, r R ) − [∆ V D ( E ) − ia D W D ( E )] ddr f D ( r, r D )+( ~ m π c ) [∆ V SO ( E ) + V SO ( E ) + iW SO ( E )] × r ddr f SO ( r, r SO )( −→ σ ·−→ L )+ V Coul ( r, r c ) , (3)where the real central potential is given by: V R ( E ) = ( V dispR + ( − Z ′ +1 C viso ( N − ZA )) e ( − λ R ( E − E F )) + C coul ZZ ′ A / ( λ R V dispR e ( − λ R ( E − E F )) ) , (4)and the imaginary surface and volume potentials aretaken as [50, 51]: W V ( E ) = ( W dispV + ( − Z ′ +1 C wviso ( N − ZA )) × ( E − E F ) ( E − E F ) + W ID V W D ( E ) = ( W dispD + ( − Z ′ +1 C wdiso ( N − ZA ) × ( E − E F ) ( E − E F ) + W ID D e ( − λ D ( E − E F )) , (5)where Z and Z ′ are, respectively, the atomic numbers ofthe target nucleus and the projectile.The real and imaginary spin-orbit potentials weretaken under the standard forms of Koning and De-laroche [50]: V SO ( E ) = V dispSO e ( − λ SO ( E − E F )) W SO ( E ) = W dispSO ( E − E F ) ( E − E F ) + W ID SO . (6)The positive quantities C viso , C wviso and C wdiso in theabove expressions are the constants of the isospin terms, C coul is the Coulomb correction constant and E F is theFermi energy for neutrons and protons. The dynamicterms, ∆ i ( E ) (with index i = V, S, SO ), are dispersivecomponents calculated from the following integral [52]:∆ V ( r, E ) = Pπ Z + ∞−∞ W ( r, E ′ ) E ′ − E dE ′ . (7)The adjustment of the OMP parameters was made inthe framework of the CC formalism. For even-A nuclei,the Davydov-Filipov (DF) model [53] accounting for the γ deformation of the nuclei was used in order to describethe collective states. The value of the γ deformation wascalculated according to the DF approach [53] using theratio: R = E +2 E +1 = 3 + p − sin (3 γ )3 − p − sin (3 γ ) , (8)where E +1 and E +2 are, respectively, the energies of thefirst and second 2 + excited states, taken from the avail-able experimental level schemes. The γ value calculatedfrom this ratio varies from 30 ◦ for R = 2 down to 0 ◦ for R = ∞ . For Si, however, the second 2 + stateis located at E x = 7380 .
59 keV above the first 3 + stateat E x = 6276 .
20 keV. This unnatural parity state is thesecond state of the γ − vibrational band. The 2 + state at7380 .
59 keV is a better candidate to form with the 0 +2 state at E x = 4979 .
92 keV the first two members of a β -vibrational band [51]. Thus, to calculate the value of γ for this nucleus, we have used the ratio R = E +1 E +1 = 183 − p − sin (3 γ ) , (9)where E +1 is the first 3 + state at E x = 6276 .
20 keV. The Mg nucleus is another exception. For this nucleus, onehas R <
2. The value of γ can be determined, instead,from the ratio of the reduced transition probbabilities: R b = B ( E +2 → +1 ) B ( E +2 → +1 ) , (10)in terms of the B ( E
2) reduced electric transition proba-bilities, expressed (see [54] and references therein) as: B ( E +2 → +1 ) = 107 (cid:18) e Q π (cid:19) sin (3 γ )9 − sin (3 γ ) B ( E +2 → +1 ) = 12 (cid:18) e Q π (cid:19) − − sin (3 γ ) p − sin (3 γ ) ! (11)where Q is the electric quadrupole moment. Glatz [55],Alons [56] and Dybdal [57] have reported experimental0reduced transition probabilities for the 2 +2 → +1 and 2 +2 → +1 ( g.s. ) transitions. Average B ( E
2) values, weightedby the experimental errors estimated by these authors,have been calculated for these transitions and are, re-spectively: B ( E +2 → +1 ) = 27 . e f m and B ( E +2 → +1 ) = 1 . e f m . Thus, the valueof the γ deformation parameter for Mg, calculated byequation (11), is γ = 27 . ◦ .For odd-A nuclei like Mg and Si, we have used theAxially-Symmetric Rigid Rotor (ASR) model [58]. In thiscase, the radii and diffusivities of the imaginary surfaceand volume potentials have been readjusted but with as-suming the same parameters for the potential depths, asin the case of the even-A isotopes. The derived results (potential depths, geometrical pa-rameters, β and γ deformations) are reported in Sec-tion V (Tables III and IV, respectively).The validity of our OMP for each isotopic chain rangesfrom E p = 0 −
250 MeV for Mg, E p = 0 −
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