Deuteron-induced reactions on manganese at low energies
M. Avrigeanu, E. Simeckova, U. Fischer, J. Mrazek, J. Novak, M. Stefanik, C. Costache, V. Avrigeanu
aa r X i v : . [ nu c l - e x ] J a n Deuteron-induced reactions on manganese at low energies
M. Avrigeanu ∗ , E. ˇSimeˇckov´a † , U. Fischer , J. Mr´azek , J. Novak , M. ˇStef´anik , C. Costache , V. Avrigeanu Horia Hulubei National Institute for R and D in Physics and Nuclear Engineering,P.O. Box MG-6, 077125 Bucharest-Magurele, Romania Nuclear Physics Institute CAS, 25068 ˇReˇz, Czech Republic and Euratom/FZK Fusion Association, Karlsruhe Institute of Technology (KIT),Hermann-von-Helmholtz-Platz, 1, 76344 Eggenstein-Leopoldshafen, Germany
Background:
The scarce data systematics and complexity of deuteron interactions demand theupdate of both the experimental database and theoretical frame of deuteron activation cross sections.Various reactions induced by neutrons and protons following the deuteron breakup (BU) should bealso taken into account. On the other hand, deuteron reaction cross sections recommended recentlyfor high-priority elements are still based on data fit without predictive power.
Purpose:
Accurate new measurements of low-energy deuteron-induced reaction cross sections formonoisotopic ( Mn) natural manganese target enhance the related database as well as the oppor-tunity of an unitary and consistent account of the related reaction mechanisms.
Methods:
Activation cross sections of , Mn, and Cr nuclei by deuterons on Mn were mea-sured at energies ≤
20 MeV by the stacked-foil technique and high resolution gamma spectrometryat the U-120M cyclotron of CANAM, NPI CAS. Then all available data for deuterons on Mn upto 50 MeV are analyzed paying particular attention to BU and direct reaction (DR) mechanisms.
Results:
Newly measured activation cross sections strengthen the deuteron database at low ener-gies, at once with a consistent account for the first time of all available data.
Conclusions:
Due account of deuteron-induced reactions on Mn, including particularly the newexperimental data at low energies, is provided by a suitable BU and DR assessment.
PACS numbers: 24.10.Eq,24.10.Ht,25.45.-z,25.60.Gc
I. INTRODUCTION
Ongoing fusion research programs (ITER, IFMIF,SPIRAL2-NFS) [1] and medical investigations using ac-celerated deuterons triggered even a decade ago anupdate of the experimental database and theoreticalaccount of deuteron-induced reactions. The relatedFENDL-library project [2] was motivated essentially bythe scarce deuteron data systematics and complexity ofdeuteron interactions. Various reactions induced by neu-trons and protons following the deuteron breakup (BU)should be also taken into account.More recently, full parametrization of the deuteronmonitor reactions and therapeutic radionuclides-production cross sections have been recommended byHermanne et al. [3], and Engle et al. [4]. Thus, beyondthe FENDL [2] concern of improved theoretical analysis,fit of the available data by a least-squares methodwith Pad´e approximations of variable order has beeninvolved to evaluate the deuteron-induced productioncross sections and corresponding uncertainties. Actually,deficiencies in describing the elastic and especially theinelastic BU that dominate the deuteron reaction crosssection at beam energies comparable with the Coulombbarrier motivated the recommended Pad´e fits [4].Consequently, the present work aims to strengthen the ∗ [email protected] † [email protected] database of deuteron-induced reactions up to 20 MeV on Mn target nucleus, as well as a deeper understandingof the involved reaction mechanisms. The weak points ofan evaluation procedure that may lead to disagreementwith experimental data are also carefully concerned.The particular choice of the Mn element for this work isrelated to the design of the structural components of ac-celerators for which the deuteron-induced activation hasa major importance for material damage and radioac-tivity risks. Thus, there is a 2% Mn presence in theSS-316L steel alloys that are considered as option for thebeam guides of the DONES project [5]. It is thereforeof interest to complete the recent analyses of deuteroninteraction with V, Cr, Fe, Co, Ni, and Cu [6–10] lookingalso for the consistent account of BU and direct reaction(DR) contributions to activation cross sections. This is aswell essential in view of significant disagreement betweenrecent measurements and calculated data [11, 12].The experimental setup as well the new measured dataare described in Sec. II. Among the models involved inthis work is firstly an energy-dependent optical potentialfor deuterons on Mn in Sec. III A. The BU analysis isdescribed in Sec. III B as well as DR account using thecomputer code FRESCO [13], while the main points ofthe pre-equilibrium emission (PE) and compound nucleus(CN) contributions of the code TALYS-1.9 [14] are givenin Sec. III C. Discussion of the measured and calculatedcross sections is in Sec. IV makes reference to the newestTENDL-2017 evaluated data library [15] as well. Finally,conclusions of this work are given in Sec. V.
II. MEASUREMENTS
The irradiation was carried out on infrastructure ofthe Center of Accelerators and Nuclear Analytical Meth-ods CANAM [16] of the Nuclear Physics Institute of theCzech Academy of Sciences (NPI CAS). Deuterons wereaccelerated by the variable-energy cyclotron U–120M.D + beam was extracted using a stripping foil and theion beam was delivered to the reaction chamber. Themean beam energy was determined with an accuracy of1%, with full width at half maximum (FWHM) of 1.8%.The collimated deuteron beam impinged the stack offoils placed in a cooled reaction chamber that served alsoas a Faraday cup. The measured MnNi foils (Goodfel-low product, 25 µ m declared thickness) containing 88%monoisotopic ( Mn) natural manganese and 12% Niwere interleaved by monitoring/degrading Al foils (Good-fellow product - 99.99% purity, 50 µ m declared thick-ness).The irradiation was carried up in two runs to check aninternal consistency of the measurement. The character-istics of the single runs are given in Table I. The meanenergy, the energy thickness and the energy spread ineach foil were simulated by the SRIM 2008 package [17].The γ rays from the irradiated foils were measuredrepeatedly by two calibrated high-purity germanium(HPGe) detectors of 50% efficiency and FWHM of 1.8keV at 1.3 MeV. Experimental reaction rates were calcu-lated from the specific activities at the end of the irradi-ation and corrected for the decay during the irradiationusing the charge measurement and MnNi foil character-istics as well. The measurement with different coolingtimes lasted up to 100 days after irradiation. The decaydata of the isotopes observed from irradiated MnNi foils[18] are given in Table II.The experimental cross sections of the Mn( d, p ) Mn, Mn( d, x ) Mn and Mn( d, x ) Cr reactions are givenin Table III. The energy errors take into account the en-ergy thickness of each foil and the initial-energy spreaderror. Cross-section errors are composed of statisticalerrors in activity determination and systematical errorsof charge measurement uncertainty ( ∼ TABLE I: Characteristics of single runs.Run Initial Total Irradiation Meanno. energy charge time current(MeV) ( µ C) (s) ( µ A)1 19.76 96.05 303 0.3172 19.5 736.87 1833 0.402 TABLE II: Half-lives, main γ lines, and their intensities [18]of the isotopes observed from irradiated Mn.Isotope T / E γ (keV) I γ (%) Mn 2.5785 h 846.77 98.91810.77 27.2 Mn 312.3 day 834.25 99.98 Cr 27.7025 day 320.08 10
III. NUCLEAR MODEL ANALYSISA. Optical potential assessment
The optical model potential (OMP) parameters ob-tained and/or validated by analysis of deuteron elastic-scattering angular distributions are then used withincalculation of all deuteron-induced reaction cross sec-tions. Consequently, the simultaneous analysis of elastic-scattering and activation data is essential for nuclearmodel calculations using a consistent input parameterset [6–10, 20, 21].However, the OMP analysis in this case makes use ofonly one measurement for deuteron elastic-scattering an-gular distribution on Mn at 7.5 MeV incident energy[22]. The best description of the measured data at a par-ticularly low incident energy has been obtained using thedeuteron OMP of Daehnick et al. [23] versus TALYS de-fault double-folding approach [14] as well as predictionsgiven by Perey-Perey [24], Lohr-Haeberli [25], and An-Cai [26] global optical potentials (Fig. 1). This potentialwas furthermore involved in the rest of this work.
TABLE III: Measured reaction cross sections (mb) fordeuterons incident on natural manganese ( Mn). The un-certainties are given in parentheses, in units of the last digit.
Energy Reaction(MeV) Mn( d, p ) Mn Mn( d, x ) Mn Mn( d, x ) Cr19.49 (27) 87.7 (61)19.22 (28) 75.2 (47) 133.1 (77) 0.353 (44)19.04 (26) 90.4 (57) 108.0 (69)18.20 (28) 84.4 (52) 89.0 (52) 0.119 (40)17.53 (28) 94.1 (76) 50.8 (36)17.13 (29) 90.9 (55) 52.7 (30)16.50 (30) 115.9 (67)16.02 (30) 100.1 (71) 30.49 (176)15.90 (32) 111.3 (71) 17.89 (124)14.85 (32) 111.4 (75) 20.32 (118)14.81 (32) 131.3 (86)14.12 (35) 148.6 (175) 16.25 (99)13.59 (35) 125.5 (101) 16.04 (92)12.22 (39) 145.6 (114) 13.37 (78)12.17 (36) 165.5 (146) 11.82 (68)10.73 (42) 169.2 (133) 10.58 (61)9.93 (45) 151.3 (312) 7.74 (55)9.08 (47) 199.4 (155) 6.84 (39)7.17 (55) 231.2 (173) 2.47 (15)7.16 (55) 256.5 (239) 1.69 (18)4.80 (72) 229.5 (137)3.13 (97) 134.4 (132) d / d R u t he r f o r d Comfort (1969) c.m. (deg) Mn(d,d)
TALYS default Perey+ (1963) Lohr+ (1974) Daehnick+ (1980) Haixia An+ (2006) E d =7.5 MeV FIG. 1: (Color online) Comparison of the measured [22]and calculated deuteron elastic-scattering angular distribu-tions using, beyond the TALYS default double-folding ap-proach [14] (dotted curve), the deuteron global OMPs ofPerey-Perey [24] (dash-dot-dotted curve), Lohr-Haeberli [25](dashed curve), Daehnick et al. [23] (solid curve), and Haixia-Chonghai [26] (dash-dotted curve) for Mn target nucleus.
B. Direct Interactions
The specific BU and DR noncompound processes makedeuteron-induced reactions substantially different fromreactions with other incident particles. Actually, no-ticeable discrepancies between the measured activationdata and theoretical model results follow mainly the dis-regard of these direct interactions (DIs) peculiarity [6–10, 20, 21].
1. Breakup
There are two distinct BU processes in the Coulomband nuclear fields of the target nucleus. The former is theelastic breakup (EB) in which the target nucleus remainsin its ground state and none of the deuteron nucleonsinteracts with it. The later is the inelastic breakup orbreakup fusion (BF), where one of these deuteron con-stituents interacts nonelastically with the target nucleus.Our description of the deuteron breakup mechanismis based on the parametrizations [27, 28] for (i) thecross sections σ pBU of total BU proton emission, and(ii) the EB cross sections σ EB . Equal inelastic-breakupcross sections σ pBF and σ nBF have been assumed for thebreakup neutron and proton, so that σ n/pBU = σ EB + σ n/pBF while the total breakup cross section is σ BU = σ EB +2 σ n/pBF [28, 29]. Actually our parametrizations have concernedthe total BU nucleon-emission and EB fractions of thedeuteron OMP total-reaction cross section σ R , i.e. f n/pBU = σ n/pBU /σ R and f EB = σ EB /σ R , respectively. The depen-dence of these fractions on the deuteron incident energy E and target-nucleus atomic Z and mass A numbers was obtained through analysis of the experimental systemat-ics of deuteron-induced reactions on target nuclei from Al to
Th and incident energies up to 80 MeV for theformer: f n/pBU = 0 . − . Z + 0 . ZA / +0 . A / E − . ZE , (1)but within a more restricted energy range up to 30 MeVfor the later [30]: f EB = 0 . − . Z + 0 . ZA / +0 . A / E − . ZE (2)More details are given elsewhere [27–29].The comparison of the measured σ pBU with microscopicbreakup cross sections [31, 32] as well as the empiri-cal parametrization pointed out the correctness of ourbreakup analysis [28, 33]. However, the improvement ofthe deuteron breakup description requires, beyond theincrease of its own data basis, also complementary mea-surements of ( d, px ) and ( n, x ), as well as ( d, nx ) and( p, x ) reaction cross sections for the same target nucleus,within the related incident-energy ranges.The energy dependence of σ R , σ BU , σ pBU , as well asthe BU components σ EB and σ pBF for deuteron interac-tions with Mn target nucleus are compared in Fig 2(a).The breakup excitation functions increase with deuteron-energy increasing, including its dominant BF componentthat is quite important for the analysis of the followingtwo opposite BU effects on deuteron activation cross sec-tions.Firstly, the leakage of the initial deuteron flux to-ward the breakup process reduces the total-reaction crosssection that should be shared among different outgoingchannels by a reduction factor (1 − σ BU /σ R ).On the other hand, the BF component brings contri-butions to different reaction channels of deuterons inter-actions with the target nuclei [6–10, 20, 21, 29]. Thus,the absorbed proton or neutron following the deuteronbreakup contributes to the enhancement of the corre-sponding ( d, xn ) or ( d, xp ) reaction cross sections, re-spectively. The compound nuclei in reactions inducedby the BF nucleons differ by one unit of the atomic massand maybe of also the atomic number in comparison withdeuteron-induced reactions, the partition of the BF crosssection among various residual-nuclei population beingtriggered by the energy spectra of the breakup nucleonsand the excitation functions of the reactions induced bythese nucleons on the target nuclei.In order to calculate the BF enhancement of, e.g., the( d, xn ) reaction cross sections, the BF proton-emissioncross section σ pBF should be (i) multiplied by the ratios σ ( p,x ) / σ pR , corresponding to the enhancing reaction, (ii)convoluted with the Gaussian line shape distribution ofthe BF–proton energy E p for a given deuteron incidentenergy E d , and (iii) integrated over the BF proton energy.Consequently, the BF–enhancement cross section has the
10 20 30 40 500.00.20.40.610 20 30 40 50 E d (MeV) R (d,t) (d,p) (b)BU DR: (d,p)+(d,t) d + Mn ( m b ) R (a)BU EB p BU p BF / R PE+CNDI=BU+DRBU DR: (d,p)+(d,t)(c)
FIG. 2: (Color online) The cross-section energy dependence of (a,b) deuteron total-reaction (short-dotted curves) and BU(dash-dot-dotted curves), (a) proton-emission BU (thin dash-dot-dotted curve) and BF (short dash-dotted), EB (dotted), (b)DR (dash-dotted), stripping ( d, p ) (thin dash-dotted) and pick-up ( d, t ) (short dash-dotted), and (c) the σ R fractions of BU(dash-dot-dotted), DR (dash-dotted), DI (solid), and PE+CN cross sections of deuteron interactions with Mn (see text). form [8, 9, 33]: σ p,xBF ( E d ) = σ pBF ( E d ) Z dE p σ ( p,x ) ( E p ) σ pR π ) w exp [ − ( E p − E p ( E d )) w ] , (3)where B d is the deuteron binding energy, σ pR is the protontotal-reaction cross section, x stands for various γ , n , d ,or α outgoing channels, while the Gaussian distributionparameters w and E p given by Kalbach [34] were used.Interpolation of experimental nucleon-induced reactioncross sections (e.g., σ ( p,x ) ) from the EXFOR library [35]or from newest TENDL library has been involved withinestimation of the BU enhancement [6–10, 20, 21, 29], inorder to reduce as much as possible the supplementaryuncertainties brought by additional theoretical calcula-tions. The nucleon total-reaction cross sections σ n/pR havebeen obtained by using the same optical potentials thathave been involved within the stripping and statisticalnucleon emission calculations.On the whole, the enhancing effect of the breakupmechanism is important mainly for describing the ex-citation functions for second and third chance emitted-particle channels. The BF enhancements due to the BUprotons and neutrons emitted during the deuteron inter-action with Mn, through the ( p, x ), and ( n, x ) reac-tions populating various residual nuclei, are discussed inSec. IV.
2. Direct reactions
In addition to the BU assessment, an accurate esti-mation of the DR cross sections is necessary to obtainfinally the correct PE+CN population of various resid-ual nuclei. However, poor attention was given so far tothis issue in deuteron activation analysis also becausethe DR cross-section account is conditioned by the avail-able experimental spectroscopic factors, outgoing particle angular distributions, or at least the differential cross-section maximum values. On the other hand, for nuclearreactions involving projectiles and ejectiles with differ-ent particle numbers, TALYS includes additionaly to PEonly the account of the continuum stripping, pick-up,breakup and knock-out reactions using Kalbach’s phe-nomenological contribution for these mechanisms [14].The appropriate calculation of the DR stripping andpick-up mechanism contributions within this work usedthe distorted-wave Born approximation (DWBA) formal-ism within the code FRESCO [13]. The post/prior formdistorted-wave transition amplitudes for stripping and re-spectively pick-up reactions, and the finite-range interac-tion have been considered. The n - p effective interactionin deuteron [36] as well as d - n effective interaction in tri-ton [37] were assumed to have a Gaussian shape, whilethe transferred-nucleon bound states were generated in aWoods-Saxon real potential [6–10, 20, 21, 29]. The popu-lated discrete levels and the corresponding spectroscopicfactors available within the ENSDF library [38] were usedas starting input for the DWBA calculations of the ( d, p )stripping [39], and ( d, t ) pick-up [40] excitation functions.Experimental angular distributions of particle emissionin deuteron-induced DRs on Mn there are only for the( d, p ) stripping [22] and ( d, t ) pick-up [41, 42] reactions.A detailed analysis of the former reaction at 7.5 MeVincident energy has made possible the calculation of al-most total ( d, p ) stripping contribution to the populationof Mn residual nucleus nucleus, of 129 discrete levelsup to the excitation energy of ∼ d, t ) cross-section calcula-tions concerned the analysis of the triton angular distri-butions measured at incident energies of 17 [41] and 18[42] MeV for 30 discrete levels up to ∼ d, p ) and ( d, t ) excitation-function calcula-tions shown in Fig. 2(b).However, due to the missing data on ( d, n ) stripping c.m. (deg) d / d ( m b / s r) g.s. Mn(d,p) Mn Comfort(1969) E d =7.5 MeV FIG. 3: (Color online) Comparison of measured (solid circles) [22] and calculated (solid curves) proton angular distributions of Mn( d, p ) Mn stripping transitions to states with excitation energies in MeV, at the incident energy of 7.5 MeV. c.m. (deg) Mn(d,t) Mn Cameron+(1981) E d =17 MeV0.010.1 d / d ( m b / s r) g.s. Mn(d,t) Mn Taylor+ (1976) E d =18 MeV FIG. 4: (Color online) Comparison of measured (solid circles) [41, 42] and calculated (solid curves) triton angular distributionsof Mn( d, t ) Mn pick-up transitions to states with excitation energies in MeV, at the incident energies of 18 and 17 MeV. and ( d, α ) pick-up reactions, the sum σ ( d,p ) + σ ( d,t ) couldstand only as a lower limit of the DR component shownalso in Fig. 2(b). It has a significant maximum around E d ∼ d, p ) strong stripping pro-cesses. Then, it results a slow decrease at higher deuteronenergies while σ R reaches its maximum value and remainsalmost constant for E d >
25 MeV. The major role of thestripping ( d, p ) reactions to the activation cross sectionsof Mn residual nucleus, for deuteron interaction with Mn, will be shown in Sec. IV. The exclusive contribu-tion of ( d, t ) pick-up process at the lowest incident en-ergies, up to the thresholds of the ( d, nd ) and ( d, np )reactions, will be also shown for the population of Mnresidual nucleus.Nevertheless, the transfer reactions are important atlow incident energies, then decreasing with the deuteronenergy increase, while the BU excitation function be-comes continuously larger. Finally, consideration of thedeuteron incident–flux decrease due to its absorptionwithin BU as well as DR processes provides the correcttotal cross-section going towards PE+CN statistical de-cay of the excited system. Thus, a reduction factor of thetotal-reaction cross section due to the direct interactions(DI) of the breakup, stripping and pick-up processes ac-counted in the present analysis is given by:1 − σ BU + σ ( d,p ) + σ ( d,t ) σ R = 1 − σ DI σ R . (4)Its energy dependence is shown in Fig. 2 (c) at once withthat corresponding to BU and DR reaction mechanisms,pointing out the role of each one in the deuteron in-teraction process with Mn target nucleus. First, onemay note the high importance of σ DI / σ R at lowest inci-dent energies due to the above-mentioned behavior of thestripping excitation function. The decrease of the DRcomponent leads to a steep increase with the deuteronenergy of the PE+CN weight, in spite of the BU in-crease. The PE+CN fraction maximum, around ∼ σ R at energiesaround 42 MeV, then DI dominates with E d increase. Itis thus pointed out the important role of the DI mecha-nisms for deuteron interactions. C. Statistical emission
The PE and CN statistical processes become impor-tant with the increase of the incident energy above theCoulomb barrier (e.g., Ref. [43]). The correspondingreaction cross sections have been calculated using theTALYS-1.9 code [14] and the reduction factor of Eq. 4in order to take into account the above-mentioned ab-sorption of he deuteron flux into the DI processes.The following input options of the TALYS-1.9 codehave been used: (a) the OMPs of Koning-Delaroche [44], Daehnick et al. [23], Becchetti-Greenlees [45], andAvrigeanu et al. [46] for neutrons and protons, deuterons,tritons, and α -particles, respectively, (b) the back-shiftedFermi gas (BSFG) formula for the nuclear level density,(c) no TALYS breakup contribution, since the above-mentioned BF enhancements is still under implementa-tion in TALYS, and (d) the PE transition rates calculatedby means of the corresponding OMP parameters also in-volved within BU, DR, and CN calculations, for a consis-tent use of the same common parameters within variousmechanism models. One may note that the same PE op-tion was used with previous similar analyses of deuteroninteraction with V, Cr, Fe, Co, Ni, and Cu [6–10] lead-ing finally to an improved agreement with the measureddata. IV. RESULTS AND DISCUSSION
The excitation functions of the residual nuclei , Mnand Cr, measured in the present work for deuteronson Mn at energies ≤
20 MeV (Sec. II), are compared inFig. 5 with the data formerly available up to 50 MeV [11,12, 47–50], the corresponding TENDL–2017 evaluation[15], and results of calculation using TALYS-1.9 code andits default input parameters [14]. The new measured dataof , Mn activation are in agreement especially with therecent measurement of Tark´anyi et al. [12], extendingto lowest energies the accurate experimental description.The same extension is provided by the new cross sectionsfor Cr activation measured for the first time below 20MeV.The comparison with the most recent evaluated [15]and TALYS-1.9 [14] default calculation results proveshowever significant cross-section differences for all thesereactions. A similar case is that of g Mn activation thatwas recently measured within a larger energy range (20–50 MeV) [11, 12] as shown in Fig. 5(c). It has also beeninvolved in this work for an overall analysis of the presentmodel approach.A first effect taken into account to obtain a bettermeasured-data account concerned the adopted input pa-rameters of the deuteron OMP. Thus, taking the advan-tage of the elastic-scattering analysis given in Sec. III A,the TALYS default option of the deuteron double-foldingOMP [51] of nucleon global OMPs [44] was replaced withthe OMP parameters of Daehnick et al. [23]. However,despite the substantial difference between the relatedelastic-scattering angular distributions shown in Fig. 1,the corresponding changes of the calculated cross sec-tions are much smaller. There is particularly apparent(i) the continuing underestimation of the ( d, p ) reactiondata with even an order of magnitude, (ii) the failure inaccounting the first decade above the effective thresholdsof , g Mn activation, and (iii) the good agreement inthe same energy range but followed then by an under-estimation with a factor ∼ Cr activation (Fig. 5).So distinct discrepancies can be obviously related to the
20 30 40 50110100 20 30 40 500.111010010 20 30 40 50210100400 10 20 30 40 50110100800 E d (MeV) Mn(d,x) Mn E d,t2n th = E d,d3nth =32.4E d,p4nth =34.7 (c) TENDL-2017TALYS-1.9 default + OMP-d (1980) Mn(d,x) Cr (d) Ditroi+ (2011)Tarkanyi+(2019)This workGilly+ (1963)Baron+ (1963)Coetzee+(1972) ( m b ) Mn(d,p) Mn (a) Ochiai+ (2008) Mn(d,x) Mn E d,t th = E d,dnth =10.6E d,p2nth =12.9 (b) FIG. 5: (Color online) Comparison of previous [11, 12, 47–50] and present (full circles) measured data, evaluated [15] (short-dashed curves), and calculated results obtained with TALYS-1.9 code [14] using either its whole default input (short-dotted)or the replacement of default deuteron OMP by that of Ref. [23] (solid curve), of deuteron-induced reactions on Mn.
20 30 40 500.111060 20 30 40 500.111010010 20 30 40 50210100400 10 20 30 40 50110100800 Mn(d,x) Mn E d,t2nth = E d,d3nth =32.4E d,p4nth =34.7 (c) Mn(d,x) Cr (d) (n,x) BF + (p,x) BF PE+CN BU+PE+CN ( m b ) Mn(d,p) Mn (a) DR TENDL-2017 PE+CN BU+DR+PE+CN E d (MeV) Mn(d,x) Mn (b) DR:(d,t) (n,2n) BF (p,d) BF BF FIG. 6: (Color online) As Fig. 5 but for present calculated results (solid curves) as well as for the PE+CN component (dashedcurves), and (a) stripping ( d, p ) and (b) pick-up ( d, t ) (dash-dotted curves), BF enhancement (dash-dot-dotted curve) as sumof either ( n, n ) (dotted curve) and ( p, d ) (short-dotted curve), or (c,d) the ( n, x ) and ( p, x ) reactions (see text). complexity of the interaction process, not entirely ac-counted for in routine evaluation/theoretical analyzes.The careful analysis of all involved reaction mecha-nisms as discussed in Sec. III may lead however to thewell improved agreement of measured data and modelcalculation results, as shown in Fig. 6. The mecha-nism detailed contributions are particularly illustratedtoo, pointing out the strength of each one. Additionalcomments concern the reaction types and residual nucleias follows. A. The Mn ( d, p ) Mn reaction
The analysis of the population of Mn residual nu-cleus through deuteron interaction with Mn repre-sents actually a distinct test of the reaction model ap-proach due to the dominant contribution of the strip-ping DR mechanism. The comparative analysis ofall reaction mechanism contributions involved in the Mn( d, p ) Mn reaction, shown in Fig. 6(a), points outthat the PE+CN component is lower by more than oneorder of magnitude than the stripping mechanism.Theinelastic breakup enhancement brought by breakup neu-trons through Mn(n, γ ) Mn reaction is practically neg- ligible and not visible in this figure.In fact, the major underestimation of the experimen-tal data by TENDL-2017 evaluation is just due to theoverlooking of the key role of direct stripping process.Actually, this proof is just in line with the previous dis-cussions of the ( d, p ) excitation functions for V [6], Cr[7], Fe [8], Ni [9], and Nb [21] target nuclei, whichshow apparent discrepancies between the measured dataand TENDL evaluations.
B. The Mn ( d, x ) Mn reaction
The analysis of the Mn( d, x ) Mn reaction [Fig. 6(b)] is the most interesting one from the viewpoint ofthe variety of contributing reaction mechanisms. Thisresidual nucleus is populated entirely through the pick–up reaction ( d, t ) at the incident energies lower than ∼ d, nd ) and ( d, p n ) reactions. The DR com-ponent becomes then not significant, with a contributionwhich is with an order of magnitude lower than the dom-inant channels above 20 MeV. The latest are PE+CNthat increase faster and reach a maximum around 29MeV. Then, two inelastic-breakup enhancing contribu-tions, through the Mn(n,2n) Mn and Mn(p,d) Mnreactions induced by breakup-nucleons, become prevail-ing with the energy increase. Thus, they are ∼
10% ofPE+CN contribution around 20 MeV incident energy,but over that above 42 MeV. This main reaction-channelinterchange leads to a slower decrease of the excitationfunction comparing to its steep increase above the thresh-old.Altogether, the sum of the five reaction contributionssucceeded to describe the measured Mn( d, pxn ) Mncross sections along the whole energy interval. Moreover,the underestimation of the lowest-energy data by theTENDL-2017 evaluation could be just the effect of the( d, t ) pick–up process overlooking as it was stressed outin previous analysis of deuteron interaction with nat
Ni[9] and Nb [21].
C. The Mn ( d, x ) Cr reaction
The new data measured in this work for Mn( d, x ) Cr reaction are important for complet-ing the Cr excitation function at incident energies justabove its effective threshold, while previous measure-ments covered higher energies from 22 up to 50 MeV[11, 12] [Fig. 6(d)]. Among possible reaction channels, Mn( d, α n ) Cr represents the main contribution tothe Cr population in the whole energy interval, as it issuggested by the shape of the excitation function.As stressed out in previous analyses of deuterons inter-acting with nat
Fe [8], nat
Ni [9], and nat
Cr [7], the mea-sured activation cross sections of Cr residual nucleus isa cumulative process (see Fig. 18 of Ref. [8]), the EC de-cay of Mn residual nucleus to Cr being much shorter( T =46.2 min) than the measurement time of the in-duced activity. However, because the population of Crresidual nucleus has been measured for incident energiesup to 50 MeV, the contribution brought by Mn decayshould be considered negligible due to the high energythresholds of the reactions populating it. These are 36.8MeV for Mn( d, t n ) and 45.6 MeV for Mn( d, p n ).A suitable account of Cr excitation function has beenobtained in this work taking into consideration the statis-tical PE+CN mechanisms as well as the inelastic-breakupenhancement brought by breakup-nucleons interactionwith Mn. The latter contribution becomes significantabove the incident energy of 40 MeV, improving well theagreement of the measured data and model calculation.
D. The Mn ( d, x ) g Mn reaction
Despite the measured cross sections in this work up toonly 20 MeV, a suitable account of the accurate recentmeasurements of g Mn activation between 20–50 MeV[11, 12] has been essential for a consistent and completeanalysis of deuteron-activation of manganese. Actually, a reliable understanding of the variety of deuteron in-teraction processes should involve nevertheless the wholerange of low incident energies, i.e. ≤
50 MeV.Population of g Mn residual nucleus follows mainlythe PE+CN statistical mechanisms, as it results fromFig. 6(c). Thus, there is a BF enhancement due tobreakup nucleons, that is weaker by at least two orders ofmagnitude. It becomes visible, in comparison with themeasured data [11, 12], only above 50 MeV. However,a sudden underestimation of these data appears below ∼
37 MeV. On the other hand, this underestimation ex-ists below the thresholds of possible reactions populat-ing Mn, as 25.9 MeV for Mn( d, t n ), 32.4 MeV for Mn( d, d n ), and 34.7 MeV for Mn( d, p n ).At this point, it became of interest to take into accountthe fact that these excitation functions [11, 12] were mea-sured using targets consisted of a natural high purityNi(2%)-Mn(12%)-Cu(86%) alloy. The authors consid-ered indeed that in principle the investigated productscould, apart from reactions on Mn, also be producedby nuclear reactions on the other two alloy components.Based on their published results for activation of theseproduct nuclides by deuterons on Ni [52, 53] and Cu,they found that only negligible corrections had to be in-troduced to their measured data derived for Mn.Nevertheless, we have included in Fig. 7 the measureddata and calculated cross sections for g Mn activationby deuterons on Mn [Fig. 6(c)] as well as on Ni [52, 53]but reduced with a correction factor 1/6 correspondingto the Ni/Mn relative amount within the target alloy.The final agreement shown by this comparison supportsindeed a Ni contribution within the measurements for Mnat the incident energies below the lowest threshold of theabove-mentioned reactions on Mn. This contributionbecomes then negligible at higher energies as well as inthe whole energy range, as well as within two orders of
20 30 40 500.010.1110 ( m b ) E d (MeV) Mn(d,x) Mn Ditroi+ (2011)Tarkanyi+(2019) TENDL-2017 Mn (BU+PE+CN) Mn+(1/6)Ni Takacs+ (2007)Hermanne+ (2013)BU+PE+CN (2016) E Mnth (1/6) x Ni(d,x) Mn FIG. 7: As Fig. 6(c) but with additional data [52, 53]and similarly calculated results (short dash-dotted curve)for Ni( d, x ) g Mn reaction, times a factor of 1/6, andthe sum (thick solid curve) of these results and those for Mn( d, x ) g Mn reaction (thin solid curve). magnitude for the other three reactions in Fig. 6.On the other hand, the calculated excitation functionof nat
Ni( d, x ) g Mn [9], with the strongest contributioncoming from ( d, α ) reaction on Ni and threshold of1.28 MeV, is different by that shown in Fig. 21 of Ref.[9]. The previous one has concerned the total activationof Mn. Finally, the addition of this calculated contri-bution of Ni activation in the target alloy of Refs. [11, 12]to the model results shown formerly in Fig. 6(c) seemsto describe well the measured data reported for g Mnactivation by deuterons on Mn. It is thus confirmed thesuitable account of all available measured cross sectionsfor deuteron activation of Mn by the present model ap-proach.
V. CONCLUSIONS
The activation cross sections for production of , Mn,and Cr radioisotopes in deuteron-induced reactions on Mn are measured at incident energies up to 20 MeV.They are in good agreement with the previously reportedexperiments [11, 12, 47–50] while all of them are the ob-ject of an extended analysis from elastic scattering untilthe evaporation from fully equilibrating compound sys-tem.A particular attention has been given at the same timeto breakup and direct reactions mechanisms. The markBU rather than BF of breakup fusion, for the sum of var-ious contributions to an activation cross section in Fig. 6,underlines the consideration of both breakup effects, i.e.,the overall decrease of σ R due to incident flux leakagetoward breakup, as well as the BF enhancement. A de-tailed theoretical treatment of each reaction mechanismhas made possible a reliable understanding of the inter-action process as well as accurate values of the calculateddeuteron activation cross sections.Furthermore, the comparison of the experimentaldeuteron activation cross sections with our model calcu-lations as well as the corresponding TENDL-2017 eval-uation supports the detailed theoretical treatment ofdeuteron interactions. The discrepancies between themeasured data and that evaluation have been the re-sult of overlooking the inelastic breakup enhancementand less appropriate treatment of stripping and pick-upprocesses. This comparison particularly indicates the im-portance of the new measured cross sections around themaximum of the Mn( d, p ) Mn excitation function aswell as the role of stripping mechanism to provide thesuitable description of these data.The measured cross sections for Mn( d, x ) Mn reac-tion at low incident energies in the present work play alsoa similar role, revealing the importance of the pick-up mechanism for the description of data around the reac-tion threshold. Actually, the main reaction-channel inter-change in the energy range up to 50 MeV for this activa-tion product underlines the complexity of the deuteron-induced reactions and need of a complete theoretical ap-proach. The first measurement of Mn( d, x ) Cr crosssections around the threshold has also been as effectivefor a suitable description of the whole excitation functionas taking into account the BF above 40 MeV.The overall agreement between the measured data andmodel calculations supports the fact that major discrep-ancies shown by the current evaluations are due to miss-ing the proper account of direct interactions. The consis-tent theoretical frame of the deuteron interactions sup-ported by advanced codes associated to the nuclear re-actions mechanisms provides predictability in additionto the use of various-order genuine Pad´e approximations[3, 4] needed in applications.However, while the associated theoretical models forstripping, pick-up, PE and CN are already settled, anincreased attention should be paid to the theoreticaldescription of the breakup mechanism including its in-elastic component. The recently increased interest onthe theoretical analysis of the breakup components (e.g.,[31, 32, 55–57]) may lead eventually to the refinement ofthe deuteron breakup empirical parametrization and in-creased accuracy of the deuteron activation cross sectioncalculations.Nevertheless, improvement of the deuteron breakupdescription requires, apart from the increase of its owndata basis, also complementary measurements of ( d, px )and ( n, x ), as well as ( d, nx ) and ( p, x ) reaction cross sec-tions for the same target nucleus, within correspondingincident-energy ranges. Moreover, as it has been provedin this work, additional measurements of deuteron-induced reaction cross sections especially just above reac-tion thresholds but also close to 50 MeV would providefurther opportunities to get a better understanding ofthese complex reactions.
Acknowledgments
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