Investigation of the one-neutron transfer in 13 C + 28 Si at E lab = 30 and 34 MeV
R. Linares, C. C. Seabra, V. A. B. Zagatto, V. Scarduelli, L. Gasques, L. C. Chamon, B. R. Gonçalves, D. R. Mendes Junior, A. Lépine-Szily
aa r X i v : . [ nu c l - e x ] J a n Investigation of the one-neutron transfer in C + Si atE lab = 30 and 34 MeV
R. Linares, ∗ C. C. Seabra, V. A. B. Zagatto, V. Scarduelli,
1, 2
L. Gasques, L. C. Chamon, B. R. Gon¸calves, D. R. Mendes Junior, and A. L´epine-Szily Instituto de F´ısica, Universidade Federal Fluminense,24210-340, Niter´oi, Rio de Janeiro, Brazil Instituto de F´ısica, Universidade de S˜ao Paulo, S˜ao Paulo, Brazil (Dated: January 29, 2020)
Abstract
Background:
Neutron transfer measurements for the O + Si system have shown thatthe experimental one-neutron and two-neutron transfer cross sections are well reproduced withspectroscopic amplitudes from two different shell model interactions for the Si isotopes: psdmod for the two-neutron transfer, and psdmwkpn for the one-neutron transfer.
Purpose:
The origin of this ambiguity can be related to a more complex mechanism in theone-neutron transfer that requires the unpairing of neutrons prior to its transfer in the ( O, O)reaction. Studying a nucleus where this characteristic is absent ( C) should help to elucidate thisquestion.
Method:
One-neutron transfer cross sections were measured for the C + Si at E lab = 30, and34 MeV, and compared with coupled reaction channel calculations using spectroscopic amplitudesderived from the psdmod and psdmwkpn shell model interactions.
Results:
The spectroscopic amplitudes from the psdmod interaction for the relevant states in Si provide a good description of the experimental data and the corresponding values agree withprevious estimates obtained from the (d,p) reaction.
Conclusions:
The experimental data for the one-neutron transfer to Si induced by ( C, C)reaction is well reproduced using spectroscopic amplitudes from the psdmod . ∗ [email protected]ff.br . INTRODUCTION Particle configurations of bound states in the atomic nuclei can be studied using transferreactions. In such studies, the optical potential and spectroscopic factors ( S ) are importantparameters in the calculations of the transfer cross sections. Experimental values for S canbe obtained from a direct comparison between experimental and theoretical cross sections,as in (d,p) [1, 2], (t,d) [3], ( Li, Li) [4] reactions. However, the experimental approach maylead to some ambiguities in the S values for many nuclei. For instance, the S value for ap / valence neutron to C ranges from 0.3 (from C(p,d) C data at 65 MeV [5]) to 1.4(from C(d,p) C data at 15 MeV [6]). The main reasons for these discrepancies are theadopted optical potentials and the coupling scheme considered in direct reaction calculation[7].Recent advances in experimental setups have renewed the use of heavy-ion probes, like( C, C) and ( O, O), in transfer reactions [8]. Some advantages over the use of light-ion are: i) avoid the inclusion of the break-up channel [9]; and ii) suppression of the effectof non-locality, that is relevant in (d,p) reactions [10, 11]. On the other hand, effects ofstrong absorption are more pronounced and the angular distributions exhibit a diffraction-like pattern as the bombarding energy increases. Moreover, second-order mechanisms suchas projectile/target excitation preceding and/or following the transfer of nucleons, mustbe taken into account properly. In addition, partial waves that contribute to the transferreaction are limited to a range of optimum Q values for a given reaction and energy.Recently, analysis of the one-neutron (1NT) and two-neutron transfer (2NT) to Si, in-duced by the ( O, O) [12] and ( O, O) [13] reactions respectively, have been reported.In these works, coupled reaction channels (CRC) were performed including S for the rel-evant states derived from nuclear shell models with suitable interactions and model spacesto describe the low-lying states in the , , Si isotopes. Best agreement between experi-mental data and calculations have been achieved adopting different interactions for the 1NT( psdmwkpn ) and 2NT ( psdmod ) processes.It is not clear how the 1NT is affected by the pre-formed paired valence neutrons inthe O nucleus. In this work, we have analyzed the 1NT to the Si using the ( C, C)probe. The C is treated as a single valence neutron bound to a C nuclear core. We havemeasured elastic cross sections at E lab = 25, 30, and 34 MeV and inelastic and one-neutron2IG. 1: (Color online) Sketch of the experimental setup with an array of 9 Si detectorsmounted in angular steps of 5 ◦ with the first one at θ lab = 25 ◦ . In panel a) top view of thesetup and b) frontal view.transfer cross sections at E lab = 30, and 34 MeV. Cross sections for elastic and inelasticscattering are used to constraint the parameters of the effective nucleus-nucleus potential.This paper is organized as follows: the experimental details and the theoretical analysis arediscussed in sections II and III, respectively. The conclusions are given in section IV. II. EXPERIMENTAL DETAILS
The experiment was performed at the 8 MV tandem accelerator of the University of S˜aoPaulo. The C beam was accelerated at E lab = 25, 30, and 34 MeV with averaged beamintensity of about 30 enA on the target. For the C + Si system, the Coulomb barrierheight is V B = 18.9 MeV (in the laboratory reference).Fig. 1 shows a sketch of the Silicon Array and Telescopes of Usp for Reactions and Nuclearapplications (SATURN) system [14], mounted in the scattering chamber for the measure-ments. A set of 9 surface barrier Si detectors was mounted at 30 cm away from the targetsand with 5 ◦ of angular step size, covering the angles from 25 ◦ to 65 ◦ (laboratory framework).A 4-position mobile target ladder, placed at the center of the chamber, was mounted with 23hin Si foils (Si-only) 99.9% isotopically enriched and 2 other foils composed of Si witha thin backing layer of
Au (Si+Au). Thicknesses of the Si layers were measured byRutherford backscattering (RBS) of He beam and were approximately 40 µ g/cm .At each beam energy, measurements were carried out with the Si+Au target, for normal-ization of the cross sections, and the Si-only target, for a clear identification of the 1NT.The energy calibration of each Si detector was performed adopting the elastic peaks associ-ated to the C scattered off the Si and
Au nuclei. The energy resolution achieved was0.2 MeV. The ratio between Au and Si foil thicknesses was determined from measurementsat E lab = 25 MeV, using the angular points at θ lab = 25 ◦ , 30 ◦ and 35 ◦ , and the theoreticalcurve.Typical Q -energy spectra, defined as the energy relative to the elastic scattering in the C + Si, are shown in Fig. 2 at a) θ lab = 25 ◦ , and b) 45 ◦ measured at E lab = 34 MeV.In this representation, the elastic scattering from Si corresponds to a peak centered at Q = 0.0 MeV. The inelastic peak associated to the excitation of Si . MeV corresponds tothe peak around Q = -1.8 MeV. At forwards angles, scattering off contaminants (oxygen)present in the target superimposes with the inelastic peak, as indicated by the asterisk inFig. 2a. Scattering off the Au corresponds to peaks with
Q > Q -energy thatdepends on the scattering angle.For the C + Si system, the
Q-value for 1NT g.s. → g.s. is +3.53 MeV and, there-fore, this reaction channel is energetically distinguished from elastic and inelastic events. InFig. 2a, the peak at Q = +3.6 MeV ( Si g.s. ) is associated to the 1NT g.s. → g.s.. At θ lab = 45 ◦ , the inelastic excitations of the Au interfere with the Si g.s. peak (see Fig. 2b).Between the elastic of Si and
Au it is also observed a peak that comes from K con-tamination in the target carried in during the manufacturing process of the thin films.The presence of this contamination was also confirmed with the Rutherford BackscatteringSpectrometry (RBS) analysis of the foils produced in the same batch, indicating a 2% Kcontamination in the target.A typical spectrum for Si-only target is shown in Fig. 3 (blue histogram). The 1NTto the Si g.s. , the elastic peak of the Si and inelastic peak of the Si . correspond topeaks 1, 4 and 6, respectively. Other peaks associated to reactions with contaminants onthe target were also identified (listed in the caption of Fig. 3), except the peak 5. This ispossibly associated to the inelastic scattering that populates the 1/2 + (2.52 MeV) in the4IG. 2: (Color online) The Q -energy spectrum for the measurements with C at 34 MeVon the Si+Au target. The spectra observed at θ lab = 25 ◦ and 45 ◦ are shown in panel a)and b), respectively. The asterisk in panel a) indicates the presence of oxygencontamination (in the target) in the inelastic peak. K. Calculation of the energies of p and α particles coming from the fusion-evaporationprocess, using the PACE4 code [15, 16], is presented in Fig. 3 (purple histogram). Thisshows that, in the energy range of the Si g.s. peak, there is no significant interference ofhigh energetic p or α particles.Yields in the elastic, inelastic and 1NT were determined from a gaussian curve on topof a linear background fitted to the experimental peaks. An example of such fits is shownin Fig. 3 in which the gaussian (yellow curve) and the linear (green curve) components arereproduced for the peak number 1. There are some counts with Q-value higher than +4.0MeV that may come from contaminant heavier than K in the the Si-only target. Possibleheavy contaminants are I, from the release agent, and
W, from the cathode used asholder for the Si powder for the manufacturing of the thin films. Such heavier contaminantswere not observed in the RBS analysis. Even though, in both cases the elastic scattering of C would produce peaks at Q-values +4.1 and +4.5 MeV, respectively. For the inelastic5 − − − − − − − C oun t s / ( . M e V ) h5 ° = 35 lab θ = 34 MeV lab E 123567 4
FIG. 3: (Color online) The Q -energy spectrum for the measurements with C at 34 MeVon the Si-only target at θ lab = 35 ◦ (blue histogram). In the same plot is shown the energyspectrum of p and α from fusion-evaporation process (purple histogram). Peak numberingas follows: 1 - Si g.s. (1NT); 2 - Si and K g.s. (1NT); 3 - elastic peak K; 4 - elasticpeak Si; 5 - possibly inelastic peak in K . ; 6 - inelastic peak Si . ; 7 - elastic peak O and C. Counts in the peak 1 were determined from the gaussian curve represented bythe yellow curve. See text for further details.peak, the background due to the presence of peak 5 at some angles was subtracted adoptinga linear behavior.
III. THEORETICAL ANALYSIS
Direct reaction calculations were performed within the coupled reaction channel (CRC)framework using the FRESCO code [17] with exact finite range and prior representation.Non-orthogonality corrections and full complex remnant terms were considered in the cou-pled channel equations. A sketch of the coupling scheme considered in the CRC calculationsis shown in Fig. 4. The inelastic channels were considered using the deformation parameterfor the collective states. For the Si target nucleus, β = 0 . C projectile nucleus, β = 0 .
143 [19]. The single-particle wave functions used inthe matrix elements were generated using Woods-Saxon potential with depth adjusted toreproduce the experimental separation energies for one neutron in C (S n = 4.95 MeV) and Si (S n = 8.45 MeV). The reduced radii and diffuseness parameters for the Si and Ccores were set to values previously used in the analysis with the O projectile. These values6IG. 4: (Color online) Coupling scheme considered in the CRC calculations.are 1.26 fm and 0.65 fm for Si core [13] and 1.25 fm and 0.80 fm for C [20], respectively.Calculations have been performed within 10% deviation in the adopted reduced radii anddiffuseness values and no significant effect were observed in the results.The S values were obtained using the NuShellX code [21]. For , C, the calculationswere performed using the psdmod interaction, that is a modified version of the psdwbt inter-action [22], which gives a reasonable description of the p-sd-shell nuclei. For , Si isotopes,two interactions are considered: again the psdmod and the psdmwkpn interaction [23]. Thelatter is a combination of the Cohen-Kurath interaction [24] for the p-shell, the Wildenthalinteraction [25] for the sd-shell and the Millener-Kurath interaction [26] for the couplingmatrix elements between p- and sd-shells. In both interactions, the model space assumes He as a closed core and valence neutrons and protons in the 1p / , 1p / , 1d / , 1d / , and2s / orbitals. The spectroscopic amplitudes of states in Si for both interactions can befound in Ref. [12]. For clarity, from now on CRC- psdmod and CRC- psdmwkpn stand for theCRC calculations using the S for the Si derived from psdmod and psdmwkpn interactions,respectively.For the CRC, the S˜ao Paulo double folding potential (SPP) [27] was used for the real andimaginary parts of the optical potential. In the entrance partition the N i was adjusted todescribe the experimental data for elastic and inelastic scatterings to account for couplingsnot explicitly considered in the coupling scheme.7 θ c.m. (degrees) -4 -3 -2 -1 σ / σ R u t h CRC (N i = 0.1)O.M. (N i = 0.7) internal pot.exp. dataE lab = 25 MeVE lab = 30 MeV (x 0.1)E lab = 34 MeV (x 0.01) FIG. 5: (Color online) Angular distributions of the elastic cross sections for the C + Siat E lab = 25, 30, and 34 MeV. The data points at θ lab = 25 ◦ , 30 ◦ , and 35 ◦ forE lab = 25 MeV were adopted for normalization of the cross sections.Fig. 5 shows the angular distributions of the elastic cross sections for E lab = 25, 30, and34 MeV. Optical model calculations using an internal imaginary potential is shown as dot-dashed purple curve. The internal imaginary potential was defined as a Wood-Saxon shapewith depth, reduced radius and diffuseness set to 50 MeV, 1.06 fm and 0.2 fm, respectively.This optical potential underestimates the cross sections at large scattering angles. A secondoptical model calculation was performed using the SPP shape for the imaginary part withadjustable N i factor. The best agreement between experimental data and theoretical curvesis achieved for N i = 0.7, in Fig. 5 represented as dashed blue curves. In the CRC calculations,experimental data are well reproduced with N i = 0.1 in the entrance optical potential.Similar results are obtained for N i = 0.2, and 0.3 (not shown in Fig. 5). This indicatesthat most relevant reaction channels (inelastic and 1NT) are accounted for in the couplingscheme and, consequently, a smaller imaginary factor is required.The angular distributions of the inelastic cross sections to the 2 + excited state in Si forE lab = 30, and 34 MeV are shown in Fig. 6, along with CRC calculations with different N i inthe imaginary term of the optical potential. Good overall agreements between experimental8 d σ / d Ω ( m b / s r) N i = 0.1N i = 0.2N i = 0.3 exp. data
20 40 60 80 θ c.m. (degrees) E lab = 30 MeVE lab = 34 MeV FIG. 6: (Color online) Angular distributions of the inelastic 2 + in Si cross sections forthe C + Si at E lab = 30, and 34 MeV.data and CRC calculations are achieved for N i = 0.1 and 0.2. The theoretical curves for theelastic scattering with these N i are almost indistinguishable. The fit to elastic and inelasticdata provides a good constrain to the parameter of the imaginary potential.The cross sections for the 1NT at E lab = 30, and 34 MeV are shown in Fig. 7. The CRC- psdmod and CRC- psdmwkpn calculations were performed using N i = 0.1 in the opticalpotential of the entrance partition. Similar results are obtained using N i = 0.2 and 0.3,meaning that the effect of N i values, between 0.1 and 0.3, is not strong to the 1NT channel.In the exit partition, the imaginary strength factor (N i ) was set 0.78, since this value providesa good description of the elastic scattering cross section for many systems in a wide energyinterval [28]. The effect of reduced radii and diffuseness parameters, used in the form-factorto construct the single-particle wave functions of the C and the Si, has been checked.The reduced radii and diffuseness values were varied within the 1.20 - 1.25 fm and 0.7- 0.8 fm ranges, respectively. These are represented in the envelope curves, for each CRCcalculation, in Fig. 7. The theoretical curves are more sensitive to the diffuseness parameter.Even though, the overall effect in the calculations is not so crucial and the CRC- psdmwkpn curves systematically lie below the CRC- psdmod . The coupling space has also been checkedand the results for elastic, inelastic and 1NT are practically the same with the removal of9 -1 d σ / d Ω ( m b / s r) CRC- psdmod
CRC- psdmwkpn exp. data
20 40 60 80 θ c.m. (degrees) -2 -1 E lab = 30 MeVE lab = 34 MeV FIG. 7: (Color online) Angular distributions of the 1NT leading to the population of theg.s. in Si cross sections for the C + Si at E lab = 30, and 34 MeV.3 / − and 5 / + states in C and the 4 + state in Si.The CRC- psdmod reproduces better the experimental values at E lab = 34 MeV and theagreement is limited at 30 MeV. Nevertheless, the CRC- psdmwkpn underestimates the crosssections at both energies. This indicates that the psdmod interaction provides a betterestimate for the S of the , Si isotopes. In Table I, it is presented a comparison betweenthe spectroscopic factors ( S ) for the Si to Si transitions derived from the psdmod and psdmwkpn interactions and experimental estimates obtained from the (d,p) reaction andDWBA calculations [1, 2, 29]. The value of S from psdmod is close to the one reported inRef. [1] whereas the psdmwkpn estimate is closer to that in Ref. [2]. All values are withinthe 1-uncertainty interval obtained from a systematic analysis of experimental data for (d,p)and using a deuteron optical potential which approximately accounts for deuteron breakupRef. [29] .The success of CRC- psdmod compared to the present data is consistent with analysisfor the 2NT in the Si( O, O) Si, for which the experimental data were reproducedadopting the S derived from the psdmod interaction for the Si isotopes [13]. In the analysisof the 1NT to Si induced by ( O, O) reaction, the experimental data were reproducedbetter using the S from the psdmwkpn interaction [12] instead. The fact that different10ABLE I: Spectroscopic factors ( S ) for the Si to Si transitions obtained by shellmodel calculations using psdmod and psdmwkpn interactions. Values obtained from Si(d,p) Si of Refs. [1, 2, 29] are also included. states |S| initial final psdmod psdmwkpn Ref. [1] Ref. [2] Ref. [29] Si g.s. 29 Si g.s. ± shell model interactions are adopted for the description of the 1NT and 2NT experimentaldata are interpreted as follows. Accurate prediction for transfer reaction demands a properdescription of the nuclear structure of the nuclear partners, represented by the S , reliableoptical potential for the scattering and also a detailed description of the transfer process. Theusual picture of the O nuclei is a dineutron valence particle bound to a O core. Therefore,the 1NT induced by O occurs first by breaking the short-range pairing interaction of thetwo neutrons and, then, one neutron is transferred to the target nuclei. Such dynamics ofpairing between two neutrons is not detailed considered into the CRC framework. The useof the psdmwkpn interaction for the ( O, O) reaction may have covered up what is, in fact,an effect of transfer mechanism instead of nuclear structure of Si.
IV. CONCLUSIONS
The 1NT cross sections in the Si( C, C) Si reaction were measured at E lab =30, and34 MeV. Within the CRC framework, the optical potential was adjusted to describe experi-mental data for elastic scattering at E lab = 25, 30, and 34 MeV and the inelastic scatteringat E lab = 30, and 34 MeV. The CRC calculation revealed the necessity to include a smallimaginary term on the the optical potential to account for reaction channels not explicitlyincluded in the coupling scheme. This was performed using the S˜ao Paulo potential withimaginary normalization of N i = 0.1 and indicates that some given channel has not beenexplicitly coupled to calculations. Elastic, inelastic and transfer data have been properlydescribed using such configuration. The spectroscopic amplitudes obtained from the psd-mod shell model interaction provides a good description of the experimental data and inaccordance with previous analysis of the (d,p) data.11 CKNOWLEDGMENT
This project has received funding from CNPq, FAPERJ, FAPESP and CAPES and fromINCT-FNA (Instituto Nacional de Ciˆencia e Tecnologia- F´ısica Nuclear e Aplica¸c˜oes). Wewould also like to thank the technical staff of LAFN for assisting in the maintenance andoperation of the accelerator. This research has also used resources of the Laboratory ofMaterial Analysis with Ion Beams - LAMFI-USP. The authors acknowledge the laboratorystaff for assistance during the RBS experiments.12
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