Experimental study of the 2n-transfer reaction 138 Ba( 18 O, 16 O) 140 Ba in the projectile energy range 61-67 MeV
A. Khaliel, T.J. Mertzimekis, F.C.L. Crespi, G. Zagoraios, D. Papaioannou, N. Florea, A. Turturica, L. Stan, N. Marginean
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Experimental study of the 2n–transfer reaction Ba ( O , O ) Ba in the projectile energy range 61–67 MeV A. Khaliel , T.J. Mertzimekis , F.C.L. Crespi , G. Zagoraios , D. Papaioannou , N. Florea ,A. Turturica , L. Stan and N. M˘arginean Department of Physics, National & Kapodistrian University of Athens, Zografou Campus, GR–15784, Athens, Greece Universit´a degli Studi di Milano and INFN sez. Milano, Milano, Italy National Institute for Physics and Nuclear Engineering, Magurele, Romania
PACS – Transfer reactions
PACS – Lifetimes,Widths
PACS – Fusion reactions
Abstract – Two–neutron transfer reactions serve as an important tool for nuclear–structurestudies in the neutron–rich part of the nuclear chart. In this article, we report on the firstexperimental attempt to populate the excited states of
Ba employing the 2n–neutron transferreaction
Ba( O, O) Ba.
Ba is highly important, as it is placed on the onset of octupolecorrelations and the lifetimes of its excited states are completely unknown, with the sole exceptionof the first 2 + state. The experiment was carried out at the Horia Hulubei National Institute forPhysics and Nuclear Engineering (IFIN–HH) in Magurele, Romania. Lower limits on the lifetimesof ground state band up to the 8 + state are reported. Furthermore, relative cross sections regardingthe 2n–transfer reaction with respect to the fusion and the total inelastic reaction channels havebeen deduced. Further investigation directions of the nuclear structure of Ba are also discussed.
Introduction. –
Multinucleon Transfer Reactions(MTR) are important tools for nuclear structure stud-ies [1–3]. Especially for energies close to the Coulombbarrier, transfer–reaction cross sections are a large frac-tion of the total reaction cross section [3], thus leading toa significant population of excited states of the producednuclei. It is under discussion that such reactions can offer anew pathway for the study of neutron–rich transuraniumisotopes and superheavy elements [4], as their expectedyields are comparable to the fusion reactions, while pro-viding the advantage of offering a wide range of populatedisotopes during the same experiment.Two–neutron transfer reactions have been successfullyused for populating the excited states of nuclei, which aremoderately rich in neutrons [5]. Recently, the neutron-rich , Ba isotopes were studied experimentally in termsof their B ( E
3) values [6, 7] using radioactive beams andCoulomb excitation. The respective B ( E
3) values, al-though featuring large uncertainties, were found to be sig-nificantly larger than any theoretical prediction. Thus,a study of
Ba is important for establishing the onset (a) email: [email protected] of octupole correlation, as well as assessing the degree ofcollectivity in the barium isotopic chain as a function ofneutron number. In addition, the lifetimes of the lower–lying states of
Ba are unknown, with the sole exceptionof the first 2 +1 state, as reported in [8].Cross–section data, either absolute or relative, are im-portant for estimating the degree of level populations ofthe reaction products. Experimental cross section dataare still scarce for such reactions, especially for barium.Barium is a material that oxidizes very quickly when ex-posed to air, thus making the manufacturing of a targetquite challenging and a “difficult” nucleus to study usingstable beams.In this work, we report on the relative cross sectionsof the 2n–transfer reaction O+ Ba → O+ Bawith respect to the fusion evaporation reaction O+ Ba → Gd+4n, as well as to the total in-elastic channel. These ratios can serve as a referencepoint for the theoretical studies, i.e. refining OpticalModel Potentials, or further experimental studies usingsuch reactions. Furthermore, lower limits on lifetimesof the observed ground–state band states are reportedby taking into consideration the limitations of thep-1 a r X i v : . [ nu c l - e x ] J a n . Khaliel et al. Doppler Shift Attenuation Method (DSAM) [9, 10] for theparticular system.Fig. 1: Partial level scheme of
Ba, showing the groundstate band and a side band [11]. The alternating parity ofthe states of two bands is a hint for significant octupolecorrelations.
Experimental Details. –
Experimental setup.
The experiment was carried outat the 9 MV Tandem Accelerator Laboratory at the HoriaHolubei National Institute of Physics and Nuclear Engi-neering (IFIN–HH) in Magurele, Romania. Four projectileenergies were studied near the Coulomb barrier of the re-action, namely 61, 63, 65 and 67 MeV. The subsequent γ decay was detected by the ROSPHERE array [12] loadedwith 15 HPGe detectors. Target manufacturing.
The manufacturing of the nat
Ba target in metallic form presents important difficul-ties, as it is a material that oxidizes extremely fast. There-fore, as it is illustrated in Fig. 2, a gold–sandwiched nat
Batarget was prepared in the Target Preparation Labora-tory of IFIN–HH [13]. The target exhibits the followingstructure: Au (4.88 mg cm − ) / nat Ba (2 mg cm − ) / Au(0.5 mg cm − ). The metallic nat Ba layer (abundance of
Ba = 71.7%) was obtained through the metalothermicreduction reaction of BaCO with La metal powder asreducing agent. For this purpose about double the sto-ichiometric amount of La metal powder was thoroughly ground with the calculated amount of BaCO , in an agatemortar set. The resulted mixture was pressed into a pel-let, which was inserted into a pinhole tantalum boat. Bothends of the boat were fixed to the high current electrodesof the Quorum technologies E6700 bench top evaporatordevice. The gold foil of 4.88 mg cm − thickness, preparedin advance by rolling, was glued to the target frame andplaced 4 cm above the tantalum boat in the evaporator.After a high vacuum of 3 . × − mbar was reached, alow current was applied through the tantalum boat to de-gassing of CO resulted from the thermal decomposition ofBaCO . Therefore, the current through the tantalum boatwas slightly increased until the reduction temperature wasreached. The evaporation process was carried out until thedesired thickness was obtained. The obtained nat Ba layerwas covered with a thin gold layer of 0.5 mg cm − with-out breaking the vacuum, to protect the metallic nat Baagainst oxidation. This deposition was made with a tung-sten basket, fixed at 9 cm distance above the substrate.The determination of the thick gold backing’s thicknesswas done by weighing, while the other two layers weredetermined by calculating the thickness from the initialamount of the substance used.
Analysis and Results. –
Lifetimes.
Lower limits on lifetimes of the states upto 8 + in the ground–state band [11], corresponding to theobserved transitions can be set, by taking into accountthe limitation of the Doppler Shift Attenuation Method(DSAM). In Fig. 3a, the two overlapping transitions ofenergies 528 and 530 keV are shown, depopulating the 4 + and 6 + states of the ground–state band. As it can be seenfor the spectra recorded in the backward (143 ◦ ) and for-ward ring (37 ◦ ), no visible lineshapes can be distinguished.The same holds for Fig. 3b, where the transition of 808 keVis depopulating the 8 + , also in the ground–state band.The maximum recoil velocity in the particular reactionmechanism is 2% the speed of light. At such recoil ve-locities, the range of lifetimes that can be measured withDSAM should be lower than approximately 1 ps [9,14–16].The present limit is established in terms of the range oflifetimes that the particular method can be applied, andnot the sensitivity of the experimental setup. Relative cross sections.
The cross section of a reactioncan be estimated by the relation: σ = N R Φ N t (1)where N R is the number of occurring reactions, N t is thenumber of target nuclei that the beam interacts with, andΦ is the incident flux of projectiles.The reactions O + Ba → O + Ba → Gd + 4 n → O + Ba ∗ p-2n–transfer study of BaFig. 2: The evaporator chamber (left) and a picture taken during the evaporation procedure (right).stem from the same entry channel and occur inside thebarium foil. In general, the relative cross section for twodifferent exit channels α , β can be estimated by: σ R = N R ( α ) N R ( β ) (2)i.e. by determining the ratios of the corresponding numberof reactions.In the present case, the number of reactions can be de-duced by measuring all observed photopeaks feeding theground state of the produced nuclei for the two above exitchannels, and then correcting with the full absolute effi-ciency of the ROSPHERE array: N R = A(cid:15) abs (3)where A is the area of the photopeak and (cid:15) abs is the ab-solute efficiency.For the 2n–reaction O+ Ba → O+ Ba, only the E γ = 602 keV transition was observed, while for the O+ Ba → Gd+4 n reaction, only the transition with E γ = 344 keV was recorded in the data (see Fig. 1).Also, for the total inelastic channel, the transition E γ =1436 keV was observed. A projection spectrum of the full γ − γ matrix is shown in Fig. 4, with the peaks of interestmarked.By extracting the ratios, and taking into account theenergy loss inside the barium foil of the target (Ta-ble 1), the results for the relative cross sections of the2n–neutron transfer reaction O + Ba → O +
Bawith respect to the fusion–evaporation counterpart O + Ba → Gd + 4n and with respect to the total inelasticchannel are shown in Fig. 5 as a function of energy in thelaboratory system.
Cross section predictions. –
In order to furtherinvestigate the experimental values of the relative crosssections measured in the present work, theoretical calcu-lations have been performed using the
GRAZING 9 [17] and
PACE4 [18] codes.The former uses Winther’s grazing model [17], which hasbeen proven successful for the description of one– or two–nucleon transfer reactions [19]. Calculations performedwith the
GRAZING 9 code use a semi–classical approachdeveloped in Ref. [20]. For a small number of nucleontransfers (up to 6–8 neutrons) and for nuclei close to themagic shell closures, the particular model describes ex-perimental data very well; however, it tends to slightlyunderestimate the data for large numbers of nucleons (seediscussion in [21]).On the other hand, the
PACE4 code is the latest ver-sion of a modified JULIAN code [22] and uses the Bassmodel [23], which was derived by using a geometric inter-pretation of available experimental data combined witha Monte–Carlo approach to determine the decay of thecompound system in the framework of Hauser–Feshbachformalism [24]. As stated in Ref. [19], the Bass modelpotential provides an overall excellent description for thefusion cross sections at energies starting from the Coulombbarrier and above. However, experimental evidence showsthat the particular model significantly underestimates thecross section data below the Coulomb barrier [19].All calculations have been performed using the defaultp-3. Khaliel et al.
Table 1: Experimental results and theoretical calculations. From left to right column: E b is the beam energy; E Ba is the incident energy of at the front of the Barium foil, by taking into consideration the beam energy loss inside thefront Au foil; ∆ E Ba is the total energy loss in the barium foil; E eff is the effective energy at the middle of the bariumfoil; σ fusR is the ratio of the 2n–transfer reaction cross section over the cross section of the fusion-evaporation channel(see eq. 2); σ inelR is the ratio of the 2n–transfer reaction cross section over the total inelastic cross section; σ Gd and σ Ba are normalized cross sections (see text for details); σ P ACE and σ GRAZING are results of
PACE4 and
GRAZING 9 calculations for the O + Ba → Gd + 4n and O + Ba → O +
Ba reactions, respectively. All values arein the laboratory system. E b E Ba ∆ E Ba E eff σ fusR σ inelR σ Gd σ Ba σ P ACE σ GRAZING (MeV) (MeV) (MeV) (MeV) (mb) (mb) (mb) (mb)61 60.04 4.91 57.59 0.3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
520 525 530 535 540E [keV]0100200300400500600700
37 deg143 deg (a)
790 795 800 805 810 815 820 825 830E [keV]020406080100120140160180
37 deg143 deg (b)
Fig. 3: Backward (143 ◦ ) and forward (37 ◦ ) spectra for (a)the 528 and 530 keV overlapping transitions, and (b) forthe 808 keV transition. The spectra show no backward–forward lineshapes.parameters each code employs. Fig. 6 shows the resultsof the calculations: Fig. 6a includes cross section calcu- lations with PACE4 (solid circles), while Fig. 6b containscalculated cross sections with
GRAZING 9 (solid squares).
PACE4 could not produce a value at the lowest energy( E eff =57.6 MeV), as was expected, since this value isfar below the barrier. The experimental absolute yield forthe fusion–evaporation channel is shown in Fig. 6 (soliddiamonds). All data points have been normalized witha single numerical factor. That factor was estimated byscaling the experimental point at the energy nearest tothe barrier ( E eff =63.7 MeV) with the respective valuecalculated with PACE4 (see overlapping points in Fig. 6a).Calculations with
GRAZING 9 are shown in Fig. 6b (solidsquares). In the same graph, experimental data of the 2n–transfer reaction O + Ba → O +
Ba are shown.These data have been extracted from the ratio in Fig. 5taking into account the scaled cross sections of the fusion–evaporation channel, as described earlier. No further scal-ing is involved.
Discussion and future investigations. –
Withinthe present framework, a study of the nucleus
Ba by us-ing the 2 n –transfer reaction O + Ba → O +
Ba,has been performed. By considering the kinematics of thereaction studied and the limitation of DSAM, lower limitson the lifetimes of 3 states of the ground state band havebeen set over 1 ps. Of course, further studies are necessaryin order to further constrain the above limit. The presentresults also sets the path for using a different technique forthe measurement of the particular lifetimes, such as theplunger technique or the fast–timing technique. For directmeasurement of the reduced transition probabilities, espe-cially for the B ( E
3) corresponding to the first 3 − state,the use of radioactive beams and Coulomb excitation tech-nique can override a lot of issues, such as possible targetcontamination and the level population strength.The relative cross sections between the 2n–transfer re-action O + Ba → O +
Ba and the competingfusion–evaporation reaction O + Ba → Gd + 4nhave been deduced by taking into account the relativep-4n–transfer study of Ba
200 400 600 800 1000 1200 1400 1600E [keV]050100150200250300 ◊ C oun t s / . k e V A u Gd A u Gd: 2 + → + G d Gd Gd G d Ba: 2 + → + 27 Al Al Ba: 2 + → +22 Ne Mg Fig. 4: Total projection spectrum from the γ − γ matrix acquired using the ROSPHERE array. Transitions in bariumisotopes are marked, as well as several from the fusion–evaporation channels. A few contaminant peaks are alsoindicated.yield of the two observed transitions feeding the groundstate of the two produced nuclei. The relative cross sec-tion behavior seems to follow a reducing pattern with re-spect to beam energy, showing that the fusion–evaporationchannel becomes stronger faster, as the Coulomb barrieris approached. This behavior is rather expected given thefact that the reactions occur in the pure–tunneling energyrange. In addition, the relative cross sections of the reac-tion O + Ba → O +
Ba and the total inelasticchannel are presented. The inelastic channel is a compet-ing reaction channel, which as can be seen from Fig. 5b,the respective cross section values are of the same order ofmagnitude within the studied energy range. The behav-ior of these cross sections follows an increasing pattern,indicating that the 2n–transfer reaction shows a strongerincrease as the energy increases towards the Coulomb bar-rier.Absolute cross sections deduced with this method, tak-ing advantage of the ratios of cross sections, may be lowerthan their actual values, as some transitions feeding theground state may not be observed in the spectra,resultingin missing strength in the overall estimation. In addition,the
Gd decay features E γ –spectrum, despite their contribution to the to-tal number of produced nuclei. While this can be usuallytreated as a weak effect, it cannot be assumed with cer- tainty.Calculations with the theoretical codes PACE4 and
GRAZING 9 have been performed to provide a compari-son with experimental data produced in the present work.The scaling of the experimental data to the
PACE4 result atthe maximum energy, almost identical to the energy of thebarrier, can be trusted to produce absolute cross sectionsfor the absolute cross sections in the fusion–evaporationchannels. This becomes evident when the deduced crosssections for the studied 2n–transfer reaction are furthercompared to
GRAZING 9 calculations. There is a very goodagreement between experimental data and theory, both intrend and in magnitude. The two lowest energy points areeffectively the same within the experimental uncertainty,while the discrepancy between the rest is of the order of20%. It has to be stressed again that this comparisoninvolves no other scaling than the one used for the fusion–evaporation channel. It would be interesting also to checkthis method in more detail for energies near and above thebarrier in the future, especially for neighboring nuclei inthis mass regime.In conclusion, the results provide useful information forthe specific case study, for both the experimental crosssections, as well as the validity of theoretical models atenergies near the barrier. 2n–transfer reactions are a veryuseful tool to study unstable, moderately neutron–rich nu-clei. To this end, the knowledge of the 2n–transfer–to–p-5. Khaliel et al. fusion cross section ratio can be extremely useful, for ex-ample, for reducing the fusion background, especially innuclear structure studies. In addition, cross section ratioscan help in constraining the optical model potential phe-nomenological parameters, for the better understanding ofsystems involving heavy–ion reactions. Such experimentaldata in the region around
Ba are very scarce, but alsovery important for studies trying to extend our knowledgeon more exotic species towards the neutron–dripline. ∗ ∗ ∗
This research work was supported by the HellenicFoundation for Research and Innovation (HFRI) andthe General Secretariat for Research and Technology(GSRT) under the HFRI PhD Fellowship Grant (GA. No.
56 58 60 62 64 66
Energy [MeV] . . . . . . σ ( B a + O ) / σ ( G d + n ) Data (a)
56 58 60 62 64 66
Energy [MeV] . . . . . σ ( B a + O ) / σ ( B a + O ) Data (b)
Fig. 5: Relative cross section of the two neutron–transferreaction O+ Ba → O+ Ba with respect to the fu-sion evaporation reaction O+ Ba → Gd+4 n (left)and the ratio with respect to the total inelastic channel O+ Ba → O+ Ba ∗ (right).
56 58 60 62 64 66
Energy [MeV] − − − σ ( G d + n ) [ m b ] DataPACE4 (a)
56 58 60 62 64 66
Energy [MeV] − − σ ( B a + O ) [ m b ] GRAZING 9Data (b)
Fig. 6: (a) Normalized cross sections of the fusion–evaporation channel after normalization to
PACE4 calcu-lations (see text). Vertical error bars are smaller than thesymbol size. (b) Deduced cross sections for the 2n–neutrontransfer channel (solid diamonds) after taking into accountthe results from panel (a), together with
GRAZING 9 cal-culations (solid squares). No scaling is involved in any ofthe data sets in panel (b). The dotted line is to guide theeye. Scales of y–axes in (a) and (b) are different.74117/2017). Partial support from ENSAR2 (EU/H2020project number: 654002) is acknowledged.
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