Investigation of complete and incomplete fusion in 7Li+124Sn reaction aroundCoulomb barrier energies

V. V. Parkar1,2∗, Sushil K. Sharma2†, R. Palit2, S. Upadhyaya3‡, A. Shrivastava1,4, S. K. Pandit1,4, K. Mahata1,4,

V. Jha1,4, S. Santra1,4, K. Ramachandran1, T. N. Nag5, P. K. Rath6, Bhushan Kanagalekar7, and T. Trivedi81Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai - 400085, India

2Department of Nuclear and Atomic Physics, Tata Institute of Fundamental Research, Mumbai - 400005, India3Department of Applied Physics, Amity University, Noida -201313, India

4Homi Bhabha National Institute, Anushaktinagar, Mumbai - 400094, India5Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai - 400085, India6Manipal Centre for Natural Sciences, Manipal University, Manipal - 576104, India7Department of Physics, Rani Channamma University, Belagavi - 591156, India and

8Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur - 495009, India

The complete and incomplete fusion cross sections for 7Li+124Sn reaction were measured usingonline and offline characteristic γ-ray detection techniques. The complete fusion (CF) cross sectionsat energies above the Coulomb barrier were found to be suppressed by ∼ 26 % compared to thecoupled channel calculations. This suppression observed in complete fusion cross sections is foundto be commensurate with the measured total incomplete fusion (ICF) cross sections. There is adistinct feature observed in the ICF cross sections, i.e., t-capture is found to be dominant thanα-capture at all the measured energies. A simultaneous explanation of complete, incomplete andtotal fusion (TF) data was also obtained from the calculations based on Continuum DiscretizedCoupled Channel method with short range imaginary potentials. The cross section ratios of CF/TFand ICF/TF obtained from the data as well as the calculations showed the dominance of ICF atbelow barrier energies and CF at above barrier energies.

PACS numbers: 25.60.Pj, 25.70.Jj, 21.60.Gx, 24.10.Eq

I. INTRODUCTION

The study of fusion involving weakly bound projec-tiles is of interest for probing the influence of low lyingstates in the continuum, the extended shape, and quan-tum tunneling at energies near the Coulomb barrier [1].In this context, the fusion reactions with radioactive ionbeams is a topic of discussion over the last two decadesfor its possible application in production of super-heavynuclei. It is expected that the extended structure of theloosely bound nuclei could in principle induce a large en-hancement of fusion which may aid to the synthesis ofsuper-heavy nuclei in fusion reactions. Alternately, forthe weakly bound nuclei, the fusion process might be af-fected by their low binding energy, which can cause themto break up while approaching the fusion barrier. Thismay effectively reduce the complete fusion cross sections,making it difficult to form the super-heavy nuclei [2, 3].

Recent studies on fusion with weakly bound stable pro-jectiles (6,7Li and 9Be) on different targets have shownthat the process of complete fusion (CF), where the en-tire projectile or all its fragments are captured, is sup-pressed when compared to predictions based on Coupled-channels model at energies above the Coulomb barrier [1].

∗vparkar@barc.gov.in†Present address : The Marian Smoluchowski Institute of Physics,Jagiellonian University, Lojasiewicza 11, 30-348 Krakow, Poland‡Present address : The Marian Smoluchowski Institute of Physics,Jagiellonian University, Lojasiewicza 11, 30-348 Krakow, Poland

In particular, experiments with 6,7Li and 9Be projectileson medium and heavy mass targets have given interestingconclusions on the systematics of CF suppression factor.The suppression in CF involving these projectiles is foundto be independent of target mass in many studies [4–7].Further the suppression factor shows an increasing trend,with decrease in the breakup threshold of the projectile[6].

The observed suppression in CF could be attributedto processes where only a part of the projectile fuseswith the target, known as incomplete fusion (ICF). Inaddition, ICF can also accommodate the two/three stepprocesses, viz .; transfer of few nucleons to/from the pro-jectile, which breaks and one of the two fragments getcaptured in the target. Influence of all such breakupprocesses on suppression in CF cross sections were dis-cussed in recent works [8–10]. For investigating the ex-tent to which ICF influences the suppression in CF, asimultaneous measurements of both CF and ICF is cru-cial. At present such information is available for verylimited cases [11–14].

In this paper, we report the measurement of completeand incomplete fusion cross sections for 7Li+124Sn reac-tion around the Coulomb barrier energies, utilizing on-line and offline characteristic γ-ray detection techniques.The dominant evaporation residues (ERs) from com-plete fusion are 126−128I (3n-5n). In addition, we havealso identified the residues from α-capture, populating126,127Te in the online measurement. In the presentcase, the residues 128I (3n) and 126I (5n) along withthe residues following t-capture, viz., 124Sn(t,1n)126Sb,

arX

iv:1

801.

0699

6v1

[nu

cl-e

x] 2

2 Ja

n 20

18

2

124Sn(t,2n)125Sb, 124Sn(t,3n)124Sb and transfer prod-ucts 124Sn(7Li,6Li)125Sn (one neutron stripping) and124Sn(7Li,8Li)123Sn (one neutron pickup) undergo ra-dioactive decay with half-lives suitable for offline mea-surements. The offline γ-ray activity measurements werecarried out at few energies for extraction of cross sectionsof these residues to get complete information of total ICFand transfer channels. For some nuclei, it was possibleto obtain cross sections using both in-beam and off-beammethods. The statistical model and coupled channel cal-culations were also carried out.

The paper is organized as follows: the experimentaldetails are described in section II. The measured CF andICF cross sections are compared with coupled channelcalculations in section III. The summary of the presentstudy is given in section IV.

II. EXPERIMENTAL DETAILS

The measurements were carried out at 14UD BARC-TIFR Pelletron-Linac accelerator facility, Mumbai using7Li beam. The details of online and offline γ-ray mea-surement methods are given here.

A. Online γ-ray Measurement

A detailed description of the experimental setup usedfor online γ-ray measurements was given in our earlierwork [5] and only a short summary pertinent to this workis presented here. The 7Li beam with energies Ebeam =17-39 MeV in one MeV step was bombarded on 124Sntarget (thickness = 2.47 ± 0.04 mg/cm2). The beamenergies were corrected for the loss at half the targetthickness and used in the further analysis. Two Comp-ton suppressed clover detectors were placed at a distanceof 25 cm from the target centre, one at 125, for the es-timation of absolute cross section of populated reactionchannels and other at 90, for identification of unshiftedγ lines. The absolute efficiency of both the detectorswas determined using a set of radioactive 152Eu, 133Baand 241Am sources mounted in the same geometry asthe target. Along with the clover detectors, one monitordetector (= 500 µm) was placed at 30. The monitordetector was utilised in the ER cross section estimationusing the measured elastic (Rutherford) scattering crosssection. The integrated beam current deposited at thebeam dump after the target was also recorded using thehigh precision current integrator. Figure 1 shows thetypical γ-ray addback spectrum from the clover kept at125 and Ebeam = 38 MeV for 7Li+124Sn reaction. Theγ lines from the possible ERs following CF; viz, 126−128Iare labeled. Also the identified γ lines following the ICFchannel; viz, from α-capture, 126,127Te are marked. Thet-capture process populates 124−126Sb nuclei, of which124Sb and 126Sb have metastable states of few minutes.Furthermore 125Sb level structure is not well studied in

600 700 800 900 1000 1100

Cou

nts

/ keV

10000

20000

30000

40000

50000

60000

Online -ray spectra7Li+124Sn

Ebeam = 38 MeV

100 200 300 400 500

20000

30000

40000

50000

60000

70000

5768

102

106

115

122

134

209

392

415

593

629

651

659

678 68

7

745

850

990

1132

124Sn*

127I126I

128I

126Te

127Te

E (keV)

666

(a)

(b)

160

695

714

FIG. 1: γ-ray addback spectrum from the clover detector at125 obtained in 7Li+124Sn reaction at Ebeam = 38 MeV. Theγ lines from the possible evaporation residues (126,127,128I)following CF are labeled. Also the γ lines following the α-capture channel (126,127Te) and inelastic 124Sn∗ are marked.

literature. Hence, it is difficult to measure their crosssections accurately in the online measurements.

B. Offline γ-ray Measurement

Six targets of 124Sn having thicknesses in the rangeof 1.5-4.0 mg/cm2 were irradiated with beam of 7Li at19.3, 22.3, 24.8, 28.8, 33 and 35.9 MeV energies. Theseenergies were chosen in such a way that after energy losscorrection at half the target thickness, they match withthat of previously measured online γ-ray measurements.The targets with the Al catcher (∼ 1 mg/cm2 thick) were

3

Offline -ray spectra 7Li+124Sn

Ebeam = 33 MeV

E (keV)200 300 400 500 600 700 800 900

Cou

nts

/ keV

2000

4000

6000

8000

10000

12000

126I

128I

124Sbg

126Sbg

125Snm

123Snm

160.

3

388.

6

442.

9

526.

6

856.

8

331.

9

414

511

666 69

572

0.7

602.

7

753.

8

125Sb

427.

946

3.4

126Sbm

573.

959

3.2

822.

5

125Sng

FIG. 2: Offline γ-ray spectrum obtained in HPGe detec-tor for 7Li+124Sn reaction at Ebeam = 33 MeV. Identified γlines from different residues following CF (126,128I), t-capture(124,125,126Sb), one neutron stripping (125Sn) and one neutronpickup (123Sn) are marked.

placed normal to the beam direction so that the recoilingresidues are stopped in target-catcher assembly. The irra-diation time was typically 7-18 hrs from highest to lowestbombarding energy. The beam current was ∼ 10-80 nA.To monitor current variations during each irradiation,a CAMAC scaler was utilized which recorded the inte-grated current in an intervals of 1 min. The irradiatedtarget-catcher assembly was then sticked to the perspexsheet and the sheet was kept at a fixed distance (∼ 10 cm)in front of the HPGe detector. The HPGe detector wassurrounded by 2 mm thick Cu and Cd sheets and 5 cmthick Pb sheets to reduce the background. The energycalibration and absolute efficiency of the HPGe detec-tor was measured by using a set of calibrated radioactive152Eu, 133Ba and 241Am sources placed at the same ge-ometry as the target. All the six targets were countedindividually at various intervals following the half lives.The residues from CF, ICF and transfer reactions wereidentified by the characteristic γ lines emitted by theirdaughter nuclei as shown in Fig. 2 and listed in Table I.

III. RESULTS AND DISCUSSION

A. Data Reduction

1. Online γ-ray Analysis

The emission cross sections for γ transitions of interestfor online measurements were calculated from the rela-tion

σγ =YγYM

dΩMεγ

dσRuthdΩ

(1)

TABLE I: List of identified residues in the offline γ-ray mea-surement for the 7Li+124Sn reaction along with their radioac-tive decay half-lives (T1/2), γ-ray energies and intensities fol-lowing their decays [15].

Reaction ER T1/2 Eγ (keV) Iγ (%)

124Sn(7Li,3n) 128I 24.99 min 442.9 12.6526.6 1.2

124Sn(7Li,5n) 126I 12.93 d 388.6 35.6753.8 4.2

124Sn(t,1n) 126Sbg 12.35 d 414.7 83.3573.9 6.7593.2 7.5666.5 99.6695.0 99.6697.0 29.0720.7 53.8856.8 17.6

126Sbm 19.15 min 414.5 86.0666.1 86.0694.8 82.0928.2 1.31034.9 1.8

124Sn(t,2n) 125Sb 2.76 yr 427.9 29.6463.4 10.5600.6 17.7636.0 11.2

124Sn(t,3n) 124Sbg 60.20 d 602.7 97.81691.0 47.6

124Sn(7Li,6Li) 125Sng 9.64 d 822.5 4.3915.6 4.11067.1 10.01089.2 4.6

125Snm 9.52 min 331.9 97.3124Sn(7Li,8Li) 123Snm 40.06 min 160.3 85.7

where Yγ is the γ-ray yield after correcting for the in-ternal conversion, YM is the monitor yield, dΩM is thesolid angle of the monitor detector, εγ is the absolute ef-ficiency of the detector for a particular γ-ray energy, anddσRuth

dΩ is the Rutherford cross section (at θM = 30) at

the same beam energy. For 126−128I and 127Te nuclei, allthe cross sections of γ transitions feeding to the groundand metastable (having ∼ few µs life times) states of theparticular residue are added to get the residue cross sec-tions. The γ lines populating the ground and metastablestates in these nuclei are taken from Refs. [16–19]. Inthe case of even-even 126Te nucleus, the identified γ lines[19] also have the contribution from offline decay eventsof 126Sbm (t1/2 = 19.15 min) which were formed after tri-ton capture followed by one neutron evaporation. Henceto extract the cross section of 126Te, we have estimatedthe contribution from 126Sbm decay, for which the crosssection was measured from offline counting at few ener-gies (explained in the next section) and interpolated forthe intermediate energies and the corrected yield for theparticular γ transition was used. Here, only the groundstate transition 2+ → O+ (666 keV) is used to get the126Te cross section.

4

FIG. 3: ER cross sections from online γ-ray measurement for3n (128I), 4n (127I), and 5n (126I) channels following CF arerepresented by open circles, open triangles, and open squares,respectively. The ER data from offline γ ray measurement for3n and 5n channels are shown by open diamonds and openstars respectively. The results of the statistical model calcu-lations for the corresponding ERs are shown by long dashed(3n), dashed dot dot (4n), and short dashed (5n) lines.

The cross sections for 128I (3n), 127I (4n), and 126I(5n) ERs following CF for 7Li+124Sn reaction are shownby open circle, open triangle and open square symbolsrespectively along with the statistical model predictionsusing PACE code [20] in Fig. 3. The error bars on thedata are due to statistical errors in the determination ofthe γ-ray yields, background subtraction and absolute ef-ficiency of the detectors. In the PACE calculations, thecross section for each partial wave (l distribution) ob-tained from the Coupled Channel (CC) calculation codeCCFULL [21] were fed as an input. The default opti-cal potentials available in the code were used. The onlyfree parameter remaining in the PACE input was thelevel density parameter ‘a’, which showed a negligibledependence on the values between a = A/9 and a =A/10. The complete fusion cross sections were deter-

mined by dividing the cumulative measured (σexpt3n+4n+5n)cross sections by the ratio R, which gives the missingER contribution, if any. Here the ratio R is defined as

R =∑xσPACE

xn/σ

PACE

fus, where x = 3, 4, 5. The ratio (R)

and the CF cross sections thus obtained are listed in Ta-ble II.

TABLE II: Measured cross sections for Σσxn(x = 3, 4, 5)evaporation residues and complete fusion along with the ratioR, obtained from PACE (defined in the text) for 7Li+124Snreaction for the measured energy range.

Elab Ec.m. σexpt3n+4n+5n R(PACE) σexptCF

(MeV) (MeV) (mb) (mb)16.4 15.5 0.41 ± 0.14 0.64 0.64 ± 0.2217.4 16.5 1.28 ± 0.20 0.76 1.69 ± 0.2618.4 17.5 6.76 ± 0.81 0.89 7.60 ± 0.9119.5 18.4 23.4 ± 0.6 0.93 25.1 ± 0.720.5 19.4 65.4 ± 8.0 0.96 68.3 ± 8.421.5 20.3 113 ± 5 0.97 116 ± 522.5 21.3 159 ± 5 0.98 162 ± 523.5 22.3 217 ± 8 0.99 220 ± 824.5 23.2 302 ± 8 0.99 305 ± 825.5 24.2 396 ± 8 0.99 400 ± 926.6 25.1 493 ± 10 0.99 498 ± 1027.6 26.1 611 ± 12 0.99 617 ± 1228.6 27.0 622 ± 11 0.99 628 ± 1129.6 28.0 676 ± 12 0.99 683 ± 1230.6 29.0 768 ± 10 0.99 776 ± 1031.6 29.9 787 ± 11 0.99 796 ± 1132.6 30.9 845 ± 21 0.99 856 ± 2233.6 31.8 838 ± 29 0.99 850 ± 3034.6 32.8 868 ± 39 0.99 881 ± 3935.6 33.7 885 ± 21 0.98 900 ± 2136.6 34.7 974 ± 26 0.98 991 ± 2637.6 35.6 978 ± 15 0.98 996 ± 1638.7 36.6 1034 ± 14 0.98 1056 ± 14

2. Offline γ-ray Analysis

For the offline γ counting experiment, the residue crosssection (σR) at a particular beam energy was obtainedusing the expression as follows:

σR =Yγλ

NtεγIγk, (2)

where

k =

m∑n=1

in(1−eλtstep)(e−λ[t1+(n−1)tstep]−e−λ[t2+(n−1)tstep]),

here, Yγ is the area under the γ-peak corresponding tothe residual nucleus with decay constant λ, Nt is the num-ber of target nuclei per unit area, εγ is the efficiency ofthe HPGe detector at the peak energy and Iγ is the inten-sity branching ratio associated with the particular γ linecorresponding to the residual nucleus. t1 and t2 are thestart and stop times of counting for the irradiated sam-ples w.r.t. the beam stop, tstep is the step size in whichthe current was recorded in the scaler, in is the currentrecorded by the scaler at the nth interval, and m is the to-tal number of intervals of irradiation. The half-lives of allthe residues of our interest were confirmed by followingtheir activities as a function of time. Typical radioac-tive decay curves obtained for 125Snm and 128I residuesare shown in Fig. 4(a) and (b), respectively. Various γ

5

125Snm

E = 331.9 keV

T1/2 = 9.6 min

Cou

nts

/ tim

e

0

1000

2000

3000

128IE= 442.9 keV

T1/2 = 25 min

time (min)20 40 60 80 100 120

0

20

40

60

80

(a)

(b)

FIG. 4: Typical radioactive decay curves obtained for (a)125Snm and (b) 128I residues.

lines corresponding to the same residue having differentIγ were also used for confirmation of the estimated chan-nel cross section.

The cross sections for 128I (3n) and 126I (5n) ERs fromthe offline measurement are shown by open diamond andopen star symbols respectively in Fig. 3. As can be seenfrom the figure, the cross sections for these two channelsfrom offline and online γ-ray measurements showed goodagreement, thus leaving no doubt about missing any ma-jor γ line feeding the ground state in online γ measure-ment. The extracted cross sections for t-capture and 1ntransfer channels are discussed in section III C.

In the offline γ-ray measurements, special care wastaken to reduce the systematic uncertainties that couldarise from different sources such as (i) beam current, (ii)target thickness, (iii) detector efficiency, and (iv) extrac-tion of γ-ray yield. The current integrator was calibratedusing a precision Keithley current source. Also the beamcurrent fluctuation was recorded by dividing the irradia-tion time in small intervals (1 min) and was used in theanalysis. This procedure reduces the uncertainty in thecurrent measurement to less than 1%. The target thick-nesses were measured using the Rutherford backscatter-ing method with 16O beam as well as α energy loss tech-nique with Am-Pu α source. Uncertainty in the thick-ness (∼ 2%) was taken into account in the analysis foreach target. The absolute detector efficiency was alsomeasured repeatedly and found to remain invariant withtime during the whole experiment. The uncertainty (∼1%) in the fitting parameters of the efficiency curve wastaken into account. The total uncertainty on the residuecross sections were obtained after adding the statisticaland the systematic errors as listed in Table III.

FIG. 5: Complete fusion cross section (filled circles) for the7Li+124Sn reaction compared with coupled (dashed lines) anduncoupled (dotted lines) results from CCFULL calculations.Solid lines were obtained by multiplying the coupled resultsby a factor of 0.74.

B. Coupled Channel Calculations

Coupled channel calculations were performed using themodified version of CCFULL [21], which can include theeffect of projectile ground-state spin and the projectileexcitation in addition to the target excitation. The po-tential parameters used were: V0 = 45 MeV, r0 = 1.17fm and a0 = 0.62 fm, obtained from the Woods-Saxonparametrization of the Akyuz-Winther (AW) potential[22]. The corresponding uncoupled barrier height VB ,radius RB , and curvature ~ω derived for the present sys-tems are 19.7 MeV, 10.3 fm and 4.13 MeV respectively.The full couplings include the coupling of the projectileground state (3/2−) and first excited state (1/2−, 0.478MeV) with β00 (β2 for the ground-state reorientation) =1.189, β01 (β2 for the transition between the ground andthe first excited states) = 1.24. These values are takenfrom Ref. [23]. Target coupling included the 3− vibra-tional excited state in 124Sn with Ex = 2.603 MeV, β3

= 0.106 [24]. The effect of coupling of 2+ excited state(β2 = 0.0953, Ex = 1.132 MeV) in 124Sn is found tobe less important compared to 3− state. The breakupor transfer coupling channel cannot be included in thesecalculations.

The results from the uncoupled and coupled calcula-tions are shown in Fig. 5 by dotted and dashed lines, re-spectively. It was observed that at sub-barrier energies,the calculated fusion cross sections with the couplings(dashed lines) are enhanced compared to the uncoupledvalues. However, at above-barrier energies, the calcu-lated values of fusion with or without couplings are higherthan the measured ones. It was interesting to observe

6

FIG. 6: Measured residue cross sections for (a) t-capture pro-cess (from offline γ-ray measurement) (b) α-capture process(from online γ-ray measurement) in 7Li+124Sn reaction areplotted. The lines are the predictions from statistical modelcalculations for the corresponding residues (see text for de-tails).

that when the calculated fusion cross sections obtainedwith the above coupling are normalized by a factor of0.74, the reduced fusion values (denoted by solid line) re-produce the experimental fusion cross sections very wellspecially at energies above the Coulomb barrier. Thus,one can conclude that the CF cross sections in this re-gion are suppressed by 26 ± 4% compared to the predic-tion of CCFULL calculations. The uncertainty of 4% insuppression factor was estimated from the uncertaintiesin VB and σCF . In recent studies [6, 7], the completefusion cross section data available with weakly boundand strongly bound projectiles on various targets wasshown to be systematically target independent. Presentwork also support this observation with 7Li projectile inmedium and heavy mass region.

C. ICF and 1n transfer cross sections

The measured cross sections for residues from incom-plete fusion; viz., 126,127Te and 124,125,126Sb along withone neutron stripping (125Sn) and pickup (123Sn) prod-ucts are listed in Table III and plotted in Fig. 6. The totalt-capture and total α-capture cross sections are obtainedfrom adding the individual residue cross-sections. Thetotal t-capture is found to be much larger than α-captureat all the measured energies. Intuitively, we expect thisbehavior as triton while approaching the target sees lowerCoulomb barrier compared to α particle. Hence the crosssection for t-capture is expected to be more compared tothose of α-capture. It is to be noted that deuteron andproton stripping from 7Li projectile would give the sameERs as those following t-capture process and subsequentfew neutron evaporation. Hence, from experiments it isdifficult to separate these three processes.

In order to investigate the behaviour of observedresidue cross-sections from t-capture and α-capture,the statistical model calculations were performed usingPACE [20] code with modified prescription for level den-sity [25]. The spectrum of the surviving α-particles, aftercapture of the complementary fragment (triton), repre-sents the cross section for breakup-fusion as a function ofthe kinetic energy of the α-particles. As seen from the lit-erature [12, 26–29] for 6,7Li induced reactions on varioustargets, the α, deuteron and triton energy spectra havewidth, σ ∼ 4 MeV centered around the 4/7 (for α) and3/7 (for triton) of beam energies in case of 7Li. AssumingGaussian distribution, the whole α spectra (or excitationenergy spectra of the intermediate nucleus formed afterICF) was divided into four bins of width 4 MeV eachas in Ref. [12] with central two bins having 34% weightand the outer two bins having 16% weight. For each7Li energy, the statistical model calculation was carriedout for these four excitation energy bins and weightedsum was taken as the predicted cross section. The cal-culated values of absolute cross sections for the residues,124,125,126Sb, are plotted in Fig. 6(a) showing reasonablygood agreement with the data. Following the same proce-dure, cross sections for residues arising from the captureof α-particles were calculated from PACE with weightfrom the corresponding triton spectra. The results ob-tained are shown for 126,127Te residues in Fig. 6(b) show-ing a similar agreement. The calculated cross sectionfor 125Te is also shown in Fig. 6(b). These calculationssuggest that these residues are populated via fragmentcapture or transfer followed by evaporation, not throughany other one step direct process.

D. Simultaneous description of CF, ICF and TFcross sections

There have been some recent theoretical works, whereseparation of the ICF and CF components have beenachieved using the calculations based on Continuum

7

TABLE III: Measured cross sections for incomplete fusion products along with 1n pickup and 1n stripping cross sectionsobtained from online and offline γ-ray measurement techniques in 7Li+124Sn reaction.

Elab127Te 126Te 126Sbm 126Sbg 125Sb 124Sbg 125Sng 125Snm 123Snm

(MeV) (mb) (mb) (mb) (mb) (mb) (mb) (mb) (mb) (mb)

18.4 5.34 ± 0.5 2.28 ± 0.2 11.8 ± 1.7 0.33 ± 0.03 0.23 ± 0.02 1.18 ± 0.16 0.17 ± 0.0121.5 20.5 ± 1.0 14.4 ± 1.2 77.0 ± 3.4 2.24 ± 0.11 2.13 ± 0.18 4.95 ± 0.05 1.11 ± 0.2022.5 0.55 ± 0.1623.5 3.05 ± 0.8824.5 6.68 ± 1.53 32.1 ± 1.9 18.3 ± 1.5 172 ± 41 8.10 ± 1.02 8.54 ± 2.62 12.0 ± 0.9 5.56 ± 0.3425.5 10.4 ± 4.0 3.50 ± 0.96 31.5 ± 1.1a

26.6 11.3 ± 2.5 7.96 ± 1.53 31.0 ± 1.1a

27.6 16.1 ± 2.2 9.87 ± 2.73 30.5 ± 1.1a

28.6 17.0 ± 2.2 12.5 ± 2.9 29.7 ± 1.6 20.6 ± 1.6 203 ± 56 15.7 ± 1.1 13.1 ± 2.6 17.3 ± 1.7 6.42 ± 1.1229.6 19.0 ± 0.7 13.3 ± 3.1 28.0 ± 1.7a

30.6 20.2 ± 1.4 15.2 ± 2.9 26.3 ± 1.7a

31.6 23.3 ± 2.4 18.4 ± 3.8 24.6 ± 1.7a

32.6 24.1 ± 3.1 21.6 ± 3.8 22.9 ± 1.3 18.4 ± 1.4 279 ± 29 23.6 ± 1.8 22.5 ± 1.3 20.8 ± 1.3 8.18 ± 1.0533.6 24.7 ± 2.1 24.5 ± 3.9 21.9 ± 1.6a

34.6 24.3 ± 1.6 24.4 ± 3.8 20.9 ± 1.6a

35.6 28.3 ± 1.9 26.3 ± 4.3 19.9 ± 1.5 16.7 ± 1.5 316 ± 22 46.9 ± 2.6 25.2 ± 1.6 24.6 ± 1.8 17.0 ± 1.236.6 30.5 ± 2.3 30.4 ± 4.6 18.9 ± 1.5b

37.6 26.9 ± 3.8 28.0 ± 3.5 17.9 ± 1.5b

38.7 28.3 ± 2.1 29.2 ± 4.2 16.9 ± 1.5b

a : interpolated value used for extraction of 126Te cross-section (see section III A 1 for details)b : extrapolated value used for extraction of 126Te cross-section

Discretized Coupled Channel (CDCC) formalism. InRef. [30], CF and ICF cross sections are separated asthe absorption from the projectile bound channels andthe projectile breakup states respectively, where the ab-sorption is calculated using a short range imaginary barepotential in the centre of mass motion. In another ap-proach, two imaginary potentials are employed for inter-action between the breakup fragments and target and theTF is defined as the cumulative absorption due to thesepotentials [31, 32]. In the work of Hashimoto et al . [33],the CF is considered to arise when both the breakup frag-ments are in the range of imaginary potentials whereas,the ICF arises when only one of the fragments is in therange of the respective imaginary potentials. They usethe complete CDCC wavefunction with two imaginarypotentials and utilize it for calculating the CF and ICFcorresponding to absorptions in different regions. In thisprocess, they use a radius parameter to divide the respec-tive absorption regions and the CF and ICF cross sec-tions were calculated for the (d,p) reactions. In the workof Parkar et al . [34], the TF and ICF cross sections wereevaluated by modifying the absorption in an approximateway by selecting different set of short range imaginary po-tentials. A sophisticated calculation method developedby Lei and Moro [35], where they explicitly calculate thenon-elastic breakup as the absorption of a given frag-ment when the other fragment survives by employing theproper outgoing boundary conditions.

Here we have followed the calculation method adoptedin our earlier work [34] where the detailed coupled chan-

nels calculations were performed using CDCC methodusing the code FRESCO 2.9 [36] for the simultaneousdescription of complete, incomplete and total fusion datafor 6,7Li+209Bi and 6,7Li+198Pt reactions. Since in thepresent work for 7Li+124Sn reaction, a complete set ofdata of CF, ICF and TF is available over a wide energyrange, similar calculations are performed. The detailsof calculation method were already described in the ear-lier work [34] and only the short summary regarding thiswork is presented here.

The binding potential for α-t in 7Li was taken fromRef. [37], while the real part of required fragment-targetpotentials (Vα−T and Vt−T ) in cluster folding model weretaken from Sao Paulo potential [38]. In the calculationspresented here, the fusion cross sections were first cal-culated by including the short-range imaginary (WSR)volume type potentials in the coordinates of both projec-tile fragments relative to the target, as in Ref. [31]. Theshort range imaginary potential for α-T and t-T are: W0

= 25 (25) MeV, rw = 0.60 (0.79) fm, aw = 0.4 (0.4)fm. Three set of CDCC calculations with the breakupcouplings were performed with three choices of opticalpotentials, where WSR was used for (i) both the projec-tile fragments relative to the target (Pot. A), (ii) the α-Tpart only (Pot. B), and (iii) the t-T part only (Pot. C).In addition, an imaginary volume type potential with pa-rameters W=25 MeV, rw=1.00 fm and aw=0.4 fm, with-out any real part was also present in the center of mass ofthe whole projectile for the projectile-target radial mo-tion. The imaginary potential ensures that the total flux

8

FIG. 7: (a) The data of CF, ICF and TF cross sectionsfor 7Li+124Sn reaction are compared with the coupled chan-nel calculations. The arrow indicate the position of Coulombbarrier. (b) Comparison of individual ICF contributions fromα-capture, t-capture along with Total ICF with the calcula-tions. (see text for details).

decreases by the absorption when the core and the va-lence cluster are in the range of the potential of targetnucleus. Using the combination of the absorption crosssections with three potentials, the cross sections for (i)Total fusion (σTF), (ii) σCF+σα, and (iii) σCF+σt werecalculated. These are further utilized to estimate theσα-capture, σt-capture and σCF explicitly. The parametersof the short range imaginary potential in the range ofrw = 0.6 to 1.0 fm and aw = 0.1 to 0.4 fm are found tobe less sensitive for the calculation of σTF . However, inthe calculation of ICF, the radius parameter of imaginarypart is optimized with the higher energy ICF data.

In Fig. 7(a) results of the calculations for the TF,CF and ICF cross sections are shown with long dashed,

FIG. 8: The ratio of cross sections, σICF/σTF and σCF/σTF

derived from the calculations as a function of Ec.m./VB for7Li+124Sn reaction is shown by dashed and dashed-dot linesrespectively. The symbols are showing the experimental data.

short dashed and dotted lines, respectively along with thecorresponding experimental data. The bare calculations(without breakup couplings) were also performed and thecalculated fusion cross sections are denoted by dashed-dot-dot line. The Coulomb barrier position is marked byarrow in the figure. It is seen that at energies above theCoulomb barrier, the calculations which include the cou-plings and calculations that omit them have negligibledifference but at energies below the barrier, the coupledTF cross sections are enhanced in comparison to bareTF cross sections. The calculated individual ICF crosssections, σα-capture and σt-capture, are shown in Figs. 7(b)along with the measured data. In this figure, the longdashed, short dashed and dotted lines are the α-capture,t-capture and Total ICF calculations, respectively. Thesimultaneous description of CF, individual ICF and To-tal ICF was achieved from these coupled channels calcu-lations. As can be seen from the Fig. 7(b), the t-capturecross sections are much more dominant than α-capturecross sections and almost equals to total ICF. Similarobservation was also made in the recent work [34] for7Li+209Bi and 7Li+198Pt reactions. Here we point outthat, experimentally the capture cross sections may in-clude the breakup and subsequent absorption in the tar-get or the transfer followed by breakup and subsequentabsorption in the target as explained in Refs. [9, 10]. Wehave not considered the transfer followed by breakup andsubsequent absorption explicitly as it is complicated pro-cess to model. Nevertheless, the breakup absorption ascalculated here is supposed to model the ICF process inan effective way.

The ratio of cross sections, σICF/σTF and σCF/σTF

derived from the calculations as a function of Ec.m./VB

are shown by dashed and dash-dotted lines respectively

9

in Fig. 8. The corresponding experimental data fromthe present measurement of σICF/σTF and σCF/σTF areshown with hollow circles and hollow triangles respec-tively in Fig. 8. From the figure it is evident that (i)for the energies above the Coulomb barrier, σICF/σTF

and σCF/σTF ratio remain approximately constant overthe energy range and CF is dominant over the ICF (ii)At the Coulomb barrier position, σICF/σTF is of similarmagnitude as σCF/σTF indicating the equal importanceof CF and ICF and (iii) for energies below the barrier,the σICF/σTF is increasing while σCF/σTF is decreasingshowing the dominance of ICF over CF cross sections.The σICF/σTF ratio at above barrier energies gives thevalue of suppression factor in CF, which is found to bein agreement (∼ 30 %) with the literature data with 7Liprojectiles from various measurements [4–7]. This valueis direct experimental number for CF suppression factorand is matching with CCFULL calculations as shown inSection III B. These results show that ICF is crucial forunderstanding the CF suppression factor.

IV. SUMMARY

The complete and incomplete fusion excitation func-tion for 7Li+124Sn reaction were measured in the energyrange 0.80 < VB < 1.90 by online and offline γ-ray de-tection techniques. At above barrier energies, the mea-sured complete fusion cross sections were found to besuppressed by a factor of 26 ± 4% in comparison with thecoupled channel calculations performed using the modeladopted in CCFULL. This suppression factor is found tobe in agreement with the literature data for the 7Li pro-jectile on various targets and seem to suggest that thesuppression factor does not vary appreciably at these en-ergies for different target mass systems. The measuredt-capture cross sections are significantly more than theα-capture cross sections at all energies. Similar obser-vations were also made on ICF data for 7Li+209Bi and7Li+198Pt reactions in Ref. [34]. The statistical modelcalculations successfully explain the measured cross sec-

tions for the residues arising from the t-capture and α-capture underlining that the residues primarily originatefrom the two-step mechanism of breakup followed fusion-evaporation. The measured ICF cross sections taken assum of t-capture and α-capture cross sections are foundto be commensurate with the suppression observed inthe CF data. Further, simultaneous measurements ofCF and ICF preferably in different target mass regionsare required to understand these aspects.

We have also performed the CDCC based coupledchannel calculations, which includes the coupling ofbreakup continuum of 7Li nucleus explicitly using thecluster folding potentials in the real part along with theshort range imaginary potentials to calculate the CF,ICF and TF cross sections. The simultaneous expla-nation of the experimental data for the CF, ICF andTF cross sections over the entire energy range was ob-tained. The calculated TF cross-sections from uncoupledand coupled were found to match at energies above thebarrier, while below barrier uncoupled TF is lower thanthe coupled one. The calculated and experimental ICFfraction, which is the ratio of ICF and TF cross sectionsis found to be constant at energies above the barrier andit increases at energies below the barrier showing the en-hanced importance of ICF contribution in TF at belowbarrier energies. Further it will be of interest to describethis complete set of data using more sophisticated theo-ries.

Acknowledgments

The authors would like to thank the Pelletron crew,Mumbai for the smooth operation of the accelerator dur-ing the experiment. We also thank Prof. J. Lubian forgiving us the code to calculate Sao Paulo potentials. Oneof the authors (V.V.P.) acknowledges the financial sup-port through the INSPIRE Faculty Program, from theDepartment of Science and Technology, Government ofIndia, in carrying out these investigations.

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