Investigation of complete and incomplete fusion in 20 Ne + 51 V system using recoil range measurement

Recoil range distributions of evaporation residues, populated in 20Ne + 51V reaction at Elab ≈ 145 MeV, have been studied to determine the degree of momentum transferred through the complete and incomplete fusion reactions. Evaporation residues (ERs) populated through the complete and incomplete fusion reactions have been identified on the basis of their recoil range in the Al catcher medium. Measured recoil range of evaporation residues have been compared with the theoretical value calculated using the code SRIM. Range integrated cross section of observed ERs have been compared with the value predicted by statistical model code


Introduction
In the last few years, study of nuclear reactions at energies near and above the Coulomb barrier have become an active topic of research [1][2][3][4].Study of nuclear reaction around the barrier energy involves the investigation of complete and incomplete fusion processes and their dependence on various entrance channel parameters [5][6][7][8].Complete fusion (CF) requires a total transfer of incident momentum from projectile to compound nucleus through the fusion of entire projectile's mass with the target.On the other hand, incomplete fusion (ICF) involves partial transfer of momentum from projectile to compound nucleus via the fusion of only a fraction of the incident projectile's mass with the target.Classically, either of these two processes will become feasible when the incident energy of projectile is higher than fusion barrier.Ever since the observation of the first ICF reaction by Britt and Quinton [9], numerous studies have been carried out to explore the mechanism involve in the ICF reactions.However, a real breakthrough was achieved by Inamura et al. [10] by performing the particle-γ coincidence measurements and claiming that ICF reactions were arising due to the break-up of incident projectile in peripheral collisions.It was suggested by Morgenstern et al. [11] and later on confirmed by several authors [5,6,12] that probability of ICF reaction increases with the increase in incident beam energy.This phenomenon of increase in ICF reaction probability with the incident beam energy was found to be a consequence of maximum angular momentum max , associated with the a e-mail: sabirjhk@gmail.comincoming projectile beam [13].max was found to be dependent on the incident beam energy through the relation [14], where R is the maximum impact parameter at which the collision leads to a nuclear fusion reaction, and V B is the fusion barrier.Liquid drop model based calculations have shown that the nuclear shape is distorted with increasing angular momentum until some critical value ( crt ) is reached at which nuclear shape is no more stable [16,17].Thus, fusion is restricted by crt above which no CF reaction is likely to occur.According to sumrule model, proposed by Wilczynski et al. [18], ICF reaction channels are localized in angular momentum space above crt .At lower energies max is close to crt , thereby precluding any window for ICF reactions.
Following the CF or ICF reaction, an excited intermediate compound system is formed which decay to ground state via the emission of particles and/or γ-rays.The phenomenon of particle and/or γ-ray emission from the excited compound system is governed by the excitation energy of the compound system which in turn depends upon the degree of momentum transferred through the CF and/or ICF processes.Evaporation residues (ERs) populated through α-emitting channels can be populated through CF as well as ICF processes.There is no theoretical model proposed so far which could predict the exact fractional contribution arising from CF and/or ICF processes in the formation of ERs populated through αemitting channels.Measurements of recoil range distribution (RRD) of ERs populated through α-emitting channels was proved to be an important tool in determining the magnitude of contributions arising from each of the possible reaction dynamics.In the present work RRDs of eight ERs, namely 67 Ge (p3n), 66 Ge (p4n), 65 Ga (α2n), 63 Zn (αp3n), 62 Zn (αp4n), 61 Cu (2α2n), 61 Co (2α2p), and 60 Cu (2α3n) populated in the 20 Ne + 51 V reaction at E lab ≈ 145 MeV have been studied.A brief detail regarding the experimental setup used to perform the present work is given in section 2. Analysis and interpretation of the results are given in section 3 whereas the conclusion drawn from the observed results are given in the last section.

Experimental details
The present experiment was performed at Variable Energy Cyclotron Centre (VECC), Kolkata using 20 Ne 6+ ion beam at energy E lab ≈ 145 MeV.The target used was 51 V foil (99.97% pure) of thickness ≈ 250 μg/cm 2 .The 51 V target was evaporated over an Al-backing of thickness ≈ 200 μg/cm 2 .The target-backing combination was mounted in a stack along with 20 thin Al-catcher foils, placed behind the target foil, to trap the recoiling nuclei.
The thickness of each Al-catcher foil was determined prior to use by weighing as well as by the α-energy loss method, and it was found to range from 100 to 150 μg/cm 2 .The projectile beam was collimated to a spot of diameter 8 mm and the beam current was found to be varying between 15-20 nA.The target was irradiated for a period of ≈ 11 hrs.The nuclear spectroscopic data used in the evaluation and measurement of the cross sections were taken from the Radioactive Isotopes Data Table of Brown and Firestone [19] and is given in Table 1 for ready reference.Details regarding the experimental setup were given in Ref. [20].

Results and analysis
The formation of ERs, populated through CF and/or ICF processes, consists of two stages.In the first stage, called 'fusion stage', an intermediate compound system is formed through the CF and/or ICF processes and the second stage, called 'evaporation stage', involves the deexcitation of the intermediate compound system through the particle and/or γ-ray emission.The intermediate compound system formed through the CF process will recoil in the Al catcher medium to a relatively larger recoil range as compared to the intermediate compound system formed through the ICF process.This discrepancy in recoil range of the intermediate compound systems formed through CF and ICF processes is arising due to the difference in degree of momentum transferred through the two processes.

RRDs of residues populated through pxn channel
CF of 20 Ne projectile with 51 V target leads to the formation of an excited intermediate compound system 71 As * .The excited intermediate compound system further decay via the emission of nucleons leading to the formation of 67,66 Ge isotope through the pxn (x = 3, 4) channels.As an example the systematics for the formation of 67 Ge through the CF process may be given as 20 Ne + 51 V ⇒ 71 As * , 71 As * ⇒ 67 Ge + p3n.
Fig. 1 shows the RRD of ER 67 Ge populated through p3n channel.As can be seen from Fig. 1, RRD of 67 Ge residue consists of a single peak at 2229.6 μg/cm 2 indicating the presence of complete momentum transfer from projectile to target through the CF process.

RRDs of residues populated through α emitting channels
ERs 65 Ga, 63 Zn, and 62 Zn populated through α2n, αp3n, and αp4n channels, respectively can be populated through CF as well ICF α processes.The formation of α channel residues through the CF and ICF α processes may be given by two different decay modes.
1. ICF α Process: The 16 O nuclei, which forms through the α break-up of 20 Ne ( 20 Ne → 16 O + α), fuses with 51 V target leading to the formation of an incompletely fused composite system 67 Ga * through the ICF α process. 67Ga * further decay via the emission of nucleons leading to the formation of ERs 65 Ga, 63 Zn, and 62 Zn trough the 2n, p3n, and p4n channels, respectively. 20Ne projectile with 51 V target leads to the formation of compound system 71 As * .ERs 65 Ga, 63 Zn, and 62 Zn have a finite probabilty of getting populated through the emission of α2n, αp3n, and αp4n, respectively from the excited compound system 71 As * .

RRDs of residues populated through 2α emitting channels
ERs 61 Cu, 60 Cu, and 61 Co were populated via 2α2n, 2α3n, and 2α2p channels, respectively.These 2α channel residues can be populated through CF, ICF α as well as ICF 2α processes.The interplay between the contributions of CF, ICF α , and ICF 2α processes in the formation of ERs populated through 2α channel may be given as: 1. ICF 2α Process: 12 C, which forms through the 2α break-up of 20 Ne projectile ( 20 Ne → 12 C + 8 Be), fuses with the 51 V target leading to the formation of an incompletely fused composite system 63 Cu * through the ICF 2α process.The excited compound system 63 Cu * further decay to 61 Cu, 60 Cu, and 61 Co residues through 2n, 3n, and, 2p channels, respectively.
2. ICF α Process: As mentioned before, due to breakup of 20 Ne projectile into 16 O and α-particle under the influence of target's field, 67 Ga * was formed through the ICF α Process. 67Ga * further decay via α2n, α3n, and α2p channels leading to the formation of ERs 61 Cu, 60 Cu, and 61 Co, respectively.
3. CF Process: Excited compound system 71 As * , formed through the CF of 20 Ne projectile with 51 V target, may further decay via the emission of 2α2n, 2α3n, and 2α2p to form the ERs 61 Cu, 60 Cu, and 61 Co, respectively.Fig. 2(a-b) shows the RRDs of ERs (a) 65 Ga, and (b) 61 Cu populated through α2n and 2α2n channels, respectively.As can be seen from Fig. 2, the RRDs of 65 Ga consist of two peaks whereas RRDs of 61 Cu consists of three peaks, which is expected.The formation of 65 Ga through α2n channel involves two different component of momentum transfer through the CF as well as ICF α processes.On the other hand, the formation of 61 Cu through 2α2n channel involves three different components of momentum transfer through the CF, ICF α and ICF 2α processes.The ex- perimentally measured most probable range R exp , along with the theoretically estimated value R theo , estimated using the code SRIM [21] for all the identified ERs populated through the CF and/or ICF processes, are tabulated in Table 2. R theo is estimated by assuming that 20 Ne projectile consist of five α-particles and the total incident momentum is equally distributed among its five α constituents.Table 3 gives the Q value of the observed ERs populated through the CF, ICF α and ICF 2α processes in the 20 Ne + 51 V raection.Table 4 gives the range integrated experimentally measured reaction cross section of ERs populated in 20 Ne + 51 V reaction at E lab ≈ 145 MeV.Last column of Table 4 gives the theoretically estimated values of rection cross section, calculated using the statistical model code PACE4 [22].It can be inferred from Table 4 that experimental reaction cross section of residues populated through the pxn channels are in good agreement with the PACE4 predictions, whereas the reaction cross section of α channel residues shows an enhancement over the PACE4 values.Such type of result is expected since the statistical model code PACE4 does not take ICF reactions into account.

Conclusion
The RRDs of eight radionuclides, namely 67 Ge(p3n), 66 Ge(p4n), 65 Ga(α2n), 63 Zn(αp3n), 62 Zn(αp4n), 61 Cu(2α2n), 60 Cu(2α3n), and 61 Co(2α2p), populated in 20 Ne + 51 V reaction at E lab ≈ 145 MeV have been studied.The analysis of measured RRDs of ERs populated through α-emitting channels reveal a significant contribution of partial momentum transfer from incident projectile to target.Different partial momentum transfer components were attributed to the fusion of 16 O and 12 C, formed through the break-up of 20 Ne projectile, with the 51 V target nucleus.

Figure 1 .
Figure 1.RRD of ER 67 Ge expected to be populated through the p3n channel.

Table 1 .
[19] of observed reaction channels populated in20Ne + 51 V reaction are given in first column along with the half-lives in the second column and other columns have spectroscopic properties taken from Ref.[19].

Table 2 .
Experimental measured most probable range (R exp ) as well as theoretically calculated range (R theo ), using the code SRIM, in Al catcher foils in unit of μg/cm 2 , for the experimentally observed reaction channels in20Ne + 51 V reaction at E lab ≈ 145 MeV.

Table 3 .
Q value of the reaction products populated through CF, ICF α , and ICF 2α processes in the20Ne + 51 V reaction at E lab ≈ 145 MeV.

Table 4 .
Experimentally measured range integrated cross sections of ERs populated in20Ne + 51 V reaction at E lab ≈ 145MeV along with the fusion cross section values calculated theoretically using the statistical model code PACE4.