Compound and non-compound nucleus contributions in the evaporation residue cross-sections of 20Ne +...

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Nuclear Physics A 884–885 (2012) 36–50

www.elsevier.com/locate/nuclphysa

Compound and non-compound nucleus contributions inthe evaporation residue cross-sections of

20Ne + 181Ta → 201Bi∗ reaction at Ec.m. = 135 MeVand 162 MeV

Gurvinder Kaur, Manoj K. Sharma ∗

School of Physics and Materials Science, Thapar University, Patiala-147004, India

Received 6 March 2012; received in revised form 17 April 2012; accepted 19 April 2012

Available online 7 May 2012

Abstract

The simultaneous existence of Compound Nucleus (CN) and Non-Compound Nucleus (NCN) processesin the decay of a nuclear system, provide a comprehensive picture of nuclear reaction dynamics and relatedphenomenon in low energy region. The CN and NCN based Evaporation Residue (ER) cross-section data isavailable for 20Ne + 181Ta → 201Bi∗ reaction at two energies i.e. Elab = 150 MeV and Elab = 180 MeV,and the same is tested in the framework of Dynamical Cluster Decay Model (DCM). Experimentally, theNCN component is reported to have major contribution from Incomplete Fusion (ICF) channel and the DeepInelastic Collision (DIC) component is shown to be negligibly small. The ER formed in CN and NCN (ICFin present case) are nicely reproduced in the framework of DCM. The available CN based ER cross-sectionsare fitted for spherical, β2 deformed and β2–β4 deformed fragmentation paths, which in turn provide a nicedescription of deformation effects in the decay of 201Bi∗ formed in 20Ne induced reaction. The role ofbarrier modification and angular momentum dependence is also addressed in addition to deformation andorientation effects.© 2012 Elsevier B.V. All rights reserved.

Keywords: Fission; Incomplete fusion; Dynamical cluster decay model; Non-compound nucleus

* Corresponding author.E-mail address: [email protected] (M.K. Sharma).

0375-9474/$ – see front matter © 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.nuclphysa.2012.04.009

G. Kaur, M.K. Sharma / Nuclear Physics A 884–885 (2012) 36–50 37

1. Introduction

In general, the measurement of fission fragments and evaporation residues in nuclear reac-tions impart a comprehensive picture of processes subsequent to the collision between projectileand target nuclei. However, depending on beam energy and entrance channel mass asymme-try, several other Non-Compound Nucleus (NCN) processes like Deep-Inelastic Collision (DIC),Quasi-Fission (QF), Incomplete Fusion (ICF) etc., start competing in addition to fully equili-brated Compound Nucleus (CN) states. In Deep Inelastic Collision (DIC), the projectile and thetarget nuclei stick together for a sufficiently long time, forming the product masses similar toprojectile and target mass. The ICF on the other hand, is associated with splitting of projec-tile nucleus before interaction with target i.e. instead of total amalgamation of projectile intotarget only a part of projectile interacts with the target nucleus. There is exchange of nucleonsbetween the colliding reaction partners in DIC, whereas ICF reactions involve the transfer ofnucleons from lighter to heavier reaction partner. Generally, asymmetric target projectile com-bination leads to an ICF process, with a low energy component in the kinetic energy spectra ofprojectile like fragments PLFs [1–4]. Moreover, the systematics of Morgenstern et al. [5], havealso shown that the contribution of ICF towards total reaction cross-section is more for massasymmetric systems as compared to mass symmetric systems. Thus, at low energies, ICF mainlycontribute to the formation of PLFs for the reaction systems with large entrance channel massasymmetry. The ICF has been investigated actively using heavy-ion beam facilities and variousmacroscopic models [6,7] have been developed and used extensively.

The dynamics of Incomplete Fusion (ICF) using light heavy ion (A� 20) beams at low energyregion has been investigated in recent times [8–11]. At energies E � 10 MeV/A, the interactiontrajectories lying within the target dimensions prominently lead to Complete Fusion (CF) andIncomplete Fusion (ICF) process [12,13]. The CF and ICF reaction modes can be disentan-gled on the basis of driving angular momenta at different interaction trajectories as suggestedby [14]. The lower angular momentum states are shown to contribute towards CF whereas, atrelatively higher � values the centrifugal potential controls the attractive nuclear potential, andconsequently the pocket in the entrance channel potential starts disappearing [15,16], giving riseto ICF contribution. In ICF the fractional mass and charge as well as the linear momentum ofprojectile are transferred to the target nucleus, due to the prompt emission of α and/or α-likeclusters in forward direction with almost projectile velocity. As a result of this, the projectile-likeand target-like partners may come into picture in the exit channel [17]. Just like Compound Nu-cleus (CN) process, the NCN process also contributes to provide worthy information regardingnuclear structure and reactions and hence it becomes mandatory for us to investigate its behaviorfor overall understanding of nuclear dynamics. An extensive work has been carried out on CNand NCN processes by Morgenstern et al. [5,18] that provides a co-relation between fractionof ICF and center-of-mass velocity with lighter reaction partner and mass asymmetry in the en-trance channel. It has helped in understanding the nuclear reaction dynamics and its dependenceon beam energy and entrance channel mass asymmetry.

The statistical evaporation codes and fission models are the two different approaches on whichthe evaporation residues, intermediate mass fragments and fission cross-sections are treated in thestandard statistical formalism [19,20]. On the contrary, the NCN processes could not be treatedwith the statistical models. Alternatively, DCM [21–33] treats ER and fission process on equalfooting using the concept of barrier penetration of preformed fragments. Although, DCM [21–33] has been quite successful in explaining the decay of compound nucleus (formed in heavyion reactions) in light, intermediate, heavy and superheavy mass region, it’s being applied here

38 G. Kaur, M.K. Sharma / Nuclear Physics A 884–885 (2012) 36–50

in reference to ICF component of ER data. In this paper DCM has been applied to study theevaporation residues formed via CN and NCN (ICF in present case) process at Elab = 150 MeVand 180 MeV in reference to [34]. This reaction is important from the point of view that theevaporation residue formed in CN process could be fitted with spherical as well as with deformedchoice of fragmentation, so there is ample opportunity to look out for the possible role of nucleardeformation and related effects in the 20Ne induced reaction. Another point of interest is that theQ-value of outgoing channel (depicted in Fig. 1) is negative at Elab = 150 MeV, whereas thesame is positive at Elab = 180 MeV.

The paper is organized as follows. The DCM model is briefly discussed in Section 2, Resultsare discussed in Section 3 and conclusions drawn from them are summarized in Section 4.

2. The Dynamical Cluster Decay Model (DCM)

DCM [21–33] is worked out in terms of the collective coordinates of mass (and charge) asym-metries η = (A1 −A2)/(A1 +A2) and ηZ = (Z1 −Z2)/(Z1 +Z2), the relative separation R, themultipole deformations βλi (λ = 2, 3, 4), and orientations θi (i = 1, 2) of two nuclei or fragments(1 and 2 stand, respectively, for heavy and light fragments). In terms of all these coordinates, for�-partial waves, the compound nucleus decay cross-section is given by

σ = π

k2

�max∑�=0

(2� + 1)P0P ; k =√

2μEc.m.

h̄2(1)

Here preformation probability P0 refers to η motion and the penetrability P to R motion,both depending on angular momentum � and temperature T . Also, μ = [A1A2/(A1 + A2)]m isthe reduced mass, with m as the nucleon mass, and �max is the maximum angular momentumwhich is fixed for the vanishing of the fusion barrier of incoming channel ηi or light particlecross-section σLP → 0. The temperature, T is related to CN excitation energy as

E∗CN = [

aT 2 − T]

(2)

In framework of DCM a = ACN/9 is taken for heavy compound systems and a = ACN/10 orACN/11 for superheavy region. In one of our recent work [32] the effect of variable level densityparameters has been studied by taking a = ACN/9, a = ACN/8 and a = ACN/6.8. The resultsof [32] indicate that with the change in level density parameter, the calculated cross-sectionsdon’t change much in the framework of DCM. In literature, different values of level densityparameter have been used and it’s temperature dependence is also explored [35,36]. Although,we have confined ourselves to a = ACN/9 in the present calculations, it would be of futureinterest to carry out the definite role of temperature dependent level density parameter in heavyion reactions.

P0 in Eq. (1) is calculated by solving stationary Schrödinger equation in η, at a fixed R = Ra ,{− h̄2

2√

Bηη

∂

∂η

1√Bηη

∂

∂η+ V (R,η,T )

}ψν(η) = Eνψν(η) (3)

where ν = 0, 1, 2, 3 referring to ground (ν = 0) and excited-states solutions, with ground-stateP0 given as

P0 = ∣∣ψR

(η(Ai)

)∣∣2√Bηη

2(4)

ACN


Fig. 1. The scattering potential for the decay of 201Bi∗ → 200Pb + X at (a) Elab = 150 MeV and (b) Elab = 180 MeV.Here X is used as notation to represent 1 proton emission for maximum angular momentum value (�max) and 1 neutronemission for minimum value (�min). The first turning point Ra , and the separation parameter R, are also shown.

The missing nuclear structure information of the Compound Nucleus in statistical modelsenters the DCM via the preformation probabilities P0 of the fragments. For the competing, non-compound ICF channel, a part of projectile interacts with target so, P0 is calculated in sameway as that for CN process with only difference that ICF leads to different composite systemdepending on break-up of the projectile nucleus.

The penetration probability P in Eq. (1) is calculated using the WKB integral as

Pi = exp

(− 2

h̄

∫ Rb

Ra

{2μ

[V (R) − Qeff

]}1/2dR

)(5)

Above equation is solved analytically [21], with the second turning point Rb satisfying V (Ra) =V (Rb) = Qeff = TKE(T ). In Eq. (3), the mass parameters Bηη are the smooth hydrodynamicalmasses [37], used for reasons of simplicity, and the fragmentation potential VR(η,T ) is definedas

VR(η,T ) =2∑

i=1

[VLDM(Ai,Zi, T )

] +2∑

i=1

[δUi] exp(−T 2/T 2

0

) + VC(R,Ai,βλi, θi, T )

+VP (R,Ai,βλi, θi, T ) + V�(R,Ai,βλi, θi, T ) (6)

Here, VLDM is T -dependent liquid drop energy of Davidson et al. [38] and δU , the ‘empirical’shell correction, from Myers and Swiatecki [39], also made T -dependent to vanish exponentiallywith T0 = 1.5 MeV [40]. VP , VC and V� are, respectively, the T -dependent, nuclear proximity,Coulomb and angular momentum �-dependent potentials for deformed, oriented nuclei (for de-tails, see [23]). For the decay of a hot CN, Ra is the first turning point of the penetration path(s),used for calculating the penetrability P , shown in Fig. 1 for different � values,


Ra = R1(α1, T ) + R2(α2, T ) + R(T ) = Rt(α,T ) + R(T ) (7)

Here Rt corresponds to touching configuration and R(T ) is the neck-length parameter, theonly parameter of DCM. In Fig. 1 the scattering plot for the light particle decay of 201Bi∗ atElab = 150 MeV and Elab = 180 MeV, enables us to access the energy transfer process at twoextreme � values i.e. �min and �max. The minimized potential is different for different angularmomentum values and therefore the corresponding preformation probability of the fragmentsgets modified accordingly. As a result, the decaying fragment is 1 proton at higher �-value and1 neutron at lower value of �. This behavior is interpreted via notation ‘X’ in Figs. 1 and 6. Thetransfer of kinetic energy of incident channel Ec.m. to internal excitation i.e. excitation energyTXE and total kinetic energy TKE can be handled as follows. For a negative Qout system as thatof Fig. 1(a) one may use the following relation

E∗CN = Ec.m. + Qin = |Qout| + TKE(T ) + TXE(T ) (8)

Qin in above expression can be positive or negative and hence could be accordingly added orsubtracted from the Ec.m. value depending on the nature and energies of target projectile combi-nation. For a positive Qout system Eq. (8) is written as

E∗CN + Qout = Ec.m. + Qin = TKE(T ) + TXE(T ) (9)

where E∗CN is calculated using Eq. (2). The neck-length parameter R(T ) allow us to define,

equivalently, the “barrier lowering” parameter VB , which simply relates V (Ra, �) and the topof the barrier VB(�), for each �, as shown in Figs. 1(a) and 1(b)

VB(�) = V (Ra, �) − VB(�) (10)

Here V (Ra, �) represent actual barrier used for the penetration and VB(�) corresponds to the topbarrier position. It may be noticed that VB appears as a negative quantity as V (Ra, �) is alwayssmaller than VB(�). Therefore, one may conclude that the actually used barrier is effectivelylowered. The validity of DCM in reference to QF has also been tested in [24,26,29] however it isbeing applied in reference to ICF data in this paper. The details of ICF related work are discussedin Section 3.2.

3. Calculations and results

The presence of NCN component makes nuclear reaction dynamics more informative andinteresting as far as nuclear structure and related phenomena are concerned. Therefore, compre-hensive analysis of possible NCN processes need to be handled with care. A sizeable amountof non-compound nucleus components like Incomplete Fusion (ICF), Deep Inelastic Collision(DIC) etc., are observed more so at higher energies for a variety of heavy ion reactions. Inorder to investigate various decay mechanisms in 20Ne + 181Ta reaction forming 201Bi∗ sys-tem, the ER, fission and ICF cross-sections have been measured in a recent experiment [34] atElab = 150 MeV and 180 MeV. It is of great interest to study the decay of 201Bi∗ nucleus andinvestigate the contribution of competing CN and NCN channels at reported energies. For 20Ne+ 181Ta reaction a significant contribution is reported for ICF channel along with normal ER andfission cross-sections. As DCM based calculations take center of mass energy Ec.m. into accountso, Ec.m. is calculated from lab energy Elab using the formula

Ec.m. = AT ∗ Elab (11)
AT + AP


Fig. 2. Variation of fragmentation potential with Fragment Mass A2 for 20Ne + 181Ta → 201Bi∗ → A1 + A2 reactionusing spherical, β2 deformed and β2–β4 deformed consideration at (a) Elab = 150 MeV and (b) Elab = 180 MeV.

The center of mass energies Ec.m. obtained from this relation are 135.07 MeV, 162.09 MeVrespectively for Elab = 150 MeV and 180 MeV. Also the compound nucleus excitation energyE∗

CN calculated using Eqs. (8)–(9) comes out to be 103.05 MeV and 130.06 MeV respectively atElab = 150 MeV and 180 MeV. Since, the deformations and orientations play a significant rolein the decay and formation process of nuclear systems, so we have presented DCM based resultsof 201Bi∗ system, for spherical consideration as well as for deformed fragmentation with highermultipole deformation effects up to hexadecapole deformations. In Section 3.1 we have discussedDCM based ER formed via CN process and Section 3.2 deals with ER having contribution fromone of the NCN process i.e. the ICF process in 20Ne induced reaction.

3.1. Evaporation Residue (ER) formed in CN process

At Elab = 150 MeV the total experimental evaporation residue (ER) cross-section is 154 mb[34] whereas at Elab = 180 MeV its value is 580 mb. This reported ER is shown to have contri-bution from CN as well as NCN process. At Elab = 150 MeV the ER formed via CN process isreported to have contribution of 15 mb whereas the remaining 139 mb (154 − 15) cross-sectionaccounts for the ER due to ICF (NCN) process. Similarly, the ER cross-section obtained due toCN at Elab = 180 MeV is 92 mb and the rest i.e. 488 mb (580 − 92) stands for cross-sectionthrough ICF (NCN) process. In this section we confine our calculations to CN based evaporationresidue cross-section data only. In order to see the deformation effects in the decay of 201Bi∗formed in 20Ne + 181Ta reaction, we have fitted the available CN channel evaporation residues(ER) cross-section using (i) spherical choice of fragmentation (ii) with inclusion of quadrupoledeformations β2 using optimum orientations [30] and (iii) using deformation effects up to hex-adecapole (i.e. β2 + β3 + β4) deformations using compact orientation approach [41,42]. The


Fig. 3. Preformation Probability P0 as a function of Fragment Mass A2 for spherical, β2 deformed and β2–β4 deformedconsideration at (a) Elab = 150 MeV and (b) Elab = 180 MeV.

Fig. 4. Variation of neck-length parameter ‘ R’ with E∗CN for spherical, β2 deformed and β2–β4 deformed choice of

fragmentation.

interesting aspect of present study is that the reported CN based ER could be fitted with either ofthese three choices of fragmentation by using different values of neck-length parameter R.


It is relevant to mention here that R is the only free parameter of the model which generallyincreases with increase in excitation energy of the compound nucleus, and its value remainswithin the range of validity of the proximity potential. The choice of this neck-length parameteris made in accordance with the experimental cross-sections. The value of R is chosen in a wayso that the calculated cross-sections start approaching the experimental data. It may be noted that R is a measure of relative separation between two decaying fragments Ai in terms of two-centershell model which is used to determine shell effects δU . For all the three cases i.e., spherical,β2 deformed and β2–β4 deformed systems the ER cross-section at energies Elab = 150 MeVand Elab = 180 MeV are successfully attained using the DCM approach. At Elab = 150 MeVthe cross-section of 15 mb could be fitted by taking R = 1.595 fm, 1.256 fm and 1.250 fmrespectively for spherical, β2 deformed and β2–β4 deformed approach. At Elab = 180 MeV theER cross-section of 92 mb is attained at R = 1.785 fm, 1.248 fm and 1.680 fm for spherical,β2 deformed and β2–β4 deformed fragmentation respectively. The dependence of neck-lengthparameter R, on compound nucleus energy and deformation effect is discussed in Fig. 4.

Figs. 2(a) and 2(b) show the behavior of fragmentation potential as a function of fragmentmass A2 at � = 0h̄ and �max at Elab = 150 MeV and Elab = 180 MeV respectively for spher-ical, β2 deformed and β2–β4 deformed choice of fragmentation. The �max is decided at pointwhere light particle cross-section become negligibly small i.e. σLP → 0. The higher �max val-ues reported in present work can be associated with the moment of inertia in sticking limit inthe angular momentum dependent potential V� in Eq. (6) for the reason discussed in [24]. InFig. 2(b) one may see that fragmentation potential at Elab = 180 MeV gets influenced at � = 0h̄

with inclusion of deformation effects contrary to Elab = 150 MeV (lower panel of Fig. 2(a)),where the fragmentation potential is almost independent of deformation effects. In other wordsat � = 0h̄, the deformation effects seem silent at Elab = 150 MeV and contribute significantly atElab = 180 MeV. One may see in lower panel of Fig. 2(b) that, the fission distribution is almostidentical for spherical and β2 choice of deformation, whereas, the same becomes relatively asym-metric with inclusion of β4 deformation. At higher value of angular momentum i.e. at � = �max,the deformation effects seem to influence fragmentation path at Elab = 150 MeV as well as atElab = 180 MeV, but the effect seems more pronounced at Elab = 180 MeV. Other point ofinterest in Fig. 2 is that spherical consideration results in symmetric fragmentation whereas thedeformed consideration results in asymmetric fragmentation at � = �max, independent of Ec.m.

values. This fact is further exploited in Fig. 3(a) and (b) where preformation probability Po

is plotted as a function of fragment mass (A2) for spherical fragmentation (upper panel), β2deformed fragmentation (middle panel) and β2–β4 deformed fragmentation (lower panel) con-sideration for Elab = 150 MeV and Elab = 180 MeV respectively. From Fig. 3 (upper panel) onemay see that fragmentation path is symmetric and fragments in the range A2 = 65–100 seem tobe contributing as fission fragments. On the contrary middle and lower panels of Fig. 3 showthat fragmentation path becomes asymmetric with inclusion of deformation effects and the frag-ments in the range A2 = 58–84 seems to be contributing towards fission. It may be noticed thatin Fig. 3, the ER contribution dominates at � = 0h̄ consideration whereas fission products startcompeting with ER at higher � values.

The variation of neck-length parameter R as a function of compound nucleus energy E∗CN

for all the three choices of fragmentation i.e. spherical, β2 deformed and β2–β4 deformed com-pact orientation approach is shown in Fig. 4. It may be noted that, R, assimilates the neckformation effects [43], and this criteria is similar to the one adopted in scission point [44] andsaddle point [45] statistical fission models. The neck-length parameter R, refers to the actuallyused barrier height and hence the concept of “barrier lowering” gets introduced in a natural


Fig. 5. VB as a function of E∗CN at Elab = 150 MeV and Elab = 180 MeV at (a) �min = 0h̄ and (b) �max .

Fig. 6. VB as a function angular momentum (�) at (a) Elab = 150 MeV and (b) Elab = 180 MeV.

way. In other words by introducing R, we are modifying the barrier penetration path i.e.V (Ra, �) as shown in Fig. 1. As with the positive value of R, V (Ra, �) increases so conse-quently VB = V (Ra) − VB decreases. Consequently the DCM supports the only acceptableexplanation for hindrance phenomenon in terms of modified shape of potential inside the barrierat sub-barrier energies. The value of neck-length parameter “ R” represents the time scale atwhich competing decay processes like neutron emission, Evaporation Residue (ER), fission andIntermediate Mass Fragment (IMF) etc., take place.

Fig. 5 represents the barrier modification, i.e. “barrier lowering” effect (see Eq. (10)) asa function of compound nucleus energy E∗ at � = 0h̄ and �max. One may clearly see
CN


Table 1Evaporation Residues formed in ICF process for 20Ne + 181Ta reaction at Elab = 150 MeV and 180 MeV.

Elab = 150 MeV Elab = 180 MeV

Projectile Elab (MeV) �max (h̄) σDCMICF (mb) Elab (MeV) �max (h̄) σDCM

ICF (mb)

4He 30 110 78.6 36 110 2628Be 60 117 36.8 72 120 13814N 105 116 9.8 126 121 4516O 120 129 12.8 144 129 40.8

ΣDCM = 138 ΣDCM = 485.8ΣExpt. = 139 ΣExpt. = 488

that barrier modification becomes more desirable at lower angular momentum i.e. at � =0h̄.

Fig. 6 shows the variation of VB as a function of angular momentum � for β2 deformedchoice of fragmentation. One neutron (1n) decay is observed at � values in the range of � =40–126h̄ and 1H for �� 126h̄ at Elab = 150 MeV. Similarly 1n-decay is observed at � values inrange of � = 40–113h̄ and 1H for �� 113h̄ at Elab = 180 MeV. One may clearly see that barriermodification becomes more prominent at lower � values. Fig. 6 also predicts the � window forER of 201Bi∗ formed in 20Ne induced reaction. The � window is seen in range of � = 40–132h̄

at Elab = 150 MeV and � = 40–136h̄ at Elab = 180 MeV. In other words the fragments with40h̄ < � < �max seem to contribute towards ER data. Therefore, Figs. 1, 5 and 6 explain thatbarrier modification is done in a natural way in the framework of DCM and it is reported to beprominent at lower �-values and higher compound nuclear energies.

3.2. Evaporation Residue (ER) formed in ICF (NCN) process

After successful explanation of CN based ER of 201Bi∗ nucleus formed in 20Ne + 181Ta reac-tion at Elab = 150 MeV and Elab = 180 MeV, we tried to test the validity of DCM in referenceto experimentally measured NCN cross-sections at reported energies. The process contributingtowards NCN cross-section in ER is reported to be the Incomplete Fusion (ICF) [34], where theprojectile breaks up prior to the fusion state. Here a part of projectile goes straight without inter-acting with the target and the residual part fuses with the target. In present case, 20Ne is supposedto break up before fusion and as a result, some of its nucleons go un-deviated and uninteractedwhile the remaining one’s fuse with the target. The four dominant channels which could accountfor the break-up process are:

Channel 1: 4He + 181Ta → 185Re → A1 + A2(4He transfer)

Channel 2: 8Be + 181Ta → 189Ir → A1 + A2(8Be transfer)

Channel 3: 14N + 181Ta → 195Hg → A1 + A2(14N transfer)

Channel 4: 16O + 181Ta → 197Tl → A1 + A2 (16O transfer)

For all these four channels, the projectile gets changed due to possible breakup of 20Neand hence the energy of projectile needs to be modified accordingly. It may be noted that af-ter the breakup of projectile, the ejectile (i.e. outgoing particle which does not fuse with thetarget) is supposed to proceed with velocity same as that of original projectile before break-up [34]. If one believes that lab. energy is shared equally among all nucleons of projectile


Fig. 7. (a) Variation of calculated ICF Cross-sections formed in 4He, 8Be, 14N, 16O transfer channels as a function ofcorresponding Elab values. (b) Fractional ICF as a function of Elab/Vb at Elab = 150 MeV and Elab = 180 MeV.

then the binding energy per nucleon E/A comes out to be 7.5 MeV and 9 MeV respec-tively for Elab = 150 MeV and Elab = 180 MeV. By knowing the energy of each nucleon ofthe original projectile (in this case 20Ne) one can find the energy of the new projectile afterbreakup.

If AP represents the mass number of projectile before break-up, then the energy of the pro-jectile would be

EProjectile = E

A∗ AP (12)

Further with reference to context that the velocity of ejectile is same as original projectile, theenergy of ejectile particle having mass AE can be obtained as

EEjectile = E

A∗ AE (13)

Hence the energy of new projectile in the ICF process due to break-up with mass number APICF

becomes

EPICF = E

A∗ AP − E

A∗ AE (14)

Alternatively, if we treat the lab energy same as that of the kinetic energy, then the veloc-ity of projectile can be obtained through it. Since this velocity is same as that of the ejectilevelocity so one can straight way deduce the kinetic energy of ejectile nucleus. Once we havethe kinetic energy of ejectile, the energy of the particle which fuses with the target via ICFprocess can be obtained by subtracting this ejectile energy from the energy of original projec-tile. The energy correction to four ICF channels i.e. 4He, 8Be, 14N and 16O transfer reactionsis applied and the energies of the new projectiles in ICF process are calculated. The modi-fied energies in reference to ICF process are tabulated in Table 1 with the corresponding ERcross-section for each channel at same value of neck-length parameter i.e. R = 1.460 fm atElab = 150 MeV and R = 1.586 fm at Elab = 180 MeV. The ER cross-section obtained for allthe four channels at same value of the neck-length parameter R = 1.460 fm comes out to be138 mb which is very close to the reported experimental value i.e. 139 mb at Elab = 150 MeV.


Fig. 8. Preformation Probability P0 as a function of Fragment Mass A2 for four ICF transfer channels at Elab = 150 MeVand R = 1.460 fm using β2 deformed fragmentation.

Similarly the evaporation residue for above mentioned four transfer reactions are worked outat R = 1.586 fm, where the sum of ER across possible break-up channels gives ER cross-section of 485.8 mb which is in good agreement with reported cross-section of 488 mb atElab = 180 MeV.

It is illustrated in Table 1 and Fig. 7(a), that 4He transfer channel contribute most in ICFprocess, followed by 8Be transfer channel, 14N transfer channel, 16O transfer channels atElab = 150 MeV and Elab = 180 MeV. There is decrease in ICF cross-sections while goingfrom 4He transfer channel to 16O transfer channel. In order to see the effect of mass asymmetrythe fractional ICF (fICF) contribution is obtained for each channel as shown in Fig. 7(b) where,fICF is plotted as a function of Ebeam/Vb .

fICF = σi(ICF)

σTF× 100

Here σi(ICF) corresponds to ICF cross-section of respective transfer channel and σTF = σCF +σICF . Although ICF cross-sections are higher at higher incident energy (as seen in Fig. 7(a))but the fractional contribution of ICF components is almost independent of energy of projectile.Moreover, the percentage of fICF is more for asymmetric transfer channel as compared to rela-tively symmetric transfer channels, in agreement with the systematics of Morgenstern [5,18]. Itmay be noted that DCM based calculations can be used to account for ICF contribution of indi-vidual transfer channels. Hence, one may access the relative contribution of competing transferchannels with ICF process using DCM based calculations. Interestingly with β2 deformed choice


of fragmentation the neck-length parameter R increases as a function of Elab for ICF channel( R = 1.460 at Elab = 150 MeV and 1.586 at Elab = 180 MeV) contrary to CN process where R is almost same at both incident energies.

Fig. 8 shows the preformation probability as a function of fragment mass for four transferchannels at Elab = 150 MeV using β2 deformation effects within optimum orientation approach.The fragmentation path for 4He, 8Be, 14N and 16O transfer reaction is quite similar to the oneobserved while fitting the CN based ER (compare middle panel of Fig. 3(a) with Fig. 8). Inother words the fragmentation path with in β2 deformed configuration remains asymmetric forCN as well as NCN channel. However a closer look of Fig. 8 shows that the contribution ofsymmetric fragments becomes more prominent while going from 4He to 16O transfer chan-nel. It may be noted that ER formed in the tabulated four ICF channels give the contributionof masses in range of A2 = 181–197, similar to the ones reported in Table III of [34]. As theICF cross-section of 20Ne + 181Ta reaction are achieved within the frame work of DCM, sowe anticipate that DCM Model can also be applied in the investigation of NCN decay alongwith CN decay where large number of applications have been done in recent past. In otherwords, DCM has been applied exclusively for the decay of CN formed in heavy ion reactiontill now [21–33] and it’s validity in reference to ICF is being tested through these calcula-tions.

4. Summary and conclusions

The evaporation residue (ER) of 201Bi∗ formed in 20Ne + 181Ta reaction has Compound Nu-cleus (CN) as well as the Non-Compound Nucleus (NCN) contributions at Elab = 150 MeVand Elab = 180 MeV. The CN based ER are nicely fitted at reported energies for spherical,β2 deformed and β2–β4 deformed choice of fragmentation. The fragmentation path at � = 0h̄

is shown to be independent of deformation effects at Elab = 150 MeV contrary to that forElab = 180 MeV. However, the deformations seem to play significant role for either of thechosen energies at higher � values i.e. at � = �max. The fragmentation path is shown to besymmetric for spherical choice of fragmentation and the same becomes asymmetric with theinclusion of deformation effects. This asymmetric fragmentation with inclusion of deforma-tion effects remain intact even in the ICF process. The neck-length parameter R, the onlyparameter of model is shown to increase linearly as a function of compound nucleus energy(E∗

CN ) for spherical and β2–β4 deformed consideration whereas the same is reported to beindependent of E∗

CN for β2 deformed effects. The barrier modification, which comes in a nat-ural way with in DCM approach, seems more desirable at lower value of angular momentum.This is the first attempt when DCM is being applied to understand ICF based decay paths. The20Ne projectile breaks into four ICF channels i.e. 4He transfer, 8Be transfer, 14N transfer, 16Otransfer channels which in turn interact with the target 181Ta to account for ICF based ER cross-sections, with 4He transfer reaction contributing maximum towards it. The ER formed in thesefour channels are accumulated to account for reported ICF cross-sections at Elab = 150 MeVand Elab = 180 MeV. Fragments in the mass range A2 = 181–197 are shown to contribute to-wards ICF process in line with experimental observations. The successful representation of ERcross-section formed in CN and ICF process enable us to conclude that DCM can be appliedsuccessfully for CN as well as NCN processes. The role of deformations, angular momentumand barrier modification is explored in context of reaction and phenomenon under considera-tion.


Acknowledgement

The financial support from the Department of Science and Technology (DST), New Delhi isgratefully acknowledged.

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