The interaction of alpha particle with ⁶⁴Zn target leads to the formation of ⁶⁸Ge^* compound system, which de-excites via various evaporation channels such as γ, p, n, 2p, nα, pα, and 2α.^[20] It is suggested in Refs. [13, 20] that within E_c.m. ∼ (5–16) MeV energy range, the one-particle (p and n) evaporation channels are dominant, whereas negligible contribution of the two- or multi-particle decay modes is observed. Moreover, the γ-channel is also not included in the present calculations due to negligible cross-sections, contributing towards the total reaction cross-sections.^[13] Apart from these decay events, the contribution from another competing channel, i.e., compound inelastic scattering is also investigated particularly at higher centre-of-mass energies. Hence in the present section, an attempt is made to address the dynamics of ⁴He+⁶⁴Zn reaction by understanding various decay modes of ⁶⁸Ge^* nucleus.

In order to understand the dynamics involved through the one particle emission, the barrier characteristics of ⁶⁸Ge^* → p+⁶⁷Ga and ⁶⁸Ge^* → n+⁶⁷Ge decay channels are plotted in Fig. 1(a) at highest incident energy E_c.m. = 15.17 MeV and extreme angular momentum states ℓ = 10ħ and 41ħ. Interestingly, both the decay channels show different barrier characteristics at different ℓ-states. Clearly, at ℓ_min = 10ħ, the barrier height (V_B) is higher for proton-emission in comparison to the neutron-decay, and is maintained upto ℓ = 22ħ as depicted from Fig. 1(b). However, these results show reverse trend at higher angular momentum states upto ℓ_max = 41ħ. This may be due to the interplay between the various potentials contributing towards the barrier height. In order to explore this, Fig. 2(a) is plotted, which shows the variation of the centrifugal potential for proton and neutron emissions at different angular momentum states. The centrifugal potential remains higher for neutron-decay for majority of ℓ-states. The same is true for the proximity potential, but not shown here. However, with the addition of the Coulomb term in Fig. 2(b), the magnitude of the potential for the neutron emission decreases for lower ℓ-values, leading to higher barrier height for the proton decay. Elaborating this, the larger barrier height for the proton emission at lowest ℓ-state is mainly due to the dominance of Coulomb term at lower angular momentum states, where the suppression in the magnitude of the centrifugal potential is simultaneously observed. At lower ℓ-states, ℓ(ℓ+1) ∼ ℓ² term in the centrifugal potential, given by Eq. (6) does not contribute much, hence the dominance of Coulomb factor can be felt for the proton decay. However, the Coulomb potential remains zero for the neutron emission resulting higher barrier for the proton at ℓ_min = 10ħ state. In contrast to this, the magnitude of the centrifugal potential competes the Coulomb term and gradually becomes larger in magnitude for the higher ℓ-values. Due to less influence of the Coulomb term at higher ℓ-states, the barrier height gets suppressed for the proton emission (see Fig. 1(b)). In other words the Coulomb and centrifugal potentials play an important role to define the barrier characteristics of the proton and neutron decays. Note that the emergence of the flip due to different barrier characteristics for proton and neutron emission channels also effect the penetration path (see Fig. 2(c)). In addition to the barrier height, barrier width also plays an important role to describe the penetration of the fragment through the barrier, as described by Eq. (8) of Sec. 2. Depending on these factors, the penetrability P shows different behavior for p- and n-decay channels, plotted in Fig. 2(c). Specifically, the variation of decay barrier width (|R_a − R_b|) can be depicted from the inset of Fig. 2(c) to illustrate the fact that penetrability increases exponentially with decrease in barrier width and vice versa. However, we notice that P increases with increase in ℓ for both decay channels and in turn sets the minimum value of angular momentum, slightly different for both particles.

In the next step, to investigate the fragmentation path of ⁶⁸Ge^* nucleus via p- and n-particle evaporation channels, the mass-fragmentation potential V(A₂) is shown in Figs. 3(a) and 3(b) at E_c.m. = 15.17 MeV. Note that the fragmentation potential goes as an input to the Schrödinger equation, which is used to estimate the preformation probability P₀, and hence the excitation functions of the nuclei. The results are obtained for both the decay channels using different separation distances (ΔR) chosen to fit the respective experimental data. In order to see the comparative contribution of energetically feasible fragments, the fragmentation paths are plotted for ℓ_min and ℓ_max values. One may notice from Figs. 3(a) and 3(b) that the structure of potential energy surfaces (PES) are almost independent at two extreme ℓ-values for the fission fragments (FF), but the characteristic behavior of fragmentation potential for light particles (LPs) is significantly different. At lower ℓ-values, the emission of light particles is favorable that means contribution of p- and n-particles is prominent, whereas fission fragments (marked in figure as FF) start competing the light particles at higher ℓ-states. Following this, an attempt is made to predict the fission cross-sections for the decay of ⁶⁸Ge^* nucleus within the framework of DCM, which may be verified by future experiment(s) (refer Table 2).

After analyzing the ℓ-dependence of fragmentation decay path for both decay channels, the effect of center-of-mass energy on the fragmentation potential (V), preformation probability (P₀) and barrier penetrability (P) is illustrated in Figs. 4(a), 4(b), and 4(c) respectively, at two common ℓ = 15ħ and 41ħ angular momentum states. These calculations are done at common neck-length parameter ΔR, chosen to fit the p-evaporation channel cross-sections. Clearly, the magnitude of fragmentation potential increases slightly with center-of-mass energies E_c.m. for p- and n-particle emissions. Interestingly, the fragmentation potentials for both particles overlaps at the ℓ = 15ħ angular momentum state, indicating the fact that neutron and proton emissions are equally probable at lower angular momentum states. On the other hand, for higher angular momentum the fragmentation behavior of the p- and n-decay channels differs significantly. For example at ℓ = 41ħ, the fragmentation potential is much higher for the neutron-emission as compared to proton-decay. Lower fragmentation potential for the proton-decay seems to suggest that the proton emission is more favorable towards decay at highest angular momentum state. This result is in accordance with the observation of Fig. 1(a), where lower barrier is reported for the proton emission at ℓ_max = 41ħ. This difference in fragmentation potential of n- and p-decay channels at higher ℓ-values enters primarily via rotational energy term due to difference in moment of inertia, as different daughter nuclei are produced in these two channels. It may be noted that ⁶⁷Ga (the daughter nucleus in p-channel) is prolate deformed with β₂ = 0.228, whereas ⁶⁷Ge (the daughter nucleus in n-channel) is oblately deformed with β₂ = −0.299. As their radii are changed significantly, so moment of inertia changes accordingly. It is important to mention here that the minima in the fragmentation potential corresponds to maxima in preformation probability and vice versa. Thus, the preformation factor P₀ shows opposite trend than that of the fragmentation potential in reference to the ℓ-value. One can see from Fig. 4(b), at lower ℓ-value, both n- and p-particles have almost same and maximum preformation probability, which in turn, represents that LPs are favorable at lower ℓ-states for all energies. Whereas, at higher ℓ, the P₀ has much lower magnitude, this is in agreement with Fig. 3(a) for the fragmentation case. Next, the variation of penetrability P is defined via Fig. 4(c), it shows similar results as shown by fragmentation potential, owing maximum magnitude at higher ℓ-state, and indicating the different barrier characteristics for both the particle emissions. Also, barrier penetrability (P) shows increment with increase in center-of-mass energy particularly at lower angular momentum.

Using the combined effect of P₀ and P values, the ER cross-sections for p- and n-decay channels are calculated within the framework of DCM, presented in Tables 1–2, and compared with experimental data.^{[13, 20]} The DCM calculated results show nice agreement with the experimental measurements. The only parameter of the model is the neck-length (ΔR), which decides the first turning point of the penetration path, obtained for best-fit of the measured data, listed in the tables and plotted in Fig. 5(a). The optimized neck-length parameter “ΔR” is observed to have larger magnitude for n-channel as compared to that of p-channel. It may be due to the reason that ⁶⁸Ge appears below the β stability line and hence seems more prone for p-emission, which is in agreement with the result depicted in Fig. 4(a). As discussed earlier, the fission fragments (FF) may also contribute in the decay of ⁶⁸Ge^* nucleus, particularly at higher ℓ-states. Thus, in this work an effort is made to predict the fission contribution presented in Table 2, using ΔR_FF = ΔR_n − 0.5 fm. It is relevant to mention that lighter fragments are generally emitted first from the hot and rotating nuclei, establishing the fact that light particle emission occurs prior to the fission process. Keeping this in mind, higher ΔR is considered for ER formation as compared to the fission decay. Similar analysis is carried out in the previous work^[41] of DCM, based on the decay of Xe-nucleus. At different neck-length parameters “ΔR_FF”, the predicted excitation functions of fission fragments (A₂ = 28–34 and their complementary fragments) are found to be negligibly small, indicating the fact that Ge-nucleus decays primarily via light particles, and fission fragments contribution is negligibly small. Moreover, if we calculate FF cross-sections at ΔR_FF = ΔR_p − 0.5 fm i.e. at the neck-length parameter of proton emission, the fission contribution reduces further. Hence the collective clusterization does not reinforce the fragmentation to follow the fission path, instead ER formation is preferred. In addition to this, the “barrier modification” (ΔV_B) another observable of DCM, which can be related to the ΔR (equivalently, R_a), is examined in Fig. 5(b) as a function of E_c.m.. Apparently, ΔV_B (in magnitude) for each particle emission is maximum for lowest E_c.m. and minimum at the highest one. It is also evident from figure that larger barrier modification is needed for the case of proton-emission in comparison with neutron one.

Table 1.

Table 1.

Table 1. The calculated decay cross-sections for p-evaporation channels using DCM at various Ec.m. for 4He+64Zn reaction and compared with experimental data.[13,20] The other related observables like neck-length parameter (ΔR) and temperature (T) are also listed. . Ec.m./MeV /MeV T/MeV ΔR/fm σp/mb DCM Exp. [13, 20] 5.79 9.14 1.168 0.606 2.63 × 10−3 (2.65 ± 0.38) × 10−3 5.86 9.21 1.172 0.617 3.01 × 10−3 (3.03 ± 0.40) × 10−3 6.16 9.51 1.190 0.716 3.73 × 10−2 (3.73 ± 0.42) × 10−2 6.26 9.61 1.196 0.721 3.69 × 10−2 (3.69 ± 0.42) × 10−2 6.39 9.74 1.203 0.805 2.94 × 10−1 (2.94 ± 0.33) × 10−1 6.52 9.87 1.211 0.804 2.72 × 10−1 (2.76 ± 0.31) × 10−1 6.80 10.15 1.227 0.830 4.32 × 10−1 (4.38 ± 0.49) × 10−1 7.01 10.36 1.239 0.854 6.98 × 10−1 (7.08 ± 0.80) × 10−1 7.04 10.39 1.240 0.846 5.76 × 10−1 (5.88 ± 0.66) × 10−1 7.15 10.50 1.247 0.915 2.49 2.52 ± 0.28 7.51 10.86 1.267 0.964 5.89 5.95 ± 0.67 7.70 11.05 1.277 0.984 7.76 7.78 ± 0.88 7.96 11.31 1.291 0.991 7.98 7.96 ± 0.89 8.07 11.42 1.297 1.017 12.2 12.4 ± 1.4 8.47 11.82 1.318 1.091 36.5 36.6 ± 4.1 8.79 12.14 1.335 1.119 49.1 49.8 ± 5.6 9.04 12.39 1.348 1.152 72.4 72.3 ± 7.3 9.68 13.03 1.381 1.204 122 122 ± 13 10.30 13.65 1.412 1.242 171 172 ± 19 10.38 13.73 1.416 1.247 176 177 ± 20 11.09 14.44 1.45 1.290 253 254 ± 28 11.24 14.59 1.457 1.293 255 255 ± 28 11.60 14.95 1.474 1.301 263 265 ± 29 12.22 15.57 1.503 1.329 317 317 ± 36 12.37 15.72 1.510 1.341 343 344 ± 40 15.17 18.52 1.633 1.398 426 428 ± 50

Table 1. The calculated decay cross-sections for p-evaporation channels using DCM at various Ec.m. for 4He+64Zn reaction and compared with experimental data.[13,20] The other related observables like neck-length parameter (ΔR) and temperature (T) are also listed. .

One-particle emission is dominant decay mode of ⁶⁸Ge^* nucleus, as explained in Sec. 1 of the present work. However, experiments^[13,20] also suggest that two-particle emission channels play significant role at energies above 20 MeV due to the large threshold of multi-nucleon clusters. Although, in this work we are dealing with energies below 20 MeV, but an effort is made here to check the relative contribution of two-particle emission for the decay of ⁶⁸Ge^* nucleus formed in ⁴He+⁶⁴Zn reaction. The cross-sections of ⁶⁸Ge^* → 2p+⁶⁶Zn and ⁶⁸Ge^* → αn+⁶³Zn decays are calculated at two extreme energies E_c.m. = 5.79 MeV and 15.17 MeV. The DCM calculated cross-sections are comes out to be σ_2p = 1.77 × 10⁻⁴ mb and σ_αn = 1.35 × 10⁻² mb at lowest E_c.m. = 5.79 MeV, which increases with increase in centre-of-mass energy and read as σ^2p = 1.27 mb and σ_αn = 15.17 mb at highest E_c.m. = 15.17 MeV. These cross-sections are calculated at same ΔR as observed for p-emission, because the previous study^[18] of DCM indicates almost similar magnitude of ΔR for one-particle and multi-nucleon emissions. Hence it is evident from above discussion that the estimated cross-sections for 2p and αn do not contribute much towards the total reaction cross-sections, as reported in the experimental work.^[20]

Table 2.

Table 2.

Table 2. Same as Table 1 but for n-evaporation channel. In addition to this, the predicted fission contributions (σFF) are also listed. . Ec.m./MeV /MeV T/MeV ΔR/fm σn/mb σFF/mb at ΔRn−0.5 fm DCM Exp. [13, 20] 9.04 12.39 1.348 1.361 10.6 10.6 ± 1.2 1.58×10−2 9.68 13.03 1.381 1.470 41.3 41.7 ± 4.6 7.98×10−2 10.30 13.65 1.412 1.553 70.2 70.4 ± 7.7 2.60×10−1 10.38 13.73 1.416 1.570 73.5 73.6 ± 8.1 2.86×10−1 11.09 14.44 1.450 1.617 106 106 ± 12 5.54×10−1 11.24 14.59 1.457 1.623 109 109 ± 12 5.84×10−1 11.60 14.95 1.474 1.640 120 120 ± 13 7.18×10−1 12.22 15.57 1.503 1.693 165 165 ± 18 14.44×10−1 12.37 15.72 1.510 1.709 178 178 ± 19 17.56×10−1 15.17 18.52 1.633 1.790 238 240 ± 26 37.20×10−1

Table 2. Same as Table 1 but for n-evaporation channel. In addition to this, the predicted fission contributions (σFF) are also listed. .

Apart from one- and two-particle evaporation channels, the compound inelastic scattering is another competing channel emerging in the decay of ⁶⁸Ge^* compound system especially at above barrier energies. In this process, the projectile is absorbed by the target nucleus and leads to formation of compound nucleus (CN), which further re-emits the incident particle with low kinetic energy, thus original nucleus remains in the excited state. Here, we have studied the compound inelastic scattering for ⁴He+⁶⁴Zn → ⁶⁸Ge^* →⁴He′+⁶⁴Zn reaction. For inelastic scattering process, the entrance channel keeps its identity, and hence the preformation probability is taken P₀ = 1 for (⁴He,⁴He′) decay channel, and penetrability is calculated using WKB approximation and presented in Fig. 6. It is evident from Fig. 6 that larger penetration probability is obtained at highest center-of-mass energy, indicating easier penetration of the projectile like fragments. Besides this, the penetrability corresponding to each ℓ-state increases with increase in angular momentum. Using P₀ and P, the measured^[13] cross-sections of (81±13.8) mb and (201±37.1) mb are best fitted at ΔR = 0.699 fm and 0.827 fm values respectively, for two highest energies E_c.m. = 11.29 MeV and 15.17 MeV, at which signature of the inelastic scattering is observed. It is relevant to mention that, if energy loss up to 30% is considered in the inelastic scattering process then the neck-length parameter “ΔR” and angular momentum effect remain almost unchanged. Hence, negligible change in ΔR and ℓ_max values is observed even with the reduction of 30% in the energy of incident flux.

Fig. 6

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	Fig. 6 Barrier penetrability P as a function of ℓ for 64Zn(4He,4He′)64Zn reaction plotted at two center-of-mass energies.

After analyzing the dynamics of tightly bound ⁴He-induced reaction, we intend to explore the decay of excited ⁷⁰Ge^* nuclear system formed via interaction of two-neutron halo “⁶He” projectile and ⁶⁴Zn target. Interestingly, in recent experiment,^{[21] 6}He+⁶⁴Zn → ⁷⁰Ge^* reaction has been studied at various energies across the barrier ranging E_c.m. = (7.54 to 16.1) MeV. The total fusion cross-sections (σ_fus) have been obtained by measuring the excitation-functions of various evaporation residues (ERs) (2n)⁶⁸Ge, (np)⁶⁸Ga, (2np)⁶⁷Ga, and (nα)⁶⁵Zn, as light charged particle emission is the primary decay mode of ⁷⁰Ge^* nuclear system. Apart from ERs, the breakup and transfer events also contribute to the total cross-sections due to loosely bound nature of the ⁶He projectile. Hence in the present section, the evaporation residue, breakup+transfer cross-sections (or equivalently incomplete fusion cross-sections) are addressed using DCM, in order to have overall understanding of the dynamics of ⁶He+⁶⁴Zn → ⁷⁰Ge^* reaction so that loosely bound nature of ⁶He nucleus be explored. The detailed analysis of the above work is carried out in the subsequent discussion.

In order to investigate the decay of ⁷⁰Ge^* nucleus, the fragmentation potential V(ℓ) and preformation probability P₀(ℓ) are presented in Fig. 7 for the evaporation residues of ⁷⁰Ge^* nucleus, corresponding to energy E_c.m. = 12.7 MeV, above the Coulomb barrier. The different ER decay modes, which are shown in figure represent multi-nucleon clusters and heavy residual nuclei, i.e., X + Y → 2n+⁶⁸Ge (solid squares), np+⁶⁸Ga (open squares), 2np+⁶⁷Ga (solid triangles) and nα+⁶⁵Zn (open triangles). Clearly, the fragmentation potentials for all ER channels show increment with increase in angular momentum. The result reflects that light charged particle emission is probable at small values of angular momentum states, due to lower fragmentation potential and larger preformation probability, as depicted from Figs. 7(a) and 7(b) respectively. It is relevant to mention that similar results are extracted for the decay of ⁶⁸Ge^* compound nucleus, where the evaporation residue formation dominates at lower angular momentum states. In addition to this, Fig. 7(a) shows that at lower ℓ-values, the fragmentation potential increases with increase in mass of the multi-particle cluster, i.e., maximum for nα and minimum for 2n cluster, whereas reverse trend is observed at higher angular momentum values. As explained earlier in Subsec. 3.1, this happens because of the relative contribution of Coulomb, proximity and centrifugal potentials to the total fragmentation potential. Due to this, an flip in the magnitude of the fragmentation potential arises around ℓ = 30ħ. Similar results are obtained from Fig. 7(b), plotted for the preformation probabilities of the decay fragments. The preformation probability shows increment upto certain ℓ-states, then sharply decreases near the ℓ_max-values of the cluster emission. The maximum values of the angular momentum can be estimated from Fig. 7(b), designated as a point where the contribution of the preformation probability is negligible. Above the ℓ_max-values the total cross-sections becomes significantly small.

Fig. 7

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	Fig. 7 The fragmentation potential (V) and preformation probability P0 vs. ℓ plotted for evaporation residues (2n)68Ge, (np)68Ga, (2np)67Ga and (nα)65Zn for the de-excitation of 70Ge* system formed via using loosely bound nucleus as a projectile at energy 12.7 MeV.

In reference to above discussion, the angular momentum window ℓ_min ≤ ℓ ≤ ℓ_max is fixed and the excitation functions for the evaporation residues of ⁷⁰Ge^* nucleus are estimated using Eq. (7). The ℓ_min for all the decay fragments lies around 0ħ, and ℓ_max-values are pointed in Fig. 7(b), which are different for different clusters. The fitted cross-sections are tabulated in Table 3 for all the mentioned clusters. The best-fit values of neck-length parameters (ΔR) for individual ER channels along with temperature (T) and center-of-mass energies (E_c.m.) are also listed in Table 3. Different ΔR values indicate unique reaction time scales for individual evaporation residue channels. It is of interest to note that the total calculated fusion cross-sections () of ⁷⁰Ge^* compound system, i.e., sum of individual ER excitation functions, deviate from the experimental measured fusion cross-sections ().^[21] It is clearly depicted from Fig. 8(a) and 8(b) that the 2n and np clusters show nice agreement with the experimental data. However, the strong mismatch of the experimental and our DCM based cross-sections is obtained for the (nα)⁶⁵Zn-cluster (see Fig. 8(c)), which is responsible for the decrement in the fusion cross-sections and signify the large contribution of breakup and transfer channels. Additionally, the cross-sections of 2np-cluster are also underestimated at above barrier energies as shown in Fig. 8(d). The results remain intact even at the maximum allowed neck-length parameters. Hence the wide range of ΔR could not address the experimental cross-sections upto ∼2.5 fm. The suppression in the nα and 2np cross-sections is governed mainly through the loosely bound nature of the ⁶He projectile, responsible for the breakup and transfer events. The loosely bound ⁶He nucleus breaks up into two parts ⁴He and 2n, which act as new projectiles and interact with the ⁶⁴Zn target nucleus individually. It may be noted that ⁶⁵Zn nucleus is not formed only via nα evaporation channel, but also find its genesis in the breakup and two-neutron transfer channels of ⁶He projectile, which is addressed in the subsequent discussion, by employing the relevant energy correction. Also, the suppression in 2np cross-sections is associated with the incomplete fusion of other part of ⁶He projectile with the target i.e. ⁴He+⁶⁴Zn. In reference to the above discussion, the contribution of breakup and transfer channels is included in the present analysis as the difference between estimated and experimental cross-sections, which are read as

Fig. 8

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	Fig. 8 Comparison of experimental cross-sections with calculated ones for (a) 2n, (b) np, (c) nα, and (d) 2np evaporation channels at various Ec.m.’s for the 6He+64Zn reaction.

Accordingly, the cross-sections are calculated for 1n decay of ⁶⁶Zn^* and 2p decay of ⁶⁸Ge^* via breakup and transfer reactions. The temperature (T) and best-fit ΔR values are reported in Table 4 and both increase with increase in energy. The angular momentum contributing to the breakup+transfer cross-sections has the limiting values ℓ_min = 12ħ and ℓ_max = 45ħ. The total sum of DCM calculated breakup+transfer and fusion cross-sections show nice agreement with the experimental fusion data (refer Fig. 9). Broadly speaking, the suppression in the total fusion cross-sections of ⁷⁰Ge^* CN due to nα and 2np channels is compensated through the breakup+transfer events leading to ⁶⁶Zn^* and ⁶⁸Ge^* nuclear systems, followed by 1n and 2p emission respectively. Conclusively, the loosely bound nature of the ⁶He projectile influences the dynamics of ⁶He+⁶⁴Zn reaction as the total contribution of breakup+transfer channel is reasonably higher than that of the fusion cross-sections.

Fig. 9

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	Fig. 9 Variation of cross-sections as a function of centre-of-mass energies for 4He+64Zn and 6He+64Zn reactions and compared with experimental data.[13,20–21]

Table 3.

Table 3.

Table 3. The DCM calculated cross-sections for individual ER 2n, np, 2np, and nα channels with best-fit values of ΔR for the decay of 70Ge* at various centre-of-mass energies. obtained by summing all ERs cross-sections and compared with experimental fusion data.[21] . Ec.m./Mev /Mev T/Mev ΔR2n/fm σ2n(68Ge)/mb ΔRnp/fm σnp(68Ga)/mb ΔR2np/fm σ2np(67Ga)/mb ΔRnα/fm σnα(65Zn)/mb /mb /mb 7.54 30.20 2.036 1.592 9.97 − − − − 1.349 14.2 24.17 128.43 9.15 31.81 2.088 1.860 44.6 − − 1.433 3.37 1.447 18.7 66.67 283.07 10.60 33.26 2.133 1.980 70.1 1.890 106 1.700 16.2 1.650 32.8 225.1 501.08 11.83 34.49 2.171 2.140 116 1.980 139 1.910 34.0 2.020 53.8 342.8 553.85 12.70 35.36 2.197 2.300 165 2.070 174 2.120 55.1 2.070 51.7 445.8 809.01 13.80 36.46 2.230 2.306 164 2.030 150 2.350 72.9 2.150 49.0 435.9 817.81 15.00 37.66 2.266 2.300 153 2.170 209 2.400 72.2 2.200 45.9 480.1 863.29 16.10 38.76 2.298 2.260 141 1.965 114 2.430 71.5 2.250 42.0 368.5 781.04

Table 3. The DCM calculated cross-sections for individual ER 2n, np, 2np, and nα channels with best-fit values of ΔR for the decay of 70Ge* at various centre-of-mass energies. obtained by summing all ERs cross-sections and compared with experimental fusion data.[21] .

Finally, the comparison of ⁴He+⁶⁴Zn and ⁶He+⁶⁴Zn reactions is investigated in Fig. 9. As mentioned above, the fusion cross-sections of nucleus formed in ⁴He+⁶⁴Zn reaction matches the experimental data nicely. On the other hand, suppression in the DCM calculated fusion cross-sections are observed for ⁶He+⁶⁴Zn reaction channel, due to mismatch in the cross-sections of nα and 2np-clusters. If one compares the fusion cross-sections for ⁴He+⁶⁴Zn and ⁶He+⁶⁴Zn reactions, sub-barrier enhancement in the fusion cross-sections of ⁶He+⁶⁴Zn reaction is observed. However, the DCM fitted σ_fus for ⁶He+⁶⁴Zn reaction bear lower magnitude at above barrier energies than the same calculated for ⁴He+⁶⁴Zn. These two results can be explained on the basis of structure properties of loosely bound projectile. The larger radius of the loosely bound projectile reduces the Coulomb barrier, as a result one can expect the fusion enhancement, as shown in Fig. 9 at sub-barrier energies.

On the other hand, the low binding energy of the outer two neutrons of the ⁶He nucleus implies large contribution of breakup+transfer channels, which could remove flux from the complete fusion and thus suppress the fusion cross-sections. The DCM results support that at the above-barrier energies, the loss of flux due to the breakup+transfer channels dominates and the resulting fusion cross-section is suppressed. Note that similar kind of results have been analyzed for the reactions of loosely bound projectile with heavy target (e.g. ¹¹Be+²⁰⁸Pb^[7]). Hence from the above discussion the loosely bound nature of the ⁶He can be easily illustrated by concluding following results: (i) The loosely bound character of the projectile is responsible for the breakup+ transfer channels, which are addressed here through the two different breakup and transfer channels of ⁶He i.e. 2n+⁶⁴Zn and ⁴He+⁶⁴Zn. (ii) The comparison of the tightly and loosely bound projectile induced reactions reveals the peculiar dynamics of ⁶He+⁶⁴Zn interacting pair. It has been emphasized that the loosely bound nature of ⁶He is responsible for the sub-barrier fusion enhancement and above barrier fusion suppression.

Table 4.

Table 4.

Table 4. The calculated breakup+transfer cross-sections using DCM for 1n decay channel for 66Zn* excited system formed in the 2n+64Zn reaction, and 2p decay channel for 68Ge* nucleus formed in 4He+64Zn reaction at modified energies . . /MeV /MeV T/MeV ΔR/fm σ/mb 2n+64Zn → 66Zn* → 1n+65Zn 2.670 22.08 1.805 1.265 89 3.229 22.64 1.827 1.340 162 3.746 23.16 1.847 1.398 241 3.824 23.24 1.850 1.366 177 4.489 23.90 1.875 1.462 349 4.878 24.92 1.889 1.472 345 5.304 24.72 1.905 1.473 320 5.690 25.10 1.920 1.475 305 4He+64Zn → 68Ge* → 2p+66Zn 9.470 12.82 1.370 1.570 17.5 10.30 13.65 1.412 2.060 76.0 11.05 14.40 1.448 2.450 112.0

Table 4. The calculated breakup+transfer cross-sections using DCM for 1n decay channel for 66Zn* excited system formed in the 2n+64Zn reaction, and 2p decay channel for 68Ge* nucleus formed in 4He+64Zn reaction at modified energies . .