Characterization of fragment emission in ^{20}Ne (7 - 10 MeV/nucleon) + ^{12}C reactions

TL;DR

This study measures the energy distributions of complex fragments emitted from ^{20}Ne + ^{12}C reactions at 145-200 MeV, revealing fully equilibrated emission and signs of orbiting-like processes at these energies.

Contribution

It provides detailed experimental data on fragment emission in ^{20}Ne + ^{12}C reactions and identifies orbiting phenomena at intermediate energies.

Findings

Damped fragment yields indicate fully equilibrated emission.

Enhanced yields of certain fragments suggest orbiting-like processes.

Comparison with statistical models shows some discrepancies.

Abstract

The inclusive energy distributions of the complex fragments (3 $\leq$ Z $\leq$ 7) emitted from the bombardment of ^{12}C by ^{20}Ne beams with incident energies between 145 and 200 MeV have been measured in the angular range 10$^{o} \leq \theta_{lab} \leq$ 50^{o}. Damped fragment yields in all the cases have been found to be the characteristic of emission from fully energy equilibrated composites. The binary fragment yields are compared with the standard statistical model predictions. Enhanced yields of entrance channel fragments (5 $\leq$ Z $\leq$ 7) indicate the survival of orbiting-like process in ^{20}Ne + ^{12}C system at these energies.

Figures

Tables

Table 1. Table 1: The angular momentum values, NOC and C fragment yield for different energies.

System	$E_{lab}$	$E^{\ast }$	$l_{cr}$	$l_{gr}$	NOCa	C yield (mb)
	(MeV)	(MeV)	($\hslash$)	($\hslash$)		expt	CASCADEb
Ne + C	109.5	60	20	26	5.2	122.6c	35.7
Ne + C	145	73	24	31	4.5	151.9$\pm$26.8	62.2
Ne + C	158	78	24	33	8.2	149.7$\pm$26.5	58.7
Ne + C	170	82	24	34	11.0	131.8$\pm$23.8	56.9
Ne + C	180	86	25	36	33.0	142.9$\pm$25.4	66.0
Ne + C	200	94	25	38	73.2	178.3$\pm$30.7	51.4
F + C	96	60	21	24	97.2	47.92$\pm$4.37 bhat96	34.5

Equations

$$A=Z\times (2.08+0.0029\times Z).$$

Full text

I Introduction

Several experiments have been done in recent years to understand the mechanism of complex fragment emission in low-energy (Elab $\lesssim$ 10 MeV/nucleon) light heavy-ion (Aprojectile + Atarget $\lesssim$ 60) reactions Sanders99 ; carlin ; pada ; bhat05 ; bhat2002 ; bhat2004 ; bhat96 ; bec98 ; beck96 ; barrow ; farrar96 ; shapi79 ; shapi821 ; shapi82 ; shiva ; dunn ; adey07 . The origin of these fragments extends from quasi-elastic (QE)/ projectile breakup carlin ; pada , deep-inelastic (DI) transfer and orbiting bhat05 ; bhat2004 ; shapi79 ; shapi821 ; shapi82 ; shiva ; dunn , to fusion-fission (FF) moretto ; Sanders91 ; Matsuse97 ; dha2 ; Szanto97 ; Szanto96 processes; and in some cases the structure of the nuclei has been found to play an important role. In most of the reactions studied, the observed fully energy-damped yields of the fragments have been successfully explained in terms of fusion-fission (FF) mechanism moretto ; Sanders91 ; Matsuse97 ; dha2 ; Szanto97 ; Szanto96 . However, the reactions involving $\alpha$ - cluster nuclei (e.g., 20Ne + 12C shapi79 ; shapi821 , 24Mg + 12C dunn , 28Si + 12C shapi82 ; shapi84 etc.) deserved special attention, where the observations of large enhancement in yield and/or resonance-like excitation function in a few outgoing channels have been indicative of a competitive role played by the deep-inelastic orbiting mechanism shapi79 ; shapi821 ; shapi82 ; shiva . In the FF mechanism, a completely equilibrated compound nucleus (CN) is formed, which decays into various exit channels. The decay probability is governed by the available phase space and barrier penetration probabilities for the respective decay channels. The process occurs in a similar time scale which is required for the complete relaxation of the entrance channel energy and angular momentum. On the other hand, deep inelastic orbiting may be described in terms of the formation of a long-lived, dinuclear molecular complex shiva , which acts as a “door way to fusion”, with a strong memory of the entrance channel. In this picture, the interacting ions are trapped in a more deformed configuration than that of the compound nucleus (trapped in the pocket of the ion-ion interaction potential due to combined effects of Coulomb and centrifugal barriers). Both orbiting and fusion-fission processes occur on similar time scale. In addition to that, for the light heavy-ion systems, the shapes of the orbiting dinuclear complexes are quite similar to the saddle and scission shapes obtained in course of evolution of the FF process. Therefore it is difficult to differentiate the signatures of the two processes.

The enhancement of fully energy damped reaction yields in light systems was first observed in the study of 20Ne + 12C inelastic scattering at backward angles shapi79 , where large cross sections have been observed in inelastic scattering yields near 180o. Subsequently, orbiting was observed in 28Si + 12C shapi82 ; shapi84 and 24Mg + 12C dunn reactions. Detailed study of 28Si + 12C system revealed that, at lower bombarding energies, the excitation spectra for the 12C fragments were dominated by single excitation and mutual excitations of the 12C and 28Si fragments, whereas at higher bombarding energies, the dominant strength for all these channels shifted to higher excitation energies shapi84 . For the higher bombarding energies, the most probable Q-values were found to be independent of detection angles and the resulting angular distributions were found to have d$\sigma$/d$\Omega\propto 1/\sin{\theta_{c.m.}}$ like angular dependence — characteristic of a long-lived, orbiting, dinuclear complex. Similar results have been obtained for 20Ne

• 12C system shapi79 ; shapi821 , where resonance-like behaviour was also found in the excitation functions for several outgoing channels, which was similar to the observation made for symmetric 16O + 16O system gobbi73 ; kovar ; kolata ; tserr78 . Enhancements of large angle, binary reaction yields have also been observed in somewhat heavier 28Si + 28Si, 24Mg + 24Mg systems Sanders99 , where significant non resonant background yield was observed at higher excitation energies. The general pattern which unfolds from these studies clearly suggests that the enhancements are manifestations of dynamics of damped nuclear reactions involving a large number of channels, rather than due to specific structure effect appearing only in a few select channels.

The enhancement in elastic and inelastic channels may be explained in terms of a long lived dinuclear configuration that decays back to entrance channel due to weak absorption which inhibits the orbiting configuration from spreading into compound nuclear states. However, the enhancement in the elastic channel can be explained with the assumption of weak absorption of grazing partial waves only; on the contrary, deep-inelastic orbiting phenomenon in general suggests weak absorption in the angular momentum window between the critical angular momentum of fusion, $l_{cr}$, and the reaction grazing angular momentum, $l_{gr}$. Besides, substantial mass and charge transfer, due to the rapid mass equilibration in light systems, would also occur during the evolution of the orbiting dinuclear complex. So, the rearrangement channels are also of interest in probing the dynamics of the orbiting process involving light nuclear systems.

It is, therefore evident that, though some qualitative understanding about the phenomenon of deep-inelastic orbiting reaction, in general ($i.e.$, correlation with number of open reaction channels beck94 , or, alternatively, to weak absorption) has been arrived at, precise mechanism of the process is still unknown. The deep-inelastic orbiting process has been observed in several light $\alpha$-like systems, for example, 20Ne + 12C shapi79 ; shapi821 , 24Mg + 12C dunn , 28Si + 12C shapi82 ; shapi84 , 28Si + 16O oliv systems, where the number of open channels are small ($\sim$ 10) beck94 . However, 16O (116 MeV) + 28Si reaction bhat2004 showed different behaviour so far as the shape of the energy distributions, variation of $<Q>$ values with angle, and yields of the fragments are concerned. For a better understanding of the orbiting process, it is interesting to study how the orbiting process evolves with energy. Intuitively, survival of long lived dinuclear configuration other than fused composite is less probable at higher excitations and there are also indications that entrance channel effect becomes smaller at higher energies Sanders99 . Shapira et al. shapi821 made detailed study of 20Ne + 12C system in the energy range Elab = 54 – 81 MeV and showed that there was large enhancement of strongly damped yields, the characteristic of a long-lived orbiting 20Ne + 12C dinuclear system. The aim of the present paper was to extend the investigation on fragment yield from 20Ne + 12C reaction at higher excitation energies, which might allow us to have a better understanding of orbiting vis-$\grave{a}$-vis fusion-fission processes for 20Ne + 12C system. If a long-lived rotating dinuclear complex is formed in these reactions, mass and charge transfer should also occur, which leads to typical deep-inelastic reaction yields. Therefore, backangle measurements for rearrangement channels became of interest. In addition to that the excitation function measurements, for the dependence of the average total kinetic energy ($E_{K}^{tot}$) loss on bombarding energy for each binary exit channel, would provide an important probe of the dynamical properties of the long-lived dinuclear complex. With this motivation, we have studied the fragment emission spectra from the reaction 20Ne + 12C at Elab = 145, 158, 170, 180 and 200 MeV, respectively. A part of the present data has already been reported bhat05 , which showed enhancement in yield of Carbon and Boron fragments well above the standard statistical model predictions.

The paper has been arranged as follows. Section II describes the experimental procedures. In Sec. III we present the analysis of 20Ne + 12C data. The results have been discussed in Sec IV. Finally, the summary and conclusions are presented in Sec. V.

II Experiments

The experiment was performed using accelerated 20Ne ion beams of energies 145, 158, 170, 180 and 200 MeV, respectively, from the Variable Energy Cyclotron at Kolkata. The target used was $\sim$ 550 $\mu$g/cm2 self-supporting 12C. Different fragments (5 $\leq$ Z $\leq$ 13) have been detected using two solid state [Si(SB)] telescopes ($\sim$ 10 $\mu$m $\Delta$E, 300 $\mu$m E) mounted on one arm of the 91.5 cm scattering chamber. Two solid state telescopes ($\sim$ 50 $\mu$m, 100 $\mu$m $\Delta$E [Si(SB)] and 5 mm E [Si(Li)]) were mounted on the other arm of the scattering chamber for the detection of light charged particles and light fragments (1 $\leq$ Z $\leq$ 4); the same detectors were also used as monitor detectors for normalization purposes. Typical solid angle subtended by each detector was $\sim$0.3 msr. The telescopes were calibrated using elastically scattered 20Ne ion from Au, Al targets and a Th-$\alpha$ source. The systematic errors in the data, arising from the uncertainties in the measurements of solid angle, target thickness and the calibration of current digitizer have been estimated to be $\approx$ 15%. Part of these uncertainties are due to the extrapolation procedures employed to extract the fully damped yields from the sequential decay components by the use of Monte Carlo simulations described in Sec. IV A.

III Results

III.1 Energy distribution

Inclusive energy distributions for various fragments (3 $\leq$ Z $\leq$ 13) have been measured in the angular range 10o - 50o for all the bombarding energies. This covered backward angles in the center-of-mass (c.m.) frame, because of the inverse kinematics of the reactions. Typical energy spectra of the emitted fragments (3 $\leq$ Z $\leq$ 13) obtained at an angle 10o at $E_{lab}$ = 170 MeV are shown in Fig. 1. It is evident that the energy spectra for lighter fragents (3 $\leq$ Z $\leq$ 6) exhibit strong peaking in energy. The peaks are nearly Gaussian in shape having its centroid at the expected kinetic energies for the fission fragments obtained from the Viola systematics corrected by the corresponding asymmetry factors viola ; beck92 and are shown by arrows in Fig. 1. The shapes of the energy spectra for the other heavier fragments (7 $\leq$ Z $\leq$ 13) are quite different from those obtained for the lighter ones. The additional contributions from DI and QE processes have been seen in the higher energy part of the spectra. Moreover, there are contributions from the recoiling nuclei (energy corresponding to $v_{CN}\cos\theta_{lab}$, shown by dashed lines in Fig. 1). All these contibutions, other than fission fragments, fall off rapidly as one moves away from the grazing angle. In this paper, we report the results from the lighter fragments (Z = 3–7).

The inclusive energy distributions for the fragments Lithium (Z = 3), Beryllium (Z = 4), Boron (Z = 5), Carbon (Z = 6) and Nitrogen (Z = 7) obtained at an angle 10o at various bombarding energies are shown in Fig. 2. It is observed that at all bombarding energies the energy spectra of the ejectiles (Li, Be, B, C, N) are nearly Gaussian in shape and they have been fitted with a single Gaussian. The non-Gaussian shapes at the low-energy side of the spectra correspond to sequential decay processes – which can be simulated by Monte-Carlo statistical model calculations (described in Sec. IV A). The Gaussian fits so obtained are shown by solid lines in Fig. 2. The centroids (shown by arrows) are found to correspond to the scission of deformed dinuclear configuration shiva ; viola ; beck92 . This suggests that, in all cases, the fragments are emitted from fully energy relaxed composite – as expected for both FF and orbiting processes. The increasing yields at lower energies may also be due to the second kinematical solution, which is a signature of binary nature of emission process.

III.2 Average velocity

The average velocities of the fragments have been computed from the measured energies and from the Z values using the empirical relation proposed by Charity et al. charity :

[TABLE]

The average velocities of the fragments obtained at different bombarding energies have been plotted in the $v_{\parallel}$ vs. $v_{\perp}$ plane in Fig. 3. It is seen that at all energies, the average velocities of different fragments fall on a circle centered around the respective $v_{CN}$, the compound nuclear velocity. This suggests that at all bombarding energies the average velocities (as well as kinetic energies) of the fragments are independent of the c.m. emission angles and indicates that at all these energies the fragments are emitted from a fully equilibrated CN-like source with full momentum transfer. The magnitude of the average fragment velocities (i.e., the radii of the circles in Fig. 3) decreases with the increase of fragment mass, which is indicative of the binary nature of the emission.

III.3 Angular distribution

The center-of-mass (c.m.) angular distributions of the fragments (Li, Be, B, C, and N) emitted in the 20Ne (145, 158, 170, 180 and 200 MeV) + 12C reactions are shown in Fig. 4. The transformations from the laboratory to center-of-mass system have been done with the assumption of a two body kinematics averaged over total kinetic energy distributions. The c.m. angular distributions of these fragments obtained at all bombarding energies follow the 1/sin$\theta_{c.m.}$ -like variation (shown by solid lines in Fig. 4) — which further corroborate the conjecture of emission from fully equilibrated composite.

III.4 Average kinetic energy

The average total kinetic energies in the center-of-mass, $E_{K}^{tot}$, for the fragments ($3\leq Z\leq 7$) obtained at all bombarding energies, have been displayed as a function of scattering angle in Fig. 5. The average fragment kinetic energies in the center-of-mass have been obtained from the respective laboratory values assuming two body kinematics. It is observed from Fig. 5 that $E_{K}^{tot}$ values are almost constant for each of the exit channel. The near constancy of $E_{K}^{tot}$ indicates that at all energies the lifetime of the dinuclear complex is longer than the time needed to completely damp the energy in the relative motion egger ; braun ; cor ; nato . The predictions of Viola systematics viola for fission fragment kinetic energies, corrected by an asymmetric factor beck92 , have been shown by solid lines in Fig. 5. The $E_{K}^{tot}$ values predicted from Viola systematics are found to be in good agreement with the experimental data at all bombarding energies.

III.5 Average Q-value distribution

The variations of average Q-value, $<Q>$, with center-of-mass emission angle for the fragments Li, Be, B, C, and N obtained at different bombarding energies are shown in Fig. 6. It is observed that the $<Q>$ of different fragments are independent of the center-of-mass emission angles at all bombarding energies. This is in contrast to the observation made earlier for other light systems (16O (116 MeV) + 27Al, 28Si, 20Ne (145 MeV) + 27Al, 59Co systems), where sharp fall off of $<Q>$ with angle have been seen bhat2002 ; bhat2004 . The $<Q>$ values remain nearly constant which further suggest that at all angles, the fragments are emitted from completely equilibrated source at all incident energies considered here.

III.6 Equilibrium cross-section

The energy distributions, velocity diagrams, angular distributions and $<Q>$ distributions indicate that the yield of these fragments (Z = 3 – 7) originates from fully energy relaxed events associated with the decay of either compound nucleus or long-lived, orbiting dinuclear system. A detailed investigation have been made to decipher the role played by aforementioned processes in the fragment yield by comparing the experimental yields with the theoretical predictions of the standard statistical model pul , extended Hauser-Feshbach model (EHFM) Matsuse97 . The experimental angle integrated yields of the fragments emitted in the 20Ne + 12C reaction at different bombarding energies are shown in Fig. 7 by solid circles (taken from Ref. shapi821 ) and triangles. The theoretical predictions of the statistical model code CASCADE pul are shown by solid lines in Fig. 7. The calculations are done considering $l$ values up to the critical angular momentum of fusion, $l_{cr}$, at each energy (given in Table 1). It is observed that at all energies the experimental yields of the fragments Li and Be are in fair agreement with the theoretical CASCADE prediction. However, the yields of the fragments B, C and N (near entrance channel) obtained at different energies are much higher than those predicted by the statistical model code CASCADE. A similar observation has been reported by Shapira et al. shapi79 ; shapi821 for the same system at lower energies for Carbon fragment. The theoretical predictions using EHFM have also been shown by dotted lines in Fig. 7 for the fragments B, C and N. The EHFM predictions also similar to those obtained from CASCADE calculations and the experimental yields are in fair excess of the theoretical estimates of both CASCADE and EHFM.

III.7 Excitation energy dependence of $<Q>$

The average Q values ($<Q>$) for the fragments Li, Be, B, C, and N have been plotted in Fig. 8 as a function of the incident energy. The linear dependence of $<Q>$ with energy provides strong evidence that the long life time may be associated with an orbiting phenomenon. This linear dependence of $<Q>$ can be expressed by simple equation of the form $<Q>=c-m*E_{c.m.}$, where $m$ is the slope and $c$ is the intercept (for example, $<Q>$ = (14.9 $\pm$ 1.0) - (0.97 $\pm$ 0.02) Ec.m. for the fragment Carbon). The experimentally determined intercepts are found to be in fair agreement with kinetic energies calculated using Viola systematics. It is interesting to note that the $<Q>$ values obtained in the present experiment between 145 MeV and 200 MeV fall on the same straight line extrapolated from the lower energy ($\sim$54 – 81 MeV) data shapi821 . This means that the energy relaxation is complete for the fragment emission studied here up to the incident energy of 200 MeV. Moreover, it also means that the final kinetic energy (E${}^{f}_{kin}$ = $<Q>$ + Ec.m.) is nearly independent of bombarding energy — which may be due to the limitation on the maximum value of angular momentum beyond which the formation of di-nucleus is not allowed due to centrifugal repulsion shapi84 .

IV Discussions

In general, the energy distributions, the angular distributions and the total fragment yields measured for 20Ne + 12C reaction at incident energies between 145 MeV and 200 MeV are similar to those obtained at lower incident energies ($\sim$ 50 - 80 MeV) for the same system (see Refs. shapi79 ; shapi821 ). Large energy damping, 1/sin$\theta_{c.m.}$ dependence of angular distribution and near constancy of $<Q>$ over a wide angular range signify that the fragment decay originates from a long lived, fully energy equilibrated system. However, the large enhancement of fragment emission cross section (5 $\leq$ Z $\leq$ 7) over the statistical-model predictions leads to the conjecture that the orbiting mechanism may still play a major role at these energies. The possibility of these enhancements, either due to feeding from the secondary deexcitation of the heavier fragments or due to orbiting mechanism, are investigated in great details and described in the following subsections.

IV.1 Contribution from secondary decay of heavier fragments

There is a possibility that the primary heavier fragments (formed due to the binary decay of composite system) may have sufficient excitation energy to deexcite through the emission of light particles and $\gamma$-rays and contribute to the yield of lighter fragments. This additional contribution from the secondary decay increases the total elemental yield of the lighter fragments. To check whether the enhancement in B, C, and N yield could be due to feeding from the secondary decay of heavier fragments of various possible binary breakup combinations, we have performed detailed simulations of secondary decay using the Monte-carlo binary decay version of the statistical decay code LILITA lilita and the statistical model code CASCADE pul and PACE4 pace2 . Secondary decay of Si∗ (binary channel 28Si + 4He), Al∗ (binary channel 26,25Al + 6,7Li), Mg∗ (binary channel 24,25,23Mg + 8,7,9Be), Na∗ (binary channel 22,21Na + 10,11B), Ne∗ (binary channel 20Ne + 12C), F∗ (binary channel 18F + 14N), O∗ (binary channel 16O + 16O), N*∗* (binary channel 14N + 18F), C*∗* (binary channel 12C + 20Ne), B*∗* (binary channel 10,11B + 22,21Na) and Be*∗* (binary channel 8,7,9Be + 24,25,23Mg) have been studied. Indeed the LILITA calculations (using the parameter set proposed in the Appendix of Ref. shapi821 and assuming the excitation energy division follows the mass ratio Sanders99 ) are in qualitative agreement with the experimental results obtained at 9 MeV/nucleon by Rae et al. Rae for the sequential decay of 20Ne + 12C. It was found that even at the highest excitation energy, secondary decay of Si∗ and Al∗ do not reach up to N; the contribution of primary Mg*∗, Na∗* decay to Z $\leq$ 7 were estimated to be $\lesssim$ 1% of the primary yield and that of Ne∗ decay to N, C, B yield were estimated to be $\sim$ 10–20%, $\sim$ 15–20% and $\sim$ 30–50% of the primary yield, respectively. Nearly $\sim$ 40–45% of the primary O∗ produced through binary exit channel 16O + 16O decays to C. The secondary decay yields from the primary excited fragments are shown in Fig. 9 for different bombarding energies. As the binary yield of O, F are small ($\sim$ 10% of the binary Ne yield, as estimated from CASCADE pul ), overall secondary decay contribution from O, F are smaller than that from Ne. Moreover, the simulations of energy distributions of the secondary decay yield of C from Ne as well as F, O using the code LILITA show that they peak at much lower energies (typically, at $\sim$ 45–50 MeV for Ne, $\sim$ 48–55 MeV for F and $\sim$ 55–60 MeV for O, compared to the peak of the experimental energy distribution at $\sim$ 75–95 MeV).

Now, the Gaussian fitting procedure for the extraction of primary fragment yield is fairly efficient in rejecting most of the low energy tail (typical rejection ratio $\sim$ 25–40% of the total yield). The energy distributions of the secondary decay have been shown in Fig. 10 for Carbon, in Fig. 11 for Boron and in Fig. 12 for Nitrogen. In the inset of these figures the spectra shown are the difference spectra; the difference between the experimental spectra and the Gaussian fitted to the spectra. It has been found that the secondary decay distributions reproduce the difference spectra very well for all the cases. It is thus evident that the secondary decay component does not interfere with the estimated primary yield for two reasons: firstly, total secondary decay yield is not quite large, and secondly, the Gaussian fitting procedure for the extraction of primary yield does take care, to a large extent, of the rejection of the contributions of the secondary decay components as their energy distributions are different from those of the primary components.

IV.2 Fragment cross-section

It has been observed that the statistical model calculations do not reproduce most of the observed experimental yields, therefore, an additional reaction component corresponding to the orbiting mechanism has to be considered. The large measured cross sections for B, C and N fragments led to the suggestion that an orbiting, di-nuclear configuration is formed that decays back to the entrance channel. After the discovery of orbiting in the 28Si + 12C system, similar enhancements of large-angle, binary-reaction yields are also observed in the present data. It is expected that the orbiting mechanism will retain a greater memory of the entrance channel than the fusion-fission process. The trapped, dinuclear complex can either evolve with complete amalgamation into a fully equilibrated compound nucleus or, alternatively, escape into a binary exit channel by way of orbiting trajectories. Orbiting can therefore be described in terms of the formation of a long-lived di-nuclear molecular complex which acts as a “doorway” state to fusion with a strong memory of the entrance channel. The equilibrium orbiting model has been used to successfully explain both the observed cross sections and total kinetic energy (TKE) values of the fully damped fragments for several lighter nuclear systems at lower energies. The theoretical prediction of the equilibrium model for orbiting and fusion shiva is denoted by dash-dotted line in Fig. 7 for the fragment B, C and N, and it also fails to explain the large enhancement in the fragment yield. The curve displayed in Fig. 7 represents the “best fit” that can be obtained by the orbiting model with a reasonable choice of the Bass potential parameters (strengths, short range, and long range of the proximity potential). It is, therefore, evident that both the equilibrium orbiting and statistical decay (CASCADE, EHFM) models result in comparable disagreement with the data. It may be interesting to note here that Shapira et al. studied the same reaction at lower energies shapi79 ; shapi821 and came to the conclusion that the large enhancements in the energy damped fragment yield observed at those energies might be due to nuclear orbiting phenomenon.

The shortcomings of the equilibrium model for orbiting does not imply that the presence of an orbiting mechanism, as distinct from fission, can be ruled out. On the contrary, there may be a large orbiting-like contribution from non fusion window (in the angular momentum window $l_{cr}\leq l\leq l_{gr}$). This is consistent, at least qualitatively, from the fact that, CASCADE calculation pul performed with $l$ values up to $l_{gr}$ (shown by dashed lines in Fig. 7) is found to reproduce the data fairly well. The values of $l_{gr}$ at different bombarding energies are given in Table 1. Yields in the transfer channels (B, N, for example) are also found to be strongly affected by the orbiting process (yield enhancement), which may be due to stochastic nucleon exchanges during long lifetime of the dinuclear system.

In Fig. 13, we show the ratio of Beryllium to Lithium (square), Boron to Lithium (circle), Carbon to Lithium (triangle) and Nitrogen to Lithium (inverted triangle) yield as a function of bombarding energies and the corresponding statistical model (CASCADE) calculations (solid lines). It is found that the observed Beryllium to Lithium ratio is well explained with the statistical model calculations. However, the other observed ratios are higher than the theoretically calculated ratios. This implies the dominance of orbiting yield over the compound nucleus yield.

IV.3 Comparison of the 20Ne + 12C and 19F + 12C reactions

The large orbiting yields that account for the largest part of the fully damped yields of 20Ne + 12C can be qualitatively understood in the framework of the Number of Open Channels (NOC) model beck94 ; beck95 . The calculated NOC are shown in Table 1 for both the 20Ne + 12C and the 19F + 12C reactions beck94 at several excitation energies along with the measured and calculated (fusion-fission cross sections as predicted by CASCADE) fully damped yields. The NOC for 20Ne + 12C exhibits the characteristic minimum for a grazing angular momentum of approximately $l_{gr}$ = 30$\hbar$ beck94 . This very deep minimum (NOC = 4.5) explains: (i) why resonant structures have been observed to be significant in 20Ne + 12C kolata ; tserr78 and, (ii) why the orbiting yields observed for C fragments are much larger than the CASCADE predictions. The comparison with 19F + 12C is instructive at $E^{*}$ = 60 MeV bhat96 (the corresponding value of the yield of fragment C for 20Ne + 12C, as given in Table 1, has been extracted from Fig. 7 to permit a direct comparison with 19F + 12C). The large NOC value for 19F + 12C beck94 (almost order of magnitude bigger) is consistent with the fact that essentially no resonances have been observed in this system Aissaoui94 ; Aissaoui97 . This was confirmed by the times scale measurements of Suaide et al. Suaide02 who found that fusion-fission (with high NOC values), a very slow mechanism, is more competitive than a faster process such as orbiting (with small NOC values) in 19F + 12C. It is worth noting from Table 1 that CASCADE predicts almost identical fusion-fission cross section for both reactions at $E^{*}$ = 60 MeV. On the other hand, due to the survival of orbiting at energies larger than 7 MeV/nucleon, the fully damped yields are much more than a factor of two bigger for the 20Ne + 12C system at $E^{*}$ = 60 MeV.

V Summary and Conclusions

The inclusive double differential cross-section for fragments having Z = 3 – 7 emitted in the reaction 20Ne ($\sim$ 7 – 10 MeV/nucleon) + 12C have been measured. Total emission cross-section for the fragments Li to N have been estimated from the experimental distributions. The c.m. angular distributions for the fragments at all the bombarding energies are found to have a 1/$\sin\theta_{c.m.}$-type of dependence which signifies the emission of these fragments from a long-lived equilibrated composite. The average velocity plots in $v_{\parallel}$ vs. $v_{\perp}$ plane indicate that the fragments are emitted from fully equilibrated source moving with compound nucleus velocity. The average kinetic energy and the average Q-value of the fragments are independent of the emission angles. This also suggests the emission from a long-lived, equilibrated composite. The angle-integrated cross-section for Li and Be fragments agree well with the theoretical predictions of statistical model but the yield of B, C and N fragments (near to entrance channel) are in excess with the theoretically predicted values. This indicates the presence of other type of reaction process, namely orbiting. In contrast, the study of the nearby system 19F (96 MeV) + 12C clearly showed that the fragments are emitted in the fusion-fission process bhat96 . Low values of NOC beck94 obtained for 20Ne + 12C system as compared to the same obtained for 19F + 12C system also confirms the conjecture of survival of orbiting in 20Ne + 12C system at higher excitations. It is interesting to mention at this point that, 16O, 20Ne + 28Si systems bhat2004 ; barrow ; farrar96 , even though $\alpha$-like, do not show the characteristics of orbiting at these energies, but orbiting-like behaviour has been observed for 28Si + 16O reaction at lower energies Szanto97 .

The present analysis also indicates that the enhancement in fragment yield for 20Ne + 12C reactions can not be explained by the equilibrium orbiting model shiva . This may be due to the fact that, the equilibrium orbiting model in its present form seems to be inadequate to explain the phenomena at higher excitations, and a more complete understanding of orbiting and vis-a-vis the angular momentum dissipation (which plays a crucial role in defining orbiting trajectories and yield) will be required.

Acknowledgements

The authors like to thank the cyclotron operating crew for smooth running of the machine, and H. P. Sil for the fabrication of thin silicon detectors for the experiment. One of the authors ( A. D. ) acknowledges with thanks the financial support provided by the Council of Scientific and Industrial Research, Government of India.