Heavy ion collision dynamics of 10 , 11 B + 10 , 11 B reactions

The dynamical cluster-decay model (DCM) of Gupta and collaborators has been applied successfully to the decay of very-light (A ∼ 30), light (A ∼ 40−80), medium, heavy and super-heavy mass compound nuclei for their decay to light particles (evaporation residues, ER), fusion-fission (ff), and quasi-fission (qf) depending on the reaction conditions. We intend to extend here the application of DCM to study the extreme case of decay of very-light nuclear systems 20,21,22Ne∗ formed in B+B reactions, for which experimental data is available for their binary symmetric decay (BSD) cross sections, i.e., σBS D. For the systems under study, the calculations are presented for the σBS D in terms of their preformation and barrier penetration probabilities P0 and P. Interesting results are that in the decay of such lighter systems there is a competing reaction mechanism (specifically, the deep inelastic orbiting of non-compound nucleus (nCN) origin) together with ff. We have emipirically estimated the contribution ofσnCN . Moreover, the important role of nuclear structure characteristics via P0 as well as angular momentum in the reaction dynamics are explored in the study.


Introduction
Compound Nucleus (CN) formed in low energy (E < 10 MeV/nucleon) heavy-ion reaction is highly excited and carry large angular momentum depending upon the energy in the entrance channel and loose it during decay by emitting γ-rays, multiple light particles (LPs: A≤4, Z≤2) like n, p, α or their heavier counterparts (referred to as evaporation residues ER), and fusion-fission (ff) consisting of symmetric and near-symmetric fission fragments, including also the intermediate mass fragments(IMFs)/ clusters [1][2][3][4][5].In addition to CN decay, non-compound nucleus (nCN) decay may also take place, like the quasifission (qf), deep-inelastic (DI) orbitting, etc., and contribute to the overall decay cross section.Reaction dynamics of light mass CN A ∼ 40 − 80 has been kind of established as the ff mechanism [4,5].In extreme case of very-light compound systems A ∼ 30, standard rotating liquid drop model (RLDM) predicts strong inhibition of ff as compared to DI scattering process/ orbiting [6].DI orbiting is referred to as the long lived dinuclear molecular process with strong memory of entrance channel.It is highly motivating to investigate the decay of very-light mass systems for competing reaction mechanims involved in the reaction dynamics.These effects could be small or large enough to compete with ff of CN.
Very light compound systems 20,21,22 Ne * formed in 10,11 B+ 10,11 B reactions are studied here, for the first time using the Dynamical Cluster-decay Model (DCM) of Gupta and collaborators [4,5].The lightest compound a e-mail: birbikram.singh@gmail.comsystem studied so far on the DCM is 28 Al * and the results are in good comparison with the available experimental data [5].It is relevant to mention here that the DCM has been developed to study the decay of hot and rotating CN formed in low-energy heavy ion reaction.It is a non-statistical description of the decay of CN as well as nCN and also to find out the role of rotational energy in the decay of CN.The DCM is so far successfully applied to the decay of a number of compound nuclei in different mass regions [4,5].In DCM, the decay of an excited CN is studied as a collective clusterization process for emissions of the LPs, as well as the IMFs and ff, in contrast to the statistical models in which each type of emission is treated on different footing.
The binary symmetric decay (BSD) of very-light mass compound systems 20,21,22 Ne * formed in 10,11 B+ 10,11 B reactions at E lab = 48 MeV and different excitation energies E * CN , is studied here by using the DCM.The 20,21,22 Ne * being negative Q out -value systems would decay only if they are produced in heavy ion reactions with compound nucleus excitation energy sufficiently enough so that where E * CN = E c.m. + Q in , and TXE(T), TKE(T) are total excitation energy and total kinetic energy of the outgoing fragments, respectively (Fig. 1(a), (b) and (c)).Within the DCM, the decay of these lighter composite systems with comparable size as well as angular momentum, with different excitation energies, is highly interesting to study, keeping in view the expected significant role of nuclear structure (via P 0 here) when a single nucleon is added.The measured cross sections for the fission like or BSD for the channels 10 B+ 10 B, 10 B+ 11 B and 11 B+ 11 B in the decay of composite systems 20 Ne * , 21 Ne * and 22 Ne * are given, respectively, in an experimental study [7], namely, the measured decay cross section for the binary symmetric decay (BSD) is maximum for 20 Ne * (σ BS D ∼ 270 mb) followed by 21 Ne * and 22 Ne * with their upper limits <130 mb amd <70 mb, respectively.The contribution of σ f f and decay cross sections due to DI orbitting σ orb in the BSD adds to give σ BS D , i.e., σ Cal.BS D = σ Cal.f f + σ Cal.orb .Note that all these components are individually measurable quantities.In case, the nCN component σ orb were not measured, it can be estimated empirically from the calculated and measured quantities, as In this work, within the DCM, we attempt to understand the decay behaviour of 20,21,22 Ne * and the role nuclear structure as well as angular momentum play in the reaction dynamics of such systems.
A brief description of the DCM is given in Sect. 2. Our calculations, using DCM, are given in Sect.3. A summary and conclusions of our study are presented in Sect. 4.

The Dynamical Cluster-decay Model (DCM)
The DCM [4,5], based on the quantum mechanical fragmentation theory (QMFT), is worked out in terms of the collective coordinates of mass asymmetry η = A 1 −A 2 A 1 +A 2 and relative separation R, which allows to define the decay cross-section, as in terms of partial waves, where the preformation probability P 0 refers to η motion and the penetrability P to R motion.With μ = mA 1 A 2 /(A 1 + A 2 ) the reduced mass and max , the maximum angular momentum, is defined for LPs cross-section σ LPs →0.The crit -value is the critical -value, in terms of the bombarding energy E c.m. , the reduced mass μ and the first turning point R a of the entrance channel η in , given by The tunneling/ penetration probability P is calculated as the WKB integral, with first and second turning points, R a and R b , (Fig. 1(a), (b) and (c)).Note that in Fig. 1(c), the value of R b is not marked since its value is too large (R b =108.052fm) to be shown conveniently on the given scale.The choice of parameter R a in Eq. ( 5), for a best fit to the data, allows us to relate in a simple way the V(R a , ) to the top of the barrier V B ( ) for each .In Eq. ( 3), P 0 , the preformation probability referring to η motion, contains the structure information of the compound nucleus, and is the solution of the stationary Schrödinger equation in η, at a fixed R=R a , with Here, the mass fragmentation potential V(η, T ), at fixed R = R a , is the sum of liquid drop energy V LDM , shell The same equation ( 3) is used for σ nCN or σ orb , calculated as the DI orbiting (orb) process, since incoming nuclei keep their identity, and hence P 0 =1, and then P is calculated for incoming channel.

Calculations and results
In this section, we present our calculations for the estimation of non-compound nucleus component σ nCN or σ orb (as DI orbitting process) in the BSD of 20 Ne * , 21 Ne * , and 22 Ne * using the DCM.First, we calulate the contribution of σ f f in the BSD and then estimated empirically from the measured and calulated quantities σ orb (= σ Expt.BS D − σ DC M f f ).Fig. 2 shows the variation of P 0 as a function of fragment mass A for the decay of a) 20 Ne * , b) 21 Ne * , and c) 22 Ne * , at different -values.Fig. 2(a) clearly shows the BSD of 20 Ne * formed in 10 B+ 10 B at E c.m. = 24MeV.Here we note that 10 B is strongly favoured at all -values.On the other hand, BSD of 21 Ne * and 22 Ne * formed in 11 B+ 10 B at E c.m. = 25.143MeV and 11 B+ 11 B at E c.m. = 24MeV, respectively, are not strongly favoured.Fig. 2(b) shows that the BSD of 21 Ne * has competition from 8 Be and 13 C. Interestingly, in Fig. 2(c) we see that the BSD of 22 Ne * in to 11 B is least favoured where 10 B and 12 B are strongly preformed follwed by 8 Li and 14 N.This result is quite important keeping into view that the experimental data for the σ Expt.
BS D [7] is maximum for 20 Ne * followed by 21 Ne * and 22 Ne * , as mentioned in the introduction also.Moreover, it is observed in Fig. 2 that the IMFs in the decay of 20 Ne * , 21 Ne * and 22 Ne * are favoured at all the -values, contrary to the observation for the decay of very light mass compound nuclei 28 Al * , 31 P * , 32 S * and light mass compound nuclei 47 V * , 48 Cr * , 56 Ni * , where the IMFs are favoured at the higher -values only [4,5].The trend for the LPs observed here is in line with that for the very light as well as light mass compound muclei, i.e., the decay of LPs is favoured at the lower -values only.

00048-p.3
Table 1.The binary symmetric decay cross section calculated using the DCM σ DC M f f for f f process, summed upto l crit ( ) for 20 Ne * , 21 Ne * , and 22 Ne * .The experimental data [7]  In Fig. 1, we notice that the barrier for the BSD of 20 Ne * , 21 Ne * and 22 Ne * starts vanishing at =12 , 13 and 15 , respectively.Coincidently, these are crit values which we obtained from Eq. ( 4) for these systems.Moreover, value of min (minimum value at which WKB integral starts contributing)=4 , 5 and 4 , respectively for the BSD of 20 Ne * , 21 Ne * and 22 Ne * .We find that the max values (=24 , 19 and 19 ) for these systems, where σ LPs →0, are very large in comparison to the crit values.At these values the scattering potential barrier already vanishes.Therefore, in the present study we have added the contribution of values upto the crit values for the respective systems.We also note in Fig. 1 that TXE(MeV) of the outgoing frgaments is maximum for the 10 B+ 10 B in the decay of 20 Ne * .Fig. 3(a) shows the variation of P 0 and P as a function for the symmetric decay of a) 20 Ne * , b) 21 Ne * , and c) 22 Ne * .Comparatively, we find that the P 0 contributes at all the values whereas P starts contributing at the higher values only.At crit , P approaches the maximum value, i.e., near to one.Here we have added the contribution of values upto the crit only while calculating the σ DC M f f for the respective systems as given in Table 1.We find that the empirically estimated value of σ orb is maximum for 20 Ne * followed by 21 Ne * and 22 Ne * .Interestingly, we see that the value of ΔR is same for 20 Ne * and 22 Ne * .

Summary and Conclusions
Concluding, the application of DCM is extended to the decay of very light mass compound systems 20 Ne * , 21 Ne * and 22 Ne * .We studied the decay of these systems and calculated σ f f for the BSD as the dynamical fragmentation process.The results clearly point out the dominant BSD for 20 Ne * in comparison to other compound systems.P 0 for the IMFs is dominant at all the -values for all the compound systems.Scattering potentials for the BSD clearly shows the vanishing of the barrier at the respective critvalues for these systems.The empirically estimated σ orb for the BSD is maximum for 20 Ne * .It will be interesting to calculate and observe the contribution of σ orb for nCN decay using Eq. ( 3) while taking P 0 =1 (with P calculated for incoming channels), the relative values of ΔR and their comparison with values fitted for the σ f f in the BSD of the systems studied.Moreover, the present calculations have been done with spherical consideration of the fragments, the effects of the oriented deformed nuclei will be matter of great interest.

Figure 2 .
Figure 2. Preformation Probability P 0 as a function of fragment mass A for the decay of a) 20 Ne * , b) 21 Ne * , and c) 22 Ne * , at different -values.

Figure 3 .
Figure 3. Preformation Probability P 0 and Penetration Probability P as a function for the symmetric decay of a) 20 Ne * , b) 21 Ne * , and c) 22 Ne * .
σ Expt.BS D is also given here for BSD due to ff as well as the DI orbitting.The contribution of σ orb is estimated from σ Expt.BS D − σ DC M f f .