1 n-transfer reaction using 6 Li with heavy mass target

Influence of 1n-transfer coupling on quasi-elastic scattering excitation function has been investigated for 6Li + 209Bi system. Coupled Reaction Channels Calculations have been carried out for the energies around the Coulomb barrier. Corresponding barrier distributions obtained with and without including 1n-transfer coupling, have been compared with experimental data. 1n-transfer effect on quasi-elastic excitation function has been observed to be insignificant for the present system. In the reaction of 6Li with 208Pb and 209Bi, an experimental relative contributions for breakup and 1n-transfer channels have been reproduced by simultaneous calculation using CDCC and CRC formalism.


Introduction
Recently, a great attention has been given to the breakup channel in the nuclear reaction studies with weakly bound nuclei [1,2].The observed enhancement and/or suppression in the fusion cross sections at around the Coulomb barrier are associated with the breakup and also other reaction channels such as transfer (pickup/ stripping), which trigger the projectile breakup [3].For example the weakly bound projectile 6 Li may directly breakup into two fragments (d + α) or the breakup may occur after some nucleon transfer (pickup/ stripping).In a very recent experimental study involving stable weakly bound projectile ( 6 Li) [3] the 1n-stripping is found more preferable channel leading to (p + α) and the contribution from 1n,1p-pick up is found negligible at below barrier energy in the reaction with 207,208 Pb and 209 Bi targets.It will be of interest to know the 1n-transfer coupling effect on quasi-elastic scattering excitation function for the 6 Li + 209 Bi system.In the present work, Coupled Reaction Channels(CRC) Calculation have been carried out to study the 1n-transfer effect on quasi-elastic scattering excitation function.In addition to that we have also done simultaneous calculation for breakup and transfer using CDCC and and CRC formalism, to understand their relative contributions which have been reported in the Ref. [3].

Experimental Details
The experiment was performed with 6 Li (3+) beam at the 14UD BARC-TIFR Pelletron facility in Mumbai, India.a e-mail: dipika.physics@gmail.comb e-mail: suryanarayan7@yahoo.comThe experimental measurements were done at 140 • employing a detector telescope with the thickness of ΔE = 15 μm and E=1.5 mm.The spectra were recorded in the energy range from 22.0 to 39.0 MeV in steps of 1.0 MeV.Two monitor detectors were placed at ±18 • for normalization and beam monitoring.A self supported 209 Bi target of thickness ∼ 1.2 mg/cm 2 was used.The bombarding energies were corrected for the energy loss in half the target thickness, ranging from 0.12 to 0.18 MeV for 6 Li.Fig. 1 shows a typical two dimensional ΔE + E total spectrum obtained at E lab = 34 MeV and θ lab = 140 • .Other details of the experiments are available elsewhere [4].

CRC calculation and Discussions
We have performed Coupled Reaction Channels (CRC) calculations using Fresco code [5]   been carried out for the energy range from 22.0 to 39.0 MeV.In these calculations the 1n-transfer was considered from ground state of 6 Li to ground state of 209 Bi, which may lead to 5 Li and final nucleus 210 Bi in its ground state, as the Q-value for this reaction is -1.058MeV.To consider the effects from target ( 209 Bi) excitation, Couplings to collective multiplet [ 208 Pb(3 − )⊗ 1h 9/2 ] j π were also included as given in table 1.The entrance channel potentials were of Woods-Saxon form with r 0 =1.2 fm and a 0 =0.67 fm.
For the 1n-transfer channel, the real part was calculated using broglia and Winther parametrization with r 0 =1.167  fm and a 0 =0.63 fm [7].The imaginary part was of short range type with W 0 = 50 MeV, r 0 =1.06 fm and a 0 =0.4 fm.The binding potentials for the valence (n) and core ( 5 Li and 210 Bi) nuclei were of the Woods-Saxon and spin orbit form.The depths were adjusted to obtain the required binding energies.These calculations were done with spectroscopic amplitudes equal to 1.
Figure .2 shows the experimental quasi-elastic (elastic + inelastic) excitation function along with the results of Coupled Reaction Channels Calculations.The dotted line indicates excitation function obtained with OM potential.The dashed and continuous lines show the excitation functions obtained with the inclusion of target inelastic and (target inelastic + 1n-transfer) respectively.The corresponding barrier distributions are plotted in the Fig. 3 which shows reasonable agreement between the present calculations and the experimental results.From the Fig. 2, it is seen that the inelastic and 1n-transfer coupling effect on quasi-elastic excitation function is negligible.The similar result can be observed in the Fig. 3 with no difference in barrier distribution heights obtained with the inclusion of target inelastic and (target inelastic + 1n-transfer).Also, no transfer coupling effect was observed on the quasielastic excitation function in the reaction of weakly bound nuclei ( 7 Li) with 144 Sm [8].

Simultaneous calculation for breakup and transfer
We have made an attempt to investigate the relative contributions for breakup and 1n-transfer in the 6 Li + 208 Pb, 209 Bi reactions using CDCC and CRC formalism.In the literature for the 6 Li + 208 Pb, 209 Bi system, it is reported that major contributions to the breakup α comes from the direct breakup as well as from 1n-stripping reaction but no theoretical investigation was made.In this work simultaneous calculations for breakup and 1n-transfer have been carried out at 26.5 and 29.0 MeV using Fresco code [5].
All the resonant states of 6 Li with finer binning and maximum excitation energy upto ∼ 8.5 MeV have been included in the CDCC calculations.Also, the target spin has been set to 1/2 − to reduce the computing time.The calculations have been carried out at 26.5 and 29.0 MeV laboratory energies.In the 1n-stripping calculation coupling to ground state has been considered and no target inelastic states have been included as the coupling to target inelastic states gives negligible cross sections.In these calculations, the binding energies for core and valence particles have been taken as 0.1MeV and the spectroscopic amplitudes were 2.0.This has been varied to assume the ground state of 5 Li to be weakly bound [9]. Figure .4 shows the results of present calculations (pink) with the inclusion of breakup as well as 1n-stripping channels and have been compared with the experimental data reported by Luong et al. [3].By adjusting the spectroscopic amplitude and binding energy of valence particle, a reasonable agreement can be observed between the present calculations and the experimental results as shown in Fig. 4. Table 2 shows the cross sections for α+d breakup and 1n-stripping at 26.5 and 29.0 MeV, in the reaction of 6 Li with 208 Pb, 209 Bi.

Summary and Conclusions
1n-transfer coupling effect on quasi-elastic scattering excitation function have been studied using CRC calculation for 6 Li + 209 Bi system.The influence from 1n-transfer coupling was observed to be insignificant on quasi-elastic scattering excitation function and no difference was observed in barrier height with the inclusion of 1n-transfer coupling in the CRC calculation.Simultaneous calculation for breakup and transfer reproduce the experimentally obtained relative contribution for breakup and 1n-stripping channels using CDCC-CRC formalism for the reaction of 6 Li with 208 Pb and 209 Bi at below barrier energies.

Figure 1 .
Figure 1.(Color online) A typical two-dimensional spectrum of ΔE vs E total for 6 Li + 209 Bi at E lab = 34 MeV and θ lab = 140 • . The calculations have DOI: 10.1051/ C Owned by the authors, published by EDP Sciences, This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 2 Figure 2 .
Figure 2. (Color online) "Qausi-elastic" excitation function for 6 Li + 209 Bi at θ lab = 140 • .The dotted line indicates excitation function obtained with OM potential.The dashed and continuous lines show results obtained with the inclusion of target inelastic coupling and with the inclusion of target inelastic coupling as well as 1n-stripping channel respectively.

Figure 3 .
Figure 3. (Color online) Corresponding barrier distribution for 6 Li + 209 Bi at θ lab = 140 • .The dotted line indicates excitation function obtained with OM potential.The dashed and continuous lines show results obtained with the inclusion of target inelastic coupling and with the inclusion of target inelastic coupling as well as 1n-stripping channel respectively.

Figure 4 .
Figure 4. (Color online) Relative contribution of direct breakup and 1n-stripping channel in the reaction of 6 Li with 208 Pb, 209 Bi