Complete fusion in ${}^7$Li+${}^{144,152}$Sm reactions

Complete fusion cross sections for ${}^7$Li+${}^{144,152}$Sm reactions have been measured at energies around the Coulomb barrier by offline $\gamma$-counting technique. Measured cross sections for the above two reactions are found to be similar at energies well above the Coulomb barrier, however, at sub-barrier energies the cross sections for the ${}^7$Li+${}^{152}$Sm system are much higher compared to the ${}^7$Li+${}^{144}$Sm system, manifesting the effect of target deformation. Cross sections for the present reactions at above-barrier energies are found to be larger than previously measured reactions involving ${}^6$Li projectile with the same targets, possibly due to smaller breakup probability of ${}^7$Li than ${}^6$Li. Coupled-channels calculations show that the experimental fusion cross sections for both the systems are enhanced at subbarrier energies and suppressed at above-barrier energies compared to the respective one-dimensional barrier penetration model predictions. The calculations by different models show that the measured complete fusion cross sections at above-barrier energies are suppressed up to $\sim$25% compared to the theoretical predictions. It also reveals that a large part of the suppression could be due to inelastic and transfer coupling.

Figure 1

Cross sections for (a) ${}^{149}$Tb ER (hollow circles), ${}^{148}$Tb ER (solid circles), ${}^{147}$Tb ER (hollow triangle-up), and ${\sigma }_{\mathrm{fus}}^{\mathrm{Expt}.}$ (hollow diamonds) obtained from the ${}^7$Li+${}^{144}$Sm reaction and (b) ${}^{156}$Tb ER (hollow stars), ${}^{155}$Tb ER (solid stars), ${}^{154}$Tb ER (hollow triangle-down), and ${\sigma }_{\mathrm{fus}}^{\mathrm{Expt}.}$ (hollow diamonds) obtained from the ${}^7$Li+${}^{152}$Sm reaction as a function of laboratory energy ($E_{\mathrm{lab}}$). Ratio of two dominant ER channels, i.e., ${\sigma }_{3n}$ to ${\sigma }_{2n}$ (solid squares) in first reaction and ${\sigma }_{4n}$ to ${\sigma }_{3n}$ (hollow squares) in second reaction at different beam energies are shown in (c) and (d), respectively. Lines represent the results of statistical model calculations (see text for details).

Figure 2

Measured complete fusion cross sections for ${}^7$Li+${}^{144}$Sm (solid circles) and ${}^7$Li+${}^{152}$Sm (open circles) in reduced scales as a function of reduced energy by two different representations: (a) ${\sigma }_{\mathrm{fus}}^{\mathrm{Expt}.}/{(A_P^{1/3}+A_T^{1/3})}^2$ versus $E_{\mathrm{c}.\mathrm{m}.}(A_P^{1/3}+A_T^{1/3})/Z_P{Z}_T$ and (b) ${\sigma }_{\mathrm{fus}}^{\mathrm{Expt}.}/\pi R_B^2$ versus $E_{\mathrm{c}.\mathrm{m}.}-V_B$. See text for details.

Figure 3

(a) Comparison of CF cross sections involving different projectiles, i.e., ${}^6$Li (solid stars) from literature (Rath 2009 [3]) and ${}^7$Li (solid circles, present data) but same target (${}^{144}$Sm), showing the effect of projectile breakup threshold. (b) Same as (a) but involving a different target (${}^{152}$Sm) and data for ${}^6$Li is from Rath 2012 [7].

Figure 4

Shown are (a) and (b) the measured complete fusion cross sections (open circles) for ${}^7$Li+${}^{144}$Sm and ${}^7$Li+${}^{152}$Sm and (c) and (d) their corresponding barrier distributions. Dash-dot-dot and dashed lines represent the results of coupled-channels calculations for the no-coupling case and with full couplings, respectively. Solid lines are obtained by normalizing the coupled results by 0.76 and 0.75 for ${}^7$Li+${}^{144,152}$Sm reactions, respectively.

Figure 5

Comparison of universal fusion function (UFF) and experimental fusion function (using the results from ccfull) as a function of reduced energy “$x$” in (a) and (b) linear scale and (c) and (d) logarithmic scale (see text for details).

Figure 6

Fusion cross sections calculated by fresco using the same WS potential parameters for entrance channel as used in ccfull with no coupling (dotted line), inelastic coupling (dashed line), and inelastic+transfer coupling (solid line) compared with the experimental data for ${}^7$Li+${}^{144,152}$Sm reactions in (a) and (b) logarithmic and (c) and (d) linear scale, respectively.

Figure 7

Comparison of UFF (solid line) and experimental fusion function (using the results from fresco) as a function of reduced energy “$x$” in (a) and (b) linear scale and (c) and (d) logarithmic scale. Stars (hollow circles) correspond to the $F_{\mathrm{Expt}.}\left(x\right)$ obtained using the fusion from fresco when the Sao Paulo (Wood-Saxon) form of potential was used for the entrance channel.

Figure 8

Fusion cross sections calculated for (a) ${}^7$Li+${}^{144}$Sm and (b) ${}^7$Li+${}^{152}$Sm reactions by Wong's model using proximity potentials “Proximity 2000” are represented by dashed lines. The above cross sections multiplied by a factor of 0.78 are represented by solid lines. Solid and hollow circles correspond to the measured CF data for ${}^7$Li+${}^{144,152}$Sm reactions, respectively.