Upper bounds for fusion processes in collisions of weakly bound nuclei

Abstract

We obtain upper limits for the contributions of the incomplete fusion and sequential complete fusion processes to the total fusion cross section. Through those upper bounds we find that these processes are negligible in reactions induced by projectiles such as 6 He and 11 Li, which break up into neutrons and one fragment containing the full projectile charge.The effects of channel coupling in fusion reactions induced by weakly bound projectiles have attracted great interest over the last decade [1]. Some theoretical studies predict strong influence of the breakup channel over the complete fusion (CF) cross section [2][3][4][5][6][7]. When one tries to compare these predictions with experimental data [8][9][10][11][12][13][14], one finds a serious problem. Sorting out complete and incomplete fusion (IF) events in an experiment may be a very difficult task, specially when uncharged fragments are produced in the breakup of the weakly bound collision partner. For this reason, most experiments measure the total fusion cross section,These results could not, in principle, be used to check theoretical predictions for σ CF . However, the situation would be different when σ IF << σ CF . In this case one can approximate σ T F σ CF and the measured cross section could be directly compared with theoretical predictions for σ CF . In the present work, we present a method to find upper limits for σ IF in collisions induced by weakly bound projectiles. With this method, we show that the incomplete fusion cross sections may be neglected when the projectile breakup produces uncharged fragments.The appropriate theoretical tool to handle this problem is the coupled-channels method. However, its implementation becomes very complicated for the breakup channel, since it involves an infinite number of states in the continuum. For practical purposes, it is necessary to approximate the continuum by a finite set of states as in the Continuum Discretized Coupled-Channels method (CDCC) [15]. This procedure has been extended to the case of fusion reactions in refs. [5][6][7]. Recently, a semiclassical alternative based on the classical trajectory approximation of Alder and Winther (AW) [16] has been proposed [17]. This approximation was used to calculate breakup cross sections and the results were compared with those of the CDCC method. The agreement between these calculations was very good. Since this semiclassical version of the CDCC method is much simpler, it may be a very useful tool to calculate cross sections for other channels in reactions with weakly bound nuclei. Although the AW method has been extensively used for several nuclear reaction processes, only very recently it was applied to the estimate of the fusion cross section [18]. For this application it was considered a simplified two-channel problem for which the fusion cross section obtained with the AW method was compared with results of a full coupled-channels calculation. In spite of the large simplification in the calculation the agreement between these two calculations was ...

Interaction of11Li with208Pb

“…[16], the effect of breakup on the fusion cross section was negligible. Recent review articles dealing with the general subject of the fusion of weakly bound nuclei are available [17][18][19] For the 11 Li + 208 Pb reaction, more recent theoretical work [20] suggests that incomplete fusion and sequential complete fusion are negligible processes. Additional theoretical treatments of the fusion of 11 Li with 208 Pb have been made recently [21,22].…”

Semiclassical coupled channels calculations in heavy-ion fusion reaction

“…where 0 describes the relative motion between the center of masses of the two nuclei involved in the collision, ℎ( ) the internal states of each of them, and ( , ) the interaction between those degrees of freedom [12]. The eigenvectors of ℎ( ) are given by the equation [14,15] ℎ| ⟩ = | ⟩.…”

“…The method developed by Alder and Winther for the study of Coulomb excitation consists of treating the relative motion by classical mechanics with the potential ( ) = ⟨ 0 | ( , )| 0 ⟩ where 0 is the ground state of the projectile using the trajectory, the coupling interaction becomes a time-dependent interaction in the − space, ( , ) = ( ( ) , ) whereas the intrinsic motion is handled as a time-dependent Quantum Mechanics problem [12,15]. The internal wave function for the excitable nucleus is found by solving the Schrödinger equation for the time dependent Hamiltonian [14] ℎ( , ) ( , ) = ℏ ( , )⁄…”

“…The geometrical model predicts that for reactions involving rotational nuclei the one dimensional Coulomb barrier is replaced by a continuous distribution of fusion barriers which correspond to the different mutual orientations of the projectile and the target nucleus. In this case the total fusion cross section is given by an integral over a continuous distribution of barriers [18,19] ( ) = 2 ( ) 2 (15) which is referred to as the barrier distribution. This quantity is directly related to the height of the potential barrier.…”

The interaction of 11Li with 208Pb

“…For the 11 Be + 209 Bi [14,15] and the 19 F + 208 Pb systems [16], the effect of breakup on the fusion cross section was negligible. Recent review articles dealing with the general subject of the fusion of weakly bound nuclei are available [17][18][19] For the 11 Li + 208 Pb reaction, more recent theoretical work [20] suggests that incomplete fusion and sequential complete fusion are negligible processes. Additional theoretical treatments of the fusion of 11 Li with 208 Pb have been made recently [21,22].…”