VOLUME 88, NUMBER 17 PHYSICAL REVIEW LETTERS 29 APRIL 2002 Angular Momentum and Cross Sections for Fusion with Weakly Bound Nuclei: Breakup, a Coherent Effect Vandana Tripathi, A. Navin,* K. Mahata, K. Ramachandran, A. Chatterjee, and S. Kailas Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India (Received 25 October 2001; published 11 April 2002) Results for the cross section and average angular momentum for complete fusion at energies around the Coulomb barrier are presented for 7 Li with 165 Ho. Comparison of the cross sections with a one- dimensional barrier penetration model, using a potential consistent with the measured elastic scattering, showed a reduction above the barrier and an enhancement below it. An increase in the measured av- erage angular momentum, , above the barrier and its consistency with that obtained from the fusion excitation function for weakly bound nuclei, is reported. These results together with a reanalysis of existing data conclusively demonstrate that the effect of breakup on fusion is coherent, like coupling to any nonelastic channel. DOI: 10.1103/PhysRevLett.88.172701 PACS numbers: 25.70.Jj, 25.60.Gc, 25.60.Pj, 25.70.Mn The understanding of the fusion process using radioac- tive ion beams (RIB) has great ramifications both for the production of superheavy elements (SHE) and in reac- tions of astrophysical interest. The weak binding of the valence nucleon(s) in RIB results in an extended spatial extent (halo/skin) and a large breakup cross section, both strongly influencing the fusion of these nuclei [1]. Fusion of heavy ions is treated as a tunneling phenomenon de- pending on the intrinsic degrees of freedom in addition to the radial separation of the colliding nuclei [2]. The role of inelastic excitations and few nucleon transfer has been illustrated from precise measurements of the fusion excita- tion function covering a wide range of Z p Z t [3]. However, the influence of the projectile breakup on fusion is not yet well understood [4]. Two theoretical models having different perspectives have been proposed to understand the effect of projectile breakup on fusion. The first [5,6] treats breakup as causing an attenuation of the flux (E and  dependent) in the inci- dent channel. The transmission coefficients for fusion are thus multiplied by a breakup survival probability leading to smaller fusion cross sections and reduced values of . This implies that the two channels, the elastic and the broken-up products, can fuse incoherently leading to com- plete and breakup fusion, respectively. In contrast to this intuitive approach, the role of breakup can be considered in a coupled channel formalism like an inelastic excitation to the continuum [7]. This would mean that the fusing system is a coherent superposition of the elastic and breakup channels and will always lead to an enhancement of the complete fusion cross section below the Coulomb barrier and a suppression above it, compared to a one- dimensional barrier penetration model (1D-BPM) predic- tion [8]. The main difference between the two approaches viz. the coherent or incoherent role of breakup on fu- sion has to be resolved experimentally. Analyses of experiments with weakly bound stable ( 9 Be) [9] and radioactive beams of 6 He [10,11] and 11 Be [4] have not resolved the issue. One of the reasons is the ambiguity in the choice of the reference potential used in the calculations. The measurement of the angular momentum of the fused system will give an additional handle to address this problem. It has been pointed out earlier [12 –14] that under simple assumptions the two observables, angular momentum and fusion cross sections, are not independent and a relationship between the moments of  and the fusion excitation function exists which is model indepen- dent. The main assumption here is that the transmission coefficient T  E follow the relationship T  E  T 0 E 0 , where E 0  E 2bE 1 1 and bE can be thought about as the inverse of a generalized moment of inertia. As pointed out by Balantekin [13] the above does not necessarily imply that the fusion process is governed by an effective one-dimensional, energy-independent local potential barrier. The transmission coefficients in the approach treating breakup as an incoherent loss of flux [5,6] do not satisfy the relationship mentioned above, because of the energy dependence of the breakup survival probability factor, while the coupled channel approach does. Hence, the measurement of  and its consistency with that derived from the fusion excitation function will be an independent test of the validity of the two models. With the aim of experimentally addressing the coherent or incoherent effect of the breakup channel on the fusion process at energies around the Coulomb barrier V b  , we report results on complete and breakup fusion cross section and average angular momentum using a weakly bound 7 Li projectile (breakup threshold of 2.45 MeV for the a1 t channel) on the 165 Ho target. A consistent analysis of the present work along with relevant work in the literature, within a coupled channel framework, is presented to illus- trate the coherent role of projectile breakup on fusion. Measurements were performed using a 7 Li beam, from the 14UD BARC-TIFR Pelletron Accelerator Facility at Mumbai, in the energy range 23 to 45 MeV correspond- ing to 0.9V b to 1.7V b . The 3.8 mgcm 2 thick 165 Ho tar- get was backed by 800 mgcm 2 thick Bi (measured using 172701-1 0031-9007 02 88(17) 172701(4)$20.00 © 2002 The American Physical Society 172701-1