(Multi-)nucleon transfer in the reactions 16 O, 3 32 S Pb

Journal of Physics: Conference Series Related content (Multi-)nucleon transfer in the reactions 16 O, 3 32 S + 208 Pb To cite this article: M Evers et al 2013 J. Phys.: Conf. Ser. 420 012129 - Quantum microscopic approach to lowenergy heavy ion collisions Cédric Simenel, Aditya Wakhle and Benoît Avez - Unexpected results in neutron-rich radioactive beams induced fusion J F Liang - Transfer/Breakup Channel Couplings in Sub-barrier Fusion Reactions C Beck View the article online for updates and enhancements. This content was downloaded from IP address 148.251.232.83 on 18/07/2018 at 00:00

doi:.88/1742-6596/420/1/012129 (Multi-)nucleon transfer in the reactions 16 O, 32 S+ 208 Pb M. Evers 1, M. Dasgupta 1, D. J. Hinde 1 and C. Simenel 1,2 1 Department of Nuclear Physics, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia 2 CEA, Centre de Saclay, IRFU/Service de Physique Nucleaire F-91191 Gif-sur-Yvette, France E-mail: maurits.evers@anu.edu.au Abstract. A detailed analysis of the projectile-like fragments detected at backward angles in the reactions 16 O, 32 S+ 208 Pb at energies below the fusion barrier is presented. Excitation functions corresponding to nucleon transfer with Z = 1 and Z = 2 were extracted, indicating surprisingly large absolute transfer probabilities at sub-barrier energies. A comparison of 2p transfer probabilities with time-dependent Hartree-Fock calculations suggests strong pairing correlations between the two protons. Excitation energies in the projectile-like fragments up to 15 MeV for the 16 O and 25 MeV for 32 S-induced reactions show the population of highly excited states in the residual nuclei, and indicate substantial dissipation of kinetic energy. A new phenomenological framework explores the effect of energy dissipation through these highly inelastic (large excitation energies) and complex (correlated few-nucleon transfer) processes on the probability for fusion in the reaction 16 O+ 208 Pb. Preliminary results show that the suppression of fusion at energies above the barrier in this reaction can be explained within the new framework. 1. Introduction Heavy-ion collisions provide an interesting field to study the effects of quantum-mechanical properties as well as classical phenomena, and how they emerge in the dynamics of the collision process at different energies. At energies well below and close to the fusion barrier, heavy-ion collisions are driven by quantum mechanics. For example, fusion at sub-barrier energies occurs through tunnelling of the projectile nucleus through the fusion barrier. Furthermore sub-barrier fusion as well as its complementary process, scattering, are affected by the internal structure of the collision partners. The coupled reaction channels formalism which considers the colliding nuclei to be in a coherent superposition of intrinsic states has proven extremely successful in the description of both fusion and scattering at sub- and near-barrier energies [1, 2, 3]. However, at deep sub-barrier energies (e.g. 5 MeV below the fusion barrier energy in the reaction 16 O+ 208 Pb) measured fusion cross sections [4, 5, 6, 7] fall below those predicted by coupled reaction channels calculations using standard Woods-Saxon potentials. This deep subbarrier fusion hindrance has been observed in a range of different reactions. A major question in nuclear physics is to explain the physical mechanisms causing this suppression of the tunnelling probability, as extrapolations of fusion probabilities (and their associated S-factors) to energies typical for astrophysical scenarios show large variations (up to 40 orders of magnitude) for different phenomenological models [8, 9, ]. Published under licence by Ltd 1

doi:.88/1742-6596/420/1/012129 16 O+ 208 Pb, E beam = 79.00 MeV 16 O ΔZ = 0 15 N ΔZ = 1 Δ ΔZ = 2 13 C 208 Pb(3 - ) 14 C 12 C 25 30 35 40 45 50 55 E Si [MeV] Figure 1. (Color online) Typical E E spectrum for the reaction 16 O+ 208 Pb at the indicated beam energy, corresponding to E c.m. /V B = 0.98. Events corresponding to the transfer of Z = 0, 1 and 2 units of charge are labelled. Calculated energy loss curves for 16 O, 15 N and 12,13,14 C are shown by the dashed curves. At energies above the fusion barrier, measured fusion cross sections also significantly fall below standard coupled-channels calculations [11, 6] using the same Woods-Saxon parametrization for the nuclear potential. A detailed analysis of this above-barrier fusion suppression for different reactions shows an increase of the suppression factor with the charge product of the colliding nuclei. Correlated with increasing above-barrier fusion suppression is increasing dissipation of kinetic energy into nucleonic degrees of freedom, known as deep inelastic collisions (DIC) [12, 11]. This becomes important with increasing matter overlap at energies near and above the fusion barrier. The importance of (multi-) nucleon transfer in these DIC processes at energies well above the fusion barrier has been discussed in a recent review [13]. Transfer processes that lead to high excitation energies in the residual nuclei were suggested [11, 14] as a key to understanding the above-barrier fusion suppression through the onset of irreversible dissipative processes. In this paper recent results are discussed suggesting that mechanisms used to explain above-barrier fusion suppression may also be responsible for the suppression of fusion through tunnelling at deep sub-barrier energies. Using the reactions 16 O, 32 S+ 208 Pb, (i) the significance of transfer processes in nuclear collisions at energies well below the fusion barrier is established, (ii) the details (e.g. excitation functions, excitation energies E x ) and underlying mechanisms of these transfer processes are explored, and (iii) for the reaction 16 O+ 208 Pb a new probabilistic framework for the description of fusion is explored which takes into account energy dissipation through high-e x transfer. 2. Measurements All measurements were done with the 14UD electrostatic accelerator of the Heavy-Ion Accelerator Facility at the Australian National University (ANU), using beams of 16 O and 32 S incident on a 208 PbS target with a thickness of 0 µg/cm 2, evaporated onto a 15 µg/cm 2 C backing. A E E detector telescope consisting of a propane gas filled ionization chamber and a Si detector located at a backward angle of θ lab = 162 was used to record the energy E Si 2

doi:.88/1742-6596/420/1/012129 Table 1. Reaction ground state Q-values for selected transfer processes in the reaction 16 O+ 208 Pb. Processes with a plus sign correspond to pickup, a minus sign indicates stripping. Predominant processes as determined by our measurements and previous work [15, 16] are highlighted in bold. Reaction Process Q gs [MeV] 208 Pb( 16 O, 17 O) 207 Pb +1n -3.225 208 Pb( 16 O, 18 O) 206 Pb +2n -1.918 208 Pb( 16 O, 15 O) 209 Pb 1n -11.727 208 Pb( 16 O, 15 N) 209 Bi 1p -8.328 208 Pb( 16 O, 14 N) 2 Bi 1p 1n -14.557 208 Pb( 16 O, 16 N) 208 Bi 1p + 1n -13.299 208 Pb( 16 O, 14 C) 2 Po 2p -13.553 208 Pb( 16 O, 13 C) 211 Po 2p 1n -17.178 208 Pb( 16 O, 12 C) 212 Po 2p 2n -16.116 208 Pb( 16 O, 15 C) 209 Po 2p + 1n -19.993 208 Pb( 16 O, 16 C) 208 Po 2p + 2n -22.7 Z = 0 Z = 1 Z = 2 Table 2. Reaction ground state Q-values for selected transfer processes in the reaction 32 S+ 208 Pb. For details see Table. 1. Reaction Process Q gs [MeV] 208 Pb( 32 S, 33 S) 207 Pb +1n +1.274 208 Pb( 32 S, 34 S) 206 Pb +2n +5.953 208 Pb( 32 S, 31 S) 209 Pb 1n -11.5 208 Pb( 32 S, 31 P) 209 Bi 1p -5.065 208 Pb( 32 S, 30 P) 2 Bi 1p 1n -12.772 208 Pb( 32 S, 32 P) 208 Bi 1p + 1n -4.589 208 Pb( 32 S, 30 Si) 2 Po 2p -7.378 208 Pb( 32 S, 29 Si) 211 Po 2p 1n -13.437 208 Pb( 32 S, 28 Si) 212 Po 2p 2n -15.902 208 Pb( 32 S, 31 Si) 209 Po 2p + 1n -8.449 208 Pb( 32 S, 32 Si) 208 Po 2p + 2n -6.214 Z = 0 Z = 1 Z = 2 and energy loss E gas of the back-scattered projectile-like fragments (PLFs). Two Si monitors positioned at ±30 were used to normalize the back-scattered events to the Rutherford cross section. A typical two dimensional spectrum for a measurement of the reaction 16 O+ 208 Pb at a beam energy corresponding to a ratio of the centre-of-mass energy to the fusion barrier energy E c.m. /V B = 0.98 is shown in Fig. 1. The three distinct regions correspond to oxygen, nitrogen and carbon PLFs, which are associated with the transfer of Z = 0, 1 and 2 units of charge. The main events at E Si 50 MeV is due to elastically scattered 16 O particles, the smaller peak at E Si 48 MeV is associated with the excitation of the lowest 3 excited state in 208 Pb at an excitation energy of 2.615 MeV. Events resulting from the transfer of three or more charged nucleons ( Z 3) are not observed for measurements at sub-barrier energies. Spectra for measurements of the PLFs following the reaction 32 S+ 208 Pb show similar features. 3

doi:.88/1742-6596/420/1/012129-1 -2 Probability P i -3 (P 1p ) 2 P 1p 208 Pb( 16 O, 15 N) 209 Bi ΔZ=2 transfer 208 Pb( 16 O, 14 C) 2 Po 208 Pb( 16 O, 12 C) 212 Po -4 12.5 13.0 13.5 14.0 14.5 15.0 r min [fm] Figure 2. (Color online) Transfer probabilities P i for the indicated transfer processes in the reaction 16 O+ 208 Pb as a function of the distance of closest approach (see text). The asymptotic behaviour for 1p transfer and predicted sequential 2p transfer are shown by the dotted straight lines. TDHF calculations for 1p and 2p transfer are shown by the solid blue and orange curves. The large open square and diamond are the measurements for N (blue) and C PLFs (black) from Videbaek et al. [15]. The smaller open squares and diamonds are the measurements for N (blue) and C PLFs (black) from Timmers [17]. 3. Transfer probabilities 3.1. Z identification of the PLFs Transfer probabilities for processes with different Z were extracted by gating on the particular region of interest in the E E spectra, and normalizing the number of events to the total number of counts in the two forward angle monitor detectors. Overall normalization of the probabilities was obtained from measurements of the total quasi-elastic scattering yields at energies well below the barrier energy, following the procedure detailed in Ref. [3]. For the reaction 16 O+ 208 Pb, deduced transfer probabilities for Z = 1 (nitrogen PLFs) and Z = 2 (carbon PLFs) are shown in Fig. 2, plotted as a function of the distance of closest approach r min assuming a trajectory in a Coulomb plus nuclear potential. A Woods-Saxon parametrization of the nuclear potential was used V N (r) = V 0 1 + exp r R 0 a 0, (1) where the parameters V 0, r 0 and a 0 were determined from analyses of the total quasi-elastic (and in the case of the reaction 16 O+ 208 Pb the inelastic 208 Pb(3 )) scattering excitation functions within a coupled-channels framework as described in Refs. [18, 2, 3]. At energies well below the fusion barrier, r min approaches the minimum distance assuming a pure Coulomb trajectory r min E c.m. V B r Coul min = Z pz t e 2 4πɛ 0 1 2E c.m. ( 1 + cosec θ ) c.m., 2 4

i 11th International Conference on Nucleus-Nucleus Collisions (NN2012) doi:.88/1742-6596/420/1/012129 1 P 1p -1 Probability P -2 (P 1p ) 2-3 208 32 31 209 Pb( S, P) Bi ΔZ = 2 transfer -4 12.5 13.0 13.5 14.0 14.5 15.0 15.5 r min [fm] Figure 3. (Color online) Transfer probabilities P i for the indicated transfer processes in the reaction 32 S+ 208 Pb as a function of the distance of closest approach r min (see text). The asymptotic behaviour for 1p transfer and predicted sequential 2p transfer are shown by the dotted straight lines. The open squares and diamonds are the measurements for F (blue) and Si (black) from Timmers [17]. where Z p, Z t are the atomic numbers of projectile and target nucleus, and E c.m. and θ c.m. are the energy and scattering angle in the centre-of-mass frame, respectively. As the energy increases r min becomes smaller than rmin Coul due to the attractive nuclear potential. The obtained absolute probabilities for transfer both in the reactions 16 O+ 208 Pb and 32 S+ 208 Pb show excellent agreement with measurements from Refs. [15, 17]. 3.2. Absolute transfer probabilities for transfer processes in the reaction 16 O+ 208 Pb Reaction Q-values for Z = 1 transfer processes in the reaction 16 O+ 208 Pb are well separated, allowing the identification of the predominant contribution to the Z = 1 events with the transfer of one proton (1p-stripping). For Z = 2 discrete peaks are not prominent in the excitation energy spectra (see top panel of Fig. 4), but an isotopic separation of the different carbon PLFs was possible using the calculated energy loss curves for different carbon isotopes as shown in Fig. 1. The contributions from 12 C, 13 C and 14 C to the integrated Z = 2 counts were determined as discussed in Ref. [19, 20]. Extracted transfer probabilities for the two dominant processes 2p-stripping 208 Pb( 16 O, 14 C) 2 Bi and α-particle stripping 208 Pb( 16 O, 12 C) 212 Bi are shown in Fig. 2 by the orange and green triangles, respectively. Transfer probabilities for the 2p1n-stripping process 208 Pb( 16 O, 13 C) 211 Bi are times smaller than those for α-particle transfer and are not shown. Contrary to what was commonly assumed [21, 22, 23, 24], at sub-barrier energies 2p transfer is the dominant process, α-particle transfer probabilities being smaller by a factor of 2 3. The difference in probabilities between 2p and α transfer increases with increasing beam energy, and is largest at E c.m. /V B 1.0. 5

doi:.88/1742-6596/420/1/012129 3.3. Absolute transfer probabilities for transfer processes in the reaction 32 S+ 208 Pb For the reaction 32 S+ 208 Pb, an equivalent analysis also indicates that 2p-stripping is the dominant Z = 2 transfer process compared to α-particle transfer. Due to the similarity in reaction Q-values of different transfer processes for both Z = 1 and Z = 2, deduced transfer probabilities may contain contributions from the channels 1p and 1p + 1n for Z = 1 and 2p 1n and 2p + 2n for Z = 2, respectively. Resulting extracted transfer probabilities for Z = 1 and Z = 2 transfer are shown in Fig. 3. 3.4. Time-dependent Hartree-Fock calculations TDHF calculations were performed for the reaction 16 O+ 208 Pb which allow the calculation of transfer excitation functions for 1p and 2p transfer using particle number projection techniques on the PLFs [25]. Since TDHF calculations are based on an independent particle picture, the calculated 2p transfer probabilities comprise sequential transfer of two uncorrelated protons. Results for the 1p and 2p transfer probabilities are shown by the solid blue and orange curves in Fig. 2. As detailed in Ref. [20] all TDHF results were scaled by a factor of 0.43 to match the experimental 1p transfer probabilities in the interval 13.2 < r min < 14.2 in which absorptive processes are negligible. The energy dependence of the TDHF calculations agree with the 1p transfer probabilities. The measured 2p probabilities are much higher than the TDHF calculations, indicating that in reality there is a strong pairing correlation between the two transferred protons, which leads to the enhanced 2p transfer probabilities. The TDHF calculations for 2p transfer are in close agreement with the predicted sequential 2p transfer probabilities (P 1p ) 2 (shown by the dotted orange line in Fig. 2), where P 1p is the experimentally measured 1p transfer probability. Overall, the agreement between TDHF calculations and the energy dependence of the extracted transfer probabilities for 1p transfer at energies below the fusion barrier is good. The calculated 2p transfer probabilities under-predict the extracted 2p transfer probabilities and therefore independently confirm a strong pairing correlation of the two protons in the observed 2p transfer probabilities. 4. Excitation energies The energies lost to excitation of the residual nuclei following Z = 1 and Z = 2 transfer were determined using the corresponding dominant transfer reactions leaving the residual nuclei in their ground states as the reference processes. Where populated, the ground-state transfers provided a good check of the energy calibration. From the excitation energy spectra, the differential transfer probabilities dp/de x were determined as dp de x d 2 σ tr dσ Ruth de x, where dσ tr /dω and dσ Ruth /dω are the differential cross sections for transfer and Rutherford scattering, respectively. Fig. 4 shows excitation energy spectra dp/de x as a function of E x for energies corresponding to E c.m. /V B = 0.96, 1.00, 1.05 for the PLFs following Z = 2 transfer in the 16 O- (top panel) and 32 S-induced reactions (bottom panel). As can be seen from the figure, average excitation energies increase with increasing charge product of the colliding nuclei, associated with increasing matter overlap between target and projectile nucleus. All reactions show the population of highly excited states, even at beam energies well below the fusion barrier. At an energy 5 MeV below the barrier, excitation energies up to 15 MeV are observed for the 16 O-induced reaction and 25 MeV for the 32 S-induced reaction. Simple optimum Q-value considerations as detailed in Ref. [20] show that there is a significant contribution to the total differential transfer probabilities dp/de x from processes leading to excitation energies higher than those expected from the optimum Q-value considerations. 6

doi:.88/1742-6596/420/1/012129 ] -1-2 (-2p) (-α) E c.m. /V B = 0.96 (-2p) (-α) E c.m. /V B = 1.00 (-2p) (-α) E c.m. /V B = 1.05 [MeV -1 dp/de x -3-4 ] -1-2 0 20 30 40 [MeV] (-2p) (-α) E x E c.m. /V B = 0.96 0 20 30 40 [MeV] (-2p) (-α) E x E c.m. /V B = 1.00 0 20 30 40 [MeV] E x [MeV dp/de x -1-3 -4 0 20 30 40 [MeV] E x 0 20 30 40 [MeV] E x Figure 4. (Color online) Excitation energy spectra showing the differential transfer probabilities dp/de x as a function of the excitation energy E x (i.e. kinetic energy loss taking into account the specific reaction Q value) of the PLFs for the indicated energies with respect to the fusion barrier energy E c.m. /V B for the Z = 2 transfer processes (2p, α transfer) in the reactions 16 O+ 208 Pb (top panel) and 32 S+ 208 Pb (bottom panel). The shaded areas show results from GRAZING calculations, see text for details. 4.1. GRAZING calculations Calculations were performed using the code GRAZING [26, 27], which is based on a semi-classical model. The code allows to include couplings to both single-nucleon transfer channels and collective excited states in the interacting nuclei. Multi-nucleon transfer occurs via a multi-step process, i.e. the calculated 2p transfer probabilities imply sequential transfer of two uncorrelated protons. The resulting coupled equations are solved in the semi-classical approximations for the relative motion of the interacting nuclei. It is important to note that GRAZING calculations give differential transfer cross sections as a function of excitation energy of the PLFs integrated over all impact parameters (i.e. angular momenta). A comparison with the measured excitation energy spectra at the angle of θ lab = 160.6 is justified since the 2p transfer angular distributions are strongly peaked at backward angles at the measured energies, see Ref. [15]. GRAZING calculations following Z = 2 transfer in the reactions 16 O, 32 S+ 208 Pb are shown in Fig. 4. All GRAZING differential transfer cross sections were scaled by the same factor, which was determined such that GRAZING calculations reproduce the total measured 2p transfer probability in the reaction 32 S+ 208 Pb at the lowest measured energy corresponding 7

doi:.88/1742-6596/420/1/012129 to E c.m. /V B = 0.96. The GRAZING differential transfer cross sections were folded with a Gaussian distribution to account for a detector energy resolution of 1 MeV. Overall GRAZING calculations fail to correctly reproduce the observed trend of increasing average excitation energy with increasing charge product of the projectile and target nuclei. Moreover and similar to the previous optimum Q-value considerations, at large excitation energies the calculated differential transfer probabilities fall below those extracted from the measured excitation energy spectra for the reaction 32 S+ 208 Pb. This is consistent with results for the kinetic energy loss spectra of the PLFs following 2p transfer in the reaction 40 Ca+ 208 Pb as shown in Ref. [28], which also show large discrepancies at high excitation energies between the calculated and measured differential transfer cross sections as a function of excitation energy for measurements at beam energies near the fusion barrier. The failure to properly reproduce the measured large kinetic energy losses in the PLFs following 2p transfer (corresponding to large excitation energies in the residual nuclei) indicates dissipative processes in 2p transfer which are not included in the GRAZING model. 5. Phenomenological dissipative optical model calculations A new phenomenological framework has been developed to investigate the effect of energy dissipation on the fusion probability for the reaction 16 O+ 208 Pb. In this approach the probability for fusion is reduced due to dissipative loss of kinetic energy into nucleonic degrees of freedom, which is linked to the measured probability for populating excited states with E x E x,thresh following 1p and 2p transfer. The fusion cross section can then be written as σ fus = ( ( π ) k 2 (2l + 1) P l(e) 1 de x A l (E x ) l E x.thresh + π ) k 2 (2l + 1) de x P l (E E x )A l (E x ), E x.thresh where P l (E) is the usual tunnelling probability for partial wave l with energy E, A l (E x ) is the probability for dissipative loss of kinetic energy by the amount E x for each partial wave, and k is the usual wave number. The partial-wave probability for dissipative energy loss is directly obtained from the measured probabilities for 1p and 2p transfer. This is done by parametrizing the probabilities using the semi-classical calculation for the transfer probability in the first Born approximation [29]. The obtained transfer probabilities (as a function of excitation energy E x and distance of closest approach r min ) are then extrapolated to the partial-wave dependent position of the barrier radius r B,l P (E x, r min ) P (E x, r B,l ) A l (E x ). The partial-wave probabilities A l (E x ) were normalized using a normalization factor given by the sum of the E x -integrated probabilities for i = 1p, 2p transfer N = i E de x,thresh x P i (E x ). Tunnelling probabilities P l (E) were calculated within a simple optical model framework, using Woods-Saxon-type nuclear potential parameters obtained from an analysis of the quasi-elastic scattering flux: V 0 = 80 MeV, r 0 = 1.19 fm, a 0 = 0.67 fm [2]. Results of calculations for three different values for the threshold excitation energy E x,thresh are shown in Fig. 5 by the blue solid curves, together with standard optical model calculations without energy dissipation (dotted black curves). The loss of kinetic energy leads to a suppression of the fusion cross section contribution of higher partial waves to the total fusion probability at above-barrier energies. The degree of suppression at above-barrier energies depends on the amount of kinetic energy lost to internal nucleonic degrees of freedom. This 8

doi:.88/1742-6596/420/1/012129 Figure 5. Fusion cross sections for the reaction 16 O+ 208 Pb. Experimental data from Refs. [30, 6]. Optical model calculations are shown by the dotted black line. Calculations taking into account energy dissipation through high-e x transfer are shown by the solid blue curves for the three indicated threshold excitation energies, see text for details. In all calculations the same Woods-Saxon-type parametrization for the nuclear potential was used: V 0 = 80 MeV, r 0 = 1.19 fm, a 0 = 0.67 fm. in turn depends on the value of the threshold excitation energy E x,thresh. As E x,thresh increases, the total transfer probability decreases (see Fig. 4) and so does the amount of fusion suppression at above-barrier energies. The best agreement with the measured fusion cross sections at energies above the barrier is obtained for a threshold of E x,thresh = 8.0 MeV. 6. Conclusion In conclusion, the following results were obtained from a detailed analysis of the projectile-like fragments detected at a backward angle in the reactions 16 O, 32 S+ 208 Pb: (i) Transfer of two protons (2p-stripping) in the reactions 16 O, 32 S+ 208 Pb occurs with a significant probability already at energies well below the fusion barrier. 2p transfer is the predominant Z = 2 transfer process, with absolute probabilities being 2 3 times larger than those for α-particle transfer. (ii) The transfer excitation functions for 2p transfer in 16 O+ 208 Pb suggest a strong pairing correlation of the two transferred protons. This is supported by TDHF calculations based on the independent particle picture. (iii) The residual nuclei following 2p and α-particle transfer are left in highly excited states, with excitation energies up to 15 MeV and 25 MeV for the 16 O- and 32 S-induced PLFs, respectively. A comparison with Q opt and GRAZING calculations show projectilelike fragments with larger kinetic energy losses than expected based on these semi-classical considerations. This suggests that dissipative and irreversible processes play an important role already at energies well below the fusion barrier. A new phenomenological and probabilistic approach to calculate fusion cross sections taking into account energy dissipation has been presented. In this approach the irreversible loss of kinetic energy due to the population of highly excited states following transfer leads to a suppression of the fusion probability at energies above the fusion barrier. Excitation energy dependent transfer probabilities were directly obtained from a parametrization of the measured 1p and 2p transfer probabilities in the reaction 16 O+ 208 Pb. Preliminary results using a simple single-channel optical model show that excellent agreement with measured fusion cross sections at energies above the 9

doi:.88/1742-6596/420/1/012129 fusion barrier can be obtained, if transfer leading to the population of excited states above 8.0 MeV is considered to lead to irreversible (and dissipative) loss of kinetic energy. These considerations strongly support the idea that few-nucleon transfer triggers the onset of dissipative and irreversible processes in the collision of nuclei already at energies well-below the fusion barrier. This would reduce the tunnelling probability, and suppress the fusion yield at these energies in a similar way as was demonstrated within the new empirical framework for the reaction 16 O+ 208 Pb at above-barrier energies. References [1] M. Dasgupta et al., Annu. Rev. Nucl. Part. Sci. 48, 401 (1998). [2] M. Evers et al., Phys. Rev. C 78, 034614 (2008). [3] M. Evers et al., Phys. Rev. C 81, 014602 (20). [4] C. L. Jiang et al., Phys. Rev. Lett. 89, 052701 (2002). [5] C. L. Jiang et al., Phys. Rev. C 71, 044613 (2005). [6] M. Dasgupta et al., Phys. Rev. Lett. 99, 192701 (2007). [7] H. Esbensen et al., Phys. Rev. C 76, 054609 (2007). [8] C. L. Jiang et al., Phys. Rev. C 75, 015803 (2007). [9] C. L. Jiang et al., Phys. Rev. C 79, 044601 (2009). [] L. R. Gasques et al., Phys. Rev. C 76, 035802 (2007). [11] J. O. Newton et al., Phys. Rev. C 70, 024605 (2004). [12] C. H. Dasso et al., Phys. Rev. C 39, 2073 (1989). [13] L. Corradi et al., J. Phys. G: Nucl. Part. Phys. 36, 1131 (2009). [14] V. Zagrebaev et al., J. Phys. G: Nucl. Part. Phys. 34, 1 (2007). [15] F. Videbaek et al., Phys. Rev. C 15, 954 (1977). [16] S. C. Pieper et al., Phys. Rev. C 18, 180 (1978). [17] H. Timmers, Ph.D. thesis, The Australian National University (1996). [18] L. R. Gasques et al., Phys. Rev. C 76, 024612 (2007). [19] M. Evers et al., Phys. Rev. C 84, 054614 (2011). [20] M. Evers et al., EPJ Web of Conferences 17, 08003 (2011). [21] R. M. DeVries et al., Phys. Rev. Lett. 35, 835 (1975). [22] H. Hasan et al., Nucl. Phys. A 318, 523 (1979). [23] I. J. Thompson et al., Nucl. Phys. A 505, 84 (1989). [24] T. Tamura et al., Phys. Rep. 65, 345 (1980). [25] C. Simenel, Phys. Rev. Lett. 5, 192701 (20). [26] A. Winther, Nucl. Phys. A 572, 191 (1994). [27] A. Winther, Nucl. Phys. A 594, 203 (1995). [28] S. Szilner et al., Phys. Rev. C 71, 0446 (2005). [29] F. Schindler et al., Nucl. Phys. A 603, 77 (1996). [30] C. R. Morton et al., Phys. Rev. C 60, 044608 (1999).