Investigating nuclear dissipation properties at large deformations via excitation energy at scission

Investigating nuclear dissipation properties at large deformations via excitation energy at scission 1 first-author 1 corresp Corresponding author, yewei@seu.edu.cn Corresponding author, yewei@seu.edu.cn yewei@seu.edu.cn Department of Physics, Southeast University, Nanjing 210096, China Department of Physics, Southeast University, Nanjing 210096, China Using the stochastic Langevin model coupled with a statistical decay model, we study nuclear dissipation properties at large deformations with excitation energy at scission ( <math id="M1"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> ) measured in experiments. It is found that the postsaddle dissipation strength required to fit <math id="M2"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data is 12 × 10 21 s -1 for 254,256 Fm and 6 × 10 21 s -1 for 189 Au, which has a smaller postsaddle deformation than the former heavy nucleus, showing a rise of nuclear dissipation strength with increasing deformation. Excitation energy at scission Langevin model Nuclear dissipation 1 Introduction 1 The precise nature of nuclear dissipation remains one of the major problems unresolved in nuclear physics. Dissipation plays a critical role in low-energy nucleus-nucleus collision dynamics [ 1 1 - 7 7 1-7 ]. It delays fission, resulting in an enhanced emission of prescission light particles and a large evaporation residue cross section with respect to the predictions of standard statistical models [ 8 8 - 10 10 8-10 ]. Accordingly, information on dissipation in fission is gained by comparing theory and experiment [ 11 11 - 14 14 11-14 ]. It has been shown [ 15 15 - 19 19 15-19 ] that dynamical Langevin models of fission describe well a great number of experimental observables, including particle multiplicities and evaporation residue cross sections, for a great number of compound nuclei (CNs) over a broad range of excitation energy, angular momentum, and fissility. Numerous theoretical investigations indicate that nuclear dissipation is shape dependent [ 11 11 , 16 16 , 20 20 , 21 21 ], and the shape dependence of the nuclear dissipation is identified as a key ingredient [ 22 22 ] in the application of Langevin models to fission of excited nuclei. Currently, intensive efforts are being put on the strength of presaddle dissipation [ 23 23 - 25 25 23-25 ], and only very few studies focus on the exploration of postsaddle dissipation characteristics. Light particles are considered to be the main indicators [ 20 20 , 21 21 , 26 26 ] for the dissipation effects. However, they can be evaporated along the whole fission path during the fission process of the CN, which causes an experimental difficulty of distinguishing particles emitted prior to saddle from those of the saddle-to-scission region. Excitation energy at scission ( <math id="M3"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> ) is observable and can be used to survey nuclear dissipation [ 27 27 ]. It is not only related to the number of prescission particles, but also depends on the energy loss taken away by these evaporated particles. Both aspects are connected with the properties of nuclear dissipation. So the quantity, <math id="M4"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> , carries ample information on nuclear dissipation. As an independent information source, the <math id="M5"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> thus constitutes an alternative tool of exploiting postsaddle dissipation properties. Till now, few researchers have used experimental <math id="M6"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data to pin down postsaddle dissipation. In the present work, the <math id="M7"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data from heavy 254,256 Fm and light 189 Au systems will be employed to probe postsaddle nuclear dissipation. 2 Theoretical model 1 A brief account of the combination of the dynamical Langevin equation with a statistical decay model (CDSM) [ 20 20 , 28 28 ] is given here. The dynamic part of CDSM is described by the Langevin equation that is expressed by entropy. We employ the following one-dimensional overdamped Langevin equation to perform the trajectory calculations. <math display="block" id="M8"><mrow><mfrac><mrow><mi>d</mi><mi>q</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mi>T</mi><mrow><mi>M</mi><mi>β</mi></mrow></mfrac><mfrac><mrow><mi>d</mi><mi>S</mi></mrow><mrow><mi>d</mi><mi>q</mi></mrow></mfrac><mo>+</mo><msqrt><mrow><mfrac><mi>T</mi><mrow><mi>M</mi><mi>β</mi></mrow></mfrac></mrow></msqrt><mi>Γ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mn>.</mn></mrow></math> Here, q is the dimensionless fission coordinate and defined as half of the distance between the center of mass of the future fission fragments divided by the radius of the compound nucleus. T is the temperature, and ⟨Γ( t )⟩ is a fluctuating force with ⟨Γ( t )⟩ = 0 . M is the inertia parameter [ 20 20 ], and β is the dissipation strength. The driving force of the Langevin equation is calculated from entropy: <math display="block" id="M9"><mrow><mi>S</mi><mo stretchy="false">(</mo><mi>q</mi><mn>,</mn><msup><mi>E</mi><mo>*</mo></msup><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><msqrt><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">[</mo><msup><mi>E</mi><mo>*</mo></msup><mo>−</mo><mi>V</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></msqrt><mn>,</mn></mrow></math> where E * is the excitation energy of the system. Equation (2) is constructed from the Fermi-gas expression with a finite-range liquid-drop potential [ 29 29 ]. The q -dependent surface, coulomb, and rotation energy terms are included in the potential V ( q ). In constructing the entropy, the following deformation-dependent level density parameter is used: <math display="block" id="M10"><mrow><mi>a</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>1</mn></msub><mi>A</mi><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><msup><mi>A</mi><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msup><msub><mi>B</mi><mtext>s</mtext></msub><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mn>,</mn></mrow></math> where a 1 = 0.073 MeV -1 and a 2 = 0.095 MeV -1 are taken from Ignatyuk et al. [ 30 30 ]. B s is the dimensionless surface area (for sphere B s = 1), which can be parametrized by the analytical expression [ 31 31 ], <math display="block" id="M11"><mrow><msub><mi>B</mi><mtext>s</mtext></msub><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo>{</mo><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mn>1</mn><mo>+</mo><mn>2.844</mn><mo stretchy="false">(</mo><mi>q</mi><mo>−</mo><msup><mrow><mn>0.375</mn><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mn>,</mn></mrow></mtd><mtd columnalign="left"><mrow><mtext>i</mtext><mi>f</mi><mtext> </mtext><mi>q</mi><mo><</mo><mn>0.452</mn></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow><mn>0.983</mn><mo>+</mo><mn>0.439</mn><mo stretchy="false">(</mo><mi>q</mi><mo>−</mo><mn>0.375</mn><mo stretchy="false">)</mo><mn>,</mn></mrow></mtd><mtd columnalign="left"><mrow><mtext>i</mtext><mi>f</mi><mtext> </mtext><mi>q</mi><mo>≥</mo><mn>0.452.</mn></mrow></mtd></mtr></mtable></mrow></mrow></mrow></math> In the CDSM, light-particle evaporation is coupled to the fission mode by a Monte Carlo procedure [ 16 16 ]. The emission width of a particle of kind ν is given by Ref. [ 32 32 ]. <math display="block" id="M12"><mtable columnalign="left"><mtr><mtd><msub><mi>Γ</mi><mi>ν</mi></msub><mo>=</mo><mo stretchy="false">(</mo><mn>2</mn><msub><mi>s</mi><mi>ν</mi></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mfrac><mrow><msub><mi>m</mi><mi>ν</mi></msub></mrow><mrow><msup><mi>π</mi><mn>2</mn></msup><msup><mi>ℏ</mi><mn>2</mn></msup><msub><mi>ρ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><msup><mi>E</mi><mo>*</mo></msup><mo stretchy="false">)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mo>×</mo><mstyle displaystyle="true"><mrow><msubsup><mo>∫</mo><mn>0</mn><mrow><msup><mi>E</mi><mo>*</mo></msup><mo>−</mo><msub><mi>B</mi><mi>ν</mi></msub></mrow></msubsup></mrow></mstyle><mi>d</mi><msub><mi>ε</mi><mi>ν</mi></msub><msub><mi>ρ</mi><mi>R</mi></msub><mo stretchy="false">(</mo><msup><mi>E</mi><mo>*</mo></msup><mo>−</mo><msub><mi>B</mi><mi>ν</mi></msub><mo>−</mo><msub><mi>ε</mi><mi>ν</mi></msub><mo stretchy="false">)</mo><msub><mi>ε</mi><mi>ν</mi></msub><msub><mi>σ</mi><mrow><mtext>inv</mtext></mrow></msub><mo stretchy="false">(</mo><msub><mi>ε</mi><mi>ν</mi></msub><mo stretchy="false">)</mo><mn>,</mn></mtd></mtr></mtable></math> where s ν is the spin of the emitted particle ν , and m ν is its reduced mass with respect to the residual nucleus. The level densities of the compound and residual nuclei are denoted by ρ c ( E * ) and ρ R ( E * - B ν - ε ν ). B ν are the liquid-drop binding energies. ε is the kinetic energy of the emitted particle, and inv ( ε ν ) is the inverse cross sections [ 32 32 ]. After each emission act of a particle, the intrinsic energy, entropy, and temperature in the Langevin equation are recalculated and the dynamics are continued. Prescission various particle multiplicities are calculated by counting the number of corresponding evaporated particle events registered in the CDSM. To accumulate sufficient statistics, 10 7 Langevin trajectories are simulated. Regarding the excitation energy at scission, it is determined by using energy conservation law, <math display="block" id="M13"><mrow><msup><mi>E</mi><mo>*</mo></msup><mo>=</mo><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup><mo>+</mo><msub><mi>E</mi><mrow><mtext>coll</mtext></mrow></msub><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>E</mi><mrow><mtext>evap</mtext></mrow></msub><mo stretchy="false">(</mo><msub><mi>t</mi><mrow><mtext>sc</mtext></mrow></msub><mo stretchy="false">)</mo><mn>,</mn></mrow></math> where E * and V ( q ) have the same meaning mentioned earlier. E coll is the kinetic energy of the collective degrees of freedom [ 20 20 ], and E evap ( t sc ) is the energy carried away by all evaporated particles by the scission time, t sc . For starting a trajectory, an orbit angular momentum value is sampled from the fusion spin distribution, which reads: <math display="block" id="M14"><mrow><mfrac><mrow><mi>d</mi><mi>σ</mi><mo stretchy="false">(</mo><mi mathvariant="script">l</mi><mo stretchy="false">)</mo></mrow><mrow><mi>d</mi><mi mathvariant="script">l</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><msup><mi>k</mi><mn>2</mn></msup></mrow></mfrac><mfrac><mrow><mn>2</mn><mi mathvariant="script">l</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>1</mn><mo>+</mo><mi>exp</mi><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mi mathvariant="script">l</mi><mo>−</mo><msub><mi mathvariant="script">l</mi><mi>c</mi></msub><mo stretchy="false">)</mo><mo>/</mo><mi>δ</mi><mi mathvariant="script">l</mi><mo stretchy="false">]</mo></mrow></mfrac><mn>.</mn></mrow></math> The parameters <math id="M15"><mrow><msub><mi mathvariant="script">l</mi><mi>c</mi></msub></mrow></math> and <math id="M16"><mrow><mi>δ</mi><mi mathvariant="script">l</mi></mrow></math> are the critical angular momenta for fusion and diffuseness, respectively. 3 Results and discussion 1 During the decay process of a CN, particle evaporation channel competes with fission channel. The nuclear friction retards fission and enhances particle emission, which lowers the excitation energy at scission. To better explore postsaddle dissipation properties with <math id="M17"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> in this work, the presaddle friction strength is set to 3 zs -1 (1 zs = 10 -21 s), in agreement with recent theoretical estimates and experimental analyses [ 12 12 , 21 21 , 28 28 , 33 33 - 35 35 33-35 ]. The postsaddle friction strength ( β ) is determined by reproducing measured <math id="M18"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> in 16 O + 238 U [ 36 36 ], 18 O + 238 U [ 36 36 ], and 20 Ne + 169 Tm [ 37 37 ] reactions. Figure 1(a) Figure 1(a) displays a comparison between experimental <math id="M19"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data of the 254 Fm system and theoretical ones which are calculated with Langevin models. It shows that <math id="M20"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> is a decreasing function of β . The reason for this behavior is that dissipation hinders fission, increasing particle emission and hence yielding a small excitation energy at scission. A detailed comparison of model calculations with experimental data reveals that the best-fit value of β is 12.5 zs -1 (represented by solid square). We also analyze the <math id="M21"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data from another heavy 256 Fm nucleus, produced in 18 O + 238 U reaction, and observe from Fig. 1(b) Fig. 1(b) that the best-fit friction strength is ∼ 11.5 zs -1 , an amplitude analogous to that of 254 Fm. Overall, the postsaddele friction strength deduced from the two heavy systems ( ∼ 12 zs -1 ) is stronger than that of presaddle friction, demonstrating a rise of the friction strength with increasing deformation. A CN undergoes deformation as it fissions. As is well known, a light CN system has a shorter saddle-to-scission distance than a heavy one. It means that the <math id="M22"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data from light and heavy fissioning systems can be employed to probe the friction strength at different deformations. To that end, we choose a light 189 Au system produced in 20 Ne + 169 Tm. The comparison between experimental data and calculated results is presented in Fig. 2 Fig. 2 . It is clear that <math id="M23"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> gets larger with the increase of incident energy as a result of a high initial excitation energy. In addition, a greater β leads to a smaller <math id="M24"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> , because more particles are evaporated at a larger friction, which significantly reduces the excitation energy at scission. By comparing the experimental and calculated <math id="M25"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> , one can notice that the friction strength of ∼ 6 zs -1 can provide a satisfactory description of the experimental data. This friction strength is slightly stronger than that of the presaddle region, a result that is consistent with that derived from the heavy Fm systems. It has been noted [ 21 21 ] that, when a modified one-body dissipation strength (which assumes a decreasing function of friction with deformation) was used in the calculation, the theoretical predictions are far below prescission particle multiplicity data of heavy fissioning nuclei with A > 250. For these very heavy nuclei, there is a longer distance between the saddle point and scission and hence a larger deformation is involved. It means that to account for the multiplicity data from heavy decaying systems, it is necessary to introduce a strong postsaddle friction in model calculations. In addition to <math id="M26"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> , we further survey particle multiplicity from light and heavy fissioning systems. As an illustration, Fig. 3 Fig. 3 shows the comparison between theoretical and experimental prescission neutrons for 256 Fm and 189 Au. The best-fit postsaddle friction value required tofit data is found to be 11 zs -1 for heavy 256 Fm and 5.5 zs -1 for light 189 Au. While the result that a stronger postsaddle friction at a larger deformation is not altered, these best-fit β values obtained from prescission neutron data are slightly different from those obtained from the <math id="M27"><mrow><msubsup><mi>E</mi><mrow><mtext>sc</mtext></mrow><mo>*</mo></msubsup></mrow></math> data. This could be due to a consequence of a difference in the sensitivity that different observables to friction. 4 Summary 1 In the framework of Langevin model of fission dynamics, we have compared calculated and measured excitation energy at scission from heavy and light fissioning systems. A postsaddle friction value of 12 × 10 21 s -1 and 6 10 21 s -1 is extracted for 248,256 Fm and 189 Au nuclei, respectively. Postsaddle deformation of 189 Au is smaller than that of 248,256 Fm, thus an evident difference in the deduced friction strength for the light and heavy nuclei shows that nuclear friction becomes strong with an increase of deformation. References D. Hilscher and H. Rossner , Ann. Phys. (Paris) 17 , 471 ( 1992 ). doi: 10.1051/anphys:01992001706047100 http://doi.org/10.1051/anphys:01992001706047100 Ann. Phys. (Paris) J. U. Andersen , J. Chevallier , J. S. Forster et al ., Attosecond time delays in heavy-ion induced fission measured by crystal blocking . Phys. Rev. C 78 , 064609 ( 2008 ). doi: 10.1103/PhysRevC.78.064609 http://doi.org/10.1103/PhysRevC.78.064609 Attosecond time delays in heavy-ion induced fission measured by crystal blocking W. Q. Shen , J. Albinski , A. Gobbi et al ., Fission and quasifission in U-induced reactions . Phys. Rev. C 36 , 115 ( 1987 ). doi: 10.1103/PhysRevC.36.115 http://doi.org/10.1103/PhysRevC.36.115 Fission and quasifission in U-induced reactions J. Velkovska , C. R. Morton , R. L. McGrath et al ., Quasifission reactions as a probe of nuclear viscosity . Phys. Rev. C 59 , 1506 ( 1999 ). doi: 10.1103/PhysRevC.59.1506 http://doi.org/10.1103/PhysRevC.59.1506 Quasifission reactions as a probe of nuclear viscosity E. Williams , D. J. Hinde , M. Dasgupta et al ., Evolution of signatures of quasifission in reactions forming curium . Phys. Rev. C 88 , 034611 ( 2013 ). doi: 10.1103/PhysRevC.88.034611 http://doi.org/10.1103/PhysRevC.88.034611 Evolution of signatures of quasifission in reactions forming curium A. K. Nasirov , G. Giardina , G. Mandaglio et al ., Quasifission and fusion-fission in reactions with massive nuclei: Comparison of reactions leading to the Z = 120 element . Phys. Rev. C 79 , 024606 ( 2009 ). doi: 10.1103/PhysRevC.79.024606 http://doi.org/10.1103/PhysRevC.79.024606 Quasifission and fusion-fission in reactions with massive nuclei: Comparison of reactions leading to the Z = 120 element Y. Aritomo , Fusion hindrance and roles of shell effects in superheavy mass region . Nucl. Phys. A 88 , 034611 ( 2013 ). doi: 10.1016/j.nuclphysa.2006.09.018 http://doi.org/10.1016/j.nuclphysa.2006.09.018 Fusion hindrance and roles of shell effects in superheavy mass region J. Benlliure , E. Casarejos , J. Pereira et al ., Transient and quasistationary dissipative effects in the fission flux across the barrier in 1A GeV 238U on deuterium reactions . Phys. Rev. C 74 , 014609 ( 2006 ). doi: 10.1103/PhysRevC.74.014609 http://doi.org/10.1103/PhysRevC.74.014609 Transient and quasistationary dissipative effects in the fission flux across the barrier in 1A GeV 238U on deuterium reactions H. Singh , K. S. Golda , Santanu Pal et al ., Role of nuclear dissipation and entrance channel mass asymmetry in pre-scission neutron multiplicity enhancement in fusion-fission reactions . Phys. Rev. C 78 , 024609 ( 2008 ). doi: 10.1103/PhysRevC.78.024609 http://doi.org/10.1103/PhysRevC.78.024609 Role of nuclear dissipation and entrance channel mass asymmetry in pre-scission neutron multiplicity enhancement in fusion-fission reactions R. Sandal , B. R. Behera , V. Singh et al ., Effect of N/Z in pre-scission neutron multiplicity for 16,18O + 194,198Pt systems . Phys. Rev. C 87 , 014604 ( 2013 ). doi: 10.1103/PhysRevC.87.014604 http://doi.org/10.1103/PhysRevC.87.014604 Effect of N/Z in pre-scission neutron multiplicity for 16,18O + 194,198Pt systems J. Sadhukhan and S. Pal , Critical comparison of Kramers’ fission width with the stationary width from the Langevin equation . Phys. Rev. C 79 , 064606 ( 2009 ). doi: 10.1103/PhysRevC.79.064606 http://doi.org/10.1103/PhysRevC.79.064606 Critical comparison of Kramers’ fission width with the stationary width from the Langevin equation W. Ye , Heavy-ion versus 3He/4He fusion-fission reactions: Angular momentum dependence of dissipation in nuclear fission . Phys. Rev. C 84 , 034617 ( 2011 ). doi: 10.1103/PhysRevC.84.034617 http://doi.org/10.1103/PhysRevC.84.034617 Heavy-ion versus 3He/4He fusion-fission reactions: Angular momentum dependence of dissipation in nuclear fission V. Singh , B. R. Behera , Maninder Kaur et al ., Neutron multiplicity measurements for 19F + 194,196,198Pt systems to investigate the effect of shell closure on nuclear dissipation . Phys. Rev. C 87 , 064601 ( 2013 ). doi: 10.1103/PhysRevC.87.064601 http://doi.org/10.1103/PhysRevC.87.064601 Neutron multiplicity measurements for 19F + 194,196,198Pt systems to investigate the effect of shell closure on nuclear dissipation Y. Ayyad , J. Benlliure , E. Casarejos et al ., Proton-induced fission of 181Ta at high excitation energies . Phys. Rev. C 89 , 054610 ( 2014 ). doi: 10.1103/PhysRevC.89.054610 http://doi.org/10.1103/PhysRevC.89.054610 Proton-induced fission of 181Ta at high excitation energies P. Fröbrich , I.I. Gontchar , Langevin fluctuation-dissipation dynamics of hot nuclei: Prescission neutron multiplicities and fission probabilities . Nucl. Phys. A 556 , 281 ( 1993 ). doi: 10.1016/0375-9474(93)90352-X http://doi.org/10.1016/0375-9474(93)90352-X Langevin fluctuation-dissipation dynamics of hot nuclei: Prescission neutron multiplicities and fission probabilities K. Pomorski , B. Nerlo-Pomorskaa , A. Surowieca et al ., Light-particle emission from the fissioning nuclei 126Ba, 188Pt and 266,272,278110: theoretical predictions and experimental results . Nucl. Phys. A 679 , 25 ( 2000 ). doi: 10.1016/S0375-9474(00)00327-4 http://doi.org/10.1016/S0375-9474(00)00327-4 Light-particle emission from the fissioning nuclei 126Ba, 188Pt and 266,272,278110: theoretical predictions and experimental results W. Ye , Role of N/Z in giant dipole resonance γ rays as a probe of post-saddle nuclear dissipation . Phys. Lett. B 681 , 413 ( 2000 ). doi: 10.1016/j.physletb.2009.10.067 http://doi.org/10.1016/j.physletb.2009.10.067 Role of N/Z in giant dipole resonance γ rays as a probe of post-saddle nuclear dissipation A. V. Karpov , P. N. Nadtochy , D. V. Vanin et al ., Three-dimensional Langevin calculations of fission fragment mass-energy distribution from excited compound nuclei . Phys. Rev. C 63 , 054610 ( 2001 ). doi: 10.1103/PhysRevC.63.054610 http://doi.org/10.1103/PhysRevC.63.054610 Three-dimensional Langevin calculations of fission fragment mass-energy distribution from excited compound nuclei Jhilam Sadhukhan and Santanu Pal , Role of saddle-to-scission dynamics in fission fragment mass distribution . Phys. Rev. C 84 , 044610 ( 2011 ). doi: 10.1103/PhysRevC.84.044610 http://doi.org/10.1103/PhysRevC.84.044610 Role of saddle-to-scission dynamics in fission fragment mass distribution P. Fröbrich and I. I. Gontchar , Langevin description of fusion, deep-inelastic collisions and heavy-ion-induced fission . Phys. Rep . 292 , 131 ( 1998 ). doi: 10.1016/S0370-1573(97)00042-2 http://doi.org/10.1016/S0370-1573(97)00042-2 Langevin description of fusion, deep-inelastic collisions and heavy-ion-induced fission P. N. Nadtochy , G. D. Adeev , and A. V. Karpov , More detailed study of fission dynamics in fusion-fission reactions within a stochastic approach . Phys. Rev. C 65 , 064615 ( 2002 ). doi: 10.1103/PhysRevC.65.064615 http://doi.org/10.1103/PhysRevC.65.064615 More detailed study of fission dynamics in fusion-fission reactions within a stochastic approach H. J. Krappe and K. Pomorski , Theory of Nuclear Fission, Lecture Notes in Physics Vol. 838 ( Springer-Verlag , Berlin , 2012 ). Theory of Nuclear Fission, Lecture Notes in Physics W. Ye and N. Wang , Significant role of level-density parameters in probing nuclear dissipation with light-ion-induced fission excitation functions . Phys. Rev. C 87 , 014610 ( 2013 ). doi: 10.1103/PhysRevC.87.014610 http://doi.org/10.1103/PhysRevC.87.014610 Significant role of level-density parameters in probing nuclear dissipation with light-ion-induced fission excitation functions B. B. Back , D. J. Blumenthal , C. N. Davids et al ., Fission hindrance in hot 216Th: Evaporation residue measurements . Phys. Rev. C 74 , 044602 ( 1999 ). doi: 10.1103/PhysRevC.74.044602 http://doi.org/10.1103/PhysRevC.74.044602 Fission hindrance in hot 216Th: Evaporation residue measurements P. D. Shidling , N. M. Badiger , S. Nath et al ., Fission hindrance studies in 200Pb: Evaporation residue cross section and spin distribution measurements . Phys. Rev. C 60 , 064603 ( 1999 ). doi: 10.1103/PhysRevC.60.064603 http://doi.org/10.1103/PhysRevC.60.064603 Fission hindrance studies in 200Pb: Evaporation residue cross section and spin distribution measurements K. Ramachandran , A. Chatterjee , A. Navin et al ., Fission time scale from prescission neutron, proton, and α particle multiplicities in 28Si+175Lu . Phys. Rev. C 73 , 064609 ( 1999 ). doi: 10.1103/PhysRevC.73.064609 http://doi.org/10.1103/PhysRevC.73.064609 Fission time scale from prescission neutron, proton, and α particle multiplicities in 28Si+175Lu W. Ye , N. Wang , Spallation reaction and the probe of nuclear dissipation with excitation energy at scission , Nucl. Sci. Techniques 24 , 050521 ( 2013 ). Spallation reaction and the probe of nuclear dissipation with excitation energy at scission P. Fröbrich , On the dynamics of fission of hot nuclei . Nucl. Phys. A 787 , 170 ( 2007 ). doi: 10.1016/j.nuclphysa.2006.12.028 http://doi.org/10.1016/j.nuclphysa.2006.12.028 On the dynamics of fission of hot nuclei P. Möller , W. D. Myers , W. J. Swiatecki et al ., Nuclear mass formula with a finite-range droplet model and a folded-Yukawa single-particle potential . At. Data Nucl. Data Tables 39 , 225 ( 1988 ). doi: 10.1016/0092-640X(88)90023-X http://doi.org/10.1016/0092-640X(88)90023-X Nuclear mass formula with a finite-range droplet model and a folded-Yukawa single-particle potential A. V. Ignatyuk , M. G. Itkis , V. N. Okolovich et al ., Fission of pre-actinide nuclei. Excitation functions for the (α,f) reaction . Yad. Fiz . 21 , 1185 ( 1975 ). Fission of pre-actinide nuclei. Excitation functions for the (α,f) reaction I. I. Gontchar , P. Fröbrich , Consistent dynamical and statistical description of fission of hot nuclei . Phys. Rev. C 47 , 2228 ( 1999 ). doi: 10.1103/PhysRevC.47.2228 http://doi.org/10.1103/PhysRevC.47.2228 Consistent dynamical and statistical description of fission of hot nuclei M. Blann , Decay of deformed and superdeformed nuclei formed in heavy ion reactions . Phys. Rev. C 21 , 1770 ( 1980 ). doi: 10.1103/PhysRevC.21.1770 http://doi.org/10.1103/PhysRevC.21.1770 Decay of deformed and superdeformed nuclei formed in heavy ion reactions C. Schmitt , P. N. Nadtochy , A. Heinz et al ., First Experiment on Fission Transients in Highly Fissile Spherical Nuclei Produced by Fragmentation of Radioactive Beams . Phys. Rev. Lett 99 , 042701 ( 2007 ). doi: 10.1103/PhysRevLett.99.042701 http://doi.org/10.1103/PhysRevLett.99.042701 First Experiment on Fission Transients in Highly Fissile Spherical Nuclei Produced by Fragmentation of Radioactive Beams W. Ye , H. W. Yang , and F. Wu , Isospin effects on the evaporation residue spin distribution . Phys. Rev. C 77 , 011302(R) ( 2008 ). doi: 10.1103/PhysRevC.77.011302 http://doi.org/10.1103/PhysRevC.77.011302 Isospin effects on the evaporation residue spin distribution B. Jurado , C. Schmitt , K.-H. Schmidt et al ., Transient Effects in Fission from New Experimental Signatures . Phys. Rev. Lett 93 , 072501 ( 2004 ). doi: 10.1103/PhysRevLett.93.072501 http://doi.org/10.1103/PhysRevLett.93.072501 Transient Effects in Fission from New Experimental Signatures D. J. Hinde , Neutron emission as a probe of fusion-fission and quasifission dynamics . Phys. Rev. C 45 , 1229 ( 1992 ). doi: 10.1103/PhysRevC.45.1229 http://doi.org/10.1103/PhysRevC.45.1229 Neutron emission as a probe of fusion-fission and quasifission dynamics J. Cabrera , Th. Keutgen , Y. El Masri et al ., Fusion-fission and fusion-evaporation processes in 20Ne+159Tb and 20Ne+169Tm interactions between E/A=8 and 16 MeV . Phys. Rev. C 68 , 034613 ( 2003 ). doi: 10.1103/PhysRevC.68.034613 http://doi.org/10.1103/PhysRevC.68.034613 Fusion-fission and fusion-evaporation processes in 20Ne+159Tb and 20Ne+169Tm interactions between E/A=8 and 16 MeV 10.1007/s41365-016-0146-y This work was supported by the National Nature Science Foundation of China (No. 11575044) 2016-08-15 2016-08-15 2016-10-08 2016-10-31 2016-12-20 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2016 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-016-0146-y http://dx.doi.org/10.1007/s41365-016-0146-y . 2016 Nuclear Science and Techniques 06 27