Nuclear Theory Group

Tohoku University

ANNUAL REPORT 2004

Academic Staff

Research Activities

(I) Low energy heavy-ion collisions and multi-dimensional quantum tunneling

• Quantum diffusion in low energy heavy-ion collisions
  (N. Takigawa, K. Washiyama, S. Ayik, B. Yilmaz, A. Gokalp and O. Yilmaz)

  In order to describe the fusion of two very heavy nuclei at near barrier energies, we proposed a generalized Langevin approach which incorporates the quantum statistical fluctuations in accordance with the fluctuation and dissipation theorem. We illustrated that the quantum statistical effects introduce an enhancement of the formation of compound nucleus, though the quantum enhancement is somewhat less pronounced as indicated in our previous calculations based on a density operator formalism.

  
  
  

• Knock-on exchange potential in the double-folding model
  (T. Takehi, K. Hagino, and N. Takigawa)

  Based on the resonating group method (RGM), we developed a novel way to compute the knock-on exchange part of the double-folding potential. This method neglects the recoil effect due to the nucleon exchange, and the resultant potential is local in the coordinate space. We compared fusion cross sections obtained with this potential to those with the trivially local equivalent potential. We found that the no-recoil approximation works well for heavy systems such as ¹⁶O + ²⁰⁸Pb reaction.

• Application of energy density formalism to subbarrier fusion reactions
  (N. Takigawa, Muhammad Zamrun F., and K. Hagino)

  We studied heavy-ion fusion reactions at sub-barrier energies using the potential given by the energy density formalism. We used the Skyrme functional and estimated the kinetic energy and spin orbit densities by the Extended-Thomas-Fermi method. We particularly analyzed the fusion excitation functions and the fusion barrier distributions for ¹⁶O + ^144,154Sm, ¹⁸⁶W, ²⁰⁸Pb reactions. In order to account for the inelastic excitations of the colliding nuclei, we fitted the potential given by the energy density formalism with the Gaussian and the Woods-Saxon forms, and performed coupled-channels calculations. Our calculations reproduced well the experimental data, suggesting that the energy density formalism provides a promising method which can be applied consistently to both the fusion reaction and the scattering problems. We also discussed the fusion cross sections computed with the energy density formalism at deep subbarrier energies.

• Surface diffuseness anomaly in heavy-ion potentials for large-angle quasielastic scattering
  (K. Hagino, T. Takehi, A.B. Balantekin, and N. Takigawa)

  Recent high precision experimental data for heavy-ion fusion reactions at subbarrier energies systematically show that a surprisingly large surface diffuseness parameter for a Woods-Saxon potential is required in order to fit the data. We pointed out that experimental data for quasi-elastic scattering at backward angles also favor a similar large value of surface diffuseness parameter. Consequently, a double folding approach fails to reproduce the experimental excitation function of quasielastic scattering for the ¹⁶O + ¹⁵⁴Sm system at energies around the Coulomb barrier. We also showed that the deviation of the ratio of the quasielastic to the Rutherford cross sections from unity at deep subbarrier energies offers an unambiguous way to determine the value of the surface diffuseness parameter in the nucleus-nucleus potential.

• Absence of structure in the ^20,22Ne + ¹¹⁸Sn quasi-elastic barrier distribution
  (K. Hagino, E.Piasecki, L. Swiderski, and N. Rowley)

  We analysed the experimental excitation function for the quasi-elastic scattering for ²⁰Ne + ¹¹⁸Sn using the coupled-channels method. In contrast to theoretical calculations based on known collective states, the experimental barrier distribution was found to be structureless. A comparison with the system ²²Ne + ¹¹⁸Sn showed that this smoothing is unlikely to be due to nucleon- or α -transfer channels, and is more likely to be due to coupling to many other weak channels.

• An extra push from entrance-channel effects
  (K. Hagino, N. Rowley, and N. Grar)

  Symmetric heavy-ion collisions are known to display an `extra-push' effect. That is, the energy at which the s-wave transmission is 0.5 lies significantly higher than the nominal Coulomb barrier. Despite this, however, the capture cross section is still greatly enhanced below the uncoupled barrier. We showed that this phenomenon can be simply explained in terms of entrance-channel effects which account for long-range Coulomb excitations.

(II) Reexamination of the screening effects on nuclear reactions at extremely low energies

• Non-linear effects
  (N. Takigawa and Y. Kato)

  We studied the screening effects of electrons on the d+d reactions in matter. By comparing the results of Kohn-Sham equations for electrons and those of linear response theory using dielectric constants, we found that non-linear effects amplify the screening effects. The obtained theoretical value of the screening energy is, however, still much smaller than the values reported by experimental analyses.

(III) Mean-field calculations for neutron-rich nuclei

• Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations
  (K. Hagino and H. Sagawa)

  We developed a perturbative model to treat the off-diagonal components in the Hartree-Fock-Bogoliubov (HFB) transformation matrix, which are neglected in the BCS approximation. Applying the perturbative model to a weakly bound nucleus $^{84}$Ni, it was shown that the perturbative approach reproduces well the solutions of the HFB method both for the quasi-particle energies and the radial dependence of quasi-particle wave functions. We found that the non-resonant part of the continuum single-particle state can acquire an appreciable occupation probability when there exists a weakly bound state close to the Fermi surface. This result originates from the strong coupling between the continuum particle state and the weakly bound state, and is absent in the BCS approximation. The limitation of the BCS approximation was pointed out in comparison with the HFB and the present perturbative model.

• Proton versus neutron deformability in ¹⁶C
  (Nyein Wink Lwin, K. Hagino, N. Takigawa, T. Futura, and T. Nakatsukasa)

  A recent publication reports that the electric quadrupole transition from the first 2⁺ to the ground states in ¹⁶C is considerably smaller than the systematics expected in stable nuclei. We discussed a possible origin for this anomolous hindrance in the B(E2) strength based on the constrained relativistic mean field (RMF) approach. To this end, we introduced a double constraint both on the proton and the neutron quadrupole moments. We found that the potential energy surface tends to be flat along the neutron deformation, while it has a relatively deep minimum along the proton deformation. This may suggest that the first 2⁺ state in ¹⁶C mainly consists of the neutron excitations.

• Scattering wave function for a deformed potential in the zero energy limit
  (K. Hagino, K. Yoshida, and K. Matsuyanagi)

  We developed a schematic model for a deformed potential in order to discuss the scattering wave function in the zero energy limit. This model consists of a spherical square well potential and a quadrupole potential whose radial dependence is given by a delta function. We argued that, for the s-wave incident, the incident wave reaches at the surface region, where the coupling is located, even at small energies. Consequently all the partial wave components have a siginificant value inside the potential range. This contrasts with the spherical case, where only the s-wave component has a significant value inside the potential in the zero energy limit.

(IV) Semi-classical methods

• WKB approximation for multi-channel barrier penetrability
  (K. Hagino and A.B. Balantekin)

  Using a method of local transmission matrix, we generalized the well-known WKB formula for a barrier penetrability to multi-channel systems. We compared the WKB penetrability with a solution of the coupled-channels equations, and showed that the WKB formula works well at energies well below the lowest adiabatic barrier. We also discussed the eigen-channel approach to a multi-channel tunneling, which may improve the performance of the WKB formula near and above the barrier.

(V) Proton radioactivity

• Fine structure in the proton radioactivity of ¹⁴⁶Tm
  (K. Hagino and K. Rykaczewski)

  We have applied the particle-core vibration coupling model to the proton emission decay of the odd-odd ¹⁴⁶Tm nucleus, which has recently been discovered at HRIBF, Oak Ridge. Assuming the spin and parity for the states in the daughter and the parent nuclei which are consistent with the known systematics and with the neigbouring nuclei, we have successfully reproduced the observed decay half lives and the branching ratios for both the ground state decay and the isomeric decay. We have also argued that the proton radioactivity provides a useful means to determin the spin and parity of single-particle levels in proton-rich nuclei.

(VI) Intermediate energy heavy ion reactions and related topics

• Nuclear liquid-gas phase transition studied with antisymmetrized molecular dynamics
  (T. Furuta and A. Ono)

  Nuclear liquid-gas phase transition was studied by using the antisymmetrized molecular dynamics (AMD). The time evolution of a many-nucleon system confined in a container is solved for a long time to get a microcanonical ensemble with given energy and volume. In order to define the temperature precisely and draw reliable caloric curves, AMD was improved with two respects. One is to treat the momentum widths of wave packets and the conserved Hamiltonian in a consistent way so that the calculated temperature is consistent with the energy conservation. The other point is to treat the interaction among gaseous nucleons correctly so that the mean field interaction is taken into account by the calculated temperature.

• Statistical calculation by antisymmetrized molecular dynamics
  (T. Furuta and A. Ono)

  In order to investigate the issue whether dynamical models can describe the equilibrated system, the microcanonical ensembles for systems confined in a given volume are generated by solving the AMD time evolution for a very long time. The obtained mass distribution is compared with the predictions by the statistical models for multifragmentation, resulting in an agreement for the global feature. However, it was found that AMD produces larger fragments and a smaller number of nucleons and alpha particles than statistical models, which may be due to the interaction among fragments that is neglected in statistical models.

• Transparency problem in heavy ion collisions
  (A. Ono)

  In the standard description by AMD for heavy ion multifragmentation reactions such as central collisions of Sn + Sn at 50 MeV/nucleon, it has been found that the emission of intermediate mass fragments to the transverse direction is not sufficient. Two possibilities were investigated to remedy this problem. One is to increase the in-medium two-nucleon collision cross section and the other is to introduce a process to directly form light fragments such as deuterons and tritons. The results show that only increasing the two-nucleon cross section cannot solve the problem but the direct process for light fragment formation can drastically improve the reproduction of the data of the fragment yields in transverse direction and the kinetic energy of fragments. This suggests that it is worth while developing a more precise formalism for the direct formation of light fragments.

(VII) Neutrino physics and nucleosynthesis

• Neutrino mixing and nucleosynthesis in core-collapse supernovae
  (A.B. Balantekin and H. Yuksel)

  In this work first a simple description of core-collapse supernovae was presented. Properties of the neutrino-driven wind, neutrino fluxes and luminosities, reaction rates, and the equilibrium electron fraction in supernova environments were discussed. Neutrino mixing and neutrino interactions that are relevant to core-collapse supernovae were briefly reviewed. The values of electron fraction under several evolution scenarios that may impact rapid neutron capture process (r-process) nucleosynthesis were calculated.

• Supernova neutrino-effects on r-process nucleosynthesis in black hole formation
  (A.B. Balantekin, T. Sasaqui, and T. Kajino)

  In the case of very massive core collapse supernova, a remnant stellar black hole is thought to be formed. Intense neutrino flux from the neutronized core and the neutrino sphere might suddenly cease during the Kelvin-Helmholtz cooling phase because of the black hole formation. Arguments have recently been given in the literature that even the neutrino mass may be determined from the time delay of deformed neutrino energy spectrum after the cease of neutrino ejection (neutrino cutoff effect). In this work we studied the expected theoretical response of the r-process nucleosynthesis to the neutrino cutoff effect in order to look for another independent signature of this phenomenon. We found a sensitive response of the r-process yield if the neutrino cutoff occurs after the critical time when the expanding materials in the neutrino-driven wind drop out of the Nuclear Statistical Equilibrium (NSE). The r-process nucleosynthesis yields change maximally if the cutoff occurs during the r-process. Using this result, connected with future detection of the time-variation of SN neutrino spectrum, we were able to identify when the black hole formation occurs in the course of SN collapse.

Publications

• Quantum effect in the diffusion along a potential barrier -- comments on the synthesis of superheavy elements
  N. Takigawa, Sakir Ayik, Kouhei Washiyama and Sachie Kimura
  Phys. Rev. C 69 (2004) 054605-1-5
  
  
• Energy Average over Regular and Chaotic States in the Decay out of Superdeformed Bands
  M.S. Hussein, A.J. Sargeant, M.P. Pato, N. Takigawa, and M. Ueda
  Prog. Theor. Phys. Suppl. 154 (2004) 146-153
  
  
• Recent Theoretical Activities of Heavy-Ion Fusion Reactions in Sendai
  N. Takigawa, Tamanna Rumin, T. Masamoto, T. Takehi, K. Washiyama and S. Ayik
  Prog. Theor. Phys. Suppl. 154 (2004) 192-200
  
  
• Influence of Tunneling on Electron Screening in Low Energy Nuclear Reactions
  S. Kimura, N. Takigawa, M. Abe, D.M. Brink and A. Bonasera
  Prog. Theor. Phys. Suppl. 154 (2004) 317-324
  
  
• Structure of positive energy states in a deformed mean-field potential
  K. Hagino and Nguyen Van Giai
  Nucl. Phys.A735 (2004), 55-76
  
  
• Subbarrier fusion in the systems ^11,10Be + ²⁰⁹Bi
  C. Signorini, A. Yoshida, Y.X. Watanabe, D. Pierroutsakou, L. Stroe, T. Fukuda, M. Mazzocco, N. Fukuda, Y. Mizoi, M. Ishihara, H. Sakurai, A. Diaz-Torres, and K. Hagino
  Nucl. Phys. A735 (2004) 329-344.
  
  
• Systematics of the diffuseness parameter in heavy-ion fusion reactions: the need for a new dynamical treatment of fusion?
  J.O. Newton, R.D. Butt, M. Dasgupta, I. Gontchar, D.J. Hinde, C.R. Morton, A. Mukherjee, and K. Hagino
  Phys. Lett. B586 (2004) 219-224.
  
  
• Large angle scattering and quasi-elastic barrier distributions
  K. Hagino and N. Rowley
  Phys. Rev. C69 (2004) 054610/1-11.
  
  
• WKB approximation for multi-channel barrier penetrability
  K. Hagino and A.B. Balantekin
  Phys. Rev. A 70 (2004)032106/1-6.
  
  
• Systematic failure of the Woods-Saxon nuclear potential to describe both fusion and elastic scattering: Possible need for a new dynamical approach to fusion
  J.O. Newton, R.D. Butt, M. Dasgupta, D.J. Hinde, I.I. Gontchar, C.R. Morton, and K. Hagino
  Phys. Rev. C 70 (2004) 024605/1-15.
  
  
• Fusion dynamics around the Coulomb barrier
  K. Hagino, N. Rowley, T. Ohtsuki, M. Dasgupta, J.O. Newton, and D.J. Hinde
  AIP Conf. Proc. 704 (2004) 82-91.
  
  
• Reaction dynamics for fusion of weakly-bound nuclei
  K. Hagino and A. Vitturi
  Prog. Theo. Phys. Suppl. 154 (2004) 77-84.
  
  
• The nuclear potential in heavy-ion fusion
  M. Dasgupta, D.J. Hinde, J.O. Newton, and K. Hagino
  Prog. Theo. Phys. Suppl. 154 (2004) 209-216.
  
  
• Near barrier fusion excitation function of ⁶Li + ²⁰⁸Pb
  Y.W. Wu, Z.H. Liu, C.J. Lin, H.Q. Zhang, M. Ruan, F. Yang, Z.C. Li, M. Trotta, and K. Hagino
  Prog. Theo. Phys. Suppl. 154 (2004) 177-183.
  
  
• Fusion and breakup in the reactions of ^6,7Li and ⁹Be
  K. Hagino, M. Dasgupta and D.J. Hinde
  Nucl. Phys. A738 (2004) 475c-478c.
  
  
• How many fusion barriers?
  L. Swiderski, P. Czosnyka, M. Kowalczyk, E. Piasecki, K. Piaseki, M. Witecki, J. Jastrzebski, A. Kordyasz, M. Kisielinski, T. Krogulski, N. Rowley, C. Marchetta, A. Pagano, M. Mutterer, W.H. Trzaska, and K. Hagino
  Int. J. Mod. Phys. E13 (2004) 315-320.
  
  
• Electric dipole transitions in neutron-rich nuclei
  T. Suzuki, H. Sagawa, and K. Hagino
  Phys. of Atom. Nucl., 67 (2004) 1674-1681.
  
  
• Antisymmetrized molecular dynamics for heavy ion collisions
  A. Ono, H. Horiuchi
  Porg. Part. Nucl. Phys. 53 (2004), 501--581.
  
  
• Symmetry energy for fragmentation in dynamical nuclear collisions
  A. Ono, P. Danielewicz, W. A. Friedman, W. G. Lynch and M. B. Tsang
  Phys. Rev. C 70 (2004), 041604(R) (5 pages).
  
  
• Ghoshal-like test of equilibration in near-Fermi-energy heavy-ion collisions
  J. Wang, T. Keutgen, R. Wada, K. Hagel, Y. G. Ma, M. Murray, L. Qin, P. Smith, J. B. Natowitz, R. Alfaro, J. Cibor, A. Botvina, M. Cinausero, Y. El Masri, D. Fabris, A. Keksis, S. Kowalski, M. Lunardon, A. Makeev, N. Marie, E. Martin, Z. Majka, A. Martinez-Davalos, A. Menchaca-Rocha, G. Nebbia, S. Moretto, G. Prete, V. Rizzi, A. Ruangma, D. V. Shetty, G. Souliotis, P. Staszel, M. Veselsky, G. Viesti, E. M. Winchester, S. J. Yennello, W. Zipper, and A. Ono
  Phys. Rev. C 71 (2005), 054608 (7 pages).
  
  
• Isospin fractionation and isoscaling in dynamical nuclear collisions
  A. Ono, P. Danielewicz, W. A. Friedman, W. G. Lynch and M. B. Tsang
  %Proc. The 8th International Conference on Clustering Aspects of Nuclear %Structure and Dynamics, Nara, November 24--29, 2003, Nucl. Phys. A738 (2004), 308c--312c.
  
  
• Nuclear liquid-gas phase transition studied with antisymmetrized molecular dynamics
  T. Furuta, A. Ono
  %Proc. YITP Workshop on Nuclear Matter Under Extream Conditions, %Kyoto, December 1--3, 2003 Prog. Theor. Phys. Suppl. 156 (2004), 147--148.
  
  
• Neutrino mixing and nucleosynthesis in core-collapse supernovae
  A.B. Balantekin and H. Yuksel
  New J. Phys. 7 (2005) 51 (18pages).
  
  
• Neutrino Physics and Nuclear Axial Two-Body Interactions
  A.B. Balantekin and H. Yuksel
  Int. J. Mod. Phys. E14 (2005) 39-46.
  
  
• Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach
  A.B. Balantekin, T. Dereli, and Y. Pehlivan
  Int. J. Mod. Phys. E14 (2005) 47-55.
  
  

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  Master Thesis (March 2005)

  • Study of heavy-ion fusion reaction with energy density formalism
    Muhammad Zamrun F.
    
    

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