Nuclear Theory Group

Tohoku University

ANNUAL REPORT 2002

Academic Staff

Research Activities

(I) LOW ENERGY HEAVY-ION COLLISIONS AND MACROSCOPIC QUANTUM TUNNELING

• Calculation of the fusion cross section using a double-folding potential
  (N. Takigawa, T. Takehi, and T. Masamoto)

  We performed the coupled-channels calculations of the fusion cross section of the ¹⁶O+¹⁵⁴Sm reaction using the double-folding potential assuming the M3Y force for the nucleon-nucleon interaction. The calculation took the effects of the excitation of the ground state rotational band of ¹⁵⁴Sm into account in the lowest order approximation. The results well reproduced the experimental data of the excitation function of the fusion cross section over a wide range from above to sub barrier energies. There appeared, however, a distinct discrepancy between the experimental data and theoretical results concerning the fusion barrier distribution.
  
  

(II) SCREENING EFFECTS ON NUCLEAR REACTIONS AT EXTREMELY LOW ENERGIES

• Influence of tunneling on electron screening in low energy nuclear reactions in laboratories
  (N. Takigawa, S. Kimura, M. Abe, and D.M. Brink)

  Using a semiclassical mean field theory, we have shown that the screening potential exhibits a characteristic radial variation in the tunneling region in sharp contrast to the assumption of the constant shift in all previous works. Also, we have shown that the explicit treatment of the tunneling region gives a larger screening energy than that in the conventional approach, which studies the time evolution only in the classical region and estimates the screening energy from the screening potential at the external classical turning point. This modification becomes important if the electronic state is not a single adiabatic state at the external turning point either by pre-tunneling transitions of the electronic state or by the symmetry of the system even if there is no essential change with the electronic state in the tunneling region.
  
  

(III) Bremsstrahlung in alpha decay

• Analysis in terms of a realistic potential
  (N. Takigawa and Y. Nozawa)

  We extended our former study of the bremsstrahlung in alpha decay using a simple potential, i.e. square well + point Coulomb interaction, by replacing it with a realistic potential. Assuming the Woods-Saxon shape, we studied the dependence of the bremsstrahlung spectrum on the depth, range and surface diffuseness parameters of the potential as well as on the choice of the preformation factor of the alpha particle. We have thus shown that the experimental bremsstrahlung spectrum is well reproduced by a shallow potential, and that the final spectrum is given by the destructive interference of the contribution from the classical and the tunneling regions in accord with the conclusion of former studies using a simple potential. A deep potential leads to a too strong bremsstrahlung originating from the strong variation of the potential in the surface region. However, it is needed to develop a theory which takes the existence of the Pauli forbidden states into account in order to exclude the deep potential from the analysis of the data of bremsstrahlung. Our calculation has shown that the magnitude of the bremsstrahlung strongly depends on the surface diffuseness parameter. We also applied the simple potential model to comparing the bremsstrahlung in the alpha decay from the three Po isotopes ^210,212,214Po and have shown that the bremsstrahlung from the tunneling region most clearly manifests itself in the isotope whose threshold energy for the alpha decay is small. We also calculated the bremsstrahlung in the alpha decay from ²¹⁴Po and ²²⁶Ra. We suggest that experiments should be redone to resolve the discrepancy among existing experimental data for these system. Also, we determined the preformation factor of the alpha particle using the threshold energy and the decay width and have shown that the preformation factor takes a noticeably small value for nuclei related to a magic number.
  
  

(IV) MEDIUM EFFECTS ON NUCLEAR INTERACTION

• Meson mixing amplitudes in asymmetric nuclear matter
  (Y. Mori and K. Saito)

  Using a purely hadronic model, the charge-symmetry-breaking ρ-ω, σ-δ, σ-ρ and δ-ω mixing amplitudes in isospin asymmetric nuclear matter is studied. The mixing amplitude is generated by nucleon and antinucleon loops and hence driven entirely by the difference between proton and neutron Fermi momenta and the proton-neutron mass difference. It is found that in neutron rich nuclei and/or neutron stars the mixing amplitudes become about 10-100 times as large as those in typical mirror nuclei.
  
  

• Study of medium effects on nuclear interaction by using polarized proton-nucleus quasi-elastic scattering
  (Y. Mori, M. Maruyama, and K. Saito)

  Recently, medium effects of spin observables have been observed in experiments at RCNP using polarized proton-nucleus quasi-elastic scattering. We study the process in the distorted wave impulse approximation based on the relativistic mean field theory. It is found that appropriate choice of spin observables brings separation of proton-proton interaction in nuclear medium into contributions from each meson exchange amplitude. We are investigating the possible origin of the anomalous behaviour appeared in spin observables, such as mass shift, change of coupling constants, off-shell effects.
  
  

(V) NONEQUILIBRIUM THERMAL FIELD THEORY

• Projection operator approach to Langevin equations in φ⁴ theory
  (T. Koide, M. Maruyama, and F. Takagi)

  By applying the projection operator method to φ⁴ theory, both quantum and semiclassical Langevin equations of motion for the soft modes are derived. It is found that except for the fluctuation force field terms, these equations are similar to the corresponding equations obtained by using the influence functional method (IFM) with the linear harmonic approximation. The differences between the fluctuation force fields can be partially eliminated by utilizing the arbitrariness of the definition of the fluctuation force field in IFM.
  
  

• Nonlinear Langevin equation of critical fluctuation in the chiral phase transition
  (T. Koide, M. Maruyama)

  By applying the projection operator method to the Nambu-Jona-Lasinio model, a nonlinear Langevin equation of critical fluctuation in the chiral phase transition is derived. The equation expresses the relaxation process of quark-antiquark condensate near the critical temperature. It is found that the critical slowing down and the thermalization can be described in terms of the linear term. We are investigating the role of the nonlinear term, which is related to the mode coupling theory.
  
  

(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 is studied by using the antisymmetrized molecular dynamics. 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. Temperature and pressure are extracted from this ensemble and caloric curves are constructed. The present work is the first time that a microscopic dynamical model which describes nuclear reactions is directly applied to get the nuclear caloric curve. The obtained constant pressure caloric curves clearly show the characteristic feature of the liquid gas phase transition, namely, plateau or backbending (negative heat capacity) which is expected for the phase transition in finite systems.
  
  

• Isospin fractionation and isoscaling in dynamical nuclear collisions
  (A. Ono, P. Danielewicz, W.A. Friedman, W.G. Lynch, and M.B. Tsang)

  Isoscaling is found to hold for fragment yields in the antisymmetrized molecular dynamics (AMD) simulations for collisions of calcium isotopes at 35 MeV/nucleon. This suggests the applicability of statistical considerations to the dynamical fragment emission. The observed linear relationship between the isoscaling parameters and the isospin asymmetry of fragments supports the above suggestion. The slope of this linear function yields information about the symmetry energy in low density region where multifragmentation occurs.
  
  

(VII) MICROSCOPIC THEORIES OF NUCLEAR COLLECTIVE MOTION

• Nuclear collective tunneling between Hartree states
  (T. Kohmura, M. Maruyama, and Y. Hashimoto)

  The nuclear collective tunneling between the Hartree states is formulated. We reform the field Hamiltonian used in the Hartree calculations into the Hamiltonian effective for the collective tunneling. For the residual interaction of s and d shell nuclei, we employs the quadrupole-quadrupole interaction which is expressed in terms of the operators that constitute SU(5) algebra. A real-time description for the collective tunneling is developed by using an adiabatic mean field model.
  
  

• Time-dependent-Hartree-Fock calculations in real time and real space
  (T. Nakatsukasa and K. Yabana)

  The Skyrme energy functional is convenient for calculations in real space because of its local nature. We studied nuclear response functions using the time-dependent version of the Skyrme energy functional. First, the ground state is constructed with the imaginary-time method, then, an external field is applied, and the time development of the wave function is calculated in the three-dimensional lattice space. In order to take into account the continuum effects, we use the absorbing-boundary-condition method and an adaptive-coordinate space. Experimental data of the giant dipole resonances (GDR) for light deformed nuclei are reasonably reproduced and we give a prediction for properties of GDR at the neutron drip lines.
  
  

• Shape-coexistence phenomena studied with the adiabatic self-consistent collective coordinate method
  (M. Kobayasi, T. Nakatsukasa, M. Matsuo, and K. Matsuyanagi)

  We studied properties of an exactly solvable multi-O(4)-model to discuss shape mixing of prolate and oblate potential minima. The adiabatic self-consistent coordinate (ASCC) theory provides us with optimal collective coordinates which are determined by the Hamiltonian's dynamics itself. We have calculated collective mass parameters and found that the cranking mass parameter is very much different from that of the ASCC. We also quantized the obtained collective Hamiltonian. The ASCC reproduces the exact quantum spectra and transition strengths.

• Elementary excitations in high-spin superdeformed band ¹⁵²Dy
  (T. Nakatsukasa)

  ¹⁵²Dy is one of a few cases for which spin values and excitation energies of the ground-state superdeformed band were measured. Recently, gamma-rays from an excited superdeformed band decaying to the ground-state superdeformed band have been also observed. Now we are able to estimate the experimental routhians (excitation energies in the rotating frame) and transition strengths. This is a good opportunity to test the prediction of the quasiparticle-random-phase-approximation in the rotating frame made by Nakatsukasa, Matsuyanagi, Mizutori, and Nazarewicz (Phys. Lett. B343 (1995) 19). The data turn out to be consistent with the interpretation of the rapidly rotating K=0 octupole vibration built on the superdeformed ground state.
  
  

(VIII) QUANTUM REACTION THEORIES OF A FEW-BODY MODEL

• Absorbing-boundary-condition method for breakup reactions of deuteron
  (M. Ueda, K. Yabana, and T. Nakatsukasa)

  Absorbing-boundary-condition approach to nuclear breakup reactions is investigated for the system of d+⁵⁸Ni. An absorbing potential outside the physical area simulates the outgoing boundary condition for scattered waves. No virtual states such as discretized continuum channels need to be introduced in the method. Results with the absorbing boundary condition accurately coincide with those with the existing method which utilizes discretized continuum channels.
  
  

(IX) Aomic and molecular physics

• Electronic dynamics of molecular elementary processes
  (T. Nakatsukasa and K. Yabana)

  We study photoabsorption and photoelectron processes of molecules using the time-dependent density-functional theory (TDDFT) on the three-dimensional real space. We have improved our programs and studied photoabsorption cross sections of hydrocarbon isomer molecules, C₃H₆ (cyclopropane and propylene). Our calculation succeeded to reproduce isomer effects and gave an interpretation of their origin.
  
  

Publications

• Fusion from an excited state
  S. Kimura and N. Takigawa, Phys. Rev. C 66 (2002) 024603 (8 pages).
  
  
• Influence of tunneling on electron screening in low energy nuclear reactions in laboratories
  S. Kimura, N. Takigawa, M. Abe, and D.M. Brink, Phys. Rev. C 67 (2003) 022801(R) (5 pages).
  
  
• Meson mixing amplitudes in asymmetric nuclear matter
  Y. Mori and K. Saito, Phys. Lett. B 552 (2003) 21-28.
  
  
• Projection operator approach to Langevin equations in φ⁴ theory
  T. Koide, M. Maruyama, and F. Takagi, Prog. Theor. Phys. 107 (2002) 1001-1035.
  
  
• Sequential decay distortion of Goldhaber model widths for spectator fragments
  Y.G. Ma, R. Wada, K. Hagel, M. Murray, J.S. Wang, L.J. Qin, A. Makeev, P. Smith, J.B. Natowitz, and A. Ono, Phys. Rev. C 65 (2002) 051602 (4 pages).
  
  
• Compatibility of localized wave packets and unrestricted single particle dynamics for cluster formation
  A. Ono, S. Hudan, A. Chbihi, and J.D. Frankland, Phys. Rev. C 66 (2002) 014603 (15 pages).
  
  
• Compatibility of the Localized Wave Packets and the Unrestricted Single Particle Dynamics for the Cluster Formation in Nuclear Collisions
  A. Ono, S. Hudan, A. Chbihi, and J.D. Frankland, Proceedings of International Symposium on Clustering Aspects of Quamtum Many-Body Systems, edited by A. Ohnishi, N. Itagaki, Y. Kanada-En'yo, and K. Kato, (World Scientific, Singapore, 2002) pp. 197-200.
  
  
• AMD Study of the EOS of Asymmetric Nuclear Matter in Nuclear Collisions
  A. Ono, Prog. Theor. Phys. Supp. 146 (2002) 378-387.
  
  
• Absorbing Boundary Condition Approach for Breakup Reactions of Halo Nuclei
  M. Ueda, K. Yabana, and T. Nakatsukasa, Proceedings of 4th Italy-Japan Symposium on Perspective in Heavy Ion Physics, edited by K. Yoshida, S. Kubono, I. Tanihata, and C. Signorini, (World Scientific, Singapore, 2002) pp. 69-76.
  
  
• 3D Real-Space Calculation of the Continuum Response
  T. Nakatsukasa and K. Yabana, Prog. Theor. Phys. Suppl. 146 (2002) 447-451.
  
  
• Absorbing Boundary Condition Approach for Breakup Reactions of Halo Nuclei
  K. Yabana, M. Ueda, and T. Nakatsukasa, Prog. Theor. Phys. Suppl. 146 (2002) 329-337.
  
  
• Atomic Spectra in Helium Bubble
  T. Nakatsukasa, K. Yabana, and G.F. Bertsch, Proceedings of the International Symposium on Clustering Aspects of Quantum Many-Body Systems, edited by A. Ohnishi, N. Itagaki, Y. Kanada-En'yo, and K. Kato, (World Scientific, Singapore, 2002) pp. 289-292.
  
  
• Application of Absorbing Boundary Condition to Nuclear Breakup Reactions
  M. Ueda, K. Yabana, and T. Nakatsukasa, Phys. Rev. C 67 (2003) 014606 (9 pages).

Doctor Thesis (March 2003)

• Theoretical study of screening effects by bound electrons on low energy nuclear reactions
  Sachie Kimura
  
  
• Theoretical study of the bremsstrahlung in alpha decay with a realistic potential
  Yoshiharu Nozawa
  
  

Master Thesis (March 2003)

• Nuclear liquid-gas phase transition studied with antisymmetrized molecular dynamics
  Takuya Furuta
  
  
• Study of medium effects on nuclear interaction by using polarized proton-nucleus quasi-elastic scattering
  Yoshiharu Mori
  
  
• Coupled-channels calculations of the fusion cross section between two heavy-nuclei using a double-folding potential
  Takayuki Takehi