Nuclear Theory Group

Tohoku University

ANNUAL REPORT 2000

Academic Staff

Research Activities

(I) PHYSICS OF HADRONS AND NUCLEI AT HIGH ENERGIES

• Parametric amplification of mesonic fields in the late stage of high energy heavy ion collisions
  (M. Ishihara and F. Takagi)

  We studied the effects of friction and expansion of the system on possible occurrence of parametric amplification of mesonic fields in the late stage of high energy heavy ion collisions within the framework of the linear sigma model.
  
  

• Chiral phase transition at high temperature and density in the QCD-like theory
  (O. Kiriyama, M. Maruyama and F. Takagi)

  Chiral phase transition at finite temperature T and/or finite chemical potential μ was studied using the QCD-like theory with a variational approach. Modified Cornwall-Jackiw-Tomboulis effective potential was derived for generally nonzero current quark mass. We then calculated the effective potential at finite T and/or μ in the chiral limit to investigate the phase structure. We found a tricritical point at T=107MeV and μ =210 MeV. It separates the second order phase transition at higher T and lower μ and the first order transition at higher μ and lower T.
  
  

• Effects of current quark mass on the chiral phase transition of QCD in the improved ladder approximation
  (O. Kiriyama, M. Maruyama and F. Takagi)

  Effects of the current quark mass on the chiral phase transition of QCD was investigated in the improved ladder approximation. We used the Schwinger-Dyson equation to modify the Cornwall-Jackiw-Tomboulis effective potential. The relevant critical exponents and the masses of the scalar and the pseudoscalar mesons at finite temperature were calculated. It was found that the effect of finite current quark mass is significant in the high temperature phase.
  
  

• A new expansion of the Heisenberg equation of motion with projection operator
  (T. Koide and M. Maruyama)

  We derived a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shing$\bar{\rm u}$. In their method, a certain restriction is imposed on the initial state. As a result, one cannot prepare arbitrary initial states. Relaxing this restriction we generalized the projection operator method in the case of a Hamiltonian both with and without explicit time dependence.

• Projection operator approach to Langevin equations in φ ⁴ theory
  (T. Koide, M. Maruyama and F.Takagi)

  We apply the projection operator method (POM) to φ ⁴ theory and derive both quantum and semiclassical equations of motion for the soft modes. These equations have no time-convolution integral term in sharp contrast with other popular results obtained from the influence functional method (IFM) and the closed time path method. However, except for the fluctuation force terms, those equations from POM are similar to the corresponding equations in IFM with the linear harmonic approximation. The quantum equation of motion in POM can be regarded as a kind of quantum Langevin equation where the fluctuation force is given in terms of the operators of the hard modes. The operators are then replaced with c-numbers by some procedure to obtain a semiclassical Langevin equation.
  
  

• Mass and wave function renormalizations in the projection operator method
  (M. Maruyama)

  We studied the time evolution of quantum systems in the projection operator method. Mass and wave function renormalizations were carried out in the Heisenberg equation of motion. We found that the results coincide with the on-mass-shell values of the self-energy and its derivative which are calculated by the Feynman rule. It was also found that the initial divergence which remains at the initial time after mass renormalization plays a important role in carrying out wave function renormalization.
  
  

• Color superconducting phase of QCD at high density
  (K. Sato, O. Kiriyama, M. Maruyama and F. Takagi)

  Color superconducting phase of QCD at high baryon number density was studied using the effective potential approach.
  
  

• Meson-baryon couplings and magnetic moments of the octet baryons in the quark-diquark picture
  (M. Iwasaki and F. Takagi)

  The quark-diquark picture of the J ^P = (1/2)⁺ octet baryons was used to study the SU(3) structure of the coupling constants between the octet baryons and the J ^P= 0^- octet mesons. The same picture was also used to calculate the magnetic moment of the octet baryons. We consider the spin-flavor configurations with both the scalar and the axial vector diquarks.
  
  

• Nucleation of hadronic bubbles from the supercooled quark-gluon plasma
  (F. Takagi)

  We studied nucleation of hadronic bubbles from supercooled quark-gluon plasma which may be formed in high energy heavy ion collisions. We found the possibility that the critical radius of the hadron droplet may be a constant independent of the temperature by considering the fluctuations of energy density, the energy conservation and the temperature change in the region of nucleation. This leads to a new scenario which is quite different from the standard Csernai-Kapusta scenario.
  
  

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

• Applicability of the orientation average formula in heavy-ion fusion reactions of deformed nuclei
  (N. Takigawa, Tamanna Rumin and K. Hagino)

  In heavy-ion fusion reactions involving a well deformed nucleus, one often assumes that the orientation of the target nucleus does not change during the reaction. We studied the accuracy of this procedure by analyzing the excitation function of the fusion cross section and the fusion barrier distribution in the reactions of ¹⁵⁴Sm target with various projectiles ranging from ¹²C to ⁴⁰Ar. It was found that the approximation gradually looses its accuracy with increasing charge product of the projectile and target nuclei because of the effects of finite excitation energy of the target nucleus. We also studied the relevance of such inaccuracy in analyzing the experimental data.
  
  

• Structure of intermediate states in dynamical collective state transitions of a nuclear system
  (H. Ohta, T. Kohmura, Y. Hashimoto, T. Kobayashi and M. Maruyama)

  We studied the dynamical collective state transitions between isolated Hartree minima with different symmetries. The time evolution of the transitons was calculated by diagonalizing the Hamiltonian. We applied our method to the tunneling process between the two lowest states with different deformations in ²⁸Si. It was found that the intermediate states are described by using multi-Slater determinants.
  
  

(III) TRANSPORT PHENOMENA

• Quantum diffusion process along a parabolic potential barrier
  (N. Takigawa, S. Kimura and S. Ayik)

  We studied the connection between dissipation and fluctuation under various circumstances for a large amplitude collective motion coupled to environments by using a linear response theory. Our method naturally leads to the well known fluctuation-dissipation theorem, i.e. the Einstein relation, and its generalization which takes both the thermal and quantum fluctuations into account when the bare potential for the collective motion is flat or a parabolic well, respectively. The same formalism has then been used to discuss the connection between the moments of the response and the correlation functions in the case, where the bare potential is a parabolic potential barrier. The analysis has been pursued in a model independent way as far as possible. When it becomes impossible, the analysis has been performed for the case of Ohmic dissipation of the Caldeira-Leggett model by introducing a cut-off frequency. We found that the frequency cut-off only slightly affects the dissipation as long as the cut-off frequency is much larger than the potential curvature. We have also shown that the frequency cut-off does not influence the fluctuation dissipation theorem for the diffusion in a flat as well as a parabolic well potentials, while it significantly influences the fluctuation property when the diffusion takes place along a parabolic potential barrier. Especially, we found a large deviation from the known fluctuation-dissipation theorem except for the cases where the temperature is much higher than the curvature of the potential barrier.

(IV)ASTROPHYSICAL NUCLEAR REACTIONS

• Screening effects on nuclear reactions at extremely low energies
  (N. Takigawa, S. Kimura and D.M. Brink)

  We studied the screening effects by a bound electron in the target atom on nuclear reactions at extremely low energies based on the semiclassical mean field theory for quantum tunneling in multi-dimensional systems. We studied the properties of the screening potential and the amount of the screening energy for D+³He²⁺, ³He⁺+d, D+d reactions at several bombarding energies. We found the followings: (1) The screening energy matches with that in the sudden tunneling limit when the bombarding energy is high. (2) The screening effects cannot be expressed by a constant shift of the potential barrier if the incident energy is so low as to make the tunneling region comparable with the Bohr radius of the unified atom or even larger. (3) The standard prescription to estimate the screening energy from the study of only classically allowed region gives a correct estimate of the screening energy only when the bombarding energy is relatively high, so that the tunneling region is much smaller than the Bohr radius of the unified atom. (4) One can expect a large screening energy, which could even exceed the the value in the adiabatic limit, if the electron initially starts from one of the excited states in the sense of the unified atom.

(V) METALCLUSTER PHYSICS

• Geometrical configurations of ions in light Na clusters and the connection to photo-absorption spectrum
  (K. Yoshizaki, A. Ono, M. Abe and N. Takigawa)

  We performed the first principle molecular dynamics calculations for Na_n, n being up to 21, clusters at zero temperature and at 370 Kelvin, which corresponds to the melting temperature of the bulk Na. We then extracted the deformation parameters (Hill-Wheeler parameters) for those light Na clusters and found that they well agree with the deformation parameters suggested from the peak positions seen in the experimantal data of photo-absorption spectrum. We also found that the results of the first principle calculations differ significantly from those of the simplified calculations of the so called empirical molecular dynamics. The first principle molecular dymanics at 370 K shows that Na₁₁ cluster dissociates into Na₃+Na₈ and gives a possible candidate of the dissociation instability of Na₁₁ cluster suggested by experimental data.

(VI) NUCLEAR STRUCTURE

• Role of chaos in the decay out of a superdeformed band
  (N. Takigawa, A.J. Sargeant, M.S. Hussein, M.P. Pato and M. Ueda)

  We studied the attenuation of the intra-band intensity of a super-deformed band which results from mixing with normally deformed configurations based on a reaction theory. We have shown that the sharp increase of the attenuation is mostly due to the tunneling through a spin dependent potential barrier and not to the chaotic nature of the normally deformed states.

(VII) MICROSCOPIC STUDY OF INTERMEDIATE ENERGY HEAVY ION REACTIONS

• Improvement of wave packet treatment in molecular dynamics
  (A. Ono)

  The quantum branching process due to the wave packet diffusion effect in antisymmetrized molecular dynamics (AMD) was improved by formulating a method to take account of the shrinking of wave packets in some phase space directions. This improvement makes AMD almost as precise as mean field models for the single particle dynamics, keeping the advantage of AMD for the fragmentation description.
  
  

• AMD analysis of Xe+Sn multifragmentation reaction
  (A. Ono, S. Hudan and A. Chbihi)

  We performed the AMD calculation for Xe+Sn central collision at 50 MeV/u, and made detailed comparison with the data taken by INDRA detector at GANIL. It was found that the multifragmentation data are well reproduced by the improvement of the wave packet treatment.
  
  

• Isoscaling in Ca+Ca collisions
  (A. Ono and B. Tsang)

  AMD results for the ⁴⁰Ca+⁴⁰Ca and ⁶⁰Ca+⁶⁰Ca central collisions were analyzed in order to investigate the isocaling property. Clear scaling property was obtained in the ratio of the fragment yields Y₁(Z,N)/Y₂(Z,N) for these two collisions with different isospin, which suggests the isospin fractionation taking place in the nuclear collisions with high isospin asymmetry.

Publications

• Chiral Phase Transition at High Temperature and Density in the QCD-like Theory
  O. Kiriyama, M. Maruyama and F. Takagi, Phys. Rev. D62 (2000) 105008.
  
  
• Parametric Amplification with Friction in Heavy Ion Collisions
  M. Ishihara, Phys. Rev. C62 (2000) 054908.
  
  
• Coulomb interaction between a spherical and a deformed nuclei
  Noboru Takigawa, Tamanna Rumin and Naoki Ihara, Phys. Rev. C 61 (2000) 044607-1-6.
  
  
• The structure of superheavy elements newly discovered in the reaction of ⁸⁶Kr with ²⁰⁸Pb
  J. Meng and N.Takigawa, Phys. Rev. C61 (2000) 064319-1-7.
  
  
• Screening Effects by Bound Electrons in Nuclear Reactions at Extremely Low Energies
  N. Takigawa and S. Kimura, Proceedings of the 1st workshop on Neutrino Oscillations and Their Origin, Feb.11-13, 2000, Mt. Fuji, Japan, Universal Academy Press, Frontiers Science Series No.35, eds. Y. Suzuki, M. Nakahata, M. Shiozawa and K. Kaneyuki, p.227-236.
  
  
• A New Expansion of the Heisenberg Equation of Motion with Projection Operator
  T. Koide and M. Maruyama, Prog. Theor. Phys. 104 (2000), 575.
  
  
• Reaction Mechanisms and Multifragmentation Processes in ⁶⁴Zn+⁵⁸Ni at 35A -- 79A MeV
  R. Wada, K. Hagel, J. Cibor, M. Gonin, Th. Keutgen, M. Murray, J. B. Natowitz, A. Ono, J. C. Stechmeyer, A. Kerambrum, J. C. Ang\'elique, A. Auger, G. Bizard, R. Brou, C. Cabot, E. Crema, D. Cussol, D. Durand, Y. El Masri, P. Eudes, Z. Y. He, S. C. Jeong, C. Lebrun, J. P. Patry, A. P\'eghaire, J. Peter, R. R\'egimbart, E. Rosato, F. Saint-Laurent, B. Tamain, and E. Vient, Phys. Rev. C 62, (2000), 034601.
  
  
• Antisymmetrized Molecular Dynamics Approach to Multifragmentation
  A. Ono, Prog. Theor. Phys. Supp. 140 (2000) 134.
  
  
• Incident-energy dependence of the fragmentation mechanism reflecting the cluster structure of the ¹⁹B nucleus
  H. Takemoto, H. Horiuchi and A. Ono, Phys. Rev. C 63 (2001), 034615.
  
  

Doctor Thesis (March 2001)

• Study of the structure of Na clusters in their ground state and at finite temperatures by first principle molecular dynamics
  Koichi Yoshizaki
  
  
• Effects of Nuclear Intrinsic Degrees of Freedom on Heavy-Ion Fusion Reactions
  Tamanna Rumin