Nuclear Theory Group

Tohoku University

ANNUAL REPORT 2001

Academic Staff

Research Activities

(I) PHYSICS OF HADRONS AND NUCLEI AT HIGH ENERGIES

• Current quark mass effects 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. The infrared behavior of the gluon propagator is modified in terms of an effective running coupling. The analysis is based on a composite operator formalism and a variational approach. We use the Schwinger-Dyson equation to give a normalization condition for the Cornwall-Jackiw-Tomboulis effective potential and to isolate the ultraviolet divergence that appears in the expression for the quark-antiquark condensate. We study the current quark mass effect on the chiral phase transition at finite temperature and/or finite density. We find a smooth crossover for T > 0, μ =0 and a first order phase transition for μ > 0, T=0. 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.
  
  

• 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.
  
  

• Study of QCD Phase Structure by Schwinger-Dyson Equations
  (K. Sato, M. Maruyama and F. Takagi)

  QCD phase structure at finite temperature and finite baryon number density is studied by evaluating simultateously the chiral condensate (the quark-antiquark condensate) and the diquark condensate using a set of Schwinger-Dyson equations. It was found that (i) there is no region in the T- μ plane where both the chiral and the diquark condensates aquire nonvanishing values simultaneously, (ii) the region of broken chiral phase is reduced appreciably at the high density side by the presence of the color superconducting phase at higer density and low temperature, and (iii) diquarks would condense even at very low temperature and density if the quark-antiquark pairs did not condense there.
  
  

• 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 result on the F/D ratios suggests a new higher symmetry.The same picture was also used to calculate the magnetic moments 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.
  
  

• Mass Spectra and the Decay widths of Glueballs in the Flux Tube Model
  (M.Iwasaki and F.Takagi)

  The mass spectra and the decay widths of the glueballs are studied using the flux tube model.
  
  

• 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 of the renormalizations coincide with the on-mass-shell value and its derivative of the self-energy which are calculated by the Feynman rule.
  
  

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

• A new theoretical approach to fusion of heavy-nuclei
  (N. Takigawa, Tamanna Rumin and Takashi Masamoto)

  We developed a new theoretical approach to the fusion between two heavy-nuclei which performs the coupled-channels calculations using the nuclear potential determined based on the double folding procedure with the parameters given by the liquid drop model. We have applied this method to the ⁶⁰ Ni+ ¹⁵⁴ Sm reaction. Since the fission barrier is expected to lie inside the fusion barrier for this system, the fusion cross section calculated in the standard way with the coupled-channels method should be called the barrier transmission cross section rather than the fusion cross section for this system. We found that thus defined barrier transmission cross section well agrees with the total experimental cross section of the fusion-fission like process for this system. This suggests that our new method provides a good estimate of the total fusion fission like process in heavy systems, while a good estimate of the total fusion cross section in lighter systems where the fission barrier lies outside the fusion barrier. Applying this method to the ⁷⁶ Ge+ ¹⁵⁰Nd reaction, we made an estimate of the cross section of the total fusion-fission like process, and found that it is much larger than the observed fusion-evaporation residue cross section suggesting the existence of the extra-push effect in this reaction.
  
  

• Applicability of the orientation average formalism to fusion reactions between heavy nuclei
  (N. Takigawa, Tamanna Rumin and Takashi Masamoto)

  We compared the fusion cross section calculated by the so called orientation average formula with that by the direct numerical integration of the coupled-channels equations for ¹⁶O+¹⁵⁴Sm, ¹⁸⁶W,²³⁸U reactions, and studied the validity of the orientation average formula. We especially examined the role of the excitation energy of the intrinsic motion, and have shown that the validity of the orientation average formalism depends on both the so called adiabaticity parameter λ =ω/ Omega, ω and Omega being the excitation energy of the 2⁺ member of the ground state rotational band and the barrier curvature, respectively, and the product of the atomic numbers of the projectile and the target nuclei representing the strength of the coupling between the relative motion and nuclear rotational excitation.
  
  

• Fusion from an excited state
  (N. Takigawa and S. Kimura)

  We studied the effects of intrinsic degrees of freedom on the barrier transmission probability of a macroscopic variable especially in the case when the intrinsic motion is initially in an excited state based on coupled-channels calculations. We analyzed in detail the dependence of channel-coupling effects on the degree of adiabaticity, the properties of the intrinsic motion such as the number of coupled intrinsic states and the nature of either vibrational or rotational couplings, and the location of the coupling form factor. We have shown that significant transitions from excited states to the ground state take place in low energy region even in the cases, where one would expect almost no non-adiabatic transitions because of the large excitation energy of the intrinsic motion. This suggests the fusion barrier to be renormalized by a tunneling assisted intrinsic transition.
  
  

(III) MICROSCOPIC THEORIES OF NUCLEAR COLLECTIVE MOTION

• Projection Operator Method for Collective Tunneling Transitions
  (T. Kohmura, M. Maruyama and Y. Hashimoto)

  Collective tunneling transitions take place in the case that a system has two nearly degenerate groud states with a slight energy splitting, which provides the time scale of the tunneling. The Liouville equation determines the evolution of the density matrix. We derive an analytical expression for the splitting of energy eigenvalues from a spectral function of the Liouville evolution. We also define the collective tunneling path of a microscopic Hamiltonian.
  
  

• Harmonic Collective Tunneling Oscillations of Nuclei
  (T. Kohmura, M. Maruyama and Y. Hashimoto)

  We investigate the nuclear collective tunneling transition from one Hartree state to another. It is shown that a nuclear system governed by the Hamiltonian symmetric between two Hartree states coherently tunnels back and forth between the two states owing to the residual interaction so that the system makes harmonic tunneling oscillations. An SU(5) model Hamiltonian is presented for the collective tunneling transitions of s and d shell nuclei.
  
  

• Shape-coexistence phenomena studied with ASCC method
  (M. Kobayashi, M. Matsuo, T. Nakatsukasa, and K. Matsuyanagi)

  We studied properties of the multi-O(4)-model Hamiltonian 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 found that the collective coordinates determined by the ASCC method are very much different from the usual assumption, namely the quadrupole degrees of freedom.
  
  

• Nuclear response functions in the continuum
  (T. Nakatsukasa, K. Yabana)

  For drip-line nuclei, the continuum effects are important for describing properties of their structure and reaction. Utilizing the Skyrme energy functional with the absorbing-boundary condition, the continuum response functions are calculated in the three-dimensional coordinate space. Large deformation splitting and soft resonance are predicted for ¹⁴Be.
  
  

(IV)ASTROPHYSICAL NUCLEAR REACTIONS

• Spatially varying potential renormalization by tunneling induced intrinsic transition
  (N. Takigawa, S. Kimura and D.M. Brink)

  We performed a semiclassical mean field analysis of a two-level coupled-channels model for a barrier transmission problem, and have shown that there can occur a strong quantum transition of the intrinsic motion from the excited to the ground states in the tunneling region, leading to a spatially dependent potential renormalization. The transition occurs effectively even in the absence of explicit coupling if the intrinsic motion is not in a pure state prior to the tunneling region because of the time evolution along the imaginary time axis. This suggests the necessity of the dynamical treatment of the electrons in the tunneling region instead of the conventional treatment in terms of a static potential shift in order to properly assess the screening effects by bound target electrons in low energy nuclear reactions in laboratories.
  
  

(V) MICROSCOPIC STUDY OF INTERMEDIATE ENERGY HEAVY ION REACTIONS

• Wave packet treatment in molecular dynamics and expansion dynamics followed by cluster formation
  (A. Ono, S. Hudan, A. Chbihi and J. D. Frankland)

  The quantum branching process due to the wave packet diffusion effect in antisymmetrized molecular dynamics (AMD) was upgraded so that one can respect the coherence of the single particle wave function evolving in the mean field. The quantum branching into Gaussian wave packets with a fixed shape is regarded as the decoherence due to the many-body correlation beyond mean field. We found that the expansion velocity of a slowly expanding big system (central Xe+Sn collision at 50 MeV/nucleon) strongly depends on the strength of the decoherence. The different expansion velocity results in the different cluster size distribution produced from the expanding system. The experimental data are reproduced if we assume a reasonably long time of the single particle coherence in this case.
  
  

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

  AMD results for the ⁴⁰Ca+⁴⁰Ca and ⁶⁰Ca+⁶⁰Ca central collisions at 35 MeV/nucleon were analyzed in order to investigate the isocaling property. Clear scaling property was obtained in the ratio of the primary fragment yields Y₁(Z,N)/Y₂(Z,N) for these two collisions with different isospin, which suggests the isospin fractionation. The AMD calculations were performed with two effective forces which correspond to the same equation of state (EOS) of isospin symmetric nuclear matter but have different density dependence of the symmetry energy. We found that the parameter of the isoscaling depends on the EOS of the asymmetric nuclear matter.
  
  

(VI) REACTIONS OF UNSTABLE NUCLEI

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

  Halo nuclei are characterized by their small separation energy for breakup. We apply the absorbing-boundary-condition method to quantum calculations for breakup reactions of three-body model. Our calculations on ¹¹Be+¹²C indicate that the eikonal approximation breaks down for energy below 50 MeV per nucleon.
  
  

(VII) ATOMIC 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. So far, we have studied photoabsorption cross sections of relatively small molecules; silane, acetylene, ethylene, cyclopropane, and propylene. Our calculation well agrees with recent experiments with synchrotron radiation.
  
  

• Excitation spectra of alkali atoms in superfluid liquid helium
  (T. Nakatsukasa, K. Yabana and G. F. Bertsch)

  Spectroscopic measurements for impurity atoms and molecules immersed in liquid helium have been performed recently. We study effects of helium perturbations on atomic spectra, utilizing the electronic and atomic density functional theory. We show that a statistical treatment of helium configuration gives reasonable line shift and broadening of alkali atoms.

Publications

• Applicability of the orientation average formula in heavy-ion fusion reactions of deformed nuclei
  Tamanna Rumin, K. Hagino and N.Takigawa, Phys. Rev. C 63 (2001) 044603.
  
  
• Attenuation of the intensity within a superdeformed band
  A.J. Sargeant, M.S. Hussein, M.P. Pato, N. Takigawa and M. Ueda, Phys. Rev. C 65 (2002) 024302.
  
  
• Semiclassical Mean Field Theory of Quantum Tunneling in a Coupled System
  N. Takigawa, S. Kimura and D.M. Brink, Soryushiron Kenkyu 104 B9.
  
  
• Current Quark Mass Effects on the Chiral Phase Transition of QCD in the Improved Ladder Approximation
  O. Kiriyama, M. Maruyama and F. Takagi,Phys. Rev. D 63 (2001) 116009.
  
  
• Projection Operator Method for Collective Tunneling Transitions
  T. Kohmura, M. Maruyama, H. Ohta and Y. Hashimoto, Prog. Theor. Phys. 107 (2002) 87.
  
  
• Time Evolution of Quantum Many Body Systems in the Projection Operator Method
  M. Maruyama, AIP Coference Proceedings on Hadrons and Nuclei; First International Symposium, held at Seoul, Korea, editted by Il-T. Cheon, T. Choi, S-W. Wong and S.H. Lee, 594 (2001) 232.
  
  
• Photoabsorption spectra in the continuum of molecules and clusters
  T.~Nakatsukasa and K.~Yabana, J. Chem. Phys. 114 (2001) 2550-2561.
  
  
• 3D Real-Space Calculation of the Continuum Response
  T.~Nakatsukasa and K.~Yabana, Proceedings of the RIKEN Symposium on ``Physics at Drip Lines'', RIKEN Review No.39, edited by H.Sagawa, T.Suzuki, and A.Ozawa, (RIKEN, Wako, 2001), pp. 96-101.
  
  
• Application of density functional theory to line broadening: Cs atoms in liquid helium
  T.~Nakatsukasa, K.~Yabana, and G.~F.~Bertsch, Phys. Rev. A65 (2002) 032512-1-6.
  
  
• Resonance and Continuum States in Weakly Bound Systems
  T.~Nakatsukasa and K.~Yabana, Proceedings of 7th International Spring Seminar on Nuclear Physics ``Challenges of Nuclear Structure'', edited by A. Covello, (World Scientific, Singapore, 2002), pp. 91-98.
  
  

Doctor Thesis (March 2001)

• Study of QCD Phase Structure by Schwinger-Dyson Equations
  Ken-ichi Sato
  
  

Master Thesis (March 2001)

• Fusion of heavy nuclei at energies near the Coulomb barrier
  Takashi Masamoto