Nuclear Theory Group ANNUAL REPORT 2005

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Nuclear Theory Group

Tohoku University

ANNUAL REPORT 2005

Academic Staff

Professor	Noboru Takigawa
Associate Professor	Kouichi Hagino
Assistant Professors	Masahiro Maruyama, Akira Ono(on leave of absence, the address in 2005: National Superconducting Cyslotron Laboratory, Michigan State University)
Secretary	Miyuki Matsushita
Research Students	Tomomasa Asano, Zakarya Mohamed(from September, 2005)
Graduate Students	Takuya Furuta, and Takayuki Takehi (D3) Yasuo Kato, Nyein Wink Lwin,and Kouhei Washiyama (D2) Muhammad Zamrun F (D1) Futoshi Minato(M2) Akihiro Suda and Yoshikazu Watanabe (M1)

Research Activities

(I) Low energy heavy-ion collisions

1.Quantum diffusion in low energy heavy-ion collisions numerical similation of a non-Markovian diffusion process
(N. Takigawa and K. Washiyama)

In order to apply the recently developed quantum diffusion theory to realistic problems of the synthesis of superheavy elements, we have developed a numerical code to handle a colored noise, and tested its accuracy in the limiting case of the diffusion along a parabolic barrier, where the barrier crossing probability can be analytically obtained.

2. Quantum diffusion in low energy heavy-ion collisions: Ito vs. Stratonovich type stochastic differential equations
(N. Takigawa and T. Asano)

In connection with the Langevin equation approach to the formation of a heavy and/or a super heavy element, we examined the difference of handling the Langevin equation as a stochastic differential equation either by an Ito-type or a Stratonovich type stochastic integration.

3. The effects of shape transition and shape coexistence on subbarrier fusion reactions
(N. Takigawa, Zakarya Mohamed Mohamed Mahmoud, Muhammad Zamrun F., and K. Hagino)

In order to test the validity and implication of understanding the structure of Ge isotopes from the point of view of shape transitions and shape coexistence, we determined the transition matrix elements needed in coupled-channels calculations for fusion reactions from the experimental data of Coulomb excitation. The preliminary calculations for the fusion reactions between two ⁷⁴Ge nuclei reproduce the experimental fusion excitation function in a comparable quality as that by a vibrational coupling model including multi-phonons.

4. No-recoil approximation to knock-on exchange potential in the double folding model for heavy-ion collisions
(K. Hagino, T. Takehi, and N. Takigawa)

We proposed the no-recoil approximation, which is valid for heavy systems, for a double folding nucleus-nucleus potential. With this approximation, the non-local knock-on exchange contribution becomes a local form. We discussed the applicability of this approximation for the elastic scattering of ⁶Li + ⁴⁰Ca system. We found that, for this system and heavier, the no-recoil approximation works as good as another widely used local approximation which employs a local plane wave for the relative motion between the colliding nuclei. We also compared the results of the no-recoil calculations with those of the zero-range approximation often used to handle the knock-on exchange effect.

5. Probing surface diffuseness of nucleus-nucleus potential with quasielastic scattering at deep sub-barrier energies
(K. Hagino, K. Washiyama, and M. Dasgupta)

We performed a systematic study on the surface property of nucleus-nucleus potential in heavy-ion reactions using large-angle quasielastic scattering at energies well below the Coulomb barrier. At these energies, the quasielastic scattering can be well described by a single-channel potential model. Exploiting this fact, we pointed out that systems which involve spherical nuclei require the diffuseness parameter of around 0.60 fm in order to fit the experimental data, while systems with a deformed target between 0.8 fm and 1.1 fm.

6. Comprehensive study of reaction mechanisms for the ⁹Be+¹⁴⁴Sm system at near- and sub-barrier energies
(K. Hagino, P.R.S. Gomes, E. Crema, M. Trotta, L.C. Chamon, M. Dasgupta, and D.J. Hinde)

We performed coupled-channels calculations for complete fusion cross sections for the ⁹Be+¹⁴⁴Sm system in order to deduce the suppression factor attributed to the breakup of ⁹Be nucleus. For this system, complete and incomplete fusion cross sections have been recently measured at near-barrier energies, using the delayed X-ray detection technique. The deduced suppression factor appeared consistent with measured incomplete fusion product yields. At about 10%, it is considerably smaller than the value of 30% previously found for a ²⁰⁸Pb target.

7. Sub-barrier fusion cross sections with energy density formalism
(Muhammad Zamrun F., K. Hagino, and N. Takigawa)

We discussed the applicability of the energy density formalism (EDF) in heavy-ion fusion reactions at sub-barrier energies. For this purpose, we calculated the fusion excitation function and fusion barrier distribution for reactions of ¹⁶O with ^154,144Sm,¹⁸⁶W and ²⁰⁸Pb with the coupled-channels method using the potential given by the energy density formalism. We also discussed the effect of saturation property on the fusion cross section for the reaction between two ⁶⁴Ni nuclei, in connection to the so called steep fall-off phenomenon.

8. Dependence on the dissipation tensor of multi-modal nuclear fission
(T. Asano, T. Wada, M. Ohta, S. Yamaji, and H. Nakahara)

A multi-dimensional Langevin equation was applied for the study of the multi-modal nuclear fission in actinide region. Two kinds of dissipation tensors, the wall-and-window formula and the wall formula, were used to investigate the dynamical effects of nuclear dissipation. The mass distribution and the total kinetic energy distribution of the fission fragments were calculated for ²⁶⁴Fm with these dissipation tensors. It was found that the dissipation tensor plays important roles in determining the fission paths. We obtained drastically different mass distributions by applying different models for nuclear friction.

(II)Nuclear reactions in matter

1. The effects of quantum motion of the target deutron
(N. Takigawa and Y. Kato)

In order to find a still missing explanation of the experimentally reported huge enhancement of the d+d reaction rates in matter and their strong host matter dependence, we developed a coupled-channels formalism to take the effects of quantum motion of the target deutron in an interstitial site into account.

(III) Structure of neutron-rich nuclei

1. Pairing correlations in nuclei on the neutron-drip line
(K. Hagino and H. Sagawa)

Paring correlations in weakly bound nuclei on the edge of neutron drip line was studied by using a three-body model. A density-dependent contact interaction was employed to calculate the ground state of halo nuclei ⁶He and ¹¹Li, as well as a skin nucleus ²⁴O. Dipole excitations in these nuclei were also studied within the same model. We pointed out that the di-neutron type correlation plays a dominant role in the halo nuclei ⁶He and ¹¹Li having the coupled spin of the two neutrons S=0, while the correlation similar to the BCS type is important in ²⁴O. Contributions of the spin S=1 and S=0 configurations were separately discussed in the low energy dipole excitations.

2. Role of low-l component in deformed wave functions near the continuum threshold
(K. Hagino and K. Yoshida)

The structure of deformed single-particle wave functions in the vicinity of zero energy limit was studied using a schematic model with a quadrupole deformed finite square-well potential. For this purpose, we expanded the single-particle wave functions in multipoles and sought for the bound state and the Gamow resonance solutions. We found that, for the K^π=0⁺ states, where K is the z-component of the orbital angular momentum, the probability of each multipole components in the deformed wave function is connected between the negative energy and the positive energy regions asymptotically, although it has a discontinuity around the threshold. This implies that the K^π=0⁺ resonant level exists physically unless the l=0 component is inherently large when extrapolated to the well bound region. The dependence of the multipole components on deformation was also discussed.

3. Deformation parameter for diffuse density
(K. Hagino, N.W. Lwin and M. Yamagami)

In extracting deformation parameters from multipole moments for deformed nuclei, one commonly uses the formulas which are based on a sharp-cut density distribution. We discussed a possible ambiguity for this procedure and clarify the role of diffuseness parameter of the density distribution. For this purpose, we used a deformed Woods-Saxon density as well as a density distribution obtained from the self-consistent relativistic mean-field (RMF) model. We showed that the formula using a root-mean-square radius instead of a sharp-cut radius requires a large correction due to a finite surface diffuseness parameter even for stable nuclei. An implication to neutron-rich nuclei was also discussed.

4. Constrained Skyrme-Hartree-Fock calculation for neutron-rich nuclei
(Nyein Wink Lwin, K. Hagino, and N. Takigawa)

We performed constrained Hartree-Fock calculations with Skyrme interaction using the 3D mesh method. We introduced a double constraint both on the proton and the neutron quadrupole moments for the ¹⁶C nucleus. We considered the configuration where the symmetry axis is parallel between the proton and neutron, as well as the configuration where the symmetry axes are perpendicular to each other.

(IV) Neutrino-nucleus reactions

1. Neutrino-nucleus reactions in a supernova environment
(F. Minato, K. Hagino, A.B. Balantekin, and N. Takigawa)

We discussed the effect of finite temperature on neutrino-nucleus reactions at a r-process site. To this end, we employed the thermal randam phase approximation (RPA) for the charged current reaction, (ν_e,e^-). We applied this method to ⁴⁰Ca(ν_e,e^-)⁴⁰Sc and ²⁰⁸Pb(ν_e,e^-)²⁰⁸Bi reactions. We found a large temperature effect for the former reaction, while the finite temperature does not play an important role in the latter. An implication to neutrino induced fission was also discussed.

2. Effect of electronic environment on neutrino-nucleus reactions at a r-process site
(F. Minato, K. Hagino, A.B. Balantekin, and N. Takigawa)

The charged-current neutrino-nucleus reactions produce an electron or positron in the final state. We discussed the effect of electron plasma in a core-collapse supernova environment on the final state interaction between the outgoing lepton and a daughter nucleus. To this end, we used the Debye-Huckel theory in order to estimate the screened potential between the electron and the daughter nucleus. We also discussed the Pauli blocking effect due to the environmental electrons. We found that both the effects hinder the cross sections of neutrino-nucleus reaction, especially at low incident energies.

(V) Dynamics and thermodynamics in many-nucleon systems

1. 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. The formula to extract the temperature (form the kinetic energy of gaseous nucleons) and its consistency with the AMD dynamics were carefully considered. The extracted temperature was found to be quite robust under the condition with which the formula is expected to be valid. The nuclear liquid-gas phase transition in the AMD description was finally confirmed.

2. Isospin fractionation in equilibrium
(T. Furuta and A. Ono)

Isospin fractionation was studied by constructing microcanonical ensembles for finite nuclear many-body systems within the framework of AMD. By comparing the systems with different proton and neutron contents, the isoscaling relation and the fractionation effect were observed.

3. Symmetry energy effects in fragment isospin composition
(A. Ono, P. Danielewicz, W.A. Friedman, W.G. Lynch, M.B. Tsang)

The antisymmetrized molecular dynamics (AMD) simulations suggest that the isospin composition of fragments produced dynamically in multifragmentation reactions is basically governed by the symmetry energy of low-density uniform nuclear matter. The effect of the statistical secondary decay of the excited fragments was studied, and it was found that the symmetry energy effect still remains in the fragment isospin composition, though the effect in the isoscaling parameter seems a very delicate problem.

4. Rare isotope production by projectile fragmentation
(M. Mocho, M.B. Tsang, A. Ono)

The AMD simulations were performed to study the production mechanism of rare isotopes from the projectile fragmentation of Ca and Ni isotopes. By taking account of the statistical decays of excited primary fragments, the experimental data of the final yields were reproduced reasonably well. Furthermore, the yields of neutron rich fragments from neutron rich projectiles were found to be sensitive to the level densities of neutron rich nuclei.

5. Cluster formation process in antisymmetrized molecular dynamics
(A. Ono, P. Danielewicz, W.G. Lynch)

The AMD model was extended by taking into account the direct formation of light clusters such as deuterons and α particles as an effect of the residual nucleon-nucleon interaction. The probability of the light-cluster formation was formulated based on the impulse approximation and by consistently avoiding the overcounting issue. A preliminary calculation shows that the light-cluster formation process has a drastic effect on the relative yields of light clusters.

Publications

Quantum statistical effects on fusion dynamics of heavy ions
S. Ayik, B. Yilmaz, A. Gokalp, O. Yilmaz and N. Takigawa,
Phys. Rev. C 71 (2005) 054611-1-8
Surface diffuseness anomaly in heavy-ion potentials for large-angle quasielastic scattering
K. Hagino, T. Takehi, A.B. Balantekin, and N. Takigawa,
Phys. Rev. C 71 (2005) 044612/1-4.
Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations
K. Hagino and H. Sagawa,
Phys. Rev. C 70 (2005) 044302/1-5.
Absence of structure in the ^20,22Ne + ¹¹⁸Sn quasi-elastic barrier distribution
E. Piasecki, L. Swiderski, P. Czosnyka, M. Kowalczyk, K. Piaseki, M. Witecki, T. Czosnyka, J. Jastrzebski, A. Kordyasz, M. Kisielinski, T. Krogulski, M. Mutterer, S. Khlebnikov, W.H. Trzaska, K. Hagino, and N. Rowley,
Phys. Lett.B 615 (2005) 55-60.
Study of fine structure in the proton radioactivity of ¹⁴⁶Tm
J. C. Batchelder, M. Tantawy, C. R. Bingham, M. Danchev, D. J. Fong, T. N. Ginter, C. J. Gross, R. Grzywacz, K. Hagino, J. H. Hamilton, M. Karny, W. Krolas, C. Mazzocchi, A. Piechaczek, A. V. Ramayya, K. P. Rykaczewski, A. Stolz, J. A. Winger, C. -H. Yu and E. F. Zganjar,
Euro. Phys. J. A 25 (2005) 149-150.
Quasi-elastic barrier distribution as a tool for investigating unstable nuclei
K. Hagino and N. Rowley,
Brazilian J. of Phys. 35 (2005) 890-893.
Pairing correlations in nuclei on the neutron-drip line
K. Hagino and H. Sagawa,
Phys. Rev. C 72 (2005) 044321/1-6.
Nuclear structure studies at the proton drip line via proton radioactivity studies
C.R.Bingham, M.N.Tantawy, J.C.Batchelder, M.Danchev, T.N.Ginter, C.J.Gross, D.J.Fong, R.Grzywacz, K.Hagino, J.H.Hamilton, M.Karny, W.Krolas, C.Mazzocchi, A.Piechaczek, A.V.Ramayya, K.Rykaczewski, A.Stolz, J.A.Winger, C.-H.Yu, and E.F.Zganjar,
Nucl. Instrum. Methods Phys. Res. B 241 (2005) 185-189.
Structure of rare-earth nuclei around the proton drip line
K. P. Rykaczewski, R. K. Grzywacz, C. R. Bingham, M. Danchev, C. Mazzocchi, M. N. Tantawy, C. J. Gross, C. H. Yu, J. C. Batchelder, M. Karny, W. Krolas, D. Fong, J. H. Hamilton, A. V. Ramayya, A. Piechaczek, E. Zganjar, J. A. Winger, T. N. Ginter, A. Stolz, and K. Hagino,
AIP Conf. Proc. 764 (2005) 223-228.
Role of low-l component in deformed wave functions near the continuum threshold
K. Yoshida and K. Hagino,
Phys. Rev. C 72 (2005)064311/1-6.
An extra push from entrance-channel effects
N. Rowley, N. Grar, and K. Hagino,
Phys. Lett. B 632 (2006) 243-246.
Disentangling the reaction mechanisms of weakly bound nuclei
P.R.S. Gomes, I. Padron, E. Crema, O.A. Capurrod, J.O. Fernandez Niellod, G.V. Marti, A. Arazi, M. Trotta, J. Lubian, M.E. Ortega, A.J. Pacheco, M.D. Rodriguez, J.E. Testoni, R.M. Anjos, L.C. Chamon, M. Dasgupta, D.J. Hinde and K. Hagino,
Phys. Lett. B 634 (2006) 356-361.
Systematic of isomeric configurations in N=77 odd-Z isotones near the proton drip line
M.N. Tantawy, C.R. Bingham, K.P. Rykaczewski, J.C. Batchelder, W. Krolas, M. Danchev, D. Fong, T.N. Ginter, C.J. Gross, R. Grzywacz, K. Hagino, J.H. Hamilton, D.J. Hartley, M. Karny, K. Li, C. Mazzocchi, A. Piechaczek, A.V. Ramayya, K. Rykaczewski, D. Shapira, A. Stolz, J.A. Winger, C.-H. Yu, and E.F. Zganjar,
Phys. Rev. C 73 (2006) 024316/1-17.
Probing surface diffuseness of nucleus-nucleus potential with quasielastic scattering at deep sub-barrier energy
K. Washiyama, K. Hagino, and M. Dasgupta,
Phys. Rev. C 73 (2006) 034607/1-5.
Tracing the evolution of temperature in near Fermi energy heavy ion collisions
J. Wang, R. Wada, T. Keutgen, K. Hagel, Y. G. Ma, M. Murray, L. Qin, A. Botvina, S. Kowalski, T. Materna, J. B. Natowitz , R. Alfarro, J. Cibor, M. Cinausero, Y. El Masri, D. Fabris, E. Fioretto, A. Keksis, M. Lunardon, A. Makeev, N. Marie, E. Martin, Z. Majka, A. Martinez-Davalos, A. Menchaca-Rocha, G. Nebbia, G. Prete, V. Rizzi, A. Ruangma, D. V. Shetty, G. Souliotis, P. Staszel, M. Veselsky, G. Viesti, E. M. Winchester, S. J. Yennello, and W. Zipper, A. Ono,
Phys. Rev. C 72 (2005) 024603-(9 pages).
Isoscaling and symmetry energy in dynamical fragment formation
A. Ono,
AIP Conference Proceedings 791 (2005) 83-92.
The Dependency on the Dissipation Tensor of Multi-modal Nuclear Fission
T. Asano, T. Wada, M. Ohta, S. Yamaji, and H. Nakahara,
J. of Nucl. and Radiochemical Sci.7 (2006) 7-11.

Master Thesis (March 2006)
- Effect of neutrino induced fission on nucleosynthesis at a core-collapse supernova
  F. Minato