HIRG 重离子反应组 Heavy Ion Reaction Group GDR as a Probe of Alpha Cluster in Light Nuclei Wan-Bing He ( 何万兵 ) SINAP-CUSTIPEN Collaborators ： Yu-Gang Ma （马余刚） Xi-Guang Cao （曹喜光） Xiang-Zhou Cai （蔡翔舟） Guo-Qiang Zhang （张国强）

Outline  Back ground and Motivation  An Extended Quantum Molecular Dynamics  Giant Dipole Resonance calculation in transport model  Characteristic spectra of different cluster structures

Cluster structures in light nuclei K. Ikeda, N. Takigawa, H. Horiuchi, Prog. Theor. Phys. Suppl. Extra Number, 464 (1968) Marin-Lámbarri D. J, Bijker R, Freer M, et al. Phys Rev Lett. 2014;113(1): Bijker R, Iachello F. Phys Rev Lett. 2014;112(15): IKEDA Picture 12 C and 16 O 12 C Hoyle state is important in triple-alpha process

Motivation ： 1.How α clustering determines the configurations and shapes? 2.What are the aspects of the collective dynamics of α clustering systems ？ 3.Can different α cluster structures of a nuclei give different GDR characteristic spectra?

An Extension of QMD model Maruyama, T., Niita, K., & Iwamoto, A. (1996). Phys. Rev. C, 53(1), 297– 304.  Gaussian wave packets of nucleons ：  Density distribution ：  Wigner function ：

 The Hamiltonian is written as ：  zero-point center-of-mass kinetic energy ：  The equations of motion ： Dynamic wave packets Zero-point energy potential energy

 effective interaction ：  Pauli potential ： Dynamic width wave packets of nucleons and the Pauli potential are the key extension of EQMD

 Friction cooling ： Add damping term Equations of motionEquations of cooling 16 O initial state before cooling 16 O cooling to ground state 19 C cooling to halo structure

Alpha cluster structures in light nuclei by EQMD

Alpha clusters at different position have different wave packets width

Density distribution of alpha clusters in different nuclei at central plane

momentum distribution of cluster state and non-cluster state

Giant Dipole Resonance in nuclei G.F. Bertsch and S.F.Tsai, Phys. Rep 180 (1975) 125

GDR calculation method 1 1. Hamiltonian written as ： 2. Dipole moments are ： 3. Dipole radiation spectrum ：

（ IQMD ） GDR gamma yield in nuclear fusion reactions Phys. Rev. C, 81(4):047602, 2010 （ IQMD ） Dependency between GDR and symmetry energy. Phys. Rev. C,87(1):014621, （ BUU ） Dependency between GDR and symmetry energy. 32 S+ 100 Mo 16MeV/u Phys. Rev. C, 88(4):47602,2013.

GDR calculation method 2  For spontaneous radiation and photon capture the Hamiltonian written as ： Ignore the A 2 term  Fermi transition rate ：

 Fermi transition rate from a to b state ：  Consider the polarized photons ， the cross-section of photon absorption as ：  In transport model ， we can define the dipole excitation operator as:  Then the perturbation as:

 The Response function of dipole excitation operator has following relationships  GDR cross-section ： Here, alpha is the fine structure constant  GDR width parameter:

Nonlinear properties of light nuclei response 4 He dipole motion frequency vs gamma energy.

GDR of 12 C and 16 O at ground state comparison between 12 C ground state and experiment data comparison between 16 O ground state and experiment data 12 C ground state may have both non-cluster and three alpha cluster with triangle structure properties. 16 O ground state may just have four alpha cluster with tetrahedron structure properties.

In the excited states of clustering light nuclei, different cluster structures shows characteristic GDR spectra.

8 Be dipole motion For 18MeV dipole motion frequency, it also shows in one alpha cluster along short axis, but the two alpha have different phase position. So the peak of this frequency is coherent subtraction.

Triangle 12 C dipole motion

Linear chain 12 C dipole motion

Linear chain 16 O dipole motion

A little bent linear chain 16 O dipole motion In bent linear chain 16 O, system can also be considered as two 8 Be. But those two substructure can not show up peak at 20 MeV like one 8 Be. The reason is those two parts have negative motion phase position. So the coherent subtraction like two alpha happens again.

Kite 16 O dipole motion

Square 16 O dipole motion

α cluster signal in fusion reactions cuts 100±5 hbarcuts 60±5 hbar cuts >95 hbar the data is from D. Pandit et al, Phys. Rev. C 81, (2010)

 Different α cluster structures of a nuclei give different GDR characteristic spectra.  30MeV is a candidate signal to probe alpha cluster formation in nuclei  High energy gamma detection may be a challenge for this study summary