THREEBODY FORCE AND FRAGMENTATION IN NUCLEAR REACTIONS Zhiqiang

THREE-BODY FORCE AND FRAGMENTATION IN NUCLEAR REACTIONS Zhiqiang Chen Institute of Modern Physics Chinese Academy of Sciences May 16, 2018 Fourth International Workshop on “State Of the Art in Nuclear Cluster Physics” May 13 -18, 2018 Galveston, TX, USA

Collaborators Zhiqiang Chen, Weiping Lin, Guoyu Tian, Rui Han Institute of Modern Physics (IMP), Chinese Academy of Sciences (CAS) Gaolong Zhang, Weiwei Qu, I. Tanihata School of Physics and Nuclear Energy Engineering, Beihang University, China Research Center for Nuclear Physics, Osaka University, Japan Roy Wada Cyclotron Institute, Texas A&M University, USA Akira Ono Department of Physics, Tohoku University, Japan

Outline • • Motivation Experiment of 12 C+12 C scattering at 100 A Me. V. AMD model simulations of nuclear fragmentation reactions. Summary and outlook

Motivation • Three-body forces(TBFs) are a frontier for understanding and predicting strongly interacting many-body systems. • TBFs are known to play an important role in the binding of nuclei and also in the equation of state(EOS) for nuclear matter. • For the binding of nuclei, ab initio type calculations that include the Fujita. Miyazawa interactions have demonstrated the importance of the attractive TBFs for understanding the structure of light nuclei. • For the EOS, TBFs are the important for reproducing the saturation properties and the compressibility at high density. • A high-density environment is produced by high-energy heavy-ion collisions so that sensitivity of the cross sections to repulsive TBFs is expected. [1] Hans-Werner Hammer, et al. , Rev. Mod. Phys. 85, 197(2013). [2] S. C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53(2001). [3] P. Navratil, et al. , Phys. Rev. Lett. 105, 032501(2010). [4]T. Otsuka, et al. , Phys. Rev. Lett. 105, 032501(2010). [5]A. Deltuva and A. C. Fonseca, Phys. Rev. C 75, 014005(2007). [6]J. Fujita and H. Miyazawa Prog. Theor. Phys. 17, 360(1957). [7]M. Baldo et al. , Astron. Astrophys. 328, 274(1997). [8]A. Lejeune, et al. , Phys. Lett. B 477, 45(2000).

TBF effects on EOS of symmetric nuclear matter 1. In order to describe reasonably the nuclear saturation properties within the nonrelativistic Brueckner-Hartree-Fock (BHF) framework, one has to take into account the TBF effect. 2. the saturation density and the saturation energy are ∼ 0. 167 fm− 3 and ∼ − 15. 9 Me. V respectively, in satisfactory agreement with the empirical values. 3. TBF contribution to the EOS is repulsive and leads to a stiffening of the EOS, especially at supra-saturation densities. 1. Wei Zuo Journal of Physics: Conference Series 420 (2013). 2. W. Zuo et al. , Nucl. Phys. A 706(2002) 418. 3. Z. H. Li et al, Phys. Rev. C 77(2008)034316.

TBF effects on high-energy heavy-ion scattering T. Furumoto et al. have proposed a theoretical model for constructing the complex optical potential for any composite projectiles through the doublefolding-model (DFM) with a newly proposed complex G-matrix NN interaction called CEG 07. real part + imaginary part T. Furumoto, Y. Sakuragi, Y. Yamamoto, PRC 78(2008) 044610, T. Furumoto, Y. Sakuragi, Y. Yamamoto, PRC 79(2009) 011601(R), T. Furumoto, Y. Sakuragi, Y. Yamamoto, PRC 80(2009) 044614 T. Furumoto, Y. Sakuragi, Y. Yamamoto, PRC 82 (2010) 029908(E) T. Furumoto, Y. Sakuragi, Y. Yamamoto, PRC 82(2010) ( 044612 )

Complex G-matrix interaction (CEG 07) T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) 044610 derived from ESC 04 “ESC 04” : the latest version of Extended Soft-Core force designed for NN, YN and YY systems Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008 1. Three-body attraction (TBA) ・ Fujita-Miyazawa diagram ・ important at low density region 2. Three-body repulsion (TBR) ・ originated the triple-meson correlation ・ important at high-density region In the ESC 04 model density-dependent effective two-body force

Saturation curve in nuclear matter with G-matrix interaction（CEG 07） ESC 04 NN force (Extended Soft-Core ) includes. Three body force ＋Three-body repulsive (TBR) ＋Three-body attractive (TBA) K=260 Me. V important Three-body force effect K=84 Me. V Two body force only

12 C +12 C elastic scattering at E/A=100~400 Me. V CEG 07 a (without TBF) CEG 07 b (with TBF) Diffractive oscillation Ø real potential : repulsive around E/A = 300～ 400 Me. V 1. E/A=100 Me. V, calculated cross section with CEG 07 a dominates over the cross sections with CEG 07 b. 2. E/A=200 Me. V, two kinds of cross sections show almost identical angular distributions. 3. E/A=400 Me. V, the situation becomes completely opposite to that of E/A=100 Me. V. 4. E/A=300 Me. V (CEG 07 b) and E/A=400 Me. V(CEG 07 a), the cross sections show a strong diffractive oscillation pattern. T. Furumoto, Y. Sakuragi and Y. Yamamoto. Phys. Rev. C 82 (2010) 044612.

Experiment of 12 C+12 C scattering at 100 A Me. V Experiment Setup 100 Me. V/u 12 C+12 C@RCNP， Osaka University Beam line: WS course Beam: 100 AMe. V 12 C Beam intensity: 0. 1 -1. 0 pn. A Beam energy resolution: 500 ke. V Target: 1. 181 mg/cm 2 natural C and 11. 400 mg/cm 2 CH 2 target Detector: VDC 1 and VDC 2, PS 1, PS 2 and PS 3 Measured angles: 1 -7. 5 degrees, Angular resolution: better than 0. 1 degree RCNP Osaka University W. W. Qu et al. , Phys. Lett. B 751, 1 (2015). W. W. Qu et al. , Phys. Rev. C 95, 044616(2017).

Magnetic spectrometer Focal plane detectors Two Vertical-type Drift Chambers(VDCs) + Three Plastic scintillators(PSs) (thickness: 3 mm, 10 mm and 10 mm ) VDC 1 and VDC 2: particle trajectory PS 1, PS 2 and PS 3: identify particles “GRAND RAIDEN”

Particle identification and spectrum fitting 12 C Particle identification during experiment. Two-dimensional plot of excitation energy and laboratory angles for outgoing 12 C particles for the spectrometer central angle of 2. 0◦. Excitation spectrum obtained at scattering angle of 1. 5◦. The fitted spectrum for the 4. 44 Me. V excited state with the target and projectile excitation components is shown.

Theoretical analysis Saturation curves Interaction model ESC: The two-body interaction ESC 08 NN interaction model. CEG 07 b: ESC 04 NN interaction model and include TBF effect. MPa: ESC 08 NN interaction model and includes a three-body repulsive part expressed by the multi-Pomeron exchange potential (MPP). Theoretical frame of microscopic coupled-channel(MCC) method W. W. Qu et al. , Phys. Rev. C 95, 044616(2017).

Results: 1 -ch calculations Reaction cross sections for 12 C + 12 C 1. 2. Elastic-scattering differential cross sections for 12 C + 12 C at 100 AMe. V The NW value is fixed by the reaction cross section. Because the cross section is very sensitive to the strength of the imaginary potential. TBF makes an important contribution to elastic scattering.

Results: Full-coupled-channel calculations Reaction cross sections for 12 C + 12 C Differential cross sections for 12 C + 12 C at 100 AMe. V ESC CEG 07 b 1. ESC fails to reproduce the measured cross sections. 2. MPa model reproduces the data better than CEG 07 b. MPa

Results: coupled-channel effect on elastic and inelastic cross sections Elastic cross sections for 12 C + 12 C at 100 AMe. V 1. 2. 3. Inelastic cross sections for 12 C + 12 C at 100 AMe. V The CC effect for the MPa interaction is seen in the elastic differential cross sections as a decrease of the cross section at large scattering angles. The inelastic scattering is better reproduced with the inclusion of the CC effect. For the inelastic cross sections, the TBF effect is also clearly seen to be important.

AMD model simulations of nuclear fragmentation reactions AMD model A. Ono, H. Horiuchi, T. Maruyama, and A. Ohnishi, Prog. Theor. Phys. 87, 1185 (1992). In AMD a reaction system with N nucleons is described by a Slater determinate of N Gaussian wave packets: The centroid of Gaussian wave packets Zi is given as: The equation of motion for Z is derived as: H is the Hamiltonian and Ciσ, jτ is a Hermitian matrix defined by: AMD treats the nucleon-nucleon collision process in the physical coordinate space. The physical coordinate. W ≡ {Wi} for a given nucleon, i, is defined as The Winger form of the ith nucleon at time t = t 0 is represented as :

Fermi boost in AMD-FM W. Lin, X. Liu, R. Wada, et al. , Phys. Rev. C 94, 064609 (2016). In AMD-FM, the Fermi motion is taken into account in the two-body collision process. When two nucleons are within the collision distance , the momentum uncertainty increases. In the actual calculations for given coordinate vectors r 1 and r 2 of two attempted colliding nucleons, the associated momenta P 1 and P 2 are given as: where P 0 i is the centroid of the Gaussian momentum distribution for the particle i and ΔP'i is the Fermi momentum randomly given along the Gaussian distribution. where G(1) is a random number generated along the Gaussian distribution with σ = 1. (ρi/ρ0)1/3 in Eq. (16) is used for taking into account the density dependence of the Fermi energy, ρi is the density at ri , and ρ0 is the normal nuclear density.

Proton energy spectra for 40 Ar+51 V at 44 Me. V/nucleon AMD Co. MD AMD-FM reproduces the experimental data well.

Proton energy spectra for 36 Ar+181 Ta at 94 Me. V/nucleon Proton energy spectra of AMD-FM at θ ∼ 110° (open squares) and 4π solid angle (open circles) are compared to the experimental spectrum (solid squares) in the center-ofmass frame for the central collision events. Proton energy spectra of AMD-FM at 75 ° (red solid histogram) and 105 °(green dashed histogram) are compared to those of experiment (solid symbols) in the laboratory frame. AMD-FM reproduces the experimental data well.

GEANT 4 calculations for 12 C +12 C at 95 Me. V/nucleon GANIL Experimental data. Energy distributions of 4 He, 6 Li, and 7 Be fragments at 4◦ and 17◦. Black points are experimental data. Histograms are for simulations with QMD, BIC, and INCL models coupled to the FBU deexcitation model. J. Dudouet, et al. , Phys. Rev. C 89, 054616 (2014) None of the toolkits provide good enough reproduction of the experimental data, especially for those from the intermediate velocity source.

Co. MD, AMD-FM calculations for 12 C +12 C at 95 Me. V/nucleon deuteron proton triton 4 He

AMD-FM calculations for 12 C +12 C at 95 Me. V/nucleon Comparing to the three transport model calculations, overall AMD-FM reproduces best the experimental data.

AMD-FM calculations for 12 C +12 C at 95 Me. V/nucleon Angular distribution for Li, Be, B and C isotopes. AMD-FM failed to reproduce IMFs experimental data.

Cluster correlations in AMD (AMD-Cluster) This extended version of AMD is developed mainly to improve the description of the IMF emission by taking into account the cluster correlation by Akira Ono, J. Phys. Conf. Ser. 420(2013) 012103. Ikeno, Ono et al. , PRC 93 (2016) 044612.

AMD-Cluster calculations for 12 C +12 C at 95 Me. V/nucleon G. Tian Phys. Rev. C 97, 034610 (2018) Angular distribution for Li, Be, B and C isotopes. AMD-Cluster reproduced the IMFs experimental data well.

Three-nucleon interaction in heavy-ion collisions Three-nucleon (3 N) interaction is incorporated into the AMD-FM model by Roy Wada. R. Wada Phys. Rev. C 96, 031601(R) (2017) Proton energy distributions for the 40 Ar+51 V. AMD-FM(circles), AMD-FM(3 N)(histograms) 1. At 100 AMe. V, the energy spectra are very similar at different angles. 2. When the incident energy increases to 200 AMe. V, the shapes of the energy spectra show a distinct difference. AMD-FM(3 N) show much harder slopes.

Proton energy distributions for the 40 Ar+40 Ca and 40 Ar+51 V. AMD-FM(dashed curves), AMD-FM(3 N)(solid curves) 1. 2. The experimental proton energy spectra at θ≥ 70°are reproduced reasonably well by AMD-FM(3 N). 3 N interaction is importance in intermediate heavy ion reactions.

100 - 400 AMe. V 12 C + 12 C proposal experiment at HIRFL-CSR (Lanzhou, China) Layout

200 AMe. V 12 C + 12 C experiment at HIRFL-CSR (test run)

Summary and outlook Ø The angular distributions of differential cross sections of 12 C +12 C elastic and inelastic scattering are precisely measured at 100 A Me. V in RCNP Osaka University. Ø The present results provide clear evidence of the important roles of the repulsive TBF and the CC effect in high-energy heavy-ion collisions. Ø The experimental energy spectra and angular distributions of light charged particles are well reproduced by the AMD-FM calculations for 12 C +12 C at 95 Me. V/nucleon. Ø The cluster correlation plays a crucial role for producing fragments in the intermediate-energy heavy ioncollisions. Ø AMD-FM (3 N) simulations indicates for the first time the importance of the 3 N interaction in intermediate heavy ion reactions. Ø In the future, 100 -400 AMe. V 12 C +12 C experiments will be done in HIRFLCSR (Lanzhou, China).

Thanks for your attention!