Heavy-ion fusion reactions for superheavy elements Kouichi Hagino
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2 Heavy-ion fusion reactions for superheavy elements Kouichi Hagino Tohoku University, Sendai, Japan 1. H.I. sub-barrier fusion reactions 2. Coupled-channels approach and barrier distributions 3. Application to superheavy elements 4. Hot fusion reactions of a deformed target 5. Summary and discussions Recent review article: K. Hagino and N. Takigawa, Prog. Theo. Phys.128 ( 12)1061. New Frontiers in Nuclear Physics and Astrophysics-1, Akdeniz Univ., Antalya, Turkey, May 28 June 1, 2018
3 Fusion reactions: compound nucleus formation P T P+T compound nucleus cf. Bohr 36 energy production in stars nucleosynthesis superheavy elements Fusion and fission: large amplitude motions of quantum many-body systems with strong interaction microscopic understanding: an ultimate goal of nuclear physics
4 Fusion reactions: compound nucleus formation fusion reactions in the sub-barrier energy region 1. Coulomb force : long range, repulsive 2. Nuclear force : short range, attractive Coulomb barrier
5 Why sub-barrier fusion? two obvious reasons: November, Zn fusion α decay superheavy elements cf. 209 Bi ( 70 Zn,n) 278 Nh V B ~ 260 MeV E cm (exp) ~ 262 MeV 83Bi 113Nh 111Rg
6 Why sub-barrier fusion? two obvious reasons: σ(e) resonance LOGARITMIC SCALE non-resonant direct measurements E 0 extrapolation needed! figure: M. Aliotta E coul Coulomb barrier nuclear astrophysics (nuclear fusion in stars) cf. extrapolation of data
7 Why sub-barrier fusion? Two obvious reasons: discovering new elements (SHE) nuclear astrophysics (fusion in stars) Other reasons: reaction mechamism strong interplay between reaction and nuclear structure cf. high E reactions: much simpler reaction mechanism many-particle tunneling many types of intrinsic degrees of freedom energy dependence of tunneling probability cf. alpha decay: fixed energy H.I. fusion reaction = an ideal playground to study quantum tunneling with many degrees of freedom
8 Discovery of large sub-barrier enhancement of σ fus potential model: V(r) + absorption cf. seminal work: R.G. Stokstad et al., PRL41( 78) 465
9 Effects of nuclear deformation 154 Sm : a typical deformed nucleus 154 Sm θ 154 Sm 16 O
10 Effects of nuclear deformation 154 Sm : a typical deformed nucleus 154 Sm deformation θ 154 Sm 16 O Fusion: strong interplay between nuclear structure and reaction
11 enhancement of fusion cross sections : a general phenomenon potential model strong correlation with nuclear spectrum coupling assisted tunneling
12 Coupled-channels method: a quantal scattering theory with excitations many-body problem still very challenging
13 TDHF simulation TDHF = Time Dependent Hartree-Fock S. Ebata, T. Nakatsukasa, JPC Conf. Proc. 6 ( 15) ab-initio, but no tunneling 16 O Pb C. Simenel, EPJA48 ( 12) 152
14 Coupled-channels method: a quantal scattering theory with excitations many-body problem still very challenging two-body problem, but with excitations (coupled-channels approach) coupling scattering theory with excitations
15 C.C. approach: a standard tool for sub-barrier fusion reactions cf. CCFULL (K.H., N. Rowley, A.T. Kruppa, CPC123 ( 99) 143) Fusion barrier distribution [Rowley, Satchler, Stelson, PLB254( 91)] single channel c.c. calculations K.H., N. Takigawa, PTP128 ( 12) 1061
16 Fusion barrier distribution (Rowley, Satchler, Stelson, PLB254( 91)) V b Data: J.R. Leigh et al., PRC52 ( 95) 3151 a nice tool to understand the reaction dynamics K.H., N. Takigawa, PTP128 ( 12) 1061
17 Recent application to SHE : Quasi-elastic B.D. hot fusion reactions 48 Ca + actinide target SHE = deformation fusion quasi-elastic Quasi-elastic barrier distribution reaction dynamics with barrier distributions? Quasi-elastic scattering : reflected flux at the barrier a sum of elastic, inelastic, and transfer easier to measure than capture H. Timmers et al., NPA584( 95)190 K.H. and N. Rowley, PRC69( 04)054610
18 previous attempts 86 Kr+ 208 Pb S.S. Ntshangase et al., PLB651 ( 07) 27 GARIS S. Mitsuoka et al., PRL99 ( 07) T. Tanaka et al., JPSJ 87 ( 18)
19 Analysis for a hot fusion reaction 48 Ca Cm 48 Ca Cm Lv * K.H. and T. Tanaka (2017) (T. Tanaka et al., JPSJ 87 ( 18) ) single-channel calculation (spherical 248 Cm)
20 Analysis for a hot fusion reaction 48 Ca Cm K.H. and T. Tanaka (2017) 48 Ca Cm (β 2 = 0.297, β 4 = 0.04) Lv * [β 2 and β 4 from P. Moller] θ 248 Cm 48 Ca
21 Analysis for a hot fusion reaction 48 Ca Cm 48 Ca Cm (β 2 = 0.297, β 4 = 0.04) Lv * K.H. and T. Tanaka (2017) Ca 4.5 MeV 1n transfer 48 Ca Cm 49 Ca Cm (Q gg = MeV)
22 Connection to the ER cross sections barrier distribution compound nucleus re-separation (quasi-fission)
23 Connection to the ER cross sections 48 Ca Cm Lv * notion of compactness: D.J. Hinde et al., PRL74 ( 95) 1295 = more compact at the touching favorable for CN
24 Extension of the fusion-by-diffusion model Fusion-by-diffusion model W.J. Swiatecki et al., Acta Phys. Pol. B34 ( 03) 2049 PRC71 ( 05) K.H., arxiv: T l simplified C.C. P CN W suv ER CN n Quasi-fission fusionfission diffusion of a 1D parabolic barrier (inner barrier) statistical model
25 2-body potential 1-body potential E P cap : quantum mechanics compound nucleus thermal fluctuation heat up re-separation
26 T l Quasi-fission diffusion of a 1D parabolic barrier P CN W suv ER CN n fusionfission V fiss (s) V Langevin in the overdamped limit: s sd s inj s s inj
27 Extension of the fusion-by-diffusion model K.H., arxiv: θ = π/2 (side collision) s (0) inj V fiss (s) V s inj s sd s s (0) inj inj s
28 Extension of the fusion-by-diffusion model K.H., arxiv:
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31 Summary and discussions Reaction dynamics for SHE formation reactions Recent measurement of barrier distributions with GARIS 48 Ca Cm coupled-channels analysis notion of compactness: ER formation with side collisions more data coming soon Open problems reaction dynamics? quantum theory for friction cf. M. Tokieda and K.H., PRC95 ( 17)
32 Quantum friction classical eq. of motion a quantization: Kanai model E. Kanai, PTP 3 (1948) 440) time-dep. wave packet approach E=5 MeV M. Tokieda and K.H., PRC95 ( 17)
33 Summary and discussions Reaction dynamics for SHE formation reactions Recent measurement of barrier distributions with GARIS 48 Ca Cm coupled-channels analysis notion of compactness: ER formation with side collisions more data coming soon Open problems reaction dynamics? quantum theory for friction shape evolution with a deformed target? how does the deformation disappear during heat-up? towards island of stability reaction dynamics with neutron-rich beams? cf. M. Tokieda and K.H., PRC95 ( 17)
34 Towards the island of stability neutron-rich beams: indispensable how to deal with low beam intensity? reaction dynamics of neutron-rich beams? capture: role of breakup and (multi-neutron) transfer? diffusion: neutron emission during a shape evolution? survival: validity of the statistical model? structure of exotic nuclei more studies are required
35 formation of SHE chemistry of SHE the origin of (S)HE reaction dynamics Nuclear Physics (RIBF/FRIB) Astrophysics structure of SHE interdisciplinary SHE science with physics, chemistry, and astronomy
36 FUSION20 November 16-20, 2020 Shizuoka, Japan Kouichi Hagino (co-chair) Tohoku University Katsuhisa Nishio (co-chair) JAEA
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