Nuclear Chart. Takashi NAKATSUKASA Theoretical Nuclear Physics Laboratory RIKEN Nishina Center. Real-space, real-time approaches ) Few-body model

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1 Takash NAKATSUKASA Theoetcal Nuclea Physcs Laboatoy RIKEN Nshna Cente Mn-WS: Real-space, eal-tme appoaches DFT, TDDFT ((Q)RPA ) Few-body model (CDCC ) Nuclea Chat 70 Los Alamos Natonal Laboatoy's Chemsty Dvson Pesents a Peodc Table of the Elements Goup** Peod 1 IA 1A 18 VIIIA 8A 1 1 H IIA A 13 IIIA 3A 14 IVA 4A 15 VA 5A 16 VIA 6A 17 VIIA 7A He L Be B C N O F Ne Na.99 1 Mg IIIB 3B 4 IVB 4B 5 VB 5B 6 VIB 6B 7 VIIB 7B VIII IB 1B 1 IIB B 13 Al S P S Cl A K Ca Sc T V C Mn Fe Co N Cu Zn Ga Ge As Se B K Rb S Y Z Nb Mo Tc (98) 44 Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La* Hf Ta W Re Os I Pt Au Hg Tl Pb B Po (10) 85 At (10) 86 Rn () 7 87 F (3) 88 Ra (6) 89 Ac~ (7) 104 Rf (57) 105 Db (60) 106 Sg (63) 107 Bh (6) 108 Hs (65) 109 Mt (66) () () () () () () Lanthande Sees* 58 Ce P Nd Pm (147) 6 Sm Eu Gd Tb Dy Ho E Tm Yb Lu Actnde Sees~ 90 Th Pa (31) 9 U (38) 93 Np (37) 94 Pu (4) 95 Am (43) 96 Cm (47) 97 Bk (47) 98 Cf (49) 99 Es (54) 100 Fm (53) 101 Md (56) 10 No (54) 103 L (57)

2 Hgh-pefomance computng ~ DFT to cove all One-to-one Coespondence Extenal potental Mnmum-enegy state Ψ Densty ρ( ) V ( ) Gound state Ψ V v-epesentatve densty ρ V ( )

3 The followng vaaton leads to all the gound-state popetes. δ { F[ ρ] ρ( ) v( ) d µ ( ρ( ) d N )} = 0 + In pncple, any physcal quantty of the gound state should be a functonal of densty. Vaaton wth espect to many-body wave functons Vaaton wth espect to one-body densty ρ( ) Physcal quantty A[ ρ( )] = Ψ[ ρ] Aˆ Ψ[ ρ] Ψ( 1, L, N ) Real nteactng system Kohn-Sham Scheme V ( ) Gound state Ψ V densty ρ( ) Vtual non-nteactng system V s ( ) Gound state Ψ S densty ρ( )

4 ρ Kohn-Sham scheme ( ) φ ( ) Ψ = det{ φ ( )} = S j h φ + v S = m [ ρ] φ ε φ KS canoncal equaton Densty functonal F [ ρ( )] = T [ ρ( )] + ( F[ ρ( )] T [ ρ( )]) = S p φ φ + V m eff S [ ρ( )] V eff [ ρ( )] Mnmzaton of ths densty functonal leads to v S [ ρ]( ) δveff = δρ ( ) S. Goely et al., ENAM 04 Nuclea DFT Global popetes, global calculatons M. Stotsov et al. * Global DFT mass calculatons: HFB mass fomula: m~700kev Takng advantage of hgh-pefomance computes

5 One-to-one Coespondence Extenal potental Tme-dependent state statng fom the ntal state Ψ( t 0 ) Tme-dependent densty V (, TD state Ψ t ( ) V ( t ) v-epesentatve densty ρ ( V, Real nteactng system TD Kohn-Sham Scheme V (, TD state Ψ( V TD densty ρ (, Vtual non-nteactng system V s (, TD state Ψ( S TD densty ρ (,

6 Skyme TDDFT n eal space Tme-dependent Kohn-Sham equaton t ψ ( στ, t ) = HF + ex t t 3D space s dscetzed n lattce Sngle-patcle obtal: η ~ ( h [ ρ, τ, j, s, J ]( t ) V ( t )) ψ ( στ, n= 1, LMt ϕ (, = { ϕ ( k, tn)} k = 1, L M, = 1, L, N ( ) y[ fm ] N: Numbe of patcles M: Numbe of mesh ponts Mt: Numbe of tme slces Spatal mesh sze s about 1 fm. Tme step s about 0. fm/c X [ fm ] Nakatsukasa, Yabana, Phys. Rev. C71 (005) Real-tme calculaton of esponse functons 1. Weak nstantaneous extenal petubaton. Calculate tme evoluton of 3. Foue tansfom to enegy doman db( ω; Fˆ ) dω V ext ( = Fˆ δ ( Ψ( Fˆ Ψ( 1 = Im t F t e π Ψ( ) ˆ Ψ( ) ωt t [ /MeV ] dt Ψ( Fˆ Ψ( db ( ω; F ˆ ) dω [ MeV ]

7 Neutons 16 O n ( ) n δρ ( ρ = ρn( 0 Tme-dep. tanston densty > 0 < 0 p ( ) p δρ ( ρ = ρ p ( 0 Potons 18 O 16 O Polate

8 4 Mg Polate 6 Mg Taxal S 30 S Oblate Oblate

9 40 A Oblate Ca Polate 40 Ca 48 Ca

10 Cal. vs. Exp. Electc dpole stengths Z N SkM* R box = 15 fm Γ = 1 MeV Numecal calculatons by T.Inakua (Unv. of Tsukuba)

11 Few-body-model calculaton of fuson coss secton Real-tme, eal-space appoach No need fo scatteng bounday condton Altenatve method to the CDCC Wave packet dynamcs of fuson eacton potental scatteng wth absopton nsde a Coulomb bae Radal Schoednge equaton fo l=0 d u, t, h h m d wth ncdent Gaussan wave packet u ( = + V () + W () u( [ ] (, t ) = k γ ( ) 0 exp 0 10Be-08Pb (A,Z=10,4 and 08,8) V0=-50 W0=-10, RV=1.6,RW=1.15, AV=0.44, AW=0.45 E_nc=8 MeV (+Coulomb at R_0), R_0=40fm, gamma=0.1fm- N=400, d=0.5, Nt=10000, dt= Be 08 Pb V ( ) Flux absobed by W() epesents fuson. W ( ) Wave packet dynamcs nclude scatteng nfomaton fo wde enegy egon. Then, how to extact eacton nfomaton fo a fxed enegy?

12 Fuson pobablty P fuson P ( E) = nt ( E) Pfnal ( E) P ( E) nt dffeental. eq. (statc cal) wave packet method Fuson pobablty fo whole bae egon fom sngle wave-packet calculaton. No bounday condton equed n the wave packet calculaton. Fuson pobablty of thee-body eacton h ψ t h h ( R,, = R + VnC ( nc ) + VCT ( CT ) + VnT ( nt ) ψ ( R,, µ J ul ( ) ( R,, R, t = m ( ) ψ J, Pl cosθ R l Intal ncdent wave Coulomb + Nuclea potental Absopton => C-T fuson Tansfe Elastc Flux loss by absopton FUSION (Complete + Incomplete) Beakup

13 P fuson ( E) P = ( E) Pf ( E) P ( E) (nc)-t 3-body n C R T C-T -body Enhancement of fuson pobablty at sub-bae eneges Case (): Weakly-bound pojectle (Neuton-halo) y n-c obtal enegy: -0.6 MeV (Halo) neuton 11 Be(n+ 10 Be)- 08 Pb head-on collson (J=0) R Coe Taget x ρ ( R,, = d( cosθ ) ψ ( R,, θ, ρ (, θ, = drψ ( R,, θ, R y x

14 Fuson pobablty of neuton-halo nucle s suppessed -body no V nt wth V nt Coe ncdent enegy deceases effectvely by neuton beakup E coe M coe M + M coe n E pojectle C n T Why dffeent fom othe studes? l l 70 Conclusons of othe studes Quantum calculatons have been done usng the dscetzed contnuum channels. Hagno et al, PRC61 (000) Daz-Toes & Thompson, PRC65 (00) Fuson was enhanced wth a weakly-bound neuton at sub-bae eneges Nuclea couplng was mpotant fo an the fuson enhancement 10 Be n R 08 Pb We need to nclude hgh-patal waves fo n- 10 Be motons. The low-patal-wave tuncaton leads to an opposte concluson!

15 Fuson Coss Secton of 11 Be Thee body full calculaton of 11 Be + 09 B Fuson pobablty s hndeed by the pesence of the halo neuton Be + 09 B Fuson coss secton ( mb ) Be + 09 B neuton 10 Be R 09 B E c.m. ( MeV ) Expement C. Sgnon et.al, Nucl. Phys. 735 (004) 39. Theoy M. Ito, M. Ueda, T. Nakatsukasa, K. Yabana, Phys. Lett. B 637, 53(006) Summay DFT/TDDFT Systematc calculatons fo all nucle ncludng those fa fom the stablty lne Descpton of lage ampltude dynamcs, such as fsson Real-tme, eal-space appoach to few-body models Accuate few-body scatteng dynamcs An altenatve appoach to CDCC