Repulsive aspects of pairing correlation in nuclear fusion reaction
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1 4C EOS and Heavy Nuclei, ARIS Univ. of Tokyo Repulsive aspects of pairing correlation in nuclear fusion reaction Shuichiro Ebata Meme Media Laboratory, Hokkaido Univ. Nuclear Reaction Data Centre, Hokkaido Univ. (JCPRG) Takashi Nakatsukasa Center for Computational Sciences and Faculty of Pure and Applied Sciences, Univ. of Tsukuba Theoretical Nuclear Physics Laboratory, RIKEN Nishina Center
2 Simulation of heavy ion collision using TDHF H.Flocard, S.E.Koonin and M.S.Weiss Phys. Rev. C17 (1978) 1682
3 Several mean-field theories No Pairing With BCS Pairing With Pairing For static Hartree-Fock(HF) HF+BCS Hartree-Fock- Bogoliubov (HFB) For dynamics Time-Dependent HF (TDHF, RPA) TDHF+BCS Cb-TDHFB TDHFB (QRPA) RPA: Random-Phase Approximation QRPA: Quasi-particle RPA
4 What kind of pairing effect is expected in low-energy Heavy ion collision? Fusion or Fission cross section Level crossing Energy Dissipation Neck formation Odd-even effects for spontaneous fission half-lives? W.J.Swiatecki, Phys. Rev. 100 (1955) 937. Spontaneous Fission Half-lives Pair transfer reaction Nuclear Josephson effect
5 Method Statics: HF+BCS Dynamics: Cb-TDHFB S.E. et al.: PRC82 (2010) ph-channel Int. : Skyrme (SkM*, SLy4d) pp(hh)-channel : δ - type (time-reversal) : spin-singlet zero-range interaction Cb-TDHFB Eqs. Points: To solve Cb-TDHFB in 3D space enable us to study nuclear dynamics including deformation and pairing, self-consistently. For the simulation of collision Prepare the target and projectile nuclei with HF+BCS, put them with some b and distance, also add velocity to them, and their time will be evolved by Cb-TDHFB. : Canonical basis (for l also) : Occupation Prob. (for l >0) : Pair Prob. (for l >0)
![Example : Photo-absorption cross section of 172 Yb 3D Cb-TDHFB β =0.32 n = 0.76 [MeV] p = 0.55 [MeV] Γ= 1.](/docs-images/86/94873081/images/6-5.jpg "0 [MeV] Cb-TDHFB can reproduce the photo-absorption cross section of 172 Yb. Heavy nucleus Deformed nucleus Including pairing Total cal.")
6 Example : Photo-absorption cross section of 172 Yb 3D Cb-TDHFB β =0.32 n = 0.76 [MeV] p = 0.55 [MeV] Γ= 1.0 [MeV] Cb-TDHFB can reproduce the photo-absorption cross section of 172 Yb. Heavy nucleus Deformed nucleus Including pairing Total cal. cost : 300 CPU hours (with a Single processor; Intel Core i7 3.0 GHz) Box size : R=15[fm], mesh=1[fm] (3D-Spherical) Canonical-basis space (HF+BCS g.s.) : 146 states for neutron, 98 states for proton Experimental data: A.M.Goryachev and G.N.Zalesnyy Vopr. Teor. Yad. Fiz. 5, 42 (1976). K=0 - K=1 - Dipole mode Proton Neutron
7 Setup for collision Incident Energy : [MeV] (E cm = [MeV], V Coul. ~ 9 MeV) Impact parameter : [fm] Effective Interaction : Skyrme force (SkM*), Contact pairing Projectile : 22 O, Target : 22 O (HF g.s. has also spherical shape) # of canonical-basis for HF+BCS g.s. ; (N, Z) = (32 (16+16), 16 (8+8)) Average of gap energy ; Calculation space (3D meshed box): Length of box for ( x, y, z ) is 36, 20, 40[fm] meshed by 1.0 [fm]
8 Simulation of 22 O + 22 O collision with b = 3.0 [fm] and E cm =10 [MeV] Time-evolution of Neutron density distribution Cb-TDHFB TDHF
![0 [fm] and E cm =10 [MeV]](/docs-images/86/94873081/images/9-2.jpg "Time-evolution of Neutron density")
9 Simulation of 22 O + 22 O collision with b = 3.0 [fm] and E cm =10 [MeV] Time-evolution of Neutron density distribution Cb-TDHFB TDHF
10 From simulation of 22 O + 22 O collision with b = [fm] and E cm =10 [MeV], Pairing correlation does not increase the fusion cross section (in this work). Up to now Same nuclei collision with the incident energy around Coulomb barrier Pairing correlation can have repulsive aspects in fusion reaction. σ H ~ 283 mb σ B ~ 246 mb be small about 15% The repulsive effects depends on the strength of pairing. From now on In a little bit heavier system? To increase pair number Case of different nuclei collision? Large difference of chemical potential will accelerate Pair transfer. Is the pairing effects visible in much heavier system?
11 In a little bit heavier system Point: increase of pair number Projectile : 52 Ca, Target : 52 Ca E cm = 51.5 MeV (V Coul. ~ 49 MeV) Effective Interaction : SkM*, Contact pairing To reproduce n of 52 Ca In both methods, the g.s. is spherical shape. Impact parameter : [fm] Cb-TDHFB TDHF σ H ~ 189 mb σ B ~ 181 mb be small about 5%
12 In a little bit heavier system Point: increase of pair number Projectile : 52 Ca, Target : 52 Ca E cm = 51.5 MeV (V Coul. ~ 49 MeV) Effective Interaction : SkM*, Contact pairing To reproduce n of 52 Ca In both methods, the g.s. is spherical shape. Impact parameter : [fm] Cb-TDHFB TDHF σ H ~ 189 mb σ B ~ 181 mb be small about 5%
13 Case of different nuclei collision Projectile : 22 O, Target : 52 Ca E cm = 25 MeV (V Coul. ~ 20.8 MeV) In both methods, the g.s. is spherical shape. Impact parameter : [fm] Effective Interaction : SkM*, Contact pairing Average of strength in 22 O and 52 Ca Cb-TDHFB TDHF Point: Difference of chemical potential σ H ~ 528 mb σ B ~ 503 mb be small about 5%
14 Case of different nuclei collision Projectile : 22 O, Target : 52 Ca E cm = 25 MeV (V Coul. ~ 20.8 MeV) Cb-TDHFB In both methods, the g.s. is spherical shape. Impact parameter : [fm] Effective Interaction : SkM*, Contact pairing Average of strength in 22 O and 52 Ca TDHF Point: Difference of chemical potential σ H ~ 528 mb σ B ~ 503 mb be small about 5%
15 Is the pairing effect visible in much heavier system? Projectile : 96 Zr, Target : 124 Sn E cm = 228 MeV (V coul. =216, 225 MeV) Effective Interaction : SLy4d, Contact pairing HF+BCS : Both ground states are spherical shape. HF : 96 Zr ; spherical, 124 Sn ; oblate shape. Very strong in order to check the effect Neglect proton pairing Coulomb barrier for 96 Zr+ 124 Sn (F.D.) HF g.s. of 124 Sn has Oblate shape. β = Zr 124 Sn V FD =225 MeV 96 Zr 124 Sn V FD =216 MeV
16 Is the pairing effect visible in much heavier system? TDHF (z Z) TDHF (x,y Z) Cb-TDHFB
17 Is the pairing effect visible in much heavier system? TDHF (z Z) TDHF (x,y Z) Time up to scission Cb-TDHFB <!!
18 Summary & Perspective Simulation of the collision phenomena with Cb-TDHFB We apply Cb-TDHFB to large amplitude collective phenomena such as collision, with a contact pairing functional. 22 O+ 22 O : Pairing effects in fusion reaction, have a repulsive aspects. 52 Ca+ 52 Ca : The repulsive aspect appears also, but its contribution becomes small. 22 O+ 52 Ca : The similar aspects can be seen. 96 Zr+ 124 Sn : The pairing effects gets the time from a contact to scission to be short. Perspective To analyze the detail of internal behavior More accurate calculation Behavior of single-particle levels in real-time cal. 40 Energy distribution, Level crossing Particle number projection for the multi-particle transfer 0 in real-time cal Nucleon transfer (Pair transfer), Nuclear Josephson effects Particle number Neutron Proton Thank you for your attention!
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