Dynamics of Quasifission in TDHF Theory

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1 Dynamics of Quasifission in TDHF Theory A.S. Umar Vanderbilt University Nashville, Tennessee, USA Collaborators: Vanderbilt: NSCL/MSU: ANU: V. E. Oberacker Z. Kohley, A. Wakhle, K. Hammerton, K. Stiefel C. Simenel, D. J. Hinde, M. Dasgupta, E. Williams, I. P. Carter, K. J. Cook, D. Y. Jeung, D. H. Luong, S. D. McNeil, C. S. Palshetkar, D. C. Rafferty Topics Covered: Time-dependent DFT theory (TDHF) Quasifission using TDHF - 40,48Ca + 238U - 48Ca + 249Bk (preliminary) - 50,54Cr + 180,186W Dynamical moment of inertia, E*, T Collective dynamics of QF Capture (time permitting) Research supported by: U.S. Department of Energy, Division of Nuclear Physics

2 Nuclear Mean Field or Energy Density Functional (EDF) 3-body DFT 2-body 1-body Mean-field - EDF ab-initio Ψ Φ Slater H H eff Ψ H Ψ = E E = Φ H eff Φ = d 3 r {H(ρ, τ, j, s,t, J μ ν ; r)+hcoulomb (ρ p )} Single-(one-) particle density etc. in terms of s.p. states A ρq ( r )= ϕ *i (r, σ, q)ϕi (r, σ, q) i=1 σ EDF in NP more complicated v=v NN eff DFT ( Hartee Fock ) v v NN eff DFT ( Kohn Sham)

3 Study Structure, Reactions, and Star Matter in Same Framework Structure Oscillations, Fusion, FIssion Neutron Star Crust Time-dependent generalization TDHF or TDDFT (variational or Runge-Gross) t2 δ S=δ dt Φ( t ) H eff i ℏ t Φ (t ) =0 t1 i ϕα =h(ρ, τ, j, s, T, J μ ν ; r)ϕ α t self-consistent TDHF gives the most probable outcome best if x-section dominated by one process

4 Modern TDHF Codes VU-TDHF Code Basis-Spline discretization for high accuracy 3-D Cartesian lattice no geometrical simplification Complete EDF including all terms (time-even, full time-odd) Coded in Fortran-95 and OpenMP 1. Umar, Oberacker, VU-TDHF, Phys. Rev. C 73, (2006) 2. Maruhn, Reinhard, Stevenson, Umar, Sky3D, Comp. Phys. Comm. 85, 2195 (2014)

5 Quasifission in TDHF 40,48Ca + 238U Heavy Systems σ capture =σ QF +σ fusion fission +σ ER - QF dominant part - Important for studying SHE dynamics Final masses: AL = 101, AR = 177 ZL = 41, ZR = 71 Ecm = 209 MeV b=1.103fm (L=20) 40 Ca + 238U V.E. Oberacker, A.S. Umar, C. Simenel, PRC 90, (2014).

6 Quasifission 40,48Ca+238U - Compare 40,48Ca+238U (b=0) - fusion implies contact-time > 35 zs (plus density shows no indication of QF) - 40Ca+238U wider energy range for QF - E* sharing seems different (calculated dynamically using DC-TDHF) Each point takes about a week on a 16 processor workstation 48 Ca+238U Ecm=203 MeV The b=0o orientation of 238U results in much smaller contact-times and mass transfer V.E. Oberacker, A.S. Umar, C. Simenel, PRC 90, (2014).

7 Impact Parameter Depenence Viola Systematics Final fragment TKE's well described by Viola systematics 40 Ca + 238U Narrow range of impact parameters at low energies Wakhle et al., PRL 113, (2014). V.E. Oberacker, A.S. Umar, C. Simenel, PRC 90, (2014).

8 Quasifission in 48Ca+249Bk (ongoing-preliminary) DC-TDHF barriers

9 Quasifission in 50,54Cr+180,186W (Ec.m./VB=1.13) Two deformed nuclei with smaller mass/charge asymmetry than Ca+U tip-side tip-tip Experiment (to be published): MORE DETAILS IN ADITYA WAKHLE's TALK TOMORROW K. Hammerton, Z. Kohley, D. J. Hinde, M. Dasgupta, A. Wakhle, E. Williams,V. E. Oberacker, A. S. Umar, I. P. Carter, K. J. Cook, J. Greene, D. Y. Jeung, D. H. Luong, S. D. McNeil, C. S. Palshetkar, D. C. Rafferty, C. Simenel, and K. Stiefel

10 Mass Angle Distributions (MAD's) TIP-SIDE

11 Contact Time versus Mass/Charge Transfer and Rotation Angle Larger the contact time larger the mass transfer Larger the contact time larger the rot. angle

12 Moment of Inertia Ecm=203 MeV, b=0 Diagonalize the moment of inertia tensor Eigenvalues give the parallel/perpendicular moment of inertia Ecm=218.3 MeV, b=2.7 fm Ratio is not well determined Equivalent sphere Enters into QF angular distribution analysis

13 Moment of Inertia Cont'd Other quantities that may be usefull via TDHF Temperature at the saddle point Pr el im in ar y Can obtain from dynamical E* using DC-TDHF Completes the ingredients of

14 Collective Dynamics with DC-TDHF Obtain collective surface seen by TDHF using dynamical density as a constraint Ca + 238U Ecm=211 MeV, b= months of computing time! Ca + 238U Ecm=203 MeV, b=0 Outgoing valley Incoming valley Incoming valley Outgoing valley 40 Ca + 238U Ecm=211 MeV, b=0

15 DC-TDHF Barriers Capture Angle average 238U alignment Experimental data: 1. M. G. Itkis et al., J. Nucl. Radiochem. Sci. 3, 57 (2002) 2. M. G. Itkis et al., Nucl. Phys. A 734, 136 (2004) 1 - x-section falls rapidly for β>10o - sin(β) multiply small angles - P(β) is in the range σ f ( E c. m. )= d βsin (β) P (β)σ ( E c. m.,β) 0 A.S. Umar, V.E. Oberacker, J.A. Maruhn, and P.-G. Reinhard, PRC 81, (2010).

16 Summary TDDFT have a strong place among the theories needed for future challenges of low-energy nuclear physics Numerical issues are resolved limitations only due to theoretical approximations (effective interactions, mean-field theory, etc.) Quasifission and deep-inelastic reactions are well suited for TDDFT We now have a reasonable handle on above- and sub-barrier fusion employing the DC-TDHF approach One major and difficult area that needs attention is the dynamics of fission