Molecular Structures in Slow Nuclear Collisions
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1 Molecular Structures in Slow Nuclear Collisions ALEXIS DIAZ-TORRES European Centre for Theoretical Studies in Nuclear Physics and Related Areas Trento, Italy
2 Nuclear Structure Reaction Dynamics FAIR Nuclear Astrophysics Motivation & Some Key Concepts Linking Nuclear Structure & Reaction Dynamics in the Formation of New Elements Summary & Outlook
3 Mass Distribution of Binary Fragmentation Thomas et al., PRC 77 (2008) Ti Er 48 Ti quantum transport (mass & charge) 170 Er
4 Quasi-Elastic Back-Scattering Energy Spectrum Evers et al., PRC 78 (2008) O+ 208 Pb complex excitations low-lying collective excitations
5 Reactions between Complex Nuclei at Low Energy Reaction Dynamics E S Nuclear Structure Coupling between nuclear structure & reaction dynamics determines the reaction observables (cross sections)
6 Time-Dependent Wave-Packet Dynamics D.J. Tannor, Quantum Mechanics: a Time-Dependent Perspective, USB, 2007 Preparation: the initial state Time propagation:, guided, by the evolution operator, where is the total Hamiltonian. Analysis: extraction of cross sections from the power spectrum of the time-dependent wave function.
7 Quantum Tunnelling in the 12C + 12C Fusion Clear physical picture facilitates data interpretation AD-T & Wiescher, EPJ Web of Conf. 93 (2015) In collaboration with Michael Wiescher (JINA)
8 Fusion Cross Section & Astrophysical S Factor Structural factor [MeV barn] Fusion cross section [barn = m2] Sommerfeld parameter S(E) represents the fusion cross section free of Coulomb suppression, which is adequate for extrapolation towards stellar energies
9 Astrophysical S-Factor Excitation Function for 12C + 12C
10 Coupled-Channels Calculations for 12C + 12C C.L. Jiang et al., PRL 110 (2013) Ec.m. (MeV) The physics of intermediate structure seems not to be included
11 12 12 Excitations in the C + C Nuclear Molecule Greiner, Park & Scheid, in Nuclear Molecules, World Scientific, 1994 Quadrupole deformation of 12C: ~ -0.5 How does this molecular structure affect low-energy fusion?
12 Sensitivity of Molecular Shell Structure to the 12C Alignment Potential Separable Expansion Method AD-T, PRL 101 (2008)
13 Quantum Partner-Dance of Two 12C Nuclei Collective Potential Energy Landscape Fusion Shape coexistence AD-T & Scheid, NPA 757 (2005) 373 AD-T, PRL 101 (2008)
14 Kinetic-Energy of Two Deformed Colliding Nuclei Gatti et al., JCP 123 (2005) Coriolis interaction
15 Initial state : the 12C nuclei are well separated Radial motion Internal rotational motion
16 Time Propagation of the Wave Function evolution operator The evolution operator is represented as a convergent series of modified Chebyshev polynomials Tannor, Quantum Mechanics from a Time-Dependent Perspective, USB, 2007
17 Power Spectrum of the Wave Function Energy projector Reflection & Transmission Coefficients E T E E E E
18 PRELIMINARY Molecular structure & fusion are closely connected AD-T & Wiescher, EPJ Web of Conf. 93 (2015) Astrophysical S-Factor Excitation Function for 12C + 12C
19 Nuclear Structure Reaction Dynamics FAIR Nuclear Astrophysics What will be the results for some experimental programmes at exotic beam facilities, if we do not properly understand the link between nuclear structure & reaction dynamics? A time-dependent quantum perspective is one useful approach for understanding, elucidating and quantifying the physics of low-energy nuclear reactions.
20 EXTRA SLIDES
21 16 16 Applying the TDWP method to O+ O
22 Two Center Shell Model: 32 S O+ O AD T & Scheid, NPHA 757 (2005) 373
23 16 16 Collective Potential & Mass Parameter: O + O AD T, Gasques & Wiescher, PLB 652 (2007) 255
24 S-Factor Excitation Curve for 16 O+16O AD T, Gasques & Wiescher, PLB 652 (2007) 255
25 Energy Projection of the Wave Function Schafer & Kulander, PRA 42 (1990) 5794 Energy spectra of at initial and final time as expectation values of the projection operator,, for instance, n = 2 :
26 Results Transmission coefficients compared with those obtained from a time-independent calculation
27 Reaction Dynamics of Weakly Bound Nuclei Useful for understanding sub-coulomb fusion data Boselli & AD-T, PRC 92 (2015) In collaboration with Maddalena Boselli, PhD student at the ECT*
28 One-Dimensional Toy Model x2 =xcm +b ξ x1 =xcm a ξ P2x Pξ 2 H= + +U 12 (ξ)+v T1 (x CM a ξ)+v T2 (x CM + b ξ) 2M T12 2m12 CM
29 Describing Fusion V, Im[W] (MeV) To simulate fusion (irreversibility): acting inside the Coulomb barrier iw T1 ( x 1) & V Rb1 Im[W] Fusion x1 (fm) iw T2 ( x2 )
30 Preparing the Initial State 4 He 2 H 6 Li
31 Time Propagation R. Kosloff, Ann. Rev. Phys. Chem. 45 (1994) 145 The Chebyshev Propagator
32 Slicing the Wave Function: A Novel Idea (Heaviside function) P i = Θ( R bi x i ) Qi = 1 Pi 209 V (MeV) Projection operator acting on the position xi of the fragment relative to the target Potential: Bi - 4He Rb1 x1(fm) Act with ( P1 +Q1 ) ( P2 +Q 2)=1 on the wave function: x1, x2, t )=ΨCF +Ψ ICF +Ψ SCATT Ψ ( x1, x 2,t )=(P 1 P2 +P 1Q 2 +Q1 P2 +Q 1 Q 2 ) Ψ(
33 Example Energy-resolved total transmission coefficient for different values of mean energy of the initial wave packet X0=120 fm sig0=10 fm
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