Lecture 1: Nuclei as Open Quantum Systems

Transcription

1 Lecture 1: Nuclei as Open Quantum Systems H. Lenske Institut für Theoretische Physik, U. Giessen

2 Open Quantum Systems An open quantum system is a quantum system which is found to be in interaction with an external quantum system, the environment. The open quantum system can be viewed as a distinguished part of a larger closed quantum system, the other part being the environment. Typical Phenomena and Concepts: Decoherence Dephasing Dissipaton Resonance trapping Level Mixing Semi-classical approximations

3 General References: Accardi L., Lu Y.G., Volovich I.V. Quantum Theory and Its Stochastic Limit. New York: Springer Verlag, Breuer, Heinz-Peter; F. Petruccione (2007). The Theory of Open Quantum Systems. Oxford University Press. Davies E. B. Quantum Theory of Open Systems. -- Academic Press, London, 1976.

4 Nuclei as Open Quantum Systems Scale Problem: hadronsnuclear many-body problemactive, effective dof Model Space Problem: P-Space (the OPEN QM system) and Q-Space (the environment) Effective Interactions in the P-Space Interplay of Many-body and Single Particle Dynamics Mixing of bound and continuum spectral regions Limits of the Mean-Field Concept?

5 Agenda: Sketch of the Theoretical Background: ab initio relativistic DFT Pairing in the Continuum Core Polarization and Fano-Resonances (New Modes of Excitation: Pygmy Resonances)

6 I. Introduction: Features of Nuclear Many-Body Dynamics

7 Nuclei as Open Quantum Systems: Hilbert-Space: H=P+Q Feshbach Projector Formalism P Q1 ; P Q 0 ; P P ; Q Q: HPP E HPQ P 0 HQP HQQ E Q H PP H P Q HQ QQ P P 0 E i H

8 Realizations in Nuclear Structure and Reaction Physics: Shell Model: active shells P-space s.p. Shell Model/HFB Theory: Space of single Slaterdeterminants P-space Bound States (P-space) and Continuum States (Qspace) Optical Potential: elastic scattering P-space

9 Approachuing the Driplines Change of Energy-Scale: S stable ~10MeV S exotic ~100keV <U MF > <V NN > Coupling to the Continuum!

10

11

12 II. Aspects of an ab initio Nuclear Density Functional Theory

13 A welknown functional the Mass Formula: a functional of neutron number N and proton number Z E(N,Z)/A = -16MeV + E surf /A 1/3 + E pair + E shell + E coul + [(N-Z)/A] 2 (a 4 + C sym /A 1/3 ) The nuclear energy density functional: a functional of neutron (q=n) and proton (q=p) densities 1 E,,... T( ) E,... 2 q q q q int q q

14 The Giessen DDRH Program: ab initio Nuclear DFT ( Seminar!) NN-Interaction in free space in-medium interactions by Dirac-Brueckner Theory adding 3-body interactions density dependent meson-nucleon vertex functionals equation of state, nuclear binding energies, single particle Thermodynamical consistentxy (Hugenholtz-van Hove theorem) spectra, excitations, reactions

15 Building blocks for a covariant nuclear DFT Dirac-Brueckner Euler-Lagrange g (, ) C. Fuchs, H. L., PRC 52 (1995), F. Hofmann, H.L., PRC64 (2001)

16 Nuclear Matter DBHF Vertices (Seminar!) Isoscalar Vertices F. de Jong, H.L., PRC57 (1998). Isovector Vertices

17 DDRH Results: B B theo B B exp exp B(A) and Charge Radii Hartree Vertices r r r 2 2 theo r 2 exp exp

18 Neutron Skins in Ni and Sn Isotopes Neutron Skin and Symmetry Energy: Bonn A : a 4 = 32 MeV Groningen : a 4 = 26 MeV Sn Data: Krasnahorkay et al. PRL 82 (1999) 3216 (from Charge Exchange Spin-Dipole sum rules) F. Hofmann et al., PR C64 (2001) N. Tsoneva. H.L., PLB586 (2004), PRC77 (2008), PRL 2009, PRL 2010

19 III. Pairing in the Continuum

20 Pairing in Infinite Nuclear Matter Free Space SE (S=0,T=1) Interaction: (Bonn-B Potential) Pairing is a LOW DENSITY Phenomenon

21 Pairing-Field in Finite Nuclei R A R A

22 Pairing Theory as Coupled Channels Problem: The Gorkov-Equations H ( H ) E ( q) ( q) ~ u j ( r) ( s) jm ; ~ v j ( r) ( s) jm Mean-Field Hamiltonian (q p,n): q nj 2 H U( ) 2m 2j1 (r) v (r) 4 2 (q) 2 nj Pairing-Field & Density (q V 1 q 2 SE q 2j1 (r) u (r)v (r) (q) (q)* q n j n j nj 4 p,n):

23 Spectrum of the Gorkov Equation:

24 Extended HFB Theory: Pairing Self-Energies Energy Shifts and Widths Spectral Functions for particles and holes

25 S. Orrigo, H.L., PLB 677 (2009) Pairing in the Continuum (q=proton,neutron)

26 11 Li : Continuum HFB Spectral Functions Neutron Spectrum:

27 g.s. Densities g.s. Densities r 2 : 2 ) ( ), ( ) ( r e v de j r q q j j q jm s r v n p q for q j q ) ( ) ( :, ) ( ) ( 11 Li : Continuum HFB g.s. Densities

28 Pairing Resonances in Dripline Nuclei 9 Li+n 10 Li r Tq Uq 2 q+eα Δq r uαq r 0 Δq r Tq Uq eα v αq S. Orrigo, H.L., PLB 677 (2009) & ISOLDE newsletter Spring 2010, p.5

29 Continuum Spectroscopy: 10 Li= 9 Li+n d( 9 Li, 10 Li)p@2.36AMeV Data: H. Jeppesen et al., REX-ISOLDE Collaboration, Nucl. Phys. A 738 (2004) 511 & Nucl. Phys. A 748 (2005) 374.

30 IV. Core Polarization and Continuum Dynamics

31 The Softness of Exotic Nuclei: Polarizability

32 Sum Rules n S1 0 T, H, T 2 S E c T 0 n 1: Polarization Sum Rule n 0 : NEWSR - Non-Energy Weighted Sum Rule n 1: EWSR - Energy Weighted Sum Rule special case EWSR : 1 c n c ~ 0 T 0 2 2M

33 The Neutron Halo in 19 C: Transition from Mean-Field to Correlation Dynamics The s.p. shell model (HFB) picture 1 U(r) U 0(r) 3U 1(r) 1 3 U c(r) 2 U (r) U ( ), n p U (r) U ( ), n p U (r) U ( ), c c c c c,n c,p H.L.,J. Prog.Part.Nucl. 561 (2004)

34 Carbon-Isotopes: HFB d-wave level density S ( E) 2( j 1) d de Carbon-Isotopes: HFB s-wave level density

35 Core Polarization and 1n-Neutron Halo States: Transition from Mean-Field to Correlation Dynamics The DCP picture: Binding by Virtual Continuum Coupling H.L.,J. Prog.Part.Nucl. 561 (2004)

36 The DCP State Operators and Eigenstates: Diagonalize the Hamiltonian of the A±1 System: H=H MF +H QRPA +V 13 nljm 0 E, jm E 0 nljm jm E z (E) z (E) c c jm nlj nljm n 'l' j'j n 'l' j' J n n 'l' j'j n z (E) z (E) 1 nlj 2 2 n 'l' j'jc n 'l' j'j c c jm e E z nlj V z 0 nlj nlj 13 n 'l' j'j e E E z V nlj z 0 n 'l' j' Jc 13 nlj n c

37 The DCP State Operators and s.p. Wave functions: Hamiltonian of the A±1 System: H=H MF +H QRPA +V 13 E, jm E 0 jm E z (E) z (E) c c jm nlj nljm n 'l' j'j n 'l' j' J n n 'l' j'j u ( ) nlj ljm (r,e) z nlj(e) nljm(r) n v nlj c jm

38 f(r)/r [1/fm^(3/2)] f(r)/r [1/fm^(3/2)] C(1/2+) DCP Wavefunctions HFB DCP C(1/2+) DCP Wavefunctions HFB DCP r [fm] r [fm] C(1/2+) DCP Wavefunctions HFB DCP r [fm] C(1/2+) DCP Wavefunctions HFB DCP r [fm]

39 Longitudinal Momentum Distributions and DCP: 17,19 C 16,18 C + n Breakup on a Carbon Target@900 AMeV 17 C Binding: Correlation Dynamics 17 C(5/2+,g.s.) S n (the.)=715kev C 2 S(g.s.) = 0.41 (the.): 132 MeV/c (exp.): 143 ± 5 MeV/c s(-1n,the.): 124 mb s(-1n,exp.): 129± 22 mb 19 C Binding: Correlation Dynamics 19 C(1/2+,g.s.) S n (the.)=263kev C 2 S(g.s.) = 0.40 (the.): 69 MeV/c (exp.): 68 ± 3 MeV/c s(-1n,the.): 192 mb s(-1n,exp.): 233± 51 mb

40 24 O Breakup at 920AMeV: 24 O a new doubly magic Nucleus (Z=8,N=16) Ebind 99 4MeV / c FWHM MeV Sn MeV open circles: exp. resolution

41 1/2 + Particle and Hole Strength Functions in 14 C Hole strength function Particle strength function

42 Correlation Dynamics in an Open Quantum System: Fano-Resonances in 15 C ~60 140keV Sonja Orrigo, H.L., Phys.Lett. B633 (2006)

43 Interference in Quantum Systems: Asymmetric Line Shapes and Fano-Resonances

44 Summary and Outlook Exotic Nuclei as Open Quantum Systems Continuum Spectroscopy and Dynamical Correlations New Generic Modes of Exotic Nuclei PDR, PQR Challenges: Many-body Dynamics at extreme Isospin Nuclear Structure at weak Binding Reaction Theory for weakly Bound Systems Credits to: Nadia Tsoneva, Urnaa Badarch, A. Ataie, A. Fedoseew, P. Konrad, Anika Obermann, Sonja Orrigo, M. Strecker