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3.04 MB
Atomic Theory of Few-Electron Systems for Nuclear Charge Radii Determination Zong-Chao Yan Department of Physics University of New Brunswick Canada [email protected] (Established 1785) March 19-21, 2012, Bad Honnef Collaborators: Gordon Drake (Univ. of Windsor) Li-Ming Wang (Univ. of New Brunswick) Hao-Xue Qiao (Wuhan University) W. Nörtershäuser GSI team Supports: NSERC, SHARCnet, ACEnet P R O J E C T S D O N E Li-11 nuclear charge radius by W. Nörtershäuser: R. Sánchez, G. Ewald, D. Albers, J. Behr, P. Bricault, B. A. Bushaw, A. Dax, J. Dilling, M. Dombsky, G. W. F. Drake, S. Götte, R. Kirchner, H.-J. Kluge, Th. Kühl, J. Lassen, C. D. P. Levy, M. R. Pearson, E. J. Prime, V. Ryjkov, A. Wojtaszek, Z.-C. Yan, C. Zimmermann Be-11 nuclear charge radius by W. Nörtershäuser: D. Tiedemann, M. Záková, Z. Andjelkovic, K. Blaum M. L. Bissell, R. Cazan, G. W. F. Drake, Ch. Geppert, M. Kowalska, J. Krämer, A. Krieger, R. Neugart, R. Sánchez, F. Schmidt-Kaler, Z.-C. Yan, D. T. Yordanov, C. Zimmermann Be-12 nuclear charge radius by W. Nörtershäuser: A. Krieger, K. Blaum, M. L. Bissell,N. Frömmgen, Ch. Geppert,M. Hammen, K. Kreim, M. Kowalska,J. Krämer, T. Neff,R. Neugart, G. Neyens, Ch. Novotny, R. Sánchez, and D. T. Yordanov Measurement of nuclear charge radii Nuclear physics: nuclear model-dependent Atomic theory & measurement: model-independent (Drake, 1980’s) ∆Enuc 2π Rnuc = 3 2 ∑ δ (r ) i i Etheory = Enr + α 2 Erel + α 3 EQED + + ∆Enuc Eexperi = Etheory (Rnuc ) ⇒ Rnuc determined Test low energy nucleon-nucleon interaction potential Review article: Halo Nuclei in Laser Light, in Lecture Notes in Physics, 745 131-153 (Springer-Verlag, Berlin, 2008). W. Nörtershäuser, et al. PRA , 83, 012516 (2011). Theoretical background For low-Z systems, we use perturbation theory: H = H 0 + α H rel + α H QED + 2 3 H 0Ψ 0 = E0Ψ 0 Etot = E0 + α 2 Ψ 0 H rel Ψ 0 + α 3 Ψ 0 H QED Ψ 0 + Variational principle: Ψ tr H 0 Ψ tr Etr ≡ Ψ tr Ψ tr then Etr ≥ E0 Etr E0 Relativistic and QED corrections H rel = − α2 8 ∑∇ + i ∑ δ (ri ) [lnα −2 ]− β (nLS ) + 4 3 ∆ EQED = α 3 Z Q= 1 4π 1 1 ( ) r r ∇ ⋅ ∇ + ⋅ ⋅ ∇ ∇ ∑ i j ij i j + 3 ij rij 2 i > j rij α2 4 i ∑ lim r (a ) −3 i> j β (nLS ) = a →0 ∑ n ij 0pn ∑ 2 19 14 164 + lnα + 30 3 15 ∑ δ (rij ) − i> j 14 Q 3 + 4π (γ + lna )δ (rij ) (En − E0 ) ln En − E0 0pn 2 ( E n − E0 ) n The Bethe logarithm β (nLS ) is very difficult to calculate. For Rydberg states of two-electron ions (Goldman and Drake): 4 ( 0.316205(6 ) Z − 1) β (nLS ) = β (1s ) + 4 3 β (nL ) + 6 Z n Z r −4 nL Derive the me/mp ratio (Paris, Dusseldorf, Amsterdan) Ground state of lithium Computational features • Quadrupole precision real*16 (32 digits) • Parallelization a) matrix elements ∝ N b) power method ∝ N • Use QD (32*2=64-digit arithmetic by Bailey) to check and find no loss of precision. 2 3 Wang, Yan, Qiao, Drake, PRA (submitted) 2 2 1s 3d D QED corrections g≈10 Difficulty: α ~1 α + β +γ Chun Li solved this problem (brand new recursion relations, unpublished) Thanks