Can the shell model be truly ab initio? and other questions

Transcription

1 Canada s national laboratory for particle and nuclear physics and accelerator-based science Can the shell model be truly ab initio? and other questions Ragnar Stroberg TRIUMF The tower of effective field theories and the emergence of nuclear phenemena CEA Saclay January 19, 2017 Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

2 Irreducible complexity? Strong vs weak emergence Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

3 Reductionism The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. Paul Dirac, 1929 i/ ψ = mψ V = e2 r +... Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

4 Can the shell model be ab initio? Outline 1. What is the shell model? 2. Is the shell model ab initio? 3. Can the shell model be derived from an underlying theory? 4. Can the shell model be formulated as an effective theory? 5. One magical chiral (-inspired) interaction, and hope for mankind Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

5 No core shell model Explicitly use harmonic oscillator basis HO forms complete basis Diagonalize with all nucleons active Extrapolate to infinite model space (variational principle) V(r) r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

6 No core shell model NCSM isn t really a model. It is a quasi-exact method for finding eigenstates of a given Hamiltonian. I will be discussing the Yes-core shell model. V(r) Explicitly use harmonic oscillator basis HO forms complete basis Diagonalize with all nucleons active Extrapolate to infinite model space (variational principle) r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

7 Analogy with atomic theory The nuclear shell model Ionization Energy (ev) He Ne Ar Kr Xe HgRn Atomic Number Z V(r) r Exp. Binding Energy - Liquid Drop Energy (MeV) Neutron number N V(r) r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

8 The nuclear shell model V(r) Valence Inert core r

9 The nuclear shell model V(r) Valence Inert core r

10 The nuclear shell model Large gap suppresses core excitations Structure due to valence particles Core provides static mean field V(r) Valence Inert core Valence particles interact via V eff 19-body problem 3-body problem But what is V eff? p 1 p 1 r V eff p 2 p 2 Pauli blocked Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

11 The nuclear shell model USD interaction: global fit to data yields spectroscopy with rms deviation 126 kev for sd shell nuclei. V(r) r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

12 The nuclear shell model Rotational band in 20 Ne V(r) r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

13 The nuclear shell model How does collectivity emerge in the shell model? H N N = mple example: a maximally coherent state Eigenvalues: { N, 0, 0,..., 0} Lowest eigenvector: 1 N (1, 1,..., 1) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

14 Is the shell model ab initio? The answer ab initio: Exact solution of exact problem 1 Degrees of freedom must be fully specified (e.g. free nucleons) 2 Hamiltonian is fundamental, i.e. not tailored to patch over deficiencies of the method 3 Solution method is exact (within estimated error) Allen and Karo, Rev. Mod. Phys. (1960) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

15 The answer Is the shell model ab initio? ab initio: Exact solution of exact problem 1 Degrees of freedom must be fully specified (e.g. free nucleons) no core shell model: Solution is exact V eff can be fundamental 2 Hamiltonian is fundamental, i.e. not tailored to patch over deficiencies of the method 3 Solution method is exact (within estimated error) Allen and Karo, Rev. Mod. Phys. (1960) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

16 The answer Is the shell model ab initio? ab initio: Exact solution of exact problem 1 Degrees of freedom must be fully specified (e.g. free nucleons) 2 Hamiltonian is fundamental, i.e. not tailored to patch over deficiencies of the method 3 Solution method is exact (within estimated error) no core shell model: Solution is exact V eff can be fundamental shell model: If V eff comes from fundamental theory, then solution is not exact If V eff is (empirically) adjusted to account for missing configurations, then it s not fundamental If V eff is derived from fundamental theory and accounts for missing configurations and operators are treated consistently Allen and Karo, Rev. Mod. Phys. (1960) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

17 Making the shell model ab initio How? Postulate: there exists some basis (d.o.f.) with identical quantum numbers, in which solution in the valence space reproduces the full solution V( r ) A fundamental Hamiltonian will induce excitations out of the valence space Valence Inert core r Change of basis corresponds to a unitary transformation H = U HU particle Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? quasi-particle Jan 20, / 28

18 Making the shell model ab initio The methods on the market Okubo-Lee-Suzuki Solve the problem exactly Obtain a valence space interaction which reproduces exact solution Valence cluster expansion? Many-body perturbation theory Treat excitations out of valence space perturbatively Q-box, resum select diagrams Does the series converge? In-medium SRG Series of unitary transformations Renormalization group flow to desired form Induced many-body forces? Coupled cluster may join in soon. Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

19 Okubo-Lee-Suzuki U A ˆP Ũ A Not unitary (excluded-space information is lost) Small-space interaction guaranteed to reproduce eigenvalues of large space But we already know those! Calculate other nuclei w/ valence cluster expansion Hope higher-body terms are negligible, justification is a posteriori Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

20 Okubo-Lee-Suzuki U A ˆP Ũ A Not unitary (excluded-space information is lost) Small-space interaction guaranteed to reproduce eigenvalues of large space But we already know those! Calculate other nuclei w/ valence cluster expansion Hope higher-body terms are negligible, justification is a posteriori core core core Core energy single-particle energy V NN Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

21 In-medium SRG U 1 U 2... U Unitary (in principle): H = e Ω He Ω No need to solve the large-space problem first work directly with H Induced 3-,4-...,A-body forces No guarantee that neglected higher-body terms will be unimportant, but... Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

22 In-medium SRG U 1 U 2... U Unitary (in principle): H = e Ω He Ω No need to solve the large-space problem first work directly with H Induced 3-,4-...,A-body forces No guarantee that neglected higher-body terms will be unimportant, but... e Ω He Ω = H + [Ω, H] + 1 [Ω, [Ω, H]] [Ω, H] 2 Ω H If Ω 1 2, then the largest source of error is likely [Ω 2b, H 2b ] 3b, and we can treat this perturbatively. Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

23 Ab initio shell model no core shell model + OLS coupled cluster + OLS in-medium SRG Dikmen et al. PRC (2015), Jansen et al. PRC(R) (2016), Stroberg et al. PRC(R) (2016) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

24 Ab initio shell model no 16 core shell model g.s. + band 8 14 coupled cluster + OLS + 24 OLS Mg γ band Energy (MeV) Experiment STD Φ 0 = 16 O TNO Φ 0 = 24 Mg USDB (fit) 8 7 in-medium10 SRG Experiment IMSRG 48 Cr Dikmen et al. PRC (2015), Jansen et al. PRC(R) (2016), Stroberg et al. PRC(R) (2016) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

25 Electric quadrupole transitions Effective charges for electric quadrupole operators O(E2) = i e i r 2 i Y (2) (θ i ) e p 1.5, e n 0.5 Can we do without them? Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

26 Electric quadrupole transitions E C E(2 + 1 ) (MeV) Exp NCSM ω=20mev Valence-space IM-SRG emax= 4 emax= 6 emax= 8 emax=10 emax=12 emax=14 EOM IM-SRG 7 core valence excluded decouple decouple B(E2; ) (e 2 fm 4 ) Nmax ω (MeV) 14 C ω (MeV) 28 NCSM results from Petr Navrátil, EOM results from Nathan Parzuchowski Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

27 Electric quadrupole transitions (3 ) core valence excluded E O decouple decouple E(2 + 1 ) (MeV) B(E2; ) (e 2 fm 4 ) Exp Valence-space IM-SRG ω (MeV) 22 O EOM IM-SRG emax= 6 emax= 8 emax=10 emax=12 emax= ω (MeV) EOM results from Nathan Parzuchowski Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

28 Electric quadrupole transitions Why??? 14 C in psd shell, compare CC, IM-SRG w/ FCI: core valence excluded E decouple decouple E(MeV) An/b 2 Ap/b C FCI psdmwk π ν neutron Nph π ν proton Nph CCS CCSD CCSDT CCSDT-1 CCSD CCS CCS CCSD CCSDT-1 π ν total Nph out of ref IMSRG(2) 0p IMSRG(2) 0p IMSRG(2) 0p π ν total Nph p sd Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

29 How should we think about the shell model? The shell model, as typically understood, is a model (but it s a pretty successful model) Fermi liquid theory: quasiparticles retain characteristics of the bare particles Quantum chemistry: separation into static and dynamic correlations An ab initio many-body method can be mapped onto the shell model nonperturbative treatment of excitations near the Fermi surface. core valence excluded static dynamic Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

30 How should we think about the shell model? The shell model, as typically understood, is a model (but it s a pretty successful model) Fermi liquid theory: quasiparticles retain characteristics of the bare particles Quantum chemistry: separation into static and dynamic correlations An ab initio many-body method can be mapped onto the shell model nonperturbative treatment of excitations near the Fermi surface. Paradigm: If a model works well but isn t fundamental, and if the fundamental theory is hard to solve, then map the fundamental theory to the model through a unitary transformation (RG flow). Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28 core valence excluded static dynamic

31 Another question Can the shell model be formulated as an effective theory? Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

32 Another question Can the shell model be formulated as an effective theory? Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

33 Another question Can the shell model be formulated as an effective theory? All of these express chiral EFT in an oscillator basis and solve exactly. Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

34 Shell model as an EFT Can the shell model be formulated as an effective theory? Answer: I don t know. Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

35 Shell model as an EFT Can the shell model be formulated as an effective theory? Answer: I don t know. Why would we want to make it an effective theory? Shell model with uncertainty estimates No need to bother mapping chiral EFT to the shell model Systematic improvements, e.g. 3N interaction, 2-body operators Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

36 First steps Degrees of freedom: quasiparticles outside of core Breakdown scale: core excitation energy Symmetries: J,π,... Small scale: shell splitting? Shell model as an EFT V(r) Valence Inert core r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

37 First steps Degrees of freedom: quasiparticles outside of core Breakdown scale: core excitation energy Symmetries: J,π,... Small scale: shell splitting? Shell model as an EFT Challenges Core shouldn t be a point-particle Is there any separation of scales? Which states to fit to? Origin of hierarchy of many-body forces? V(r) Valence Inert core Energy (MeV) /2+ 5/2 1/2 3/2 +5/2+ + 9/2 7/2 5/2 3/2 1/2 3/2+ 3/2 3/2 + 5/2 1/2 Energy (MeV) 17 F 1/2 + 5/ Energy (MeV) 16 O /2 5/2 3/2 + 7/2 5/2 1/2 1/2 +5/2+ 3/2+ 9/2 3/2 3/2 3/2 + 5/2 1/2 17 O 1/2 + 5/2 + r Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

38 One magical chiral (or chiral-inspired) interaction NN 3N EM 500/400 EM 1.8/2.0 N 3 LO same Λ 2N = 500 MeV same non-local regulator same fit to NN scattering, 2 H same λ SRG = 1.88 fm 1 same N 2 LO same Λ 3N = 400 MeV same local regulator non-local regulator fit to 3 H BE, t 1/2 fit to 3 H BE, 4 He r ch consistently SRG evolved no SRG for 3N Empirical saturation point EM 1.8/2.0 Hebeler et al. PRC(R) (2011), Drischler et al. PRC (2016), monis et al. (in prep.) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

39 One magical chiral (or chiral-inspired) interaction NN 3N EM 500/400 EM 1.8/2.0 N 3 LO same Λ 2N = 500 MeV same non-local regulator same fit to NN scattering, 2 H same λ SRG = 1.88 fm 1 same N 2 LO same Λ 3N = 400 MeV same local regulator non-local regulator fit to 3 H BE, t 1/2 fit to 3 H BE, 4 He r ch consistently SRG evolved no SRG for 3N Empirical saturation point EM 1.8/2.0 EM 500/400 EM 1.8/2.0 Hebeler et al. PRC(R) (2011), Drischler et al. PRC (2016), monis et al. (in prep.) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

40 One magical chiral (or chiral-inspired) interaction NN 3N EM 500/400 EM 1.8/2.0 N 3 LO same Λ 2N = 500 MeV same non-local regulator same fit to NN scattering, 2 H same λ SRG = 1.88 fm 1 same N 2 LO same Λ 3N = 400 MeV same local regulator non-local regulator fit to 3 H BE, t 1/2 fit to 3 H BE, 4 He r ch consistently SRG evolved no SRG for 3N Empirical saturation point EM 1.8/2.0 EM 500/400 EM 1.8/2.0 Neither interaction is fully consistent however... Saturation properties appear important for finite nuclei Hebeler et al. PRC(R) (2011), Drischler et al. PRC (2016), monis et al. (in prep.) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

41 EM 1.8/2.0 interaction E(2 + 1 ) A A Experiment EM1.8/2.0 SDPFMU E(2 + 1 ) A Ca Experiment EM 500/400 EM1.8/2.0 SDPFMU A Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

42 The neutron dripline S 26 P S 27 P Ar 29 S 28 P Ar 31 Cl 30 S 29 P Ar 32 Cl 31 S 30 P K 34 Ar 33 Cl 32 S 31 P K 35 Ar 34 Cl 33 S 32 P K 36 Ar 35 Cl 34 S 33 P K 37 Ar 36 Cl 35 S 34 P K 38 Ar 37 Cl 36 S 35 P K 39 Ar 38 Cl 37 S 36 P K 40 Ar 39 Cl 38 S 37 P K 41 Ar 40 Cl 39 S 38 P K 42 Ar 41 Cl 40 S 39 P K 43 Ar 42 Cl 41 S 40 P K 44 Ar 43 Cl 42 S 41 P K 45 Ar 44 Cl 43 S 42 P K 46 Ar 45 Cl 44 S 43 P K 47 Ar 46 Cl 45 S 44 P K 48 Ar 47 Cl 46 S 45 P K 49 Ar 48 Cl 47 S 46 P 51 K 50 Ar 49 Cl 48 S 52 K 51 Ar 50 Cl 53 K 54 K 55 K 56 K 52 Ar 51 Cl 53 Ar Proton number Z He 4 He 6 He 1 H 2 H 3 H PRELIMINARY 9 C 8 B 7 Be 10 C 13 O 12 N 11 C 10 B 9 Be 14 O 13 N 12 C 11 B 10 Be 6 Li 7 Li 8 Li 9 Li 8 He 17 Ne 15 O 14 N 13 C 12 B 11 Be 20 Mg 18 Ne 17 F 16 O 15 N 14 C 13 B 12 Be 11 Li 22 Al 21 Mg 20 Na 19 Ne 18 F 17 O 16 N 15 C 14 B 23 Al 22 Mg 21 Na 20 Ne 19 F 18 O 17 N 16 C 15 B 14 Be 24 Al 23 Mg 22 Na 21 Ne 20 F 19 O 18 N 17 C 25 Al 24 Mg 23 Na 22 Ne 21 F 20 O 19 N 18 C 17 B 26 Al 25 Mg 24 Na 23 Ne 22 F 21 O 20 N 27 Al 26 Mg 25 Na 24 Ne 23 F 22 O 21 N 20 C 28 Al 27 Mg 26 Na 25 Ne 24 F 23 O 22 N 29 Al 28 Mg 27 Na 26 Ne 25 F 24 O 23 N 22 C 30 Al 29 Mg 28 Na 27 Ne 26 F 31 Al 30 Mg 29 Na 28 Ne 27 F 32 Al 31 Mg 30 Na 29 Ne 33 Al 32 Mg 31 Na 30 Ne 29 F Neutron number N 34 Al 33 Mg 32 Na 31 Ne 35 Al 34 Mg 33 Na 32 Ne 31 F 36 Al 35 Mg 34 Na 33 Ne 37 Al 36 Mg 35 Na 34 Ne 38 Al 37 Mg 36 Na 39 Al 38 Mg 37 Na 40 Al 39 Mg 41 Al 40 Mg 42 Al 43 Al Heaviest known neutron dripline FRDM 1995 HFB-8 EM1.8/2.0 Baumann et al. Nature (2007), Möller et al. (1995), Samyn et al. (2004), Holt et al. (in prep.) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

43 The heavy-mass frontier The tin isotopes (Z = 50) 100 Sn: 50 protons, 50 neutrons core valence excluded decouple decouple Open shell valence space: full gds shell m-scheme dimension Need importance truncation to diagonalize! Ground state energy (MeV) emax = 10, E3max = 14 emax = 12, E3max = 14 emax = 14, E3max = 14 emax = 14, E3max = 16 emax = 14, E3max = 18 EM 1.8/ Sn Experiment ω (MeV) monis et al. (in prep.), Stumpf et al. PRC(R) (2016) Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

44 Ground state energy (MeV) Isotopic chain with ω = 16, e max = 14, E3 max = 16 PRELIMINARY Tin isotopes Experiment EM 1.8/ (Z = 50) A S2n (MeV) Experiment EM 1.8/ A Sn (MeV) 3pt (MeV) Open shell tin isotopes 15 Experiment 14 EM 1.8/ A Experiment EM 1.8/ A Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

45 Collaborators The shell model can be derived ab initio The SM can be seen as an efficient separation of degrees of freedom Attempts at ab initio effective charges aren t yet successful Formulating the SM as an effective theory appears frought with difficulties EM 1.8/2.0 interaction suggests that once you get N N scattering and saturation, things fall into place Collaborators: A. Calci, J. Holt, J. Kozaczuk, D. Morrissey, P. Navrátil NSCL/MSU S. Bogner, H. Hergert, N. Parzuchowski TU Darmstadt R. Roth, A. Schwenk, J. monis ORNL/UT G. Hagen, T. Morris Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

46 Backup slides Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

47 Ψ Φ E/A (MeV) AME SM (C=R) ENO ngle Ref. 22 O 24 O 28 O S 36 S 36 Ca 40 Ca Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

48 E E3 + (MeV) E E3 + (MeV) B Λ 3N =400 MeV Λ 3N =500 MeV 10 B (a) 10 IT-NCSM B 8 He 4 He (full 3N) IM-SRG ref. Λ 3N =400 MeV Na Λ 3N =500 MeV 22 Na (b) 22 Exp. Na 16 O IM-SRG ref V Λ 3N = 400 MeV Λ 3N = 500 MeV ( ) see 3 + text 46 V (c) 46 Exp. V 40 Ca IM-SRG ref. Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28

49 Egs (MeV) Egs (MeV) (a) (d) 260 A C (Z=6) Experiment CCSD(T) IT-NCSM MR-IM-SRG IM-SRG(ENO) A A Na (Z=11) Experiment IM-SRG(SM) IM-SRG(ENO) A A N (Z=7) Experiment SCGF GGF IT-NCSM IM-SRG(ENO) (b) A A Ca (Z=20) CRCC MR-IM-SRG IM-SRG(SM) IM-SRG(ENO) (e) A (c) A O (Z=8) Experiment SCGF GGF CCSD(T) IT-NCSM MR-IM-SRG IM-SRG(SM) IM-SRG(ENO) A A Ni (Z=28) CRCC MR-IM-SRG IM-SRG(SM) IM-SRG(ENO) (f) A Ragnar Stroberg (TRIUMF) Can the shell model be truly ab initio? Jan 20, / 28