Weak decays from coupled cluster computations

Transcription

1 Weak decays from coupled cluster computations Gaute Hagen Oak Ridge National Laboratory Topical Collaboration meeting on DBD + fundamental symmetries INT, June 20, 2017

2 @ ORNL / UTK: G. R. Jansen, T. Morris, T. Papenbrock, M. Schuster, Z. H. Chalmers: B. Carlsson, A. Ekström, C. Hebrew U: N. Barnea, D. MSU/ U Oslo: M. Trento: G. TRIUMF: S. Bacca, J. Holt, M. Miorelli, P. Navratil, S. R. TU Darmstadt: C. Drischler, C. Stumpf, K. Hebeler, R. Roth, A. Schwenk, J. LLNL: K. Wendt Collaborators

3 Outline CC computations of beta decays in 8 He and 14 C. Benchmark GT with other methods (CI-IM-SRG, NCSM). The quenching of g A Role of 2BCs and correlations on super allowed Gamow-Teller transition in 100 Sn Compute 2νββ and 0νββ decay in 48 Ca with full-space coupled-cluster

4 Quenching of Gamow-Teller strength in nuclei Long-standing problem: Experimental beta-decay strengths quenched compared to theoretical results. Renormalizations of the Gamow-Teller operator? Missing correlations in nuclear wave functions? Model-space truncations? Meson exchange currents (2BCs)? G. Martinez-Pinedo et al, PRC 53, R2602 (1996) Surprisingly large quenching Q (50%) obtained from (p,n) experiments. The excitation energies were just above the giant Gamow-Teller resonance ~10-15MeV (Gaarde 1983).

5 Charge exchange equation-of-motion coupled method Diagonalize H = e T H N e T via a equation-of-motion technique: R " = % r ( ' p * ( n ' % r '/ (0 p * ( N * 0 N / n ' % r '/4 (05 p * ( N * 0 N * 5 N 4 N / n ' A. Ekström, G. Jansen, K. Wendt et al, PRL (2014) Compute spectra of daughter nuclei as beta decays of mother nuclei Level densities in daughter nuclei increase slightly with 3NF Predict several states in neutron rich Fluorine

6 Charge exchange equation-of-motion coupled method Diagonalize H = e T H N e T via a equation-of-motion technique: R " = % r ( ' p * ( n ' % r '/ (0 p * ( N * 0 N / n ' % r '/4 (05 p * ( N * 0 N * 5 N 4 N / n ' A. Ekström, G. Jansen, K. Wendt et al, PRL (2014) Compute spectra of daughter nuclei as beta decays of mother nuclei Level densities in daughter nuclei increase slightly with 3NF Predict several states in neutron rich calcs Fluorine r (05 '/4 has massive requirements for realistic

7 8 He (g.s.) [MeV] Benchmarks for Gamow-Teller transitions in 8 He NCSM IM-SRG L-CCSD(T) 8 Li (1 + ) - 8 He(g.s.) [MeV] N 3 LO(500), λ srg = 1.8fm -1-9 N 3 LO(500), λ srg = 1.8fm NCSM IM-SRG EOM-CC M GT N max NCSM IM-SRG EOM-CC N 3 LO(500), λ srg = 1.8fm N max M GT N max NNLO opt NCSM EOM-CCSDT-1 EOM-CCSD IM-SRG N max

8 Normal ordered one- and two-body current Gamow-Teller matrix element: Normal ordered operator: Ô GT = O 0 N + O 1 N + O 2 N ON 0 = X hi O (1) ii + 1 X hij O (2) iji 2 iapplee f i,japplee f ON 1 = X hp O (1) qi{p q} + X X hpi O (2) qii{p q} pq pq iapplee f O 2 N = 1 4 X hpq O (2) rsi{p q sr} pqrs

9 One- and two-body currents and normal ordering in Coupled-Cluster CCSD similarity transformed normal-ordered current operator: T = T 1 + T 2 3-body terms 6-body terms O GT = e T O N e T = e T O 1 N e T + e T O 2 N e T Normal-ordered 1-body approximation J. Menéndez, D. Gazit, A. Schwenk PRL 107, (2011) Normal order with respect to free Fermi gas. One-body normal ordered approximation gives quenching of g A by a factor q = for different set of couplings constants

10 Benchmarks for Gamow-Teller transitions in 14 C N3LO(500) + 3N(L=400), λ srg = 2.0fm-1 NCSM EOM-CC IM-SRG M GT J π NCSM EOM-CC GT GT+MEC GT GT+MEC : l 3max /N max

11 Quenching of Ikeda sum rule in 14 C Quenching factor: Sum rule calculated in CC: A. Ekström, G. Jansen, K. Wendt et al, PRL (2014) N3LO(500) + 3N(L=400), λ srg = 2.0fm-1

12 Accurate BEs from light à heavy à infinite matter from a chiral interaction 1.8/2.0 (EM) from K. Hebeler et al PRC (2011) The other chiral NN + 3NFs are from Binder et al, PLB (2014) Accurate binding energies up to mass 100 from a chiral NN + 3NF Fit to nucleon-nucleon scattering and BEs and radii of A=3,4 nuclei Reproduces saturation point in nuclear matter within uncertainties Deficiencies: Radii are less accurate

13 Quenching of g A from two-body currents EOM-CC ESPM Experiment quenching factor BC uses same cutoff and LECs as the 1.8/2.0(EM) interaction A

14 Quenching of g A from two-body currents quenching factor EOM-CC ESPM Experiment P. Klos et al, arxiv: (2016) BC uses same cutoff and LECs as the 1.8/2.0(EM) interaction A

15 Gamow-Teller transition in 100 Sn Heaviest self-conjugate doubly magic nucleus Largest known strength in allowed nuclear β-decay In the closest proximity to the proton dripline At the endpoint of the rapid proton capture process (Sn-Sb-Te cycle) Unresolved controversy regarding s.p. structure of 101 Sn Sewernyiak et al PRL (2007) predicted a 5/2+ groundstate as presumably in 103 Sn Darby et al, PRL (2010) Hinke et al, Nature (2012)

16 Structure of the ligthest tin isotopes Faestermann, Gorska, & Grawe (2013) t=4 High 2 + energy in 100 Sn Predict 7/2 + ground-state in 101 Sn Experimental splitting between 7/2 + and 5/2 + reproduced Ground-state spins of Sn will be measured at CERN (CRIS collaboration)

17 100 In from charge exchange coupled-cluster equation-of-motion method Hinke et al, Nature (2012) 2.93(34) MeV 3p-3h charge-exchange EOM: H N R µ 0i = E µ R µ 0i Reproduce known 1 + state at 2.93(34) MeV Predict a 7 + ground-state for 100 In Ground-state spin of 100 In can be measured by CRIS collab. at CERN

18 Super allowed Gamow-Teller decay of 100 Sn Effects of triples excitations about 10%

19 Neutrinoless ββ-decay of 48 Ca 0νββ Nuclear matrix element for neutrinoless double beta decay in 48 Ca using different methods. From Y. Iwata et al, PRL (2016). The NME for 0νββ differ by a factor two or three depending on the method Need to determine the NME more precisely with quantified uncertainties What does ab-initio calculations add to this picture?

20 Neutrinoless ββ-decay of 48 Ca h 48 Ti O 48 Cai 2 = h 48 Ti O 48 Caih 48 Ca O 48 Tii Closure approximation with Gamow-Teller, Fermi and Tensor contributions: M 0 GT + gv g A 2 M 0 F + M 0 T The ground-state of 48 Ca is computed in the CCSD approximation: H N 0i = E 0 0i, H N = e T H N e T, T = T 1 + T 2 The CC energy functional is expressed in term of left/right ground-states h 0 (1 + )H N 0i = E 0, h 0 (1 + ) 0i =1. = X ia i aa a a i X ijab ij ab a ba a a i a j

21 Neutrinoless ββ-decay of 48 Ca 48 Ti is computed using a double charge exchange equation of motion method with 2p2h and 3p3h excitations R µ = 1 4 L µ = 1 4 X ijab X ijab r ab ij p ap b n in j l ij ab p bp a n i n j H N R µ 0i = E µ R µ 0i h 0 L µ H N = h 0 L µ E µ X ijkabc X ijkabc r abc ijk p ap b N c N k n i n j The Nuclear matrix element for 0νββ in 48 Ca is given by: l ijj abc p ap b N c N k n i n j h 48 Ti O 48 Cai 2 = h 48 Ti O 48 Caih 48 Ca O 48 Tii = h 0 L 0 O N 0ih 0 (1 + )O N R 0 0i

22 48 Ti from CR-EOM-CCSD(T) R " = 1 4 % r (0 '/ p * ( p * 0 n / n ' + 1 3! : % r (05 '/4 p * ( p * 0 N * 5 N 4 n / n '

23 48 Ti from CR-EOM-CCSD(T) R " = 1 4 % r (0 '/ p * ( p * 0 n / n ' + 1 3! : % r (05 '/4 p * ( p * 0 N * 5 N 4 n / n '

24 EOM-CR-CCSD(T)

25 Neutrinoless ββ-decay of 48 Ca NME for 0νββ Method GT Fermi Tensor CCSD CCSDT-1(10) CCSDT-1(12) CCSDT-1(14) NME computed with the chiral NN + 3N interaction 1.8/2.0 (EM) [K. Hebeler et al PRC (2011)] Model-space N max =10, hw = 22MeV. Not converged with respect to modelspace or truncation in 3p3h amplitudes Preliminary CC results agree with QRPA

26 quenching factor EOM-CC ESPM Experiment Summary Quenching of GT strength in nuclei from two-body currents A NME for 0νββ Method GT Fermi Tensor CCSD CCSDT-1(10) CCSDT-1(12) CCSDT-1(14) Super allowed GT transition in 100 Sn The NME for 0νββ in 48 Ca from coupledcluster calcualtions