Shape coexistence and beta decay in proton-rich A~70 nuclei within beyond-mean-field approach

Transcription

1 Shape coexistence and beta decay in proton-rich A~ nuclei within beyond-mean-field approach A. PETROVICI Horia Hulubei National Institute for Physics and Nuclear Engineering, Bucharest, Romania

2 Outline complex EXCITED VAMPIR beyond-mean-field model shape-coexistence effects on structure and dynamics of Se shape-coexistence effects on - superallowed Fermi β-decay of the ground state of Br - Gamow-Teller β-decay of the 9 isomer of Br

3 A~ proton-rich nuclei exhibit drastic changes in structure with number of nucleons, spin, excitation energy generated by shape coexistence and shape mixing competing T=0 and T= pairing correlations isospin-symmetry-breaking interactions Challenges for theory realistic effective Hamiltonians in adequate model spaces, beyond-mean-field methods comprehensive understanding of structure phenomena and β-decay properties

4 complex VAMPIR model family the model space is defined by a finite dimensional set of spherical single particle states the effective many-body Hamiltonian is represented as a sum of one- and two-body terms the basic building blocks are Hartree-Fock-Bogoliubov (HFB) vacua the HFB transformations are essentially complex and allow for proton-neutron, parity and angular momentum mixing being restricted by time-reversal and axial symmetry (T= and T=0 neutron-proton pairing correlations already included at the mean-field level ) the broken symmetries (s=n, Z, I, p) are restored by projection before variation * The models allow to use rather large model spaces and realistic effective interactions

5 Beyond mean field variational procedure complex VAMPIR complex EXCITED VAMPIR

6

7 A ~ mass region 40 Ca - core model space for protons and neutrons p / p 3/ 0f 5/ 0f 7/ d 5/ 0g 9/ (charge-symmetric basis Coulomb contributions to the π-spe from the core) renormalized G-matrix (OBEP- Bonn CD) pairing properties enhanced by short range Gaussians for: T = : pp ( -35 MeV), np ( -0 MeV), nn ( -35 MeV) T = 0: np ( -35 MeV) onset of deformation influenced by monopole shifts: <0g 9/ 0f; T=0 G 0g 9/ 0f;T=0> (0f 5/, 0f 7/ ) <d 5/ p; T=0 G d 5/ p;t=0> (p /, p 3/ ) Coulomb interaction between valence protons added

8 Shape mixing in the analogue states of the A = isovector triplet: 36 Kr Br Se 36 Se I(h) - Prolate content Oblate content 0 4(4)()() % 5() % 56() % 39() % 5() % 43() % 6 76(3)()() % 7() % A. Petrovici, Phys. Rev. C 9, 0430 (05) Phys. Scr.9, (07)!ground state > dominated by oblate components in Se, but prolate ones in Br Br I(h) - Prolate content Oblate content 0 68() % 6()() % 66() % 9() % 68()() % 6() % 6 8(4)()()() % 0() %!similar structure for Br and Kr Kr I(h) - Prolate content Oblate content 0 69(3) % 4(3) % (3) % 4() % 75(3) % 9() % 6 86(3)() % 7() %

9 Shape-coexistence effects in low-energy spectra Excitation energy / MeV Se Br Kr Exp Theory Exp Theory Exp Theory Kr 4 p(o) o(p) Excitation energy / MeV EXVAM

10 Shape mixing in the lowest two bands of Kr wave functions - yrast states dominated by prolate deformed configurations - yrare states manifest oblate dominated content I(h) - Prolate mixing Oblate mixing 0 69(3)% 4(3)% 0 3(4)(4)(3)()()% 48(3)()% (3)% 4()% 5()()% 7()% 4 75(3)% 9()% 4 9()% 78% 6 86(3)()% 7()% 6 8()()% 87()% B(E;ΔI=) (e fm 4 ) confirmed by recent experimental data I(h) - p(o)-band o(p)-band 589() (3) (44) 88(33) spectroscopic quadrupole moments (efm ) I(h)

11 Shape mixing in the lowest bands of Se Se p(o) o(p) p-bands Excitation energy / MeV (8 ) (6 ) 8 (6 ) EXP 0 EXVAM

12 Wave functions and electromagnetic properties for Se - yrast states dominated by prolate deformed configurations - yrare states manifest oblate dominated content I(h) - Prolate Oblate content content I(h) - Prolate mixing Oblate mixing 58% 4% 4% 59% 8 84(3)()() % % 4 54% 46% 8 47()(7)(4)(4)(3)() % 8 % 4 45% 55% 8 3 (5)()() % 73 % 6 8% 9% 0 5(39)()() % 6 9% 8% 0 40(40)(7)(5)()()() % 0 5 0() % 84% Precise quadrupole moments could test the oblate-prolate mixing scenario I(h) - I(h) B(E;ΔI=) (e fm 4 ) I(h) - p(o)-band o(p)-band Exp (9) (4) 6 738(9) 730(58) 530(96) 8 78(78) 404(09)(49)(54) 0 564(86)(55) 477(09)(53)(47)

13 Self-consistent weak interaction rates Fermi transition probabilities B if (F )= J i g V 4π M F M F (ξ f J f ˆ ξ i J i ) = δ Ji J f M F (ab)(ξ f J f [c a c b] 0 ξ i J i ) ab M F (ab) =(a ˆ b) Gamow-Teller transition probabilities B if (GT )= J i M GT (ξ f J f ˆσ ξ i J i ) g A 4π M GT = M GT (ab)(ξ f J f [c a c b ] ξ i J i ) ab M GT (ab) =/ 3(a ˆσ b) Independent chains of variational calculations for the parent and daughter nuclei

14 Shape coexistence effects on weak interaction rates Isospin-symmetry-breaking and shape-coexistence effects on superallowed Fermi β-decay A. Petrovici, J. Phys.: Conf. Series 74 (06) 0038 test of the CVC hypothesis test of the unitarity of CKM matrix δc isospin-symmetry-breaking correction Kr Q EC = MeV /4π) V B(F) (g Kr -> 0 0 gs /4π) V B(F) (g -> Kr yrast Excitation energy (MeV) Excitation energy (MeV) % δ c.5% Nonanalog branches: % δ c 3 % Nonanalog branches: 0 IV, 0 V 0.4 % IV.3 %

15 Shape coexistence effects on superallowed Fermi β-decay of Br /4π) V B(F) (g Br 0 gs -> Excitation energy (MeV) Br Q EC = 9.9 MeV δ c %

16 Shape coexistence and Gamow-Teller β-decay of Kr A. Petrovici and O. Andrei, Phys. Rev. C9, (05) Large variety of deformations in daughter states revealed by spectroscopic quadrupole moments ) ) (efm Q sp Br Gamow-Teller states Excitation energy (MeV) (efm Q sp 80 Br 60 3 Gamow-Teller states Excitation energy (MeV)

17 Gamow-Teller strength distributions for the decay of 0 and states in Kr Specific shape mixing for each parent and daughter state influences the strength distributions B(GT) (g /4π) A -> Kr 0 gs B(GT) (g /4π) A -> Kr 0 exc Excitation energy (MeV) Excitation energy (MeV) B(GT) (g /4π) A -> Kr yrast B(GT) (g /4π) A -> 3 Kr yrast Excitation energy (MeV) Excitation energy (MeV) Contributions from p ν(π) / pπ(ν) 3/, pν 3/ pπ 3/, f ν 5/ f π 5/, f ν(π) 5/ f π(ν) 7/, gν 9/ gπ 9/ (coherent / cancelling effect) matrix elements

18 T / = D Terrestrial half-lives 0<E f <Q EC f(z, E f )[B if (GT )B if (F )] T / exp = 5(7) ms T / GT = 58 ms T / EXVAM = 5 ms T / F = 63 ms

19 Shape coexistence and Gamow-Teller β-decay of the 9 isomer in Br!prolate configurations dominate the structure of the 9 isomer in Br!large variety of deformations revealed by spectroscopic quadrupole moments of daughter states in Se Q sp (efm ) Se lowest 35 8 states Excitation energy (MeV) Q sp (efm ) Se lowest 0 states Excitation energy (MeV)

20 Gamow-Teller strength distributions for the decay of the 9 isomer in Br 0 - Br 9 8 Specific shape mixing for parent and daughter states influences the strength distributions Br Contributions from p ν(π) / pπ(ν) 3/, pν 3/ pπ 3/, f ν 5/ f π 5/, dν 5/ dπ 5/, gν 9/ gπ 9/ matrix elements (coherent / cancelling effect)

21 Br isomer half-life T / = K E f f (Z, E f )B if (GT ) Q EC =.90 MeV T / exp =. () s T / EXVAM =.3 s

22 Summary complex EXCITED VAMPIR scenario concerning shape-coexistence effects on structure and dynamics of Se superallowed Fermi β-decay of the ground state of Br Gamow-Teller β-decay of the 9 isomer of Br