variational approach to isospin symmetry breaking in medium mass nuclei a. petrovici institute for...
DESCRIPTION
Complex EXCITED VAMPIR approach the model space is defined by a finite dimensional set of spherical single particle states 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 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 basic building blocks are Hartree-Fock-Bogoliubov (HFB) vacua the HFB transformations are essentially complex and allow for proton-neutron, parity the HFB transformations are essentially complex and allow for proton-neutron, parity and angular momentum mixing being restricted by time-reversal and axial symmetry and angular momentum mixing being restricted by time-reversal and axial symmetry the broken symmetries (s=N, Z, I, p) are restored by projection before variation the broken symmetries (s=N, Z, I, p) are restored by projection before variationTRANSCRIPT
![Page 1: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/1.jpg)
Variational approach to isospin symmetry breaking in medium mass nuclei
A. PETROVICI
Institute for Physics and Nuclear Engineering, Bucharest, Romania Institut für Theoretische Physik, Universität Tübingen, Germany
![Page 2: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/2.jpg)
Characteristics of N~Z nuclei in the region :• shape coexistence and mixing• competition between T=0 and T=1 pairing correlations, isospin mixing• rapid structural changes with particle number, angular momentum and excitation energy
Isospin symmetry breaking effects in the A~70 mass region on - Superallowed Fermi beta decay - Mirror Energy Differences
Self-consistent description of proton-rich A~70 nuclei based on:
- beyond mean field variational VAMPIR approaches - realistic effective interactions in large model spaces
![Page 3: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/3.jpg)
Complex EXCITED VAMPIR approach
• the the model spacemodel space is defined by a finite dimensional set of is defined by a finite dimensional set of spherical single particlespherical single particle states states
•• the effective many-bodythe effective many-body Hamiltonian Hamiltonian is represented as a sum of is represented as a sum of one- and two-bodyone- and two-body
termsterms•• the basic the basic building blocksbuilding blocks are Hartree-Fock-Bogoliubov ( are Hartree-Fock-Bogoliubov (HFBHFB) vacua) vacua
•• the HFB transformations are the HFB transformations are essentially essentially complexcomplex and allow for and allow for proton-neutron, parity proton-neutron, parity
and angular momentum mixingand angular momentum mixing being restricted by time-reversal and axial symmetry being restricted by time-reversal and axial symmetry
• the broken symmetries (the broken symmetries (s=N, Z, I, ps=N, Z, I, p) are restored by ) are restored by projection before variationprojection before variation
![Page 4: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/4.jpg)
Beyond mean field variational procedure
complex VAMPIR
complex EXCITED VAMPIR
![Page 5: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/5.jpg)
A ~ 70 mass region
<1p 1d5/2; T=0|G| 1p 1d5/2;T=0>
renormalized G-matrix (OBEP, Bonn A/Bonn CD)• short range Gaussians in pp, np, nn channels
• monopole shifts:<0g9/2 0f ; T=0|G| 0g9/2 0f ;T=0>
model space for both protons and neutrons:
1p1/2 1p3/2 0f5/2 0f7/2 1d5/2 0g9/2
40Ca - core
(charge-symmetric basis + Coulomb contributions to the π-spe from the core)
![Page 6: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/6.jpg)
Superallowed Fermi β decay between 0+ T=1 analog states
δc – isospin-symmetry-breaking correction
test of the CVC hypothesis
test of the unitarity of CKM matrix
![Page 7: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/7.jpg)
Isospin-symmetry-breaking contributions: electromagnetic interaction • Coulomb contribution to the single particle energies resulting from the Ca core • Coulomb two-body matrix elements charge-dependent strong interaction • Bonn CD potential
Charge-symmetric effective Hamiltonian: • same single particle energies for and •• Bonn A potential
Isospin-symmetry-breaking effective Hamiltonians: Bonn A + Coulomb
Bonn CD + Coulomb
Isospin operator a
bsingle particle state of the model space )
MF = <f |+ |i>
Strategy:
![Page 8: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/8.jpg)
![Page 9: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/9.jpg)
![Page 10: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/10.jpg)
Petrovici et al. Nucl. Phys. A747 (2005) 44
![Page 11: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/11.jpg)
br ms
GANIL, J. Garces Narro et al, PRC63 (2001) 044307
![Page 12: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/12.jpg)
![Page 13: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/13.jpg)
![Page 14: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/14.jpg)
A. Petrovici et al, Phys. Rev. C78 (2008) 064311
![Page 15: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/15.jpg)
A. M. Hurst et al, Phys. Rev. Lett.98 (2007) 072501 (70Se: No evidence for oblate shapes)
J. Ljungvall et al, Phys. Rev. Lett. 100 (2008) 102502 (70Se: Evidence for oblate shapes)
G. de Angelis et al, Eur. Phys. J. A12 (2001) 51 (70Br)
Complex Excited Vampir predictions: oblate-prolate mixing specific for each nucleus (varying with increasing spin).
Mirror Energy Differences A= 70, 82, 86
![Page 16: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/16.jpg)
Strong oblate-prolate mixing up to spin 6+ : oblate components dominate the yrast states of 70Se, but the yrare states of 70Br
![Page 17: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/17.jpg)
Precise quadrupole moments for low spin states could clarify the open problem.
![Page 18: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/18.jpg)
![Page 19: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/19.jpg)
High spin states obtained within the Excited Vampir approach (Bonn A + Coulomb)
![Page 20: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/20.jpg)
![Page 21: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/21.jpg)
Analog states obtained within the complex Excited Vampir approach
![Page 22: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/22.jpg)
![Page 23: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/23.jpg)
![Page 24: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/24.jpg)
![Page 25: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/25.jpg)
![Page 26: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/26.jpg)
![Page 27: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/27.jpg)
A. Petrovici et al, Phys. Rev. C78 (2008) 064311
![Page 28: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/28.jpg)
A. Petrovici, J. Phys.G: Nucl. Part. Phys 37 (2010) 064036
![Page 29: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/29.jpg)
Summary and outlook
• strategy for calculating the isospin-symmetry-breaking effects on the superallowed Fermi β decay based on a self-consistent description of the analog and non-analog branches (experimental branching ratios are needed)
• in progress: systematic derivation of improved effective interaction in larger model spaces
• trends in mirror energy differences correlated with shape mixing in the structure of the analog states ( precise quadrupole moment measurements are required)
complex Excited Vampir variational approach to coexistence phenomena
![Page 30: Variational approach to isospin symmetry breaking in medium mass nuclei A. PETROVICI Institute for Physics and Nuclear Engineering, Bucharest, Romania](https://reader035.vdocument.in/reader035/viewer/2022062311/5a4d1af87f8b9ab059982ab3/html5/thumbnails/30.jpg)
In collaboration with:
K. W. Schmid, Amand Faessler
Tuebingen University, Germany
O. Andrei
National Institute for Physics and Nuclear Engineering, Bucharest, Romania