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Mirror Symmetry

Isospin symmetry and independence in analogue excited states. Mirror Symmetry. Silvia Lenzi University of Padova and INFN. 11th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS . Silvia M. Lenzi Dipartimento di Fisica e Astronomia“Galileo Galilei ” Università di Padova and INFN.

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Mirror Symmetry

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  1. Isospinsymmetry and independence in analogue excited states Mirror Symmetry Silvia Lenzi University of Padova and INFN 11th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS Silvia M. LenziDipartimentodiFisica e Astronomia“GalileoGalilei” UniversitàdiPadova and INFN

  2. p n Neutron-proton exchange symmetry • Charge symmetry : Vpp = Vnn Charge independence: (Vpp + Vnn)/2= Vnp Deviations are small Electromagnetic interactions lift the degeneracy of the analogue states, but do not generally affect the underlying symmetry.

  3. 2+ 0+ MeV MeV 5 5 4 4 4+ 4+ 4+ 3 3 2 2 2+ 2+ 1 1 4+ 0+ 0+ 0 0 0.693 1+ 3+ Analogue states in the A=22, T=1 triplet T=1 T=1 T=0and T=1 LARGE differences in mass/binding energy mainly due to Coulomb effects SMALL differences in excitation energy

  4. Differences in analogue excited states Z Mirror Energy Differences (MED) N=Z N Test the charge symmetry of the interaction Triplet Energy Differences (TED) Test the charge independency of the interaction

  5. Mirror symmetry is (slightly) broken Isospin symmetry breakdown, mainly due to the Coulomb field, manifests when comparing mirror nuclei. This constitutes an efficient observatory for a direct insight into nuclear structure properties.

  6. Measuring MED and TED Can we reproduce such small energy differences? What can we learn from them? They contain a richness of information about spin-dependent structural phenomena We measure nuclear structure features: • How the nucleus generates its angular momentum • Evolution of radii (deformation) along a rotational band • Learn about the configuration of the states • Isospin non-conserving terms of the interaction

  7. 8 6 4 2 0 MED and nucleon spatial correlations J J probability distribution for the relative distance of two like particles in the f7/2 shell j j j j ΔEC 8 courtesy P. Van Isacker 6 neutron align. proton align. 4 MED 2 0 I=8 j j A(N,Z) A(Z,N) angular momentum J=0 Shifts between the excitation energies of the mirror pair at the backbending indicate the type of nucleons that are aligning j j

  8. MED and nucleon alignment D.D. Warner, M.A. Bentley and P. Van Isacker, Nature Physics 2 (2006) 311 51Fe 51Mn Energy (MeV) Experiment Shell Model 25 21 17 13 9 5 6 + Coulomb MED Alignment 2J 3 0 100 0 -100 MED (keV)

  9. Including monopole Coulomb effects Can we do better? When we “normalize” to the g.s. energy, large Coulomb effects vanish, however… a small but important effect remains as a function of the angular momentum, and it is related to changes of the nuclear radius, or deformation and to single-particle effects.

  10. Improving the description of Coulomb effects VCMMultipole part of the Coulomb energy: Between valence protons only radial effect: radius changes with J VCmMonopole part of the Coulomb energy: L2 term to account for shell effects change the single-particle energies electromagnetic LS term

  11. The radial term The difference between the Coulomb energy of the ground states (CDE): J If RC changes as a function of the angular momentum… In f7/2 nuclei the radial contribution can be calculated from the relative p3/2 occupation number along the yrast band in the shell model framework z and n are the number of protons and neutrons in the p3/2 orbit, relative to the g.s. (J=0)

  12. f7/2 j=l+½ d3/2 j=l-½ d3/2 j=l-½ f7/2 j=l+½ ΔEp ~ 220 keV The electromagnetic spin-orbit term Analogous to the atomic case, the nuclear electromagnetic spin-orbit coupling has relativistic origin. s ℓ ℓ s π ν Its contribution to the MED becomes significant for configurations with a pure single-nucleon excitation to the f7/2 shell: a proton excitation in one nucleus and a neutron excitation in its mirror

  13. Are Coulomb corrections enough? VCM+VCm VCM Exp VCm Another isospin symmetry breaking (ISB) term is neededand it has to be big!

  14. πππννν Looking for an empirical interaction In the single f7/2 shell, an interaction V can be defined by two-body matrix elements written in the proton-neutron formalism : We can recast them in terms of isoscalar, isovector and isotensor contributions Mirrors We assume that the configurations of these states are pure (f7/2)2 Isovector Isotensor Triplet

  15. Looking for an empirical interaction VC is calculated for every J state in the f7/2 shell and then subtracted to MED and TED to estimate VB This suggests that the role of the isospin non conserving nuclear force is at least as important as the Coulomb potential in the observed MED A. P. Zukeret al., PRL 89, 142502 (2002)

  16. The “J=2 anomaly” Is this just a Coulomb two-body effect? Spatial correlation probability for two nuclons in f7/2 Calculation (using Harmonic Oscillator w.f) Two possibilities: Increase the J=2 term Decrease the J=0 term We choose 1) but there is not much difference See talk by M. Bentley Coulomb matrix elements (MeV) Angular momentum J

  17. Looking for an empirical interaction From the yrast spectra of the T=1 triplet 42Ti, 42Sc, 42Ca we deduce the interaction Calculated estimate VBf7/2 (1) estimate VBf7/2 (2) Simple ansatzfor the application to nuclei in the pf shell: A. P. Zuker et al., PRL 89, 142502 (2002)

  18. Calculating MED and TED We rely on isospin-conserving shell model wave functions and obtain the energy differences in first order perturbation theory as sum of expectation values of the Coulomb (VC)andisospin-breaking (VB) interactions

  19. Calculating the MED with SM Theo 49Mn-49Cr VCM:givesinformation on the nucleonalignmentor recoupling VCM Exp VCm: gives information on changes in the nuclearradius VCm Important contribution from the ISBVB term: of the same order as the Coulomb contributions VB A. P. Zuker et al., PRL 89, 142502 (2002)

  20. MED in T=1/2 states Verygoodquantitative descriptionof data without free parameters A = 47 A = 45 A = 49 A = 51 A = 53 M.A. Bentley and S.M.L., Prog. Part. Nucl. Phys. 59, 497-561 (2007)

  21. MED in T=1 states A = 46 A = 42 A = 48 A = 50 A = 54 M.A. Bentley and SML, Prog. Part. Nucl. Phys. 59, 497-561 (2007) Same parameterization for the whole f7/2 shell!

  22. Some illustrative examples

  23. Evidenceof the monopoleradialeffect Multipole (alignment) effects are cancelled out radial term Most important contribution The nucleus changes shape towards band termination M.A. Bentley et al., PRL 97, 132501 (2006)

  24. 23/2- 23/2- 19/2- 19/2- 15/2-2 15/2-1 15/2-2 15/2-1 11/2-2 11/2-2 Negative parity The electromagnetic spin-orbit effect:disentangling configurations 35Cl 35Ar 11/2-1 11/2-1 From the MED experimentalvalues we can identifythosestateswithconfigurationsof pure proton (neutron) excitationto the f7/2shell. 11/2-1 MED > 300 keV 11/2-2 F. Della Vedova et al., Phys.Rev. C 75, 034317 (2007)

  25. A=54 A=42 T=1 A=54/42 MED: the VB term no collectivity: only multipole effects: smooth recoupling and J=2 anomaly 2 particles / holes A=54 A=42 A.Gadea et al., PRL 97, 152501 (2006)

  26. TED in the f7/2shell TED (keV) TED (keV) TED (keV) TED (keV) Only multipole effects are relevant. The ISB term VB is of the same magnitude of the Multipole Coulomb term

  27. Some questions arise… What happens farther from stability or at larger T in the f7/2 shell? The same prescription applies (see M. Bentley’s talk) Can we understand the origin of this term? Work in progress with A. Zuker Is the ISB term confined to the f7/2shell or is a general feature? If so the same prescription should work

  28. Looking for a systematic ISB term • Necessary conditions for such studies: • good and enough available data • good shell model description of the structure Ideal case: the sdshell But…few data at high spin and no indications of J=2 anomaly in A=18

  29. A systematic analysis of MED and TED in the sd shell

  30. The method We apply the same method as in the f7/2shell However, here the three orbitals, d5/2, s1/2 and d3/2 play an important role VCr (radial term): looks at changes in occupation of the s1/2

  31. MED: different contributions A=29 T=1/2 T=1/2 A=26 T=1

  32. MED in the sd shell MED (keV)

  33. TED in the sd shell TED (keV) The prescription applies successfully also in the sd shell!

  34. What about other mass regions? The next mass region is the upper pf and fpg shells but… not much data to perform a systematic analysis The shell model description is not that good. The development of deformation and shape coexistence enter into play

  35. MED and TED in the upper pf shell

  36. The method We apply the same method as in the f7/2shell However, here the three orbitals, p3/2, f5/2 and p1/2 play an important role VCr (radial term): looks at changes in occupation of both p orbits

  37. MED in the upper pf shell MED (keV)

  38. TED in the upper pf and fpg shells

  39. N~Z nuclei in the A~68-84 region Around N=Z quadrupole correlations are dominant. Prolate and oblate shapes coexist. The fpg space is not able to reproduce this behaviour, the fpgds space is needed. MED are sensitive to shape changes and therefore a full calculation is needed, which is not always achievable with large scale SM calculations s1/2 d5/2 g9/2 quasi SU3 40 pseudo SU3 f5/2 p A.P. Zuker, A. Poves, F. Nowacki and SML, arXiv:1404.0224 Experimentally it is not clear if what we measure are energy differences between analogue states, as ISB effects may exchange the order of nearby states of the same J

  40. Conclusions Z N~Z nuclei present several interesting properties and phenomena that can give information on specific terms of the nuclear interaction. N=Z N The investigation of MED and TED allows to have an insight on nuclear structural properties and their evolution as a function of angular momentum such as: alignments, changes of deformation, particular s.p. configurations. The need of including an additional ISB term VB shows up not only in the f7/2 shell but also in other mass regions (sd, upper pf and fpg). Investigation of its origin is in progress.

  41. In collaboration with Mike Bentley Rita Lau Andres Zuker

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