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Carpathian Summer School of Physics 2007 Sinaia, Romania, August 20th-31st, 2007 Mirror Nuclei: symmetry breaking and nuclear dynamics Silvia M. Lenzi Dipartimento di Fisica and INFN, Padova, Italy Symmetries Symmetries help to understand Nature Examination of fundamental symmetries: a key question in Physics conservation laws good quantum numbers In nuclear physics, conserved quantities imply underlying symmetries of the interactions and help to interpret nuclear structure features Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Symmetries in nuclear physics p n Isospin Symmetry: 1932 Heisenberg SU(2) Spin-Isospin Symmetry: 1936 Wigner SU(4) Seniority Pairing: 1943 Racah J 0 j Spherical Symmetry: 1949 Mayer J 0 J 2 Nuclear Deformed Field (spontaneous symmetry breaking) Restore symm. rotational spectra: 1952 Bohr-Mottelson SU(3) Dynamical Symmetry: 1958 Elliott Interacting Boson Model (IBM dynamical symmetry): 1974 Arima and Iachello Critical point symm. E(5), X(5) …. 2000… F. Iachello Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Outline What’s isospin symmetry? Why studying isospin symmetry? How do we study it? Experimental methods Theoretical methods What do we learn from the data? Few illustrative recent examples Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Bibliography • Isospin in Nuclear Physics, Ed. D.H. Wilkinson, North Holland, Amsterdam, 1969. • Review article on CDE: J.A. Nolen and J.P. Schafer, Ann. Rev. Nucl. Sci 19 (1969) 471; S. Shlomo, Rep. Prog. Phys.41 (1978) 66; N. Auerbach, Phys. Rep. 98 (1983) 273 • Recent on CDE: J. Duflo and A.P. Zuker, Phys. Rev. C 66 (2002) 051304(R) • Theory on CED: A.P. Zuker, S.M. Lenzi, G. Martinez-Pinedo and A. Poves, Phys. Rev. Lett. 89 (2002) 142502; • Theory on CED: J.A. Sheikh, D.D. Warner and P. Van Isacker, Phys. Lett. B 443 (1998) 16 • Shell model reviews: B.A. Brown, Prog. Part. Nucl. Phys 47 (2001) 517; T. Otsuka, M. Honma, T. Mizusaki and N. Shimitzu, Prog. Part. Nucl. Phys 47 (2001) 319; E. Caurier, G. Martinez-Pinedo, F. Nowacki, A.Poves, and A.P. Zuker, Rev. Mod. Phys. 77 (2005) 427 • Review article on CED: M.A. Bentley and S.M. Lenzi, Prog. Part. Nucl. Phys. (2006). • Review article on N~Z: D. D. Warner, M. A. Bentley, P. Van Isacker, Nature Physics 2, (2006) 311 - 318 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 The nucleus: a unique quantum laboratory Composed by two types of fermions differing only on its charge Strong interaction: largely independent of the charge Proton – Neutron exchange symmetry Proton and neutron can be viewed as two alternative states of the same particle: the nucleon. The quantum number that distinguish the two charge states is the isospin t 1 2 proton : tz 1 2 neutron : tz 1 2 This is in analogy to the two intrinsic spin states of an electron Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Charge invariance and isospin 1932 Heisenberg applies the Pauli matrices to the new problem of labeling the two alternative charge states of the nucleon. 1937 Wigner: isotopic spin is a good quantum number to characterize isobaric multiplets. A Tz t z ,i i 1 N Z 2 NZ NZ T 2 2 Isobaric analogue multiplets: States with the same J,T in nuclei with the same A=N+Z Nuclear interaction: • Charge Symmetry: Vpp=Vnn • Charge Independence: Vpp=Vnn=Vpn π Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 ν Two-nucleon system For a two-nucleon system four different isospin states can exist: Triplet T=1 Singlet T=0 The isospin quantum number T directly couples together the two effects of charge symmetry/independence and the Pauli principle Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Isobaric spin (isospin) In the absence of Coulomb interactions between the protons, a perfectly charge-symmetric and charge-independent nuclear force would result in the binding energies of all these isobaric analogue nuclei being identical; that is, they would be structurally identical. Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Symmetry breaking… 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. Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 IMME and Coulomb Displacement Energies IMME: Isobaric Multiplet Mass Equation M BE((TT TTz z))aabT bTz z cT cT 22 zz a: isoscalar (~100 MeV) b: isovector (~10 MeV) c: isotensor (~300 keV) -145 CDE ,T ,Tz M ,T ,Tz M ,T ,Tz 1 M np b c2Tz 1 M np Isobaric Analogue States -150 -BE(MeV) For a set of isobaric analogue states, the difference between the masses or BE of two neighbours defines the CDE Ground States -155 CDE -160 A=21 Isobars -165 -170 8 9 10 Z 11 12 13 Nolen-Schiffer anomaly: calculated CDE underestimate the data by 7% (100’s keV) Recent works show that this discrepancy can be reduced to the order of ~200 keV The understanding of Coulomb effects at the level of less than 100 keV seemed likely to be very difficult… Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Excited analogue states Normalize the ground state energies and look at the excited analogue states… Mirror nuclei with Tz = ±1/2 27 13 Al14 27 14 Si13 Tests isospin symmetry Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 T=1 isobaric triplets The nucleus can be characterized by isospin quantum numbers which restrict the possible states in which the many-nucleon system can exist. 22 22 22 Mg Na 12 10 11 11 10 Ne12 Look at the isobaric triplet: We expect: T=1 states low in energy in 22Mg and 22Ne T=0 and T=1 states in 22Na (N=Z) Tests isospin independence MeV MeV 5 5 4 4 4+ 3 4+ 4+ 2 3 2 1 2+ 0 0+ 22 12 Mg10 0.693 4+ 3+ 22 11 Na11 2+ 2+ 1 0+ 0+ 0 22 10 Ne12 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 T=3/2 Isobaric quadruplets: the spectra 21 9 F12 21 10 Ne11 21 11Na10 21 12 Mg 9 T=3/2 T=1/2 Small differences in excitation energy due (mainly?) to Coulomb effects Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Coulomb energy differences (differences of excitation energies) Z Mirror Energy Differences (MED) MED J E *J ,Tz 1 / 2 E *J ,Tz 1 / 2 ΔbJ N Tests the charge symmetry of the interaction Triplet Energy Differences (TED) TED J E *J ,Tz 1 E *J ,Tz 1 2E *J ,Tz 0 2ΔcJ Tests the charge independency of the interaction MED and TED are of the order of 10’s of keV Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 A classical example: MED in T=1/2 states Coulomb effects in isobaric multiplets: - bulk energy (100’s of MeV) - displacement energy (g.s.) CDE (10’s of MeV) - differences between excited states (10’s of keV) Mirror Energy Differences MEDJ EJ (Z N ) EJ (Z N ) 49 25Mn24 49 24Cr25 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Measuring the Isospin Symmetry Breaking Can we reproduce such small energy differences? What can we learn from them? Interestingly 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 the radii (deformation) along a rotational band Learn about the configuration of the states Isospin non-conserving terms in the nuclear interaction Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Mirror energy differences and alignment J j j j ΔEC 8 j 8 6 6 J=6 neutron align. 4 4 proton align. 2 0 2 0 A(N,Z) j A(Z,N) j J=0 j j j MED j probability distribution for the relative distance of two like particles in the f7/2 shell 0 I=8 angular momentum Shifts between the excitation energies of the mirror pair at the back-bend indicate the type of nucleons that are aligning Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Nucleon alignment at the backbending J.A. Cameron et al., Phys. Lett. B 235, 239 (1990) C.D. O'Leary et al., Phys. Rev. Lett. 79, 4349 (1997) 49Mn j j Experimental MED 49Cr j j J=6 Alignment MED are a probe of nuclear structure: reflect the way the nucleus generates its angular momentum Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Coulomb energy differences: Experimental methods Studying the f7/2 shell The 1f7/2 shell is isolated in energy from other major orbits Wave functions dominated by (1f7/2)n configurations N=Z High-spin states experimentally reachable f5/2 p1/2 p3/2 f7/2 28 28 proton number 55Ni 56Ni 27 52Co 53Co 54Co 55Co 26 50Fe 51Fe 52Fe 53Fe 54Fe 25 48Mn 49Mn 50Mn 51Mn 52Mn 53Mn 24 20 54Ni 46Cr 47Cr 48Cr 49Cr 50Cr 51Cr 23 44V 45V 46V 47V 48V 43Ti 44Ti 45Ti 46Ti 47Ti d3/2 s1/2 22 42Ti d5/2 21 41Sc 42Sc 43Sc 44Sc 45Sc 20 40Ca 41Ca 42Ca 43Ca 44Ca 20 21 22 23 24 25 49V neutron number 26 Experimental issue : proton-rich Tz< 0 isobars very weakly populated Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 27 28 Experimental requirements High efficiency for γ detection Low cross section at high spin (small masses) High energy transitions High selectivity: particle detectors Many channels opened: high efficient charged-particle det. Kinematics reconstruction for Doppler broadening Mass spectrometers Neutron detectors to select proton rich channels Polarimeters and granularity (J, π, δ) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Gamma spectroscopy Anti-Compton gamma ray Constructing a level scheme γ1 Gamma array Ge crystal 156Dy γ2 γ3 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Gamma-ray spectrometers Present GASP GAMMASPHERE e ~ 10 — 5 % ( Mg=1 — Mg=30) Next future AGATA GRETA e ~ 40 — 20 % ( Mg=1 — Mg=30) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Techniques for proton-rich spectroscopy Three basic techniques for selecting proton-rich systems 1. High efficiency & high granularity gamma-ray spectrometer (e.g. Euroball, Gammasphere) - high fold gn (n 3) coincidence spectroscopy 2. Gamma-ray array + 0o recoil mass spectrometer + focal plane detectors - identify A,Z of recoiling nucleus tag emitted gamma-rays 3. Identify cleanly all emitted particles from reaction - needs a charged-particle detector (p, ) + high-efficiency & high granularity neutron detector array Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 1. High fold gn (n > 3) coincidence spectroscopy Rely on the power of the array: • high-fold gamma ray coincidences • high granularity… and on the similarity between the energy of the transitions with those of the known mirror nucleus 260 ms Double-coincidence spectra after gating on 2 analogue transitions S.J. Williams et al., Phys. Rev. C 68 (2003) 011301 32 S 24 Mg,1p2n 53 Co Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 2. Identification of A,Z of the recoiling nucleus E.g.: Fragment Mass Analyser (FMA) at 0o @ Argonne National Lab GS • Combined electric and magnetic dipoles beam rejection & A/q separation • A/q identified by x-position at focal plane • Z identified by energy loss (E-DE) in gas-filled ionisation chamber • FMA information used to “tag” coincident gamma-rays at target • Efficiency - up to ~ 15% Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Z identification Example: Ca 20 B5 Mn 10 5 50 25 * 25 48 25 No excited states known in 48Mn DE 40 20 V25 2 p 48 23 Mn 23 2n 48 Mn 4 ~ 10 48 V Z identification essential… Ionisation Chamber Fe Mn Cr E V Ti Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 γ-γ coincidence analysis (A/q = 3, Z=25)-gated gg coincidence analysis… 48 25 Mn 23 M.A. Bentley et al., Phys.Rev. Lett. 97, 132501 (2006) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 48 23 V25 3. Measuring the evaporated particles With this method we do not measure directly the final residue but the particles emitted from the compound nucleus charged particles neutrons We need high efficiency detectors for: Advantage: more flexible than recoil mass spectrometry more channels can be measured! Disadvantage: not as clean as RMS and, if neutrons are needed, it can be much less efficient Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Observation of excited states in 50Fe sum of gates (*) counts 50Fe 50Cr sum of gates (*) 50 26 Fe 50 24 24 Cr 26 Eg (keV) σ(Fe)/ σ(Cr) ≈ 10-4 S. M. Lenzi et al., Phys. Rev. Lett. 87, 122501 (2001) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Coulomb energy differences: Theoretical methods Cranked shell model and alignment alignment Cranked shell-model Approximations: • one shell only • fixed deformation • no p-n pairing CSM: good qualitative description of the data J.A. Sheikh, P. Van Isacker, D.D. Warner and J.A. Cameron, Phys. Lett. B 252 (1990) 314 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Ingredients for the Shell Model calculations 1) an inert core 2) a valence space 3) an effective interaction that mocks up the general hamiltonian in the restricted basis the valence space The choice is determined by the limits in computing time and memory: large dimension of the matrices to be diagonalised. 28 f5/2 p1/2 p3/2 f7/2 20 d3/2 s1/2 inert core d5/2 8 Current programs diagonalise matrices of dimension ~109 p1/2 p3/2 2 s1/2 N or Z Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Shell model and collective phenomena Shell model calculations in the full fp shell give an excellent description of the structure of collective rotations in nuclei of the f7/2 shell • Excitation energies • Transition probabilities Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 -50 D.D. Warner et al., Nature Physics 2 (2006) 311 -100 51Fe Energy -150 (MeV) 6 -200 5 7 51Mn 9 Experiment Experiment fp-shell Model Shell Model 11 13 15 17 19 21 23 25 27 Alignment in A=51 Experiment 0 fp-shell Model 50 25 11 13 15 17 19 21 23 25 27 MED 21 Alignment 17 2J 3 9 9 5 MED (keV) -200 -100 -150 -50 0 -100 M.A. Bentley et al, PRC 62 (2000) 051303 100 100 0 0 50 7 100 keV 5 13 J.Ekman et al, EPJ A9 (2000) 13 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Improving the description of Coulomb effects Can we do better? Multipole term of the Coulomb energy VCM: Monopole term of the Coulomb energy Vcm interaction with the core VC VCM VCm What is missing? Between valence protons only 3 e 2 Z ( Z 1) radial effect: ECr radius changes with J 5 R ECll 4.5Z cs13/12[2l (l 1) N ( N 3)] keV A1/ 3 ( N 3 / 2) ECls ( g s gl ) 1 1 dVC l.s 4mN2 c 2 r dr change the single-particle energies A.P. Zuker Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 The radial term Coulomb energy of a charged sphere: 3Z ( Z 1 )e 2 EC 5 RC The difference between the energy of the ground states (CDE): 3n2 Z n e 2 EC J 0 EC Z EC Z 5RC If RC changes as a function of the angular momentum… n Tz 2 J 1 3 1 ECr J EC J EC 0 n2Z n e 2 5 RC J RC 0 3 2 RC 0 RC J n2Z n e 2 5 RC Radial contribution to the MED RC J 3 n2Z n e 2 5 RC2 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Evidencing the monopole radial effect Multipole (alignment) effects are cancelled out 48 25 Mn 23 f 7/32 f 73/ 2 48 23 V25 f 73/ 2 f 7/32 radial term VCr Most important contribution M.A. Bentley et al., PRL 97, 132501 (2006) The nucleus changes shape towards band termination Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Electromagnetic single-particle effects: the ℓ·s term ECls 1 g s gl 2mN2 c 2 Ze 2 l s R 50 times smaller than the nuclear spin-orbit term!!! Acts differently on protons and neutrons s ℓ f7/2 ΔEp ~ 220 keV j=l+½ ℓ s d3/2 j=l-½ f7/2 j=l+½ d3/2 j=l-½ 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 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 The T=1/2 mirror nuclei A=35 35Ar 35Cl 23/2- 19/2- 19/2- Large MED for the 13/2is found A=35 15/2-in 15/2state 2 F. Della Vedova et al., PRC 75, 034317 (2007) 1 15/2-1 15/2-2 >300 keV!!! 13/2- 11/2-2 13/2- 11/2-2 J. Ekman et al., PRL 92 (2004) 132502 Negative parity The two 11/2 states have very different configurations 13/2- Measured very large MED values for all high spin states! Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 MED in the sd shell: the EMSO The mirror pair 35Ar – 35Cl Calculations in the sdfp space Large and similar contributions from the multipole Coulomb and the electromagnetic spin-orbit terms F. Della Vedova et al., PRC 75, 034317 (2007) The mirror pair 39Ca – 39K Exp. data: Th. Andersson et al., EPJA 6, 5 (1999) Small effects due to the orbital term Puzzling results… deformation effects? Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 EMSO effect in the fp and f7/2 shell The mirror pair 61Ga – 61Zn 61 31 VCM+ls+ll+VCr f5 / 2 Exp Ga 30 VCM+ls+ll VCM+ls VCM p3 / 2 Data: L-L. Andersson et al., PRC (2005) The mirror pair 48Mn – 48V 48 25 Mn 23 48 25 48 23 V25 Mn 23 f7 / 2 d3 / 2 M.A. Bentley et al., PRL 97, 132501 (2006) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Are Coulomb corrections enough? 49 25 Mn 24 49 24 Cr25 sum of Coulomb terms Another term of nuclear nature is needed, but it has to be big! Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Looking for an empirical interaction In the single f7/2 shell, an interaction V can be defined by twobody matrix elements written in the proton-neutron formalism : V , V , V We can recast them in terms of isoscalar, isovector and isotensor contributions ππ πν νν U (0) V V V U (1) V V U (2) V V 2V Mirrors ) (1) configurations MEDJ (42 Ti- 42We Ca)assume U (f17)/ 2 , J that VC(1the V Isovector ,J B, J of these states are pure (f7/2)2 Triplet TEDJ (42 Ti 42 Ca - 242 Sc) U (f72/)2 , J VC(,2J) VB(,2J) Isotensor If the energy differences are due only to VC one expects very small numbers for all J couplings for VB 42Ti 42Sc 42Ca A. P. Zuker et al., Phys. Rev. Lett. 89, 142502 (2002) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Learning from MED and TED in A=42 From the yrast spectra of the T=1 triplet 42Ti, 42Sc, 42Ca we deduce: VC VCh.o. ( f 7 / 2 ) J=0 J=2 J=4 J=6 81 24 6 -11 MED-VC 5 93 5 -48 estimate VBf7/2 (1) TED-VC 117 81 3 -42 estimate VBf7/2 (2) VC Calculated 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 and TED J=2 anomaly Simple ansatz for the application to nuclei in the pf shell: (1) VBpf 100 keV ( J 2) ( 2) VBpf 100 keV ( J 0) A. P. Zuker et al., Phys. Rev. Lett. 89, 142502 (2002) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Evidence of ISB of the nuclear interaction Very good quantitative agreement between theory and data The multipole Coulomb contribution gives information on the nucleon alignment MED (keV) The monopole Coulomb contribution gives information on changes in the nuclear radius (deformation) Important contribution from the “nuclear” ISB term, of the same order as the Coulomb contributions!!!!! Now, without changing the parametrization, see how the rest of the MED for nuclei along the f7/2 shell are described by the calculations… A. P. Zuker et al., PRL 89, 142502 (2002) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 A=49 Coulomb energy differences (CED): Results MED and TED in the shell model framework Good quantitative description of data without free parameters A = 47 47 24 A = 48 48 25 A = 49 Mn 23 4823V25 49 25 Mn 24 49 24 Cr25 54 28 Ni26 54 26 Fe 28 Cr23 4723V24 140 A = 54 120 100 A = 51 51 26 51 Fe25 25 Mn 26 A = 53 53 27 53 Co26 26 Fe27 80 60 40 20 0 -20 -40 0 2 4 6 M.A. Bentley and S.M. Lenzi, Prog. Part. Nucl. Phys. (2006) in press Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Rotational T=1/2 analogue states A=47/49 7 particles/holes in the f7/2 shell Band termination state: 72 52 32 12 8 72 52 32 152 J max 31 2 Deformed nuclei Rotational bands All terms contribute significantly to the MED Monopole effects: Cr Multipole effects: CM and VB Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 T=1 A=54/42 triplet: MED and TED A=54 A=42 J=2 anomaly 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) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 More results of MED measurements P.E. Garrett et al., PRC 75, 014307 (2007) Rising and GANIL: T=2 mirror in A=36 P. Doorneball et al., Phys.Lett. B 647, 237 (2007) F. Azaiez et al., to be published Rising stopped-beam campaign: J=8,10 in A=54 D. Rudolph et al., to be published Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Summary and outlook These studies allow to learn about: Mechanism of nucleon alignment at the backbending Evolution of the radii along a rotational band Importance of the single-particle effects: - test interactions and basis - information on the configurations Evidence of isospin-non-conserving terms in the nuclear interaction f5 / 2 p3 / 2 J=2 anomaly Other interesting facets can be, and are being, studied in isobaric multiplets: - lifetimes and decay probabilities - magnetic and giromagnetic moments - isospin mixing ….. These investigations will improve with the advent of intense stable and radioactive beams and the next generation gamma-arrays and ancilaries Much effort has to be put in the development of theoretical methods Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Thanks to… Theory: A.P. Zuker, F. Nowacki (Strasbourg) Experiments: M. A. Bentley (York) N. Marginean, A. Gadea, F. Della Vedova, (LNL and Padova) J. Ekman, D. Rudolph (Lund) P.E. Garrett (Guelph) Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Monopole Coulomb single-particle effects: 2) the ℓ2 (orbital) term J. Duflo and A.P. Zuker, Phys. Rev. C 66 (2002) 051304(R) The monopole Coulomb term accounts for shell effects. It changes the single-particle energy of the protons proportionally to the square of the orbital angular momentum. For a proton in a main shell N above a closed shell Zcs is: ECll 13 / 12 2 1 N N 3 keV 4.5Z cs A1 / 3 N 32 Eg. in the fp shell: Z cs 20 N 3 150 keV p3/2 f7/2 proton s.p. relative energy is increased by 150 keV Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007 Alignment and shell model Define the operator A a a a a J 6 51Fe-51Mn J 6 0 “Counts” the number of protons coupled to J=6 Calculate the difference of the expectation value in both mirror as a function of the angular momentum ΔA,J J A Z J ' J A Z ' J 7/2 5/2 3/2 1/2 51Fe p 51Mn n p n In 51Fe (51Mn) a pair of protons (neutrons) align first and at higher frequency align the neutrons (protons) M.A.Bentley et al. Phys Rev. C62 (2000) 051303 Silvia Lenzi, Carpathian Summer School of Physics 2007, Sinaia, Romania, 20 August 2007
