Probing the Symmetries of Isobaric Analogue States M.A.Bentley University of York, UK. in collaboration with. Dave Warner

Transcription

1 DDW Symposium CCLRC Daresbury February Probing the Symmetries of Isobaric Analogue States M.A.Bentley University of York, UK in collaboration with Dave Warner Overview

2 Overview DDW Symposium CCLRC Daresbury February Daresbury, December 1991 (Hatton Arms)

3 DDW Symposium CCLRC Daresbury February Probing the Symmetries of Isobaric Analogue States Overview Outline: Introduction The symmetry of isospin A=45 T=1/2 mirror nuclei Coulomb Matrix Elements the J=2 anomaly Towards the experimental limit N=Z-3 49 Fe

4 Symmetries of Isobaric Multiplets DDW Symposium CCLRC Daresbury February e.g. A=20 isobaric analogue states, look at d 5/2 occupations Na9 10Ne 10 9 F T=1 Triplet state 8 8 T=0 Singlet state T z = -1 T z = 0 T z = +1 =(N-Z)/2 T 1 allowed T 0 allowed T 1 allowed

5 Symmetries of Isobaric Multiplets DDW Symposium CCLRC Daresbury February MeV Expect: T=1 states low in energy in 20 Na and 20 F T=0 and T=1 states in 20 Ne (N=Z) MeV MeV Na9 10Ne 10 9 F MeV

6 Nolen Schiffer Anomaly DDW Symposium CCLRC Daresbury February Coulomb Displacement Energy (CDE) -145 Isobaric Analogue States -BE(MeV) Ground States T=3/2 5/2 + states A=21 Isobars ~5 MeV CDE Z Understanding the absolute energy difference (mass) CDE = Difference in mass: ( CDE) = MJ, T, T + 1 MJ, T, T + ΔMnp J, T, T e.g. Difference in g.s. mass of mirror pair ~ 9 MeV for A~ 50 Models only accounted for ~95% of this - ~500keV discrepancy. Nolen-Schiffer Anomaly (Ann. Rev. Nuc. Sci. 1969) Differences in excitation energy typically 10 s kev! z z z

7 Energy Differences in Isobaric Multiplets Study energy displacement of excited states (MED) MED = ( J ) ( J ) E x T = 1 2 E x T = 1 2 z z Yields Coulomb energies if charge-symmetry is assumed M.A.Bentley et al, PRC 62 (00) J.Ekman et al, E. J. P. A9 (00) 13 DDW Symposium CCLRC Daresbury February

8 Energy Differences in Isobaric Multiplets Energy (MeV) 6 51 Fe 51 Mn Experiment Shell Model 25 CED J 13 Experiment fp-shell Mod 0 M.A.Bentley et al, PRC 62 (00) J.Ekman et al, E. J. P. A9 (00) MED (kev) DDW Symposium CCLRC Daresbury February

9 / / A=45 Mirror Pair Euroball + Euclides + Neutron Wall Experiment: High spin yrast and intruder analogue states * 12Mg12+ 12Mg12 24Cr Ti V p, n p,2n σ σ fus fus ~ 300mb ~ 1mb Need to select pure 2-neutron evaporated events 1. Require 2n detected in n-wall Counts pure 2n spectrum 44 Ti 45 V 2. Reject nearest neighbour coincidences 3. Require similar time of flight recorded Energy (kev) DDW Symposium CCLRC Daresbury February

10 A=45 Mirror Pair DDW Symposium CCLRC Daresbury February V Ti 22 23

11 A=45 Mirror Pair DDW Symposium CCLRC Daresbury February

12 A=45 Mirror Pair DDW Symposium CCLRC Daresbury February J π = 3/2 + BAND 45 V: ν(f 7/2 ) 2 π(f 7/2 ) 4 π(d 3/2 ) -1 OR ν(f 7/2 ) 3 π(f 7/2 ) 3 ν(d 3/2 ) -1 T=1 J π = Cr T=1 J π = V 45 Ti: π(f 7/2 ) 2 ν(f 7/2 ) 4 ν(d 3/2 ) -1 OR π(f 7/2 ) 3 ν(f 7/2 ) 3 π(d 3/2 ) -1 T=1 J π = Ti T=1 J π = V

13 A=45 Mirror Pair DDW Symposium CCLRC Daresbury February M.A.Bentley et al, PRC in press (2006) Also couples to J π = 3 + T=0 core configurations mix. Assume: Charge-independence, perfect isospin symmetry Isospin Coupling Rules Contribution depends on. ( core core ) T T t t TT 2 z, z z Thus: can predict MED based on CG 2 and the data from the A=46 isobaric triplet

14 Missing/weak E1s DDW Symposium CCLRC Daresbury February E1 decay intensity from 5/2 + VERY different (factor ~ 10)

15 Missing/weak E1s DDW Symposium CCLRC Daresbury February p1n - gated spectrum 2n - gated spectrum

16 Missing/weak E1s DDW Symposium CCLRC Daresbury February /2-5/2 + F. Della Vedova et al 2003 INFN LNL Ann. Rep. D.G.Jenkins et al, Phys Rev C 72(2005)031303

17 Missing/weak E1s DDW Symposium CCLRC Daresbury February /2 ( ) /2 ( ) (9/2 ) Ar Ar 35 Cl / / / /2 ( ) / (7/2 ) / / / MED (kev) 35 Ar- 35 Cl /2 3/2 7/2-5/2 + 7/2-5/2 + 0 J.Ekman et al PRL 92(2004)132502

18 Missing/weak E1s DDW Symposium CCLRC Daresbury February What is expected? T z -dependence of transition matrix element between isobaric analogue states? ASSUME: Charge-symmetry and charge independence No isospin mixing Wigner-Eckart theorem extracts T z -dependence (ΔT=0) f ; TT z H 0 + H 1 i; TT z = f H 0 i + T z f ; T H i; T f i ( 2T + 1)( T + 1) T 1 E1 E1s identical in mirror nuclei ISOSPIN MIXING: T T+1 and T+1 T components independent of sign of T z Cancellations can occur..

19 Coulomb Matrix Elements DDW Symposium CCLRC Daresbury February Coulomb Matrix Elements: Coulomb energy of proton pair as a function of J (=0, 2, 4 and 6 for f 7/2 shell) ingredient for SM Spatial correlation probability for two nuclons in f 7/2 P.Van Isacker (p.c.) Calculation (using Harmonic Oscillator w.f)

20 J=2 Anomaly Single-j shell model picture, the wave functions in 53 Fe can be written J = a jn =, jp = J J p; J p 2 J p J 7 2 where J p = 0, 2, 4, and 6. Thus - can fit the CED to predictions of (f 7/2 ) n model Extract Coulomb Matrix Elements (CME) f7/2 Coulomb Matrix 450 f7/2 f7/2 Coulomb Coulomb Matrix Matrix f7/2 Coulomb Elements 400 Matrix Elements Elements Elements Jp Jp CME(keV) CME (kev) A=42 A=54 A=53 A=47/49 - Empirical FIT - FIT to to CME shell model A Gadea et al, LNL Ann Rep J=2 Anomaly appears across whole shell. DDW Symposium CCLRC Daresbury February

21 The Mirror Pair 53 Co/ 53 Fe Three holes in the 56 Ni doubly-magic core band terminating state S.J.Williams et al. PRC68 (2003) R. π(f 7/2 ) -1 ν(f 7/2 ) -2 π(f 7/2 )-2 ν(f 7/2 ) Experiment Shell Model 53 Co Z=27, N=26 Alignment of a single f 7/2 pair of protons in 53 Fe and neutrons in 53 Co Smooth alignment of ~ 100 kev fp-shell Model multipole and monopole Coulomb contributions 53 Fe Z=26, N=27 MED (kev) MED (kev) DDW Symposium CCLRC Daresbury February I.N.C. Multipole Radial (a) (b)

22 J=2 Anomaly DDW Symposium CCLRC Daresbury February Anomalous CME: Clearly not just Coulomb two-body effects measured Configuration mixing? But, same across whole shell? Charge-symmetry breaking has been suggested? Effect hinted at in B.A.Brown and R.Sherr, NPA 322 (1979) 61 Global fit to CDE with variable CME.

23 J=2 Anomaly DDW Symposium CCLRC Daresbury February Effect hinted at in B.A.Brown and R.Sherr, NPA 322 (1979) 61 Global fit to CDE with variable CME.

24 Towards Larger Isospin DDW Symposium CCLRC Daresbury February Mg9 11Na10 10Ne 11 9 F12 T=3/2 quadruplet T=1/2 doublet DeShalit & Fesbach 1990 T z = -3/2 T z = -1/2 T z = +1/2 T z = +3/2 T 3/2 only T 1/2 only T 1/2 only T 3/2 only Mirror Pair Mirror Pair

25 Towards Larger Isospin DDW Symposium CCLRC Daresbury February F12 10Ne11 11Na10 12Mg9

26 Towards Larger Isospin DDW Symposium CCLRC Daresbury February N=Z-3 (T z =-3/2) nucleus 49 Fe: The experimental limit?? Experiment due ~ April 2006 Gammasphere + Fragment Mass Analyser GS Ion Ch. Ti Foc.Pl 40 Ca + 12 C, 230 MeV, v/c ~ 8.5 %, E rec ~ 160 MeV A/Q from dispersion, Z from Ion Chamber Recoils too energetic for FMA Ti degraders used Test run December 2004 (with DDW)

27 A=49 T=3/2 mirrors σ( 49 Fe) ~ 1μb cf. σ( 49 Mn) ~ 500μb Z-identification essential, high recoil velocity helps Contaminants need to be removed Scattered beam, A/Q ambiguities, reactions from Ti ΔE E tot DDW Symposium CCLRC Daresbury February

28 A/Q DDW Symposium CCLRC Daresbury February A=49 T=3/2 mirrors Additional (rough) mass identification from energy (E tot ) and time-of-flight (T) A α E tot T 2 ET 2

29 DDW Symposium CCLRC Daresbury February Ion Chamber gated by ET 2. A=49 T=3/2 mirrors ΔE E tot 49 Fe identified, σ ~ 1.5 μb measured Clean high-spin spectroscopy feasible

30 A=49 T=3/2 mirrors DDW Symposium CCLRC Daresbury February

31 (some of the) collaborators DDW Symposium CCLRC Daresbury February Analysis & interpretation C. Chandler (Keele), S.J. Williams (Surrey), J. Ekman (Lund), S.M. Lenzi (Padova), M.J.Taylor (York), D.G.Jenkins (York), D.D.Warner (Daresbury) Calculations A.Poves (Madrid), A.P. Zuker (Strasbourg), S.M. Lenzi (Padova), J.Ekman (Lund) Experimental Teams: Argonne, Strasbourg, Legnaro, ORNL, GANIL

32 Collaborators DDW Symposium CCLRC Daresbury February Dedicated to: David D Warner