1. Nuclear moment measurements of neutron-rich Al isotopes using spin-polarized RI beams Daisuke Kameda Nuclear moment measurements of neutron-rich Al isotopes using spin-polarized RI beams - Determination of the boundary of the “island of inversion” - Daisuke Kameda RIKEN, Asahi Applied Nuclear Physics Laboratory The 17th International Spin Physics Symposium, SPIN2006 October. 2 nd –7 th, 2006, Kyoto, Japan K. Asahi, H. Ueno, A. Yoshimi, T. Haseyama, H. Watanabe Y. Kobayashi and M. Ishihara RIKEN, Asahi Applied Nuclear Physics Laboratory K. Asahi, D. Nagae, K. Shimada, M. Takemura, K. Takase, T. Arai, S. Suda, T. Inoue and M. Uchida Department of Physics, Tokyo Institute of Technology J. Murata and H. Kawamura Department of Physics, Rikkyo University Collaborators:

2. Introduction :  Nuclear moment studies in the vicinity of the island of inversion  Why 32 Al(Z=13, N=19) ? Experiment and Result Comparison with shell models Summary Outline:

3. Nuclear moment studies in the vicinity of the island of inversion Ne Mg Al Na F Si P 20 Z N Island of Inversion E.K. Warburton, J. A. Becker and B. A. Brown, PRC41(1990)1147. Monte Carlo shell model with sdpf model space: Y. Utsuno, et al., Phys. Rev. C70(2004) 044307. 20 s 1/2 f 7/2 d 5/2 d 3/2 p 3/2 f 7/2 d 3/2 p 3/2 Normal sd-shell configuration d 5/2 s 1/2 0p0h, spherical2p2h (intruder), deformed In the case of Na isotope chain:

4. Nuclear moment studies II: neutron-rich N=19 isotones  ( 31 Mg, I  =1/2 + ) : G. Neyens et al., Phys. Rev. Lett. 94 (2005) 022501. 32 Al (Z=13) : Our previous work Phys. Lett. B615 (2005)186. The Q-moment for the ground state of 32 Al is expected to provide the conclusive answer.  ( 32 Al) is well reproduced by sd (0p0h) shell models  2p2h dominance, deformed Ne Mg Al Na F Si P N=19 Z N=20 |  ( 32 Al gs ;1 + ) |= 1.959(9) μ N 1.2p2h dominating state 2.~50% mixing of a 2p2h state to a 0p0h state 3.Normal sd shell The low-lying levels are not reproduced well by the sd shell models. M. Robinson et al., Phys. Rev. C53(1996)R1465. Indication of reducing the shell gap :

5. Experiment for Q ( 32 Al g.s. ) in RIKEN Procedure : 1, Produce spin-polarized 32 Al beam via projectile fragmentation 2, Detect the quadrupole resonance using the  -NMR technique

6. Production of spin-polarized 32 Al beam Primary beam 40 Ar 95 AMeV, 40pnA Nb targetNb, 0.37 g/cm 2 Secondary beam 32 Al Emission angle1.3 – 5.2 deg. Momentum12.6 GeV/c ±3 % Intensity@F25 x 10 3 particle/sec. Purity85% Polarization~ 0.7 % RIKEN Projectile fragment separator (RIPS): B  = (mv 0 /e) AZAZ  = 3.6 m) ∝Z2 ∝Z2 dEdxdEdx Isotope separation: Particle identification:  E @ F2 SSD TOF (F2 PPAC - RRC) Selected momentum region: 40 Ar K. Asahi, et al., Phys. Lett. B251 (1990) 488 Key technique for polarization : To produce polarization, the Fermi motion of nucleons in the projectile and fragment was utilized.

7.  -NMR apparatus 55° ~0.5 Tesla R = W(0)/W(  ) = (1+A  P)/(1-A  P) β-ray angular distribution for pol. nuclei : W(  ) 1 + A  P cos  ~ = [A   32 Al)=  -0.85] R ’ = (1-A  P)/(1+A  P)  -ray up/down ratio: NMR effect (AFP) : P  -P 0 + - freq. + - = 0 3 cos 2  c - 1 2 3 Q 4 + - 0 = g  N B 0 /h (Larmor frequency) Q = e 2 qQ/h (Quadrupole coup. const.)  c = 0 ( crystal c-axis // B 0 ) The resonance frequencies of 32 Al( I =1) in a stopper of single-crystal  -Al 2 O 3 : In the present work,  -ray asymmetry change observed: ~ = 1- R’ / R 4AP4AP Crystal structure of  -Al 2 O 3 : h.c.p. pol. 32 Al stopper surface

8. Quadrupole resonance spectra with  -Al 2 O 3 stopper |Q( 32 Al)| Q ( 27 Al) Q ( 32 Al) |Q( 27 Al)| ref. Q ( 27 Al) in  -Al2O3: J. Magn. Reson. 89 (1990) 515. Q( 27 Al): Phys. Rev. Lett. 68 (1992) 927. Crystal c-axis // B 0 Q ( 32 Al) = 407(34) kHz = |Q( 32 Al)| = 24(2) mb Temperature : ~ 80 K = 140.2(10) mb 2389(2) kHz Fitting analysis : Gaussian function taking into account the efficiency for AFP spin reversal Chemical shift :0.00188(3) % (negligible) J. Magn. Reson. 128 (1997) 135. taking the overall error into account Q (= e 2 qQ/h) kHz to be submitted.

9. Systematic comparison :  and Q for Al isotopes Experimental data : N.J. Stone, Atomic Data and Nucl. Data. Tables 90 (2005) 75. Calculation code : OXBASH, B.A. Brown, A. Etchegoyen, W.D.M.Rae, MSU Cycl. Lab. Rep. No.524(1986). USD Hamiltonian (for sd-shell nucluei) : B.Wildenthal, Prog. Part. Nucl. Phys. 11 (1984) 5 Effective operators : B.A. Brown and B.H. Wildenthal, Nucl. Phys.A 474 (1987) 290-306 (e p, e n ) = (1.3, 0.5) Monte Carlo shell model calc. by Utsuno (in private communication) sd -normal configurations : 87 % fp-intruder configurations : 13 % 32 Al g.s : Single-particle-like configurations Very small Q-moment 0h0h 0h0h The calculated sd-configurations of 32 Al g.s.  2 = 79 %,  2 < 3.8 % | 32 Al g.s ( I  =1 + ) |  d -1 5/2 d -1 3/2 J=1+ =  +  |  d 3 5/2 d 2 3/2 ) d -1 3/2 J=1+ + …

10. Why is so small the Q-moment of 32 Al ? = = 92 e p radial part: Harmonic Osci.(M. Carchidi et al, PRC34(1986)2280 ) A(I,j,j’) + B(I,j,j’) = 20 e p + 5 e n Reduced E2 matrix elements : = 70 e n Geometrical terms involving 6j symbols: A(I,j,j’),B(I,j,j’) Small geometrical factors in are main source of the small Q-moment of 32 Al. I (total spin) A(I,5/2,3/2)B(I,5/2,3/2) 10.0220.068 20.1600.070 30.0560.134 40.2240.244 The case of 32 Al g.s (I=1, j=d 5/2, j’=d 3/2 ) Dominant (~80%) configuration for 32 Al g.s. :  coupl.  [  d -1 5/2 d -1 3/2 ] I=1 The small E2 matrix element for the ψ coupl. state is consistent with the small exp. value, Q( 32 Al g.s. )=24(2) mb  29 mb, taking ( e p, e p )=(1.3, 0.5) E2 matrix element for the ψ coupl. state : (Off-diagonal contributions are negligibly small according to the USD calculation by OXBASH.)

11. The location and variation of the boundary region The location and variation of the boundary region Ne Mg Al Na F Si P Present work sd-normal shell structure pf-Intruder structure Transitional structure : a mixing between sd-normal and pf-intruder configurations N=20 The inversion occurs gradually via a transitional nucleus 29 Na Inversion process along the Z=11 line Inversion process along the N=19 line The inversion occurs suddenly between 31 Mg and 32 Al with a drastic change on shape Island of Inversion

12. Summary and Conclusion Experiment on nuclear moments for the 32 Al ground state: 40 Ar + Nb  pol. 32 Al |Q( 32 Al g.s )| = 24(2) mb in cooled single crystal a-Al 2 O 3 (T~80K) ( |g( 32 Al g.s. )| = 1.951(5)  N in single crystal Si stopper ) Comparison with nuclear moments for Al isotopes and shell model calculations: Small Q( 32 Al g.s ) indicates that 32 Al has a spherical shape. The good agreements with the USD calculation indicates that 32 Al is a normal sd -shell nucleus.  The single-particle-like configuration about the [  d -1 5/2 d -1 3/2 ] J=1+ state Comparison with recent reports on the N=19 isotones 30 Na, 31 Mg and 32 Al: The clear-cut borderline of the island of inversion is located between 32 Al (normal) and 31 Mg (intruder), in sharp contrast to the case of the sodium isotope chain. Thank you for your attentions. Further investigation is needed, in particular, ,Q( 33 Al) and the low-lying level structure for 32 Al

13. Low-lying levels in 32 Al 1.The 4 + 1st isomer state above 2 + 1st state M. Robinson, et al., PRC53(1996)R1465 2.Lowering of the negative parity state M. Robinson, et al., PRC53(1996)R1465. B. Fornal, et al., PRC55(1997)762. 3.The  -decay branching ratio to the ground state from 32 Mg. G. Grevy et al., NPA734(2004)369. The g-factor of the isomer (  =200ns) is interesting. USDA from Home page of B. A. Brown

14. Mechanism for the sudden transition along the N =19 chain Z=12 Deformation Z=13 Upward shift of the proton valence orbits at Z=13 in the prolate deformation region Suppression of the prolate deformation for 32 Al g.s.

15. Analyses of Q-moments for Al isotopes Q cal =  (e p A p + e n A n ) A p(n) : E2 matrix elements for proton (neutron)  A p (mb)  A n (mb) The small Q-moment of 32 Al is constructed almost only by the E2 matrix element of USD cal. OXBASH  =0.77  =0.58  =0.77  =0.73

16. Production of pol. RI beam via PF reaction - Principle - Advantages ： 1.chemically independent 2.very fast process R vv v0+vv0+v Projectile fragment Target nucleus Participant : v0v0 Orbital angular mom.  L=R×m  v K. Asahi, et al., Phys. Lett. B251 (1990) 488 near side far side P > 0  L P > 0 P < 0 H. Okuno et al., Phys. Lett. B 335 (1994) 29 Projectile, MeV/u 14 N 40 15 N 68 15 N 110 15 N 67 15 N 68 targetAu NbAl fragment 12 B 13 B  frag. (deg.) 5.04.02.02.51.0

17.  theo (USD) (  N )  exp. (  N ) Prediction power of USD calculation - magnetic moments for sd -shell nuclei : B.H. Wildenthal. Prog. Part. Nucl. Phys. 11 (1984) 5. B.A. Brown and B.H. Wildenthal, et al., Nucl. Phys. A474 (1987) 290-306 USD interaction : Effective g-factos : Root mean square ~ 0.119  N

18. → | μ ( 30 Al GS ;3 + ) | = 3.010(7) μ N ΔF/F (1-sweep) = 1.1 (%) → | μ ( 32 Al GS ;1 + ) | = 1.959(9) μ N H. Ueno et al., Phys. Lett. B 615 (2005) 186.  -NMR spectra for 30 Al and 32 Al in sc.  -Al 2 O 3 - with the magic angle “ = 55° ” -  -NMR spectra for 30 Al and 32 Al in sc.  -Al 2 O 3 - with the magic angle “  c = 55° ” -

19. Intruder states of the neutron-rich N=19 isotones 30 Na (Z=11) 31 Mg (Z=12) MCSM : Y. Utsuno et al., Phys. Rev. C70 (2004) 044307. Nuclear moments: M. Keim et al., Eur. Phys. J. A8 (2000) 31.  moment and spin: G. Neyens et al., Phys. Rev. Lett. 94 (2005) 022501. 32 Al (Z=13) intruder normal ?  moment : H. Ueno et al., Phys. Lett. B615 (2005) 186.  suggests the normal state However, the low-lying levels are not reproduced well by the sd -shell model. M. Robinson et al., PRC53(1996)R1465. B. Fornal et al., PRC55(1997)762 G. Grevy et al., Nucl. Phys. A734(2004)369 The Q-moment may be more sensitive to the intruder effect than the  -moment. We can see the sensitivity in Q( 29 Na).

20. Where is the border of the “ island of inversion ” ? Ne Mg Al Na F Si P N=20 energy income (  E c ) energy expense (2  E g ) The border Island Normal 32 Al 31 Mg 30 Na 1. Monopole term  Effective shell gap (E g ) : 2. Multipole term  Correlation energy (E c ) proton neutron d 5/2 d 3/2 s 1/2 EgEg f 7/2 N=16 N=20 Y. Utsuno, et al., Phys. Rev. C 60 (1999) 054315

21. 0 1,0 0,-1 32 Al(   =1 + ) Q-moment search using sc.  -Al 2 O 3 freq. F+F+ F-F-  c = 90°(c-axis ⊥ B 0 )

22. Origin of the [  d -1 5/2 d -1 3/2 ] I =1 state dominance in 32 Al g.s. 1, Energetic favor of the I =1 coupling state between neutron-proton spin-orbit partners. Isoscalar part of USDIsovector part of USD  general trend of effective interactions cf. Cohen-Kurath(p-shell), USD(sd-shell), GXPF(fp-shell) For example, 2, Neutron configurations are highly restricted in the closed-shell plus one-hole system.

23. Why is the Q( 32 Al g.s. ) so small ? 2, Energetic favor of the I =1 + coupling state between proton-neutron spin-orbit partners in effective interactions. 1, Dominance of the [  d -1 5/2 d -1 3/2 ] I=1+ state by about 80 %  force the Q-moment to be small 3, Neutron configurations are highly restricted in the one-hole system (N=19). origin Answer :

24. The other example : small Q( 12 B g.s. I =1 + ) 12 B Neutron number Q-moments (mb) code: OXBASH proton neutron 12 B( I =1 + ) =  p3/2  p1/2 p3/2 p1/2 75 % + 13% | > + … Al isotopes (1.3e n, 0.5e n ) = 10 e p

25.  measurement for 33 Al(N=20) - normal sd-shell structure - The  -decay scheme is well-described with the USD interaction. A.C. Morton et al., PLB544(2002)274. 33 Al 89 % 33 Si 5/2+ 3/2+ P n =8.5(7)% (norma sd-shell) 32 Si Further investigation for the low-lying levels for 33 Al and nuclear moments is really needed.

26. 33 Al (Z=13, N=19) : transitional or not ? MCSM, PRC64(2001)011301(R) For N=20 isotones According to the MCSM prediction, the intruder mixing for N=20 isotones gradually occurs via a transitional nucleus 33 Al. 33 Al The  -decay of 33 Al, however, found no indication of the intruder mixing. A.C. Morton et al., PLB544(2002)274.

27.  -Decay time spectrum 32 Al A e – ( t /  ) + B A 3443(86) B 167(96)  present 45(2) ms Red.  2 0.97 ref. Table of Isotopes Least  2 fitting :  reported = 48(6) ms

28. Experiment on  and Q for 32 Al 1. Production of spin-polarized RI beam using projectile fragmentation reaction :   40 Ar (95 A MeV) + Nb (target)  pol. 32 Al 2. Catch of 32 Al(, ) in a stopper : 2. Catch of 32 Al( T 1/2 =33 ms, I p =1 + ) in a stopper :   Single crystal Si stopper (g-factor measurement)   Single crystal a-Al 2 O 3 stopper (Q-moment measurement) 3. Observation of the Nuclear Magnetic Resonance (NMR) through  -ray asymmetry changes using the  -NMR technique Procedure : RIKEN Accelerator Research Facility : RIKEN Ring Cyclotron

29. Preparation of a  -Al2O3 stopper X-ray diffraction h.c.p. structure How to hold : Quadrupole splitting for I=1 case 0 + - freq. = 0 3 cos 2  c - 1 2 3 Q 4 + - + - 0 = g  N B 0 /h (Larmor frequency) Q = e 2 qQ/h (QCC)  c = 0 ( crystal c-axis // B 0 )

30.  -NMR apparatus 55° The resonance frequency of 32 Al in sc.  -Al 2 O 3 : 0 = g  N B 0 /h (Larmor frequency) Q = e 2 qQ/h (QCC) m, m- 1 = 0 － 3cos 2  c - 1 2 3 Q 2 I (2 I -1) ( m -1/2 ) Stopper :  single-crystal Si (room temp.)  single-crystal -Al 2 O 3 (T=80K) ~0.5 Tesla W(0)/W(180) = (1+A  P)/(1-A  P) 0 1,0 0,-1 In the case of I  =1 +,  c : angle between the B 0 field and the crystal c-axis freq. X-ray diffraction β-ray angular distri. for pol. nuclei : W(  ) 1 + A  P cos  ~ = A   32 Al)=  -0.85 W(0)/W(180) = (1-A  P)/(1+A  P)  -ray up/down ratio: NMR effect : P  -P

31.  -NMR apparatus β-ray emission from pol. RI : W(  ) 1 + A  P cos  ~ = (U/D) OFF (U/D) ON 1 - 4A  P ~ ~ (U/D) OFF = (1+A  P ) / (1-A  P ) (U/D) ON = (1-A  P ) / (1+A  P )  -ray up/down count ratio : A   -0.85 for 32 Al degrader How to measure the Q-moment ? 0 + - freq. = 0 3 cos 2  c - 1 2 3 Q 4 + - + - 0 = g  N B 0 /h (Larmor frequency) Q = e 2 qQ/h (QCC)  c = 0 ( crystal c-axis // B 0 )