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The 17th International Spin Physics Symposium, SPIN2006 October. 2 nd –7 th , 2006, Kyoto, Japan

The 17th International Spin Physics Symposium, SPIN2006 October. 2 nd –7 th , 2006, Kyoto, Japan.

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The 17th International Spin Physics Symposium, SPIN2006 October. 2 nd –7 th , 2006, Kyoto, Japan

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  1. The 17th International Spin Physics Symposium, SPIN2006 October. 2nd –7th,2006, Kyoto, Japan Nuclear moment measurements of neutron-rich Al isotopes using spin-polarized RI beams- Determination of the boundary of the “island of inversion” -Daisuke KamedaRIKEN, Asahi Applied Nuclear Physics Laboratory Collaborators: 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

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

  3. Nuclear moment studies in the vicinity of the island of inversion In the case of Na isotope chain: P Si Al Mg Z Na Ne F 20 N Normal sd-shell configuration Island of Inversion E.K. Warburton, J. A. Becker and B. A. Brown, PRC41(1990)1147. 0p0h, spherical 2p2h (intruder), deformed p3/2 p3/2 f7/2 f7/2 20 d3/2 d3/2 s1/2 s1/2 d5/2 d5/2 Monte Carlo shell model with sdpf model space: Y. Utsuno, et al., Phys. Rev. C70(2004) 044307. n n

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

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

  6. Selected momentum region: Production of spin-polarized 32Al beam RIKEN Projectile fragment separator (RIPS): 40Ar Isotope separation: A Z Br = (mv0/e) (r = 3.6 m) dE dx ∝Z2 • Particle identification: • DE @ F2 SSD • TOF (F2 PPAC - RRC) Key technique for polarization : K. Asahi, et al., Phys. Lett. B251 (1990) 488 To produce polarization, the Fermi motion of nucleons in the projectile and fragment was utilized.

  7. W(q )1 + Ab Pcosq ~ ~ = = + - 3nQ 3 cos2qc - 1 - n = n0 + 2 4 β-ray angular distribution for pol. nuclei : b-NMR apparatus ~0.5 Tesla [Ab(32Al)=-0.85] b-ray up/down ratio: R=W(0)/W(p) = (1+AbP)/(1-AbP) 55° NMR effect (AFP) : P -P pol. 32Al R’ = (1-AbP)/(1+AbP) b-ray asymmetry change observed: 4AbP 1- R’ / R The resonance frequencies of 32Al(I=1) in a stopper of single-crystal a-Al2O3: In the present work, qc = 0 ( crystal c-axis // B0 ) Crystal structure of a-Al2O3: h.c.p. stopper surface freq. n+ n0 n- n0= gmNB0/h (Larmor frequency) nQ= e2qQ/h (Quadrupole coup. const.)

  8. Quadrupole resonance spectra with a-Al2O3 stopper Crystal c-axis // B0 Temperature : ~ 80 K 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. nQ(32Al) = 407(34) kHz taking the overall error into account |Q(32Al)| |Q(27Al)| 140.2(10) mb = = nQ(27Al) nQ(32Al) 2389(2) kHz ref. nQ(27Al) in a-Al2O3: J. Magn. Reson. 89 (1990) 515. Q(27Al): Phys. Rev. Lett. 68 (1992) 927. |Q(32Al)| = 24(2) mb nQ (= e2qQ/h) kHz to be submitted.

  9. 0hw 0hw Monte Carlo shell model calc. by Utsuno (in private communication) 32Alg.s : sd-normal configurations : 87 % fp-intruder configurations : 13 % Systematic comparison : m and Q for Al isotopes Experimental data : N.J. Stone, Atomic Data and Nucl. Data. Tables 90 (2005) 75. (ep, en)= (1.3, 0.5) 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.A474 (1987) 290-306 Calculation code : OXBASH, B.A. Brown, A. Etchegoyen, W.D.M.Rae, MSU Cycl. Lab. Rep. No.524(1986). The calculated sd-configurations of 32Alg.s. • Single-particle-like configurations • Very small Q-moment |32Alg.s(Ip=1+) = | pd-15/2nd-13/2J=1+ + a • | p(d35/2d23/2) nd-13/2J=1+ + … a2= 79 %, b2< 3.8 %

  10. Why is so small the Q-moment of 32Al ? Dominant (~80%) configuration for 32Alg.s. : ψcoupl. = [pd-15/2nd-13/2]I=1 E2 matrix element for the ψcoupl. state : <ψcoupl.|E2(p) + E2(n)|ψcoupl.> = A(I,j,j’)<pd-15/2 || E2(p) || pd-15/2>+B(I,j,j’) <nd-13/2 || E2(n) || nd-13/2>=20ep + 5en 29 mb, taking (ep,ep)=(1.3, 0.5) The small E2 matrix element for the ψcoupl. state is consistent with the small exp. value, Q(32Alg.s.)=24(2) mb • Reduced E2 matrix elements : <pd-15/2 || E2(p) || pd-15/2> = 92ep <nd-13/2 || E2(n) || nd-15/2> = 70en radial part: Harmonic Osci.(M. Carchidi et al, PRC34(1986)2280) • Geometrical terms involving 6j symbols: A(I,j,j’), B(I,j,j’) The case of 32Alg.s (I=1, j=d5/2, j’=d3/2) Small geometrical factors in < [pd-15/2nd-13/2]I=1.|E2(p) + E2(n)| [pd-15/2nd-13/2]I=1 > are main source of the small Q-moment of 32Al. (Off-diagonal contributions are negligibly small according to the USD calculation by OXBASH.)

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

  12. Summary and Conclusion Experiment on nuclear moments for the 32Al ground state: • 40Ar + Nb  pol. 32Al • |Q(32Alg.s)| = 24(2) mb in cooled single crystal a-Al2O3 (T~80K) ( |g(32Alg.s.)| = 1.951(5) mNin single crystal Si stopper ) Comparison with nuclear moments for Al isotopes and shell model calculations: • Small Q(32Alg.s)indicates that 32Al has a spherical shape. • The good agreements with the USD calculation indicates that 32Al is a normal sd-shell nucleus.  The single-particle-like configuration about the [pd-15/2nd-13/2]J=1+ state Comparison with recent reports on the N=19 isotones 30Na, 31Mg and 32Al: • The clear-cut borderline of the island of inversion is located between 32Al (normal) and 31Mg (intruder), in sharp contrast to the case of the sodium isotope chain. Further investigation is needed, in particular, m,Q(33Al) and the low-lying level structure for 32Al Thank you for your attentions.

  13. Low-lying levels in 32Al • 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 b-decay branching ratio to the ground state from 32Mg. G. Grevy et al., NPA734(2004)369. USDA from Home page of B. A. Brown The g-factor of the isomer (t=200ns) is interesting.

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

  15. Analyses of Q-moments for Al isotopes Qcal = a (ep Ap + en An) Ap(n) : E2 matrix elements for proton (neutron) USD cal. OXBASH a=0.77 a=0.58 a=0.77 a=0.77 a=0.77 a=0.77 a=0.77 aAp (mb) a=0.73 aAn (mb) The small Q-moment of 32Al is constructed almost only by the E2 matrix element of <pd5/2|r2Y2|pd5/2>

  16. Production of pol. RI beam via PF reaction - Principle - K. Asahi, et al., Phys. Lett. B251 (1990) 488 Projectile fragment P > 0 P > 0 -dL near side v0+dv v0 R dv Participant : far side Orbital angular mom. dL=R×md v Target nucleus P < 0 H. Okuno et al., Phys. Lett. B 335 (1994) 29 • Advantages ：　 • chemically independent • very fast process

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

  18. b-NMR spectra for 30Al and 32Al in sc. a-Al2O3- with the magic angle “qc = 55°”- ΔF/F (1-sweep) = 1.1 (%) → | μ(30AlGS;3+) | = 3.010(7) μN → | μ(32AlGS;1+) | = 1.959(9) μN H. Ueno et al., Phys. Lett. B 615 (2005) 186.

  19. Intruder states of the neutron-rich N=19 isotones intruder intruder normal ? 30Na (Z=11) 31Mg (Z=12) 32Al (Z=13) • Nuclear moments: M. Keim et al., • Eur. Phys. J. A8 (2000) 31. m moment and spin: G. Neyens et al., Phys. Rev. Lett. 94 (2005) 022501. • m moment : H. Ueno et al., • Phys. Lett. B615 (2005) 186.  suggests the normal state • MCSM : Y. Utsuno et al., • Phys. Rev. C70 (2004) 044307. 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 m-moment. We can see the sensitivity in Q(29Na).

  20. Y. Utsuno, et al., Phys. Rev. C 60 (1999) 054315 Where is the border of the “island of inversion” ? P Si Al Mg Na Ne F N=20 f7/2 N=20 Eg d3/2 The border Normal N=16 s1/2 energy expense (2DEg) 32Al 31Mg 30Na d5/2 neutron proton 1. Monopole term  Effective shell gap (Eg) : 2. Multipole term  Correlation energy (Ec) Island energy income (DEc)

  21. 32Al(I p=1+) Q-moment search using sc. a-Al2O3 F- F+ qc = 90°(c-axis ⊥ B0) freq. n0 n0,-1 n1,0

  22. Origin of the [pd-15/2nd-13/2]I=1 state dominance in 32Alg.s. 1, Energetic favor of the I=1 coupling state between neutron-proton spin-orbit partners.  general trend of effective interactions cf. Cohen-Kurath(p-shell), USD(sd-shell), GXPF(fp-shell) 2, Neutron configurations are highly restricted in the closed-shell plus one-hole system. For example, Isoscalar part of USD Isovector part of USD

  23. Why is the Q(32Alg.s.) so small ? Answer : 1, Dominance of the [pd-15/2nd-13/2]I=1+ stateby about 80 %  force the Q-moment to be small origin 2, Energetic favor of the I=1+ coupling state between proton-neutron spin-orbit partners in effective interactions. 3, Neutron configurations are highly restricted in the one-hole system (N=19).

  24. The other example : small Q(12Bg.s. I=1+) Al isotopes (1.3en, 0.5en) Q-moments (mb) 12B code: OXBASH Neutron number pp1/2 np1/2 + 13% |F> + … 12B(I=1+) = 75 % pp3/2 np3/2 neutron proton < [pp-13/2np-11/2]I=1 | epQ(p) + enQ(n) | [pp-13/2np-11/2]I=1> = 10 ep

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

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

  27. b -Decay time spectrum 32Al Least c2 fitting : Ae – (t / t ) + B treported = 48(6) ms ref. Table of Isotopes

  28. Experiment on m and Q for 32Al RIKEN Accelerator Research Facility : RIKEN Ring Cyclotron • Production of spin-polarized RI beam using projectile fragmentation reaction : • 40Ar (95 A MeV) + Nb (target)  pol. 32Al • Catch of 32Al(T1/2=33 ms, Ip=1+) in a stopper : • Single crystal Si stopper (g-factor measurement) • Single crystal a-Al2O3 stopper (Q-moment measurement) • Observation of the Nuclear Magnetic Resonance (NMR) through b-ray asymmetry changes using the b-NMR technique Procedure :

  29. + - Preparation of a a-Al2O3 stopper h.c.p. structure Quadrupole splitting for I=1 case freq. n+ n0 n- 3nQ 3 cos2qc - 1 - n = n0 + 2 4 n0= gmNB0/h (Larmor frequency) nQ= e2qQ/h (QCC) qc = 0 ( crystal c-axis // B0 ) X-ray diffraction How to hold :

  30. W(q )1 + Ab Pcosq ~ = X-ray diffraction X-ray diffraction β-ray angular distri. for pol. nuclei : b-NMR apparatus ~0.5 Tesla Ab(32Al)=-0.85 b-ray up/down ratio: 55° W(0)/W(180) = (1+AbP)/(1-AbP) NMR effect : P -P W(0)/W(180) = (1-AbP)/(1+AbP) Stopper : • single-crystal Si (room temp.) • single-crystal a-Al2O3 (T=80K) The resonance frequency of 32Al in sc. a-Al2O3 : 3nQ 3cos2qc - 1 nm,m-1 = n0 － (m -1/2) 2 2I(2I-1) qc : angle between the B0 field and the crystal c-axis n0= gmNB0/h (Larmor frequency) nQ= e2qQ/h (QCC) In the case of I p=1+, freq. n0 n0,-1 n1,0

  31. b-NMR apparatus W(q )1 + Ab Pcosq ~ = + - ~ ~ • β-ray emission from pol. RI : Ab= -0.85 for 32Al • b-ray up/down count ratio : (U/D)OFF = (1+AbP)/(1-AbP) degrader (U/D)ON = (1-AbP)/(1+AbP) (U/D)ON 1 -4Ab P (U/D)OFF How to measure the Q-moment ? 3nQ 3 cos2qc - 1 - n = n0 + 2 4 freq. n0= gmNB0/h (Larmor frequency) nQ= e2qQ/h (QCC) n+ n0 n- qc = 0 ( crystal c-axis // B0 )

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