Nuclear moment measurements of neutron-Nuclear moment measurements of neutron-rich Al isotopes using spin-polarized RI beamsrich Al isotopes using spin-polarized RI beams

- Determination of the boundary of the “island of inversion” -

Daisuke KamedaDaisuke KamedaRIKEN, Asahi Applied Nuclear Physics Laboratory

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

K. Asahi, H. Ueno, A. Yoshimi, T. Haseyama, H. Watanabe Y. Kobayashi and M. IshiharaRIKEN, 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:

Introduction : Nuclear moment studies in the

vicinity of the island of inversion Why 32Al(Z=13, N=19) ?

Experiment and ResultComparison with shell models Summary

Outline:Outline:

Nuclear moment studies in the vicinity of the island of inversion

Ne

MgAl

Na

F

SiP

20

Z

N

Island of Inversion 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

s1/2

f7/2

d5/2

d3/2

p3/2

f7/2

d3/2

p3/2

Normal sd-shell configuration

d5/2

s1/2

0p0h, spherical 2p2h (intruder), deformed

In the case of Na isotope chain:

Nuclear moment studies II: neutron-rich Nuclear moment studies II: neutron-rich NN=19 =19 isotonesisotones

(31Mg, I=1/2+) :

G. Neyens et al., Phys. Rev. Lett. 94

(2005) 022501.

32Al (Z=13) : Our previous work Phys. Lett. B615 (2005)186.

The Q-moment for the ground state of 32Al is expected to provide the conclusive answer.

((3232Al) is well reproduced by Al) is well reproduced by sdsd ( (0p0h0p0h) shell models ) shell models

2p2h dominance, deformed

Ne

MgAl

Na

F

SiP

N=

19

Z

N=

20

| (32Algs;1+) |= 1.959(9) μN

1. 2p2h dominating state2. ~50% mixing of a 2p2h state to a 0p0h state3. 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 :

Experiment for Q (32Alg.s.) in RIKEN

Procedure : 1, Produce spin-polarized 32Al beam via projectile fragmentation 2, Detect the quadrupole resonance using the -NMR technique

Production of spin-polarized Production of spin-polarized 3232Al beam Al beam

Primary beam 40Ar

95 AMeV, 40pnA

Nb target Nb, 0.37 g/cm2

Secondary beam 32Al

Emission angle 1.3 – 5.2 deg.

Momentum 12.6 GeV/c ±3 %

Intensity@F2 5 x 103 particle/sec.

Purity 85%

Polarization ~ 0.7 %

RIKEN Projectile fragment separator (RIPS):

B = (mv0 /e) AZ

= 3.6 m)

∝Z2 　 dEdx

Isotope separation:

Particle identification: • E @ F2 SSD • TOF (F2 PPAC - RRC)

Selected momentum region:

40Ar

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.

-NMR apparatus -NMR apparatus

55°

~0.5 Tesla

R = W(0)/W() = (1+AP)/(1-AP)

β-ray angular distribution for pol. nuclei :W() 1 + AP cos ~=

[A32Al)=-0.85]

R’ = (1-AP)/(1+AP)

-ray up/down ratio:

NMR effect (AFP) : P -P

0+ -

freq.

+- = 0

3 cos2 c - 1

2

3Q

4+-

0= gNB0/h (Larmor frequency)

Q= e2qQ/h (Quadrupole coup. const.)

c = 0 ( crystal c-axis // B0 )

The resonance frequencies of 32Al(I=1)in a stopper of single-crystal -Al2O3:

In the present work,

-ray asymmetry change observed:~=1- R’ / R 4AP

Crystal structure of -Al2O3: h.c.p.

pol. 32Al

stopper surface

Quadrupole resonance spectra with Quadrupole resonance spectra with -Al-Al22OO3 3 stopper stopper

|Q(32Al)|

Q(27Al)Q(32Al)

|Q(27Al)|

ref. Q(27Al) in -Al2O3: J. Magn. Reson. 89 (1990) 515. Q(27Al): Phys. Rev. Lett. 68 (1992) 927.

Crystal c-axis // B0

Q(32Al) = 407(34) kHz

=

|Q(32Al)| = 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 (= e2qQ/h) kHz to be submitted.

Systematic comparison : Systematic comparison : and and QQ for Al for Al isotopesisotopes

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.A474 (1987) 290-306

(ep, en) = (1.3, 0.5)

Monte Carlo shell model calc. by Utsuno (in private communication)

sd-normal configurations : 87 %fp-intruder configurations : 13 %

32Alg.s :

• Single-particle-like configurations• Very small Q-moment

0h

0h

The calculated sd-configurations of 32Alg.s.

2 = 79 %, 2 < 3.8 %

|32Alg.s(I=1+)

| d-15/2 d-1

3/2 J=1+=

+| d3

5/2d23/2) d-1

3/2 J=1+ + …

Why is so small the Q-moment of Why is so small the Q-moment of 3232Al ? Al ?

<ψcoupl.|E2() + E2()|ψcoupl.> =

< d-15/2 || E2() || d-1

5/2 > = 92ep

radial part: Harmonic Osci.(M. Carchidi et al, PRC34(1986)2280)

A(I,j,j’) < d-15/2 || E2() || d-1

5/2 >+B(I,j,j’) < d-13/2 || E2() || d-1

3/2 >=20ep + 5en

•Reduced E2 matrix elements :< d-1

3/2 || E2() || d-15/2 > = 70en

•Geometrical terms involving 6j symbols: A(I,j,j’), B(I,j,j’)

Small geometrical factors in < [d-15/2 d-1

3/2]I=1.|E2() + E2()| [d-1

5/2 d-13/2]I=1 >

are main source of the small Q-moment of 32Al.

I (total spin) A(I,5/2,3/2) B(I,5/2,3/2)

1 0.022 0.068

2 0.160 0.070

3 0.056 0.134

4 0.224 0.244

The case of 32Alg.s (I=1, j=d5/2, j’=d3/2)

Dominant (~80%) configuration for 32Alg.s. : ψcoupl.[d-15/2 d-1

3/2]I=1

The small E2 matrix element for the ψcoupl. state is consistent with the small exp. value, Q(32Alg.s.)=24(2) mb

29 mb, taking (ep,ep)=(1.3, 0.5)

E2 matrix element for the ψcoupl. state :

(Off-diagonal contributions are negligibly small according to the USD calculation by OXBASH.)

The location and variation of the boundary The location and variation of the boundary regionregion

Ne

MgAl

Na

F

SiP 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 29Na

Inversion process along the Z=11 line

Inversion process along the N=19 line

The inversion occurs The inversion occurs suddenlysuddenly between between 3131Mg and Mg and 3232Al with a Al with a drastic change on shape drastic change on shape

Island of Inversion

Summary and ConclusionSummary and ConclusionExperiment 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) N in 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 [d-1

5/2d-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.

Thank you for your attentions.

Further investigation is needed, in particular, Further investigation is needed, in particular, ,,QQ((3333Al) and the low-lying level structure for Al) and the low-lying level structure for 3232AlAl

Low-lying levels in Low-lying levels in 3232AlAl1. 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 32Mg.

G. Grevy et al., NPA734(2004)369.

The g-factor of the isomer (=200ns) is interesting.

USDAfrom Home page of B. A. Brown

Mechanism for the Mechanism for the suddensudden transition transition along the along the NN=19 chain=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 32Alg.s.

Analyses of Q-moments for Al isotopes Analyses of Q-moments for Al isotopes Qcal = (ep Ap + en An) Ap(n) : E2 matrix elements for proton (neutron)

A

p (

mb

)

A

n (m

b)

The small Q-moment of 32Al is constructed almost only by the E2 matrix element of <d5/2|r2Y2|d5/2>

USD cal.OXBASH

=0.77=0.58=0.77=0.77=0.77=0.77=0.77=0.73

Production of pol. RI beam via PF reaction - Principle - Production of pol. RI beam via PF reaction - Principle -

Advantages ：　1. chemically independent2. very fast process

R

v

v0+v

Projectile fragment

Target nucleus

Participant :

v0

Orbital angular mom. 　L=R×mv

K. Asahi, et al., Phys. Lett. B251 (1990) 488

near side

far side

P > 0LP > 0

P < 0

H. Okuno et al., Phys. Lett. B 335 (1994) 29

Projectile,MeV/u

14N40

15N68

15N110

15N67

15N68

target Au Au Au Nb Alfragment 12B 13B 13B 13B 13Bfrag. (deg.) 5.0 4.0 2.0 2.5 1.0

theo(USD) (N)

ex

p.

(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

→ | μ (30AlGS;3+) |

= 3.010(7) μ N

ΔF/F (1-sweep) = 1.1 (%)

→ | μ (32AlGS;1+) |

= 1.959(9) μ N

H. Ueno et al., Phys. Lett. B 615 (2005) 186.

-NMR spectra for-NMR spectra for 30 30Al and Al and 3232Al in sc. Al in sc. -Al-Al22OO33

- with the magic angle “- with the magic angle “c = 55°”- = 55°”-

Intruder states of the neutron-rich Intruder states of the neutron-rich NN=19 =19 isotonesisotones

30Na (Z=11) 31Mg (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.

32Al (Z=13)intruder 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 effectthan the -moment.We can see the sensitivity in Q(29Na).

Where is the border of the “island of inversion” ?

Ne

MgAl

Na

F

SiP

N=20

energy income (Ec)

energ

y e

xpense

(2

Eg)

The

bord

er

Island

Normal

32Al31Mg30Na 1. Monopole term

Effective shell gap (Eg) : 2. Multipole term Correlation energy (Ec)

proton neutrond5/2

d3/2

s1/2

Eg

f7/2

N=16

N=20

　　　　　　　　　 Y. Utsuno, et al., Phys. Rev. C 60 (1999) 054315

0 1,00,-1

3232Al(Al(=1=1++) ) QQ-moment search using sc. -moment search using sc. --AlAl22OO33

freq.

F+F-

c = 90°(c-axis B⊥ 0)

Origin of the [Origin of the [dd-1-15/25/2dd-1-1

3/23/2]]II=1 =1 state dominance in state dominance in 3232AlAlg.s.g.s. 1, Energetic favor of the I=1 coupling state between neutron-proton spin-orbit partners.

Isoscalar part of USD Isovector 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.

Why is the Q(Why is the Q(3232AlAlg.s.g.s.) so small ?) 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-15/2 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 :

The other example : small The other example : small QQ((1212BBg.s. g.s. II=1=1++))

12B

Neutron number

Q-m

om

ents

(m

b)

code: OXBASH

proton neutron

12B(I=1+) = p3/2

p1/2

p3/2

p1/2

75 % + 13% |> + …

Al isotopes

(1.3en, 0.5en)

< [p-13/2 p-1

1/2]I=1 | epQ() + enQ() | [p-13/2 p-1

1/2]I=1 > = 10 ep

measurement for measurement for 3333Al(Al(NN=20)=20)- normal - normal sdsd-shell structure --shell structure -

The -decay scheme is well-described with the USD interaction.

A.C. Morton et al., PLB544(2002)274.33Al

89 %

33Si

5/2+

3/2+

Pn=8.5(7)%

(norma sd-shell)

32Si

Further investigation for the low-lying levels for 33Al and nuclear moments is really needed.

3333Al (Al (ZZ=13, =13, NN=19) : transitional or =19) : transitional or not ?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 33Al.

33Al

The -decay of 33Al, however, found no indication of the intruder mixing.

A.C. Morton et al., PLB544(2002)274.

-Decay time spectrum -Decay time spectrum

32Al

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

Experiment on Experiment on and and QQ for for 3232AlAl

1.1. Production of spin-polarized RI beam using projectile fragmentation Production of spin-polarized RI beam using projectile fragmentation reaction :reaction :

40Ar (95 A MeV) + Nb (target) pol. 32Al 2.2. Catch of Catch of 3232Al(Al(T1/2=33 ms, , Ip=1+) in a stopper : ) in a stopper :

Single crystal Si stopper (g-factor measurement) Single crystal a-Al2O3 stopper (Q-moment measurement)

3.3. Observation of the Nuclear Magnetic Resonance (NMR) through Observation of the Nuclear Magnetic Resonance (NMR) through -ray asymmetry changes using the -ray asymmetry changes using the -NMR technique-NMR technique

Procedure :

RIKEN Accelerator Research Facility :

RIKEN Ring Cyclotron

Preparation of a Preparation of a -Al2O3 -Al2O3 stopper stopper

X-ray diffraction

h.c.p. structure

How to hold :

Quadrupole splitting for I=1 case

0+ -

freq.

= 0 3 cos2 c - 1

2

3Q

4+-+-

0= gNB0/h (Larmor frequency)

Q= e2qQ/h (QCC)

c = 0 ( crystal c-axis // B0 )

-NMR apparatus -NMR apparatus

55°

The resonance frequency of 32Al in sc. -Al2O3 :

0= gNB0/h (Larmor frequency)

Q= e2qQ/h (QCC)

m,m-1 = 0 － 3cos2 c - 1

2

3Q

2I(2I-1)(m -1/2)

Stopper : single-crystal Si (room t

emp.) single-crystal -Al2O3 (T

=80K)

~0.5 Tesla

W(0)/W(180) = (1+AP)/(1-AP)

01,0 0,-1

In the case of I =1+,

c : angle between the B0 field and the crystal c-axis

freq.

X-ray diffractionX-ray diffraction

β-ray angular distri. for pol. nuclei :W() 1 + AP cos ~=

A32Al)=-0.85

W(0)/W(180) = (1-AP)/(1+AP)

-ray up/down ratio:

NMR effect : P -P

-NMR apparatus-NMR apparatus β-ray emission from pol. RI : W() 1 + AP cos ~=

(U/D)OFF

(U/D)ON1 - 4AP~~

(U/D)OFF = (1+AP)/(1-AP)

(U/D)ON = (1-AP)/(1+AP)

-ray up/down count ratio :

A-0.85 for 32Al

degrader

How to measure the Q-moment ?

0+ -

freq.

= 0 3 cos2 c - 1

2

3Q

4+-+-

0= gNB0/h (Larmor frequency)

Q= e2qQ/h (QCC)

c = 0 ( crystal c-axis // B0 )