Magnetic Moment

of Proton Halo Nucleus 28P

The XIV International Conference on

Hyperfine Interactions & XVIII

International Symposium on Nuclear

Quadrupole Interactions

August 5-10

Iguassu Falls, Brazil

Presented by Shengyun Zhu

CIAE D.M. Zhou, Y.N. Zheng, D.Q Yuan, Y. Zuo,

P. Fan, X.Z. Zhang, S.Y. Zhu

Osaka Univ. K. Matsuta, M. Mihara, M. Fukuda, D. Nishimura,

J. Komurasaki, D. Ishikawa, R. Matsumiya

Niigata Univ. T. Izumikawa, S. Takahashi, H. Hirano, T.

Ohtsubo

RIKEN T. Nagatomo

NIRS, HIMAC A. Kitagawa, M. Kanazawa, M. Torikoshi, S.

Sato

Kochi Univ. of Tech. S. Momota, Y. Nojiri

Fukui Univ. of Tech. T. Minamisono

Tokyo Univ. of Sci. T. Sumikama

LBL J.R. Alonso, G.F. Krebs, T.J.M. Symons

Nihon Univ. T. Suzuki

31 people from 10 institutions

Outline

1, Background

2, Experimental

3, Results and discussion

1, Background

• Proton-rich unstable nucleus 28P has one

proton outside the 27Si Core

• The last proton lies in the 2s1/2 orbital and

its separation energy is Sp = 2.065 MeV

• 28P nucleus in ground state (Ip= 3+, T1/2 = 270.3 ms)

a good candidate of proton halo nucleus

27Si

P

28P decay

270.3ms11.3%3.57.6%4.82.76%4.72.45%4.869.2%4.83.64%4.33+9315.928588.717933.457799.016276.201779.0300stable

Q

EC

=14332

02815P0+2+3+3+2+3+3+2814Si1.92%5.84617.864+ 図

1.1:28P

の崩壊図

11.3% 3.5

3+ 270.3 ms

3.64% 4.3

2.45% 4.8

2.76% 4.7

7.6% 4.8

28P

28Si

69.2% 4.8

1.92% 5.8

8588.71

9315.92

7799.01

7933.45

4617.86

6276.20

stable

1779.030

00+

4+

2+

3+

3+

3+

3+

2+

QEC = 14332 keV

T=1 (IAS)

p n

state state

2s1/2

1p1/2

1p3/2

1d5/2

1d3/21d3/2

1d5/2

2s1/2

1s1/2 1s1/2

1p3/2

1p1/2

28P nuclear structure

Proton halo structure of 28P

• Coulomb barrier may hinder the formation

of proton halo

the size of proton halo much smaller than

neutron halo

• It is not easy to investigate proton halo by

cross section measurements

The experimental results are controversial

• H.Y. Zhang et al did not observe proton halo in 28P

by measuring the reaction cross section for 28P+12C

• Z.H. Liu et al measured

the reaction cross section

for28P+Si at 40 AMeV

detected an enhancement

of reaction cross section

for which the proton halo

is responsible

28P

• Navin et al confirmed the existence of proton halo in 28P by measuring de-excitation g ray I coincidence

with the momentum distribution of the projectile

residues

• Chen et al & Ren et al calculated the density

distribution of 28P

& showed proton halo

in 28P

(RMF, Shell model, SHF)

Magnetic moment of 28P

• Measurement of magnetic moment can

provide detailed information on the wave

function of halo nucleons in combination

with theoretical analysis

• The magnetic moment of 28P in ground state

has not been measured so far.

St able Nuclei

~1990年

Recent 15y

He

Li

Be

B

C

F

O

Ne

8 10 1 1 12 13 1 4 15 17 19

9 10 11 12 147

8 9 1 16 7

6 8

9 1 0 11 12 13 1 4 15 1 6 17 1 8 19 20 22

12 1 3 14 1 5 16 17 18 19 2 0 21 22 23

13 1 4 15 1 6 17 1 8 19 20 21 2 2 23 24

1 7 18 1 9 20 2 1 22 2 3 2 4 2 5 26 27

17 18 19 2 0 21 2 2 23 24 25 26 27 28 29 30 3231

2 0 21 2 2 23 24 25 26 27 28 29 30 3231 33 34 35

N

Na

20 21 22 23 24 25 26 27 28 29 30 3 231 33 34 35 36 37 38

22 23 2 4 25 2 6 27 2 8 29 3 0 3231 33 3 4 35 3 6 37 3 8 39 4 0

2 2 23 24 25 2 6 27 2 8 29 3 0 3 231 33 3 4 35 3 6 37 3 8 39 4 0 41

26 2 7 28 2 9 30 323 1 3 3 34 3 5 36 3 7 38 3 9 40 4 1 42

27 2 8 29 3 0 3231 33 3 4 35 3 6 37 3 8 39 4 0 41 42 43

323 1 3 3 34 3 5 36 3 7 38 3 9 40 4 1 42 4 3 44

3231 33 3 4 35 3 6 37 3 8 39 4 0 41 42 43 44 45

35 3 6 37 3 8 39 4 0 41 42 43 44 45 46

35 36 37 38 39 40 41 42 43 44 45 4 6 47

4 0 41 42 43

39 4 0 41 4 2 43

44 45 46 4 7

4 4 45 46 4 74 8

48

49

Al

Si

P

S

Mg

Cl

Ar

KCa

ScTi

Z

N

Recent situation of

magnetic moment measurement

T=1/2

T=3/2N=20

T=1

• The present work was motivated to measure

the magnetic moment of 28P

by -NMR with a new spin polarized beam

technique

• Magnetic moment of 28P in ground state &

density distributions of protons were also

calculated by modified shell model

2, Experimental

• Magnetic moment of proton-rich nucleus 28P

has been measured by -NMR combined with

a new polarization technique of charge

exchange reaction product

in intermediate energy heavy ion collisions

(reported at this conference)

Heavy Ion Medical Accelerator in Chiba (HIMAC)

National Institute of Radiological Sciences (NIRS), Japan

28Si

100 MeV/u

Charge exchange

28Si+Be 28P + X

fAsym

metr

y

• 28P nuclei were produced by

the charge exchange reaction 28Si+Be 28P + X

2-mm thick Be target was bombarded

with a primary beam of 100 MeV/u 28Si

from heavy ion synchrotron accelerator (HIMAC)

• 28P nuclei were separated out with a fragment

separator installed in the secondary beam line

• By selecting ejection angle q=0.7°

& momentum Δp/p0 = -2.0

nuclear spin polarization

was introduced in the 28P nuclei

Obtained P~1%

• Polarized 28P nuclei slowed down

by a thickness controllable energy

degrader & implanted into a Pt catcher

cooled at 15 K, placed under a strong magnetic field of 0.9 or 1.0 T, to preserve polarization

• Beta-rays emitted from 28P were detected

by a pair of plastic scintillation counter telescopes placed above and below the Pt catcher relative to the polarization direction

• The -NMR was detected by the -ray asymmetry

• The spin relaxation time was long enough compared with the half-life of 28P

(reported at this conf.)

3, Results & discussion

Experimental sequence

Beam 200 ms

rf 15 ms

-ray counting

500 ms

coling 1285 ms

28P beam mixed

with 27Si as

background

S/N ~5.6

for the sequence

using in the exp.

Time spectrum

2 s repetition, flat Top 800 ms, by fast extraction to get 200 ms width.

400 600 800 1000 1200

-0.004

-0.002

0.000

0.002

0.004

0.006400 450 500 550 600 650 700 750 800 850 900 9501000105011001150120012501300

-0.004

0.000

0.004

0.008

FM=15KHz

-ray

asy

mm

metr

y c

han

ge

AP

Frequency(kHz)

FM=50KHz

Typical -NMR spectra obtained at H = 1.0 T with an FM of 50 kHz (up)

& at H = 0.9 T with an FM of 15 kHz (down)

-NMR spectra

• The -NMR spectra give

the resonant frequency

f = 0.7055(49) MHz

• via m = hnLI/mNH

the g-factor and magnetic moment deduced to be

g = 0.1028 (21)

︱m(28P)︱= 0.309(9) mN

correcting 0.10% of the theoretical diamagnetism

& including 0.27% of Knight shift in the error

• Due to the configuration mixing

the magnetic moment is strongly quenched

from the Schmidt value of 0.88msch = 0.880 mN

400 600 800 1000 1200

-0.004

-0.002

0.000

0.002

0.004

0.006400 450 500 550 600 650 700 750 800 850 900 9501000105011001150120012501300

-0.004

0.000

0.004

0.008

FM=15KHz

-ray

asy

mm

metr

y c

han

ge

AP

Frequency(kHz)

FM=50KHz

mexp = 0.309 (9) mN

p

m(29P + 27Si) = 0.370 mN

+ =

28P

n hole

27Si

n hole

-0.865 mN

p

29

P

1.235 mNm : cf. 0.370

particleP particle

• OXBASH calculations of the magnetic moment and the density distributions of protons & neutrons performed

• An improved shell-model Hamiltonian with enhanced spin-flip proton-neutron interaction and modified single-particle energies was used

• The interaction parameters were adjusted for the sd shells

• Three kinds of one-body transition densities for isovectors and isoscalars were obtained from the shell model wave functions for computing the magnetic moment and quadrupole moment and the density distributions of protons, neutrons and matter, respectively

(many body wave function)

Shell model calculation

Magnetic moment

mshell = 0.306 mN

Experimentally measured magnetic moment

mexp = 0.309 (9) mN

well reproduced by the shell model value

In addition, shell model calculation shows

that the magnetic moment is resulted from

the cancellation of the 2s1/2 orbital and the d orbitals

The 2s1/2 acts as an important part

Data??

Magnetic moments of states

for 28P

1d3/2 0.0163

1d3/2 & 1d5/2 -0.2526

1d3/2 & 2s1/2 0

1d5/2 & 1d3/2 -0.2526

1d5/2 -0.6253

2s1/2 & 1d3/2 0

2s1/2 1.4202

Particle numbers (shell)

1/2 state EN1 0.3767

FP1 1.0980

3/2 state EN3 0.3759

FP3 0.6212

5/2 state EN5 4.2471

FP5 5.2805

HF can not

Density distribution

Density distribution of protons has

a much longer tail than that of neutrons

0 5 10 15 20

de

nsity(f

m-3)

r(fm)

proton

neutron

matter

0

10-2

10-4

10-6

10-8

10-10

Shell model

0 5 10 15 20

de

nsity(f

m-3)

r(fm)

proton

total matter

neutron

0

10-2

10-4

10-6

10-8

10-10

Skyrme-Hartree-Fock

Summary

• Magnetic moment of 28P in the ground state (Ip=3+, T1/2=

270.3 ms) has been measured by –NMR with spin polarized RI beams technique through charge

exchange reaction 28Si + Be→28P + X

Obtained P ~ 1%

• Measured magnetic moment ︱m(28P)︱= 0.309mN is well reproduced by the shell model value of +0.306mN

• Proton density distribution calculated by the shell model shows a long tail

• The present results provide a strong confirmation of the configuration of the 2s1/2 proton which should lead to the halo structure

Future work

To carry out an more precise

measurement

for the magnetic moment of 28P

To measure the quadrupole moment Q of 28P

and perform shell model calculation of Q

Thank you