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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