1. Unexpected nonquenching of the isoscalar spin-M1 transitions
Hiroaki MATSUBARA
Tokyo Women’s Medical University
2015 Nov

2. Collaborators

3. Quenching problem of GT strength
(p,n) reaction
GT sum rule (model independent)
K. Ikeda PL 3, 271 (1963)
Only 50% strength has been observed in experiment.
Where is missing strength?
Measured area
Δ-h?
~50%
B(GT)
2p2h? 25 50
300 　　Ex. (MeV)
・Δ-h excitation （excitation of quark）　~300 MeV IV only
M. Ichimura, H. Sakai and
T. Wakasa; PPNP. 56, 446 (2006).
・2p2h excitation （tensor force effect） ~50MeV IS / IV

4. Quenching of spin strength
12B (12N) 0+ 1+
T=1
T=0
Quenching factor (sd-shell): Experiment / Theory of transition
Ikeda Sum-rule
(up to Ex=50 MeV)
Shell-Model Calc.
(within 0-hw)
GT (στ±)
0.9
0.6
IV spin-M1 (στz) --
0.6—1.0 (*)
IS spin-M1 (στ)
0.5—0.7 (*)
Uncertain results
・Quench is dominant
・Consistent with
　　　　　 2p2h theories
However,
・ Large error bar
・ Nuclear dependence
(*) Taken from G.M. Crawley PRC(1989): (p,p’) on sd-shell nuclei

5. Quenching of spin strength
12B (12N) 0+ 1+
T=1
T=0
Quenching factor (sd-shell): Experiment / Theory of transition
Ikeda Sum-rule
(up to Ex=50 MeV)
Shell-Model Calc.
(within 0-hw)
GT (στ±)
0.9
0.6
IV spin-M1 (στz) --
0.6—1.0 (*)
IS spin-M1 (σ)
0.5—0.7 (*)
Present work
(within 0-hw) --
0.61(6)
1.01(9)
Nonquench!
(*) Taken from G.M. Crawley PRC(1989): (p,p’) on sd-shell nuclei

6. Nonquenched IS spin-M1 strength
was found by the present work.
- Is it consistent with Δ-h excitation?
- Is it consistent with 2p2h excitation? No
Yes
Quenching factor (sd-shell): Experiment / Theory of transition
Ikeda Sum-rule
(up to Ex=50 MeV)
Shell-Model Calc.
(within 0-hw)
GT (στ±)
0.9
0.6
IV spin-M1 (στz) --
0.6—1.0 (*)
IS spin-M1 (σ)
0.5—0.7 (*)
Present work
(within 0-hw) --
0.61(6)
1.01(9)
Nonquench!
(*) Taken from G.M. Crawley PRC(1989): (p,p’) on sd-shell nuclei

7. Experiment and analysis

8. (p,p’) experiment at the RCNP
A. Tamii, NIMA605, 326 (2009)
Meas. Angle =0—14 deg
Proton beam : 295 MeV
ΔE (FWHM)：　40 keV
→　20keV
MWDCs
Plastic Scinti.
Dispersion matching

9. Targets 12C, 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca
Systematic study of all the T=0 (stable, N=Z even-even) nuclei
12C, 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca
Five targets will be reported in this talk.
12C, 24Mg, 28Si : Self-supporting metal foil
32S : Cooled self-supporting elemental foil
36Ar : Gas cell target
H. Matsubara, NIMA 267 (2009).
H. Matsubara, NIMA 678 (2012).
Liquid nitrogen temperature
Aramid window (6um-thickness)

10. High energy-resolution spectrumSn Sp

11. Energy spectra at 0-degrees
24Mg
36Ar
28Si

12. Jπ assignment from shape of ang. dist.
・Distorted wave Born approximation by DWBA07
NN interaction. : Franey and Love, PRC31(1985)488. (325 MeV data)
Trans. density : USD, USDA, USDB　(from shell model calculation) 1+ 1+ 1+ 1+
Forward peaking for L=0 transition.
M1 has the maximum at 0 degree.
0+, IS-1+, IV-1+ and others
Distributions at 0-5 degree are similar.
Difference between IS and IV
is due to exchange tensor term.

13. IS, IV spin-M1 angular dist. (28Si)0+ 1- 2+

14. Unit cross section (UCS)
・ Conversion factor from cross-section to squared nuclear matrix element (SNME)
・ Calibration from β andγ-decay measurements (assuming the isospin symmetry)
(T= IS or IV)
UCS
Kinematical factor
SNME (To be obtained)
・ Mass dependence established in GT study
T.N. Taddeucci, NPA469 (1987).

15. IS/IV spin-M1 strength dist.
Squared Nuclear Matrix Element

16. Summation of spin-M1 SNME
・ Summation up to 16 MeV (up to 0-hw).
・ Compared with shell-model calculations using USD-int.
Squared Nuclear Matrix Elem.
(Bare g)
(Eff. g)
Averaged quenching factors:
IS spin-M1 trans. is not quenched.
IS spin-M1
IV spin-M1
1.01(9)
0.61(6)

17. Consistency with the IS Magnetic Moment and the effective g-factor
Effective g-factors were determined to reproduce <S>.
The factors come from
the g-factors in free space.
Spin-matrix
Data taken from B.A. Brown, NPA (1987).
Magnetic moment
Spin-matrix <S>
Quenching is dominant at the shell-edge.

18. Consistency with the IS Magnetic Moment and the effective g-factor
Effective g-factors were determined to reproduce <S>.
The factors come from
the g-factors in free space.
Spin-matrix
Data taken from B.A. Brown, NPA (1987).
Magnetic moment
Spin-matrix <S>
Quenching is dominant at the shell-edge.
Quenching is suppressed at the mid-shell.

19. What does the nonquench suggest?
Spin alignment in the ground state
Suggesting 2p2h excitation due to
tensor force

20. Spin alignment in the ground state
: total spin operator in a nucleus
: spin alighment in the g.s.
Nonquench suggests

21. How to deduce <Sp・Sn>?
IS : in-phase transition for p and n
IV : out-phase transition for p and n
Sum of IS :
(Closure approx.)
Sum of IV :
Subtraction of IS-sum minus IV-sum

22. <Sp・Sn> values
USD with eff. g-factors
by Arima, Towner, Brown

23. <Sp・Sn> values
Experimental results suggest spin alignment.

24. <Sp・Sn> values Shell-model : USD interaction
Correlated Gaussian Meth.: W. Horiuchi
AV8’: 0.135
(stronger tensor)
G3RS: 0.109
(weaker tensor)
Minnesota:
-0.020
(no tensor)

25. <Sp・Sn> values Shell-model : USD interaction
Correlated Gaussian Meth.: W. Horiuchi
No-Core Shell-model: P. Navratil

26. Spin alignment is supported by state-of-the-art calc. with tensor force.

27. Open questions Experimental results are up to 16 MeV.
No experimental data at high Ex.
What makes dependence of quench/nonquench at sd-shell ?
Large quench for shell-edge nuclei
Nonquench for mid-shell nuclei

28. Summary Non-quenching was observed in the IS spin-M1 transitions.
Introducing <Sp・Sn>, the present result suggests that the quenching in spin transitions are due to 2p2h excitations preliminary resulting from tensor interaction.
State-of-the-art calculations support the new interpretation of the spin alignment in the g.s.
Thanks for the attention.

30. <Sp・Sn>

31. Proportionality of UCS (28Si)
Detection limit
Detection limit
Theoretical study (DWBA calc.) suggests 10% uncertainty for IS.

32. Isospin breaking in 24Mg

33. Model space dependence
USD = sd-shell
SDPFM = sdpf-shell
唯一計算できた20Neの例
Free gs-factor
モデル空間の拡張でも RIS/IV　の絶対値は改善しない

36. Unit cross section (UCS)
For isoscalar part …
Mirror states of γ-decay widths of 11B/11C
were employed to deduce B(M1)IS.
Y.Fujita, PRC 62 (2000)
Decomposition of IS spin and orbital pats
T.Kawabata, PRC 70, (2004)

37. Total-spin-product in g.s.
SM calc.
Realistic-int. calc.
12C(e,e’): P.von Neumann-C., NPA(2000)

38. Another approach to GT quenching
M1 transition is analogous to GT transition.
(p,p’) → spin-M1
(p,n) or (n,p) → GT
analogous
1) Δ-N-1 configuration only IV
2) 2p-2h configuration both IS and IV
2p-2h
Δ-h
M1-IS (στ)
possible
impossible
M1-IV(στz)
GT (στ±) SM
QIS　 > QIV　= QGT
QIS　 = QIV　= QGT
Difference of quenching degree between M1-IS and IV provides us
essential information of GT quenching.

39. What is spin-quenching?
Exp.
Calc.
Origin
GT-quenching GT
Sum-rule
2p-2h >> Δ-h
Truncation of high-order config. mix.
( e.g. 2p-2h, core-pol.)
SM-quenching
GT, IS/IV-M1
S.M.
BW: B.A. Brown, NPA (1987).
TK: I.S. Towner, NPA (1983).
Ar: A. Arima, ANP (1987).
Spin-quenching at A=17 and 39
Well studied
M. Ichimura, PPNP (2006).
Understood ?

40. How are the exp. data of spin-M1?
(p,p’) experiment on 28Si
1, Sensitive to spin excitation
2, T=0 target
→ Separable IS from IV
Spin-quenching at A=28 (28Si)
2p-2h
・Large uncertainty
・No systematic study
-Only 28Si and 32S
・Incomprehensive trend
Why is IS-M1 so quenched?
Δ-h : Typical naive example
TK, Ar : Assumed mass-dependence
Exp. : G.M. Crawley et at. PRC (1989)