Unexpected nonquenching of the isoscalar spin-M1 transitions Hiroaki MATSUBARA Tokyo Women’s Medical University matubara@twmu.ac.jp 2015 Nov-16-19 HST15@Osaka

Collaborators

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

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

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

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

Experiment and analysis

(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

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)

High energy-resolution spectrum Sn Sp

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

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.

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

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).

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

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)

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.

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.

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

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

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

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

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

<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)

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

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

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

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.

<Sp・Sn>

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

Isospin breaking in 24Mg

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

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) 044314 Decomposition of IS spin and orbital pats T.Kawabata, PRC 70, (2004)

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

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.

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 ?

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)