np Spin-Correlation in the Ground State Studied by Spin-M1 Transitions

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np Spin-Correlation in the Ground State Studied by Spin-M1 Transitions Atsushi Tamii Research Center for Nuclear Physics (RCNP) Osaka University, Japan for RCNP-E299 Collaborations 2nd International Workshop and 12 th RIBF Discussion on Neutron-Proton Correlations July 6-9, 2015, University of Hong Kong 1

np Spin-Correlation in the Ground State Studied by Spin-M1 Transitions H. Matsubara 1, A. Tamii 2 and RCNP-E299 collaboration 1 National Institute of Radiological Sciences 2 RCNP, Osaka University Submitted to PRL* *Accepted for publication in PRL after the conference 1

RCNP, Osaka U. Univ. of Witwatersrand Collaborators A. Tamii, T. Adachi, K. Fujita, K. Hatanaka, D. Ishikawa, M. Kato, H. Okamura, Y. Tameshige, K. Suda, M. Yosoi J. Carter, H. Fujita IKP, Tech. U. of Darmstadt P. Von Neumann-Cosel, B. Ozel, I. Poltoratska, A. Richter, A. Shevchenko Kyusyu U. Dept. of Phys. M. Dozono, S. Kuroita, Y. Yamada Osaka U. Dept. of Phys. Y. Fujita CNS, Univ. of Tokyo Chiba U. Dept. of Phys. T. Kawabata, K. Nakanishi, S. Sakaguchi, H. Nakada Y. Sasamoto, Y. Shimizu Miyazaki U. Dept. of App. Phys. IFIC-CSIC, Valencia CYRIC, Tohoku U. N. Fujita, A. Nonaka, B. Rubio M. Itoh, Y. Sakemi H. Sakaguchi ithemba LABs Niigata U. Kyoto U. Dept. of Phys. F.D. Smit, R. Neveling Y. Shimbara J. Zenihiro Hokkaido Univ. TRIUMF W. Horiuchi, P. Navratil

Outline 1. np Pairing Correlations 2. np Spin-Correlation Function and Spin-M1 Sum-rule 3. Experimental Methods 4. Results 5. Discussions 6. Summary

np Pairing Correlations spin-aligned np-pairs np pairing, mass analysis B. Cederwall et al., Nature 469, 68 (2011) Frauendorf and Macciavelli, PPNP78, 24 (2014) high-momentum correlated nucleon pairs R. Subedi et al., Science 320, 1476 (2008); I. Korover et al., PRL 113, 022501 (2014) pn contact pairing vibrations low-e super GT state R. Weiss et al., PRL114, 012501 (2015); S. Tan Ann. Phys. 323, 2952(2008) F. Cappuzzello et al., Nature Comm. 6, 6743 (2015). Y. Fujita et al., PRL (2014). transfer reactions/knock out reactions We d like to add one more alternative approach.

IS and IV pairings n p IS (T=0, S=1) Isoscalar np-paring IV (T=1, S=0)

pairing in the ground state W.F. independent particles unperturbed ground state

pairing in the ground state W.F. independent particles + paring interactions

pairing in the ground state W.F. independent particles + paring interactions

pairing in the ground state W.F. P 1,i P 1, j P 1,i P 1, j P 1,i = ν i ν i P 1,i = π i π i isovector pairing correlation = BCS type correlation

pairing in the ground state W.F. P 1,i P 1, j P 1,i P 1, j occupation probability P 1,i = ν i ν i P 1,i = π i π i isovector pairing correlation = BCS type correlation

np pairing in the ground state W.F. D 0,i D 0, j D 0,i = 1 ( 2 ν π i i π i ν ) i isoscalar pairing correlation by e.g. tensor correlation

np pairing in the ground state W.F. D 0,i D 0, j n-spin and p-spin: aligned isoscalar pairing correlation by e.g. tensor correlation s n s p > 0

np pairing in the ground state W.F. D 0,i D 0, j n-spin and p-spin: aligned s n s p > 0 sn s p = S 2 = s n + s p ( ) 2 = s n 2 + s p 2 + 2 s n s p isoscalar pairing correlation by e.g. tensor correlation + 1 4 3 4 for IS np pair (deuteron) for IV np pair

np pairing in the ground state W.F. D 0,i D 0, j n-spin and p-spin: aligned s n s p > 0 sn s p = isoscalar pairing correlation by e.g. tensor correlation + 1 4 3 4 for IS np pair (deuteron) statistical weight = 3 for IV np pair statistical weight = 1

np pairing in the ground state W.F. D 0,i D 0, j s n s p > 0 n-spin and p-spin: aligned isoscalar pairing correlation by e.g. tensor correlation induces correlation between the directions of the n-spin and p-spin

np spin correlation function S n N i S n S p s n,i S p Z i s p,i : np spin correlation function of the nuclear ground state

S n N i S n S p s n,i S p Z i s p,i : np spin correlation function of the nuclear ground state unperturbed ground state S n S p = 0 also for IV pp/nn parings IS np pairing S n S p > 0 IV np pairing S n S p < 0

How to Study the np Spin Correlation Function? IS/IV spin-m1 excitations and Sum-Rule S n + S p = S n S p = ( S n S p ) 2 = 1 ( 4 σ" τ z ) 2 = = = 1 4 1 4 1 4 ( S n + S p ) 2 = 1 4 A 1 " σ i 2 i A 1 " σ iτ z 2 i f f 0 στ f z σ τ z f f στ 0 0 ( ) M σ τ z M ( " σ ) 2 2 2 z S n S p = 1 4 S 2 n + S closure 2 p = 1 16 ( S n + S ) 2 p ( S n S ) 2 p ( M ( " σ ) 2 M ( " σ τ ) 2 ) z ( S n + S ) 2 p + ( S n S ) 2 p = 1 4 = 1 ( M ( " σ ) 2 + M ( " σ τ ) 2 ) z 16 IV spin-m1 squared nuclear matrix elements (SNME) IS spin-m1 SNME

M1 Operator ( ) ( ) N A Z k k n s k n l Z k k p s k p l s g l g s g l g M O µ " # $ % & + + + = + = = 1 1 1) ( ˆ " " Spin- M1 Reduced Transition Strength ( ) 2 2 2 1 2 1 4 3 1 i g l g g l g f J M B z IV s IV l IS s IS l i τ σ σ π $ $ % & ' ' ( ) + + + = ( ) 2 2 2 2 1 2 1 4 3 1 N IS s i i f g J M B µ σ π σ # # $ % & & ' ( + = ( ) 2 2 2 2 1 2 1 4 3 1 N z IV s i i f g J M B µ στ π στ $ $ % & ' ' ( ) + = T=0 Isoscalar (IS) Spin- M1 Reduced Transition Strength T=1 Isovector (IV) Spin- M1 Reduced Transition Strength M1 Reduced Transition Strength ( ) i f M σ σ = ( ) i f M z στ στ = IS Reduced Matrix Element IV Reduced Matrix Element

Experimental Methods

CREX WS, March 17-19, 2013 RCNP, Osaka Univ. KYOTO RIKEN J-PARC TOKYO OSAKA July 28 2008 seminar @ LNL

Research Center for Nuclear Physics, Osaka Univ. High-resolution Spectrometer Grand Raiden High-resolution WS beam-line

Spectrometer Setup for 0- deg (p,p ) at RCNP As a beam spot monitor in the vertical direction Transport : Dispersive mode Intensity : 3 ~ 8 na

Self-Conjugate (N=Z) even-even Nuclei ground state: 0 + ;T=0 We focus on these nuclei. Stable self-conjugate even-even nuclei: ( 4 He), 12 C, 16 O, 20 Ne, 24 Mg, 28 Si, 32 S, 36 Ar, 40 Ca

Targets 12 C, 24 Mg, 28 Si: self-supporting target Cooled 32 S self-supporting target Gas Cell Target ( 36 Ar) H. Matsubara et al., NIMB 267, 3682 (2009) H. Matsubara et al., NIMA 678, 122 (2012) Aramide window of 6 "m t

Energy spectra at 0-degrees 12 C 28 Si 24 Mg 32 S 36 Ar

Angular distribution for J π assignment Distorted wave Born approximation by DWBA07 Trans. density : USD, USDA, USDB (from shell model calculation) NN interaction. : Franey and Love, PRC31(1985)488. (325 MeV data) 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. ( 28 Si) IV IS 0 + 1-2 +

Unit cross section (UCS) Conversion factor from cross-section to Squared Nuclear Matrix Elements (SNME) Calibration from β andγ-decay measurements (on the assumption of the isospin symmetry). dσ dω σˆ T ( 0 ) = ˆ F( q, E ) M ( O) 2 UCS ( A) = N σ T Kinematical factor exp x ( xa 1/3 ) T.N. Taddeucci, NPA469 (1987). Function taken from the mass dependence of GT UCS f (T= IS or IV) SNME

IS/IV-spin-M1 distribution

Spin-M1 SNME Summed up to 16 MeV. Compared with shell-model predictions using the USD interaction bare-g effective-g Squared Nuclear Matrix elements Non-quenching Isoscalar spin-m1 SNME is not quenching.

np Spin Correlation Function Shell-Model: USD interaction S n i S p eff:g eff /g is multiplied to the SNME Positive np spin correlation functions were observed systematically, showing the IS np pairing.

Correlated Gaussian Calculation of the 4 He System with Realistic NN Interactions Spin matrix elements of the 4 He ground state S n 2 + S p 2 S n S p by W. Horiuchi S=0 S=1 S=2 AV8 Stronger tensor int. G3RS Weaker tensor int. Minnesota No tensor int. 0.572 0.135 85.8% 0.4% 13.9% 0.465 0.109 88.5% 0.3% 11.3% 0.039-0.020 100% 0% 0% Y. Suzuki, W. Horiuchi et al., FBS42, 33(2007) H. Feldmeier, W. Horiuchi et al., PRC84, 054003(2011) S = S + S p n

np Spin Correlation Function AV8 : 0.135 (stronger tensor) Shell-Model: USD interaction Correlated Gaussian Method: W. Horiuchi G3RS: 0.109 (weaker tensor) S n i S p Minnesota: -0.020 (no-tensor)

np Spin Correlation Function Shell-Model: USD interaction Correlated Gaussian Method: W. Horiuchi Non-Core Shell Model: P. Navratil S n i S p

np Spin Correlation Function NCSM P. Navratil Correlated Gaussian Method: W. Horiuchi Non-Core Shell Model: P. Navratil Shell-Model: USD interaction S n i S p

np Spin Correlation Function Shell-Model: USD interaction Correlated Gaussian Method: W. Horiuchi Non-Core Shell Model: P. Navratil S n i S p Further theoretical studies on the sd-shell nuclei by ab-initio type calculations with realistic interactions are very interesting.

Discussion/Criticism

Model Space Dependence No significant difference between sd and sdpf in the shell-model predictions for 20 Ne The case of 20 Ne USD = sd-shell SDPFM = sdpf-shell Free g s -factor

Contribution from Strengths at Higher E x. No significant difference in the shell-model predictions. Shell Model in sd-shell, USD E x <16.1MeV E x =all A M(σ) M(στ) Diff M(σ) M(στ) Diff ------------ ---------------------------------+-------------- 24 0.23 0.23 0.00 0.27 0.28-0.01 28 0.37 0.42-0.05 0.41 0.46-0.05 32 0.40 0.45-0.05 0.42 0.48-0.06 36 0.22 0.24-0.02 0.23 0.25-0.02 ~85% in Ex<16 MeV >90% in Ex<16 MeV Measurement was done only below E x =16 MeV. Still a part of strength may be fragmented to upper excitation energies like B(GT).

Relation to Fujii-Fujita-Ikeda Sum-Rule for GT transitions and its quenching No clear relation Fujii-Fujita-Ikeda Sum-Rule S ( GT ) S + GT = 3( N Z) is the difference between S - and S + and the main contribution is T 0-1 In the present work, IV spin-m1 corresponds to T 0 +1. 42

Unit Cross Section and Proportionality (theoretical study) 28 Si(p,p ) IS 28 Si(p,p ) IV Detection Limit Detection Limit H. Matsubara, thesis ~ 28 Si(p,n) 26 Mg( 3 He,t) R.G.T. Zegers et al., PRC74, 24309(2004).

Relation to the IS Magnetic Moment and the effective g-factor consistent with the present result Empirical values were obtained to reproduce <S>. µ IS = 0.38 s + 0. 5J Spin-matrix The factors come from the g-factors in free space. Adapted from B.A. Brown, NPA (1987) Quenching is large at the shell-edge. Quenching is suppressed in the mid-shell.

Future Experimental Possibilites Mass dependence of the np spin correlation function along the N=Z line Target nuclei are unstable above A=40. - (p,p ) and (d,d ) in inverse kinematics Isospin dependence of the np spin correlation function for N Z nuclei IS and IV transitions need to be selectively excited. For stable nuclei: - ( 6 Li, 6 Li γ) for IV spin-m1 excitations - (d,d) or ( 6 Li, 6 Li ) for IS spin-m1 excitations Strength in the continuum and in unstable nuclei - ( 12 C, 12 C(1 +,T=1;15.11 MeV)) in inverse kinematics for IS spin-m1 12 C+γ - ( 12 C, 12 C(1 +,T=0;12.71 MeV)) in inverse kinematics for IV spin-m1 α+ 8 Be α+α+α 45

Future Experimental Possibilites In general, the difference of IS and IV SNMEs in any spin-isospin mode can be a probe of np correlation for the relevant operator. e.g IS SDR and IV SDR for L=1 component of the IS np-pairing 46

IS/IV spin-m1 response ν-opacity and ν-transportation in SNe and PNS SNe dynamics, nucleosynthesis, cooling of a proton neutron star - GT, IS/IV-spinM1 response of nuclear matter - IS-spinM1 response of pure neutron matter Spin (magnetic) susceptibility and response to a strong magnetic field Inversely energy weighted sum-rule χ σ 2n = 4 3N 1 ω f σ 0 i f i 2 of spin-m1 transition strengths. G. Shen et al., PRC87, 025802 (2013) Magnetic response of nuclear matter in a magnetar

Summary IS/IV-spin-M1 SNMEs have been studied by a high-resolution (p,p ) measurement at E p =295 MeV No-quenching is observed in the IS-spin-M1 SNME while quenching is observed in the IV-spin-M1 SNME as is expected from the analogous GT transitions. The np spin correlation function extracted from the experimental data show systematically positive numbers, implying the IS np correlation in the ground states. A shell model calculation using the USD interaction does not reproduce the positives. However, predictions of the correlated Gaussian method on 4 He, and the non-core shell model look more consistent with the data.

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