1. Neutron skin thickness determined from charge exchange reactions on 90 Zr Kentaro Yako (University of Tokyo) INPC, Jun. 6, 2007 0

2. Experiment: K. Y., H. Sakai, and RCNP-E149 collaborators Theory: H. Sagawa, S. Yoshida [E149 members] K. Yako, H. Sakai, M.B. Greenfield, K. Hatanaka, M. Hatano, J. Kamiya, H. Kato, Y. Kitamura, Y. Maeda, C.L. Morris, H. Okamura, J. Rapaport, T. Saito, Y. Sakemi, K. Sekiguchi, Y. Shimizu, K. Suda, A. Tamii, N. Uchigashima, T. Wakasa Collaborators: 1

3. Neutron skin thickness Neutron skin thickness: related to physics on nuclear matter. Sagawa et al. has linear correlations with symmetry energy EOS of neutron matter : well known … : poorly known … proton and neutron distributions : fundamental properties of nuclei 2 ± 0.04 fm accuracy of better than ± 0.04 fm is needed.

4. Charge exchange spin dipole operator: Model independent sum rule: e scattering(p,n)(n,p) J π = 0 -, 1 -, 2 - 90 Zr(p,n) [Wakasa et al.] and 90 Zr(n,p) data taken at RCNP extract total SD strengths from proton elastic scattering isovector GDR excitation by scattering antiprotonic x-ray parity-violation electron scattering isovector spin-dipole sum rule Method of obtaining electron elastic scattering model dependent 3

5. (p,n) and (n,p) reactions at 300 MeV (p,n) & (n,p): Reaction mechanism is simple. 300 MeV: Distortion effects are smallest. ⇒ analysis with DWIA is reliable. Spin-flip excitations are favored ⇒ effect of nonspin dipole component is small. Advantages: 4 Double differential cross sections Small dipole peaks at 3 MeV, 6 MeV, 10 MeV multipole decomposition analysis... total strengths

6. Multipole decomposition analysis 0 -, 1 -, 2 - : inseparable 90 Zr(n,p) angular dist. ω = 20 MeV NN interaction: t-matrix by Franey & Love @325 MeV optical model parameters: Global optical potential (Cooper et al.) one-body transition density: pure 1p-1h configurations n-particle 1g 7/2, 2d 5/2, 2d 3/2, 1h 11/2, 3s 1/2 p-hole 2p 1/2, 2p 3/2, 1f 5/2, 1f 7/2 radial wave functions … W.S. / H.O. MDA DWIA DWIA inputs 5

7. Decomposed spectra (p,n) at 4.6 deg SDR at 20 MeV (n,p) at 4-5 deg c.s. below 10 MeV … due to L=1 PLB615(2005)193 6

8. Proportionality relation & unit cross section The averaged value works if you discuss the sum rule value rather than state-by-state strengths. Uncertainty of calculated … 14%. optical potential, radial wave function Differences are due to: tensor interaction ph combinations of… - different radial quantum numbers - “ j < j < ” data“unit cross section” (p,n) … at 4.6 deg DWIA 7

9. SD strength distributions T=4,5,6 T=6 MD analysis single SDR bump [(p,n)] asymmetric shape … strength extends to ～ 50 MeV unstable analysis above 40 MeV [(n,p)] 8 shifted by +17 MeV

10. SD strength distributions T=4,5,6 HF+RPA two or more bumps good agreement below 25 MeV with quf = 0.68 2p-2h is necessary above 25 MeV T=6 MD analysis single SDR bump [(p,n)] asymmetric shape … strength extends to ～ 50 MeV unstable analysis above 40 MeV [(n,p)] 9 (SRPA) shifted by +17 MeV

11. Sum rule value Integrated strength Exp values approach HF+RPA values at 50 MeV excitation. Sum rule value almost constant S-S- S+S+ S - -S + 247 4(stat.) 12(MD) 98 4(stat.) 5(MD) 148 6(stat.) 7(MD) 7(syst.) Strengths (fm 2 ) below 40 MeV stable at 30 < E x < 50 MeV 10

12. Neutron skin thickness methodnucleus(fm) Ref. p elastic scatt. antiprotonic x-ray 90 Zr 0.09 0.07 0.09 0.02 Ray, PRC18(1978)1756 IVGDR by α scatt. 116,124 Sn … 0.12 Krasznahorkay, PRL66(1991)1287 SDR by ( 3 He,t) 114--124 Sn … 0.07 SDR by (p,n) & (n,p) 90 Zr0.07 0.04 this work, PRC74(2006)51303R Trzcinska, PRL87(2001)082501 11 Krasznahorkay, PRL82(1999)3216 goal of parity violation electron scattering: 0.04 (1%)

13. Summary We studied SD excitations from 90 Zr by the (p,n) and (n,p) reactions by MD analysis. This is the first attempt to obtain the SD strength distributions of both channels. The strength distributions below 25 MeV excitation are well reproduced by HF+RPA calculations with quf=0.68. Integrated SD strengths (in fm 2 ) below 40 MeV: S - = 247 4(stat.) 12(MD) S + = 98 4(stat.) 5(MD) S - - S + = 148 6(stat.) 7(MD) 7(syst.) Neutron skin thickness: 0.07 0.04 fm 12

14. Constraint on EOS ? Constraint on EOS is not strong. 90 Zr 17

15. Things to do (in future) Calibration SD unit cross section (14%) …comparison with decay measurements validity check of DWIA calculations for SD 39 Y 89 38 Sr 89 5/2 + 1/2 - (n,p) β decay 99.99% 50.53d Q β =1495.1 MeV (Plan by M. Sasano)

16. (p,n) & (n,p) work (p,n) & (n,p) at 300 MeV advantages: 300 MeV: Distortion effects are smallest ( ). ⇒ analysis with DWIA is reliable. Tensor interaction is smallest ( ). ⇒ Proportionality relation is reliable. Simple reaction mechanism tensor FraneyLove disadvantage: low energy resolution (ΔE = 500 keV ～ 1 MeV) … Multipole decomposition analysis works best.

17. Realistic transition densities Radial transition densities obtained by HF+TDA Angular distribution 2-2-

18. (n,p) 実験施設 (n,p) experiment at RCNP （ n,p ） facility 5 7 Li(p,n) 2x10 6 neutrons/s

19. Proton elastic scattering elastic scattering Complete measurement differential cross section analyzing power spin rotation parameter Analysis: folding model NN interaction Pauli blocking (density dependence) Relativistic or Non-rel “medium modification” … ⇒ model dependent σ AyAy R vs energy data at 500 MeV …time reversal invariance denoted error: ±0.07 fm

20. dσ/dΩ (μb/sr) Isovector GDR Excitation by α Scattering α ： isoscaler probe ⇒ is responsible for excitation of isovector GDR. transition potential: δ np /R 0 (%) E α =120 MeV, 0 deg α+ 124 Sn Krasznahorkay, KVI δ np /R 0 = 4±2 % ⇒ uncertainty of δ np …±0.12 fm de-excitation γ was detected.

21. Parity violating electron scattering Z boson couples primarily to the neutron at low Q 2. parity-violating asymmetry in polarized elastic scattering → weak-charge density → neutron density

22. Decomposed angular distributions 90 Zr(n,p) Reasonable fits are obtained. σ(θ=4-5deg) is the most sensitive to dipole component.

23. Proportionality relation JπJπ # of ph config. (mb/sr/fm 2 ) 0-0- 40.28±0.03 1-1- 120.24±0.06 2-2- 140.29±0.05 total300.27±0.06 The averaged value works if you discuss the sum rule value rather than state-by-state strengths. Uncertainty of calculated … ±14%. optical potential, radial wave function Differences are due to: tensor interaction ph combinations of… - different radial quantum numbers - “ j < j < ” ph- and J π - dependence data“unit cross section” (p,n) … at 4.6 deg DWIA 10

24. Proportionality relation unit cross section … dependence on ph config.: ～ 30% ph config. (fm 2 )(mb/sr)(mb/sr/fm 2 ) 12.843.8850.303 4.991.3990.280 2.140.4280.200 1.430.3580.251 total21.406.0700.284 Estimation of 0 - unit cross section at 0 MeV Difference of radial quantum number affects proportionality. data“unit cross section” (p,n) … at 4.6 deg DWIA 9

25. ω dependence of unit cross section SD cross sections at high excitation region is suppressed in the exp spectra. (p,n)-(n,p) difference… Coulomb term of the optical potential. 11

26. 2p2h contributions Drozdz et al. … second RPA [PLB 189(1987)271] one-body potential.: Woods-Saxon type residual interaction: G-matrix (Nakayama) ～ 35% … above 28 MeV Rijsdijk et al. … dressed particle RPA [PRC48(1993)1752] one-body potential.: HO residual interaction: G-matrix (Dickhoff) 14