Nuclear radii and density distributions Y. Matsuda Kyoto - PowerPoint PPT Presentation

Nuclear radii and density distributions Y. Matsuda Kyoto University GCOE Symposium Feb. 12 2012 Kyoto University Clock Tower Centennial Hall International Conference Hall 2013 年 2 月 12 日火曜日 1

Contents Introduction Proton elastic scattering from stable nuclei Elastic Scattering of Protons with RI beams Summary Present work 2013 年 2 月 12 日火曜日 2

Introduction 2013 年 2 月 12 日火曜日 3

Nuclear radii and density distributions - Fundamental properties of nuclei - Inputs and/or guidelines to describe the nuclear reactions and structures Stable nuclei Charge radius Muonic atom By unfolding the charge Proton distribution Electron scattering distribution By using the well inferred Neutron distribution Proton elastic scattering proton distribution 2013 年 2 月 12 日火曜日 4

History of Universe Big Bang Elementary particles 10 20 Hadron Temperature [K] Light nuclei 10 10 Stars Nucleosynthesis 1 Today Nuclear Physics 10 -10 10 -20 1 10 20 10 40 Time after Big Bang [seconds] Background: http://www.nscl.msu.edu/~austin/nuclear-astrophysics.pdf 2013 年 2 月 12 日火曜日 5

Nuclear chart stable nuclei ~300 nuclei unstable nuclei observed so far ~2700 nuclei drip-lines (limit of existence) （ theoretical predictions) ~6000 nuclei magic numbers Projectile Fragmentation In-flight U fission & P.F. protons neutrons http://www.nishina.riken.go.jp 2013 年 2 月 12 日火曜日 6

Introduction Proton elastic scattering from Stable nuclei 2013 年 2 月 12 日火曜日 7

Proton elastic scattering E p =200 - 400 MeV The longest mean free path in nuclei ( 2 fm -1 ) 10 3 Cross section [mb] pp pn np 10 2 10 1 10 100 1000 E lab. [MeV] 2013 年 2 月 12 日火曜日 8

Relativistic Impulse Approximation D. P. Murdock and C. J. Horowitz, Phys. Rev. C 35, 1442(1987). Relativistic Love-Franey model: (0) � (1) µ � F PV q � 5 q � 5 / / F S + F V � µ + F T � µ � (0) � (1) µ � + F A � 5 (0) (1) (0) � µ (0) � 5 F = (1) � (1) µ 2M 2M N 1 N 0 L = S, V, PV, T, A k c � k c q = k c � k c � 2 � 2 � 2 + q 2 � L � I � 2 + q 2 � L � I i M 2 g g 0 1 F L (q, E c ) F L D (q) + F L = X (Q) 1 2E c k c q 2 + m 2 L,L (j ) { � 0 · � 1 } I j f j (q) F L D (q) = � k c � k c j N 0 N 1 B L (j ),L { � 0 · � 1 } I j f j (Q) F L ( � 1) T X (Q) = Direct j 2 N 0 N 1 2 2 g 2 � 2 g 2 � f j (q) j j j j = � i 2 + q 2 q 2 + m 2 q 2 + m j 2 k c � k c � 2 j + q 2 � j � 2 Q = k c + k c � 2 � 2 + Q 2 � L � I � 2 + Q 2 � L � I g g 0 1 1 Q 2 + m 2 F L (pp) F L (T = 1) = k c � k c 1 F L (pn) 2 F L (T = 0) + F L (T = 1) = N 0 N 1 Exchange 2013 年 2 月 12 日火曜日 9

Relativistic Impulse Approximation Phenomenological medium modification H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998). g 2 j g 2 , → j ρ ( r ) 1 + a j ρ 0 � ρ ( r ) � 1 + b j m j m j , → ρ 0 N 0 N 1 m g g N 0 J.Zenihiro et al., N 1 Phys. Rev. C 82, 044611 (2010) 2013 年 2 月 12 日火曜日 10

Sn) Ay (124 Ay (122 Ay (118 Sn) Ay (116 (degree) Sn) Sn) Sn) (degree) Ay (120 Proton elastic scattering form stable nuclei Experimental data at RCNP, Osaka University Trial density + medium effect Search density + medium effect 116 Sn(x10 4 ) 118 Sn(x10 2 ) � (mb/sr) 120 Sn(x1) d � /d 122 Sn(x10 -2 ) 124 Sn(x10 -4 ) � c.m. � c.m. S.Terashima et al., J.Zenihiro et al., Phys. Rev. C 77, 024317 (2008) Phys. Rev. C 82, 044611 (2010) 2013 年 2 月 12 日火曜日 11

Proton elastic scattering form stable nuclei Experimental data at RCNP, Osaka University S.Terashima et al., J.Zenihiro et al., Phys. Rev. C 77, 024317 (2008) Phys. Rev. C 82, 044611 (2010) 2013 年 2 月 12 日火曜日 12

Introduction Proton elastic scattering from Stable nuclei Elastic Scattering of Protons with RI beams 2013 年 2 月 12 日火曜日 13

Recoil Proton Spectrometer (RPS) NaI(Tl) E 1 pΔE up RPS RDCup p SHT p E 7 E 8 RDCdown Beam pΔE down X Y E 14 1 m Solid H 2 (SHT) RDC p Δ E E material Para H 2 Ar+C 2 H 6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm 2 440 x 440 mm 2 431.8 x 45.72 mm 2 thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Resolution 500 μ m TOF : 0.1 nsec 0.3 %(80 MeV) 2013 年 2 月 12 日火曜日 14

Recoil Proton Spectrometer (RPS) NaI(Tl) E 1 pΔE up RPS RDCup p SHT p E 7 E 8 RDCdown Beam pΔE down X Y E 14 Solid para hydrogen target φ 30 mm, 1 mm t 1 m Solid H 2 (SHT) RDC p Δ E E material Para H 2 Ar+C 2 H 6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm 2 440 x 440 mm 2 431.8 x 45.72 mm 2 thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Resolution 500 μ m TOF : 0.1 nsec 0.3 %(80 MeV) 2013 年 2 月 12 日火曜日 14

Recoil Proton Spectrometer (RPS) NaI(Tl) E 1 pΔE up RPS RDCup p SHT p E 7 E 8 RDCdown Beam pΔE down X Y E 14 Solid para hydrogen target φ 30 mm, 1 mm t 1 m Large, thin solid hydrogen target using para-H 2 , Solid H 2 (SHT) RDC p Δ E E Y. Matsuda et al., Nucl. Instr. and Meth. A 643 6-10 (2011). material Para H 2 Ar+C 2 H 6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm 2 440 x 440 mm 2 431.8 x 45.72 mm 2 Scintillating fiber detector for momentum tagging light nuclei at intermediate energies, thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Y. Matsuda et al., Nucl. Instr. and Meth. A 670 25-31 (2012). Resolution 500 μ m TOF : 0.1 nsec 0.3 %(80 MeV) 2013 年 2 月 12 日火曜日 14

Elastic Scattering of Protons with RI beams Z Equation of state of 66 Ni 70 Ni asymmetric nuclear matter (@GSI) A drastic growth of the density distribution with an increase of the neutron number 20 O (@NIRS-HIMAC) 9 C 10 C 11 C N 2013 年 2 月 12 日火曜日 15

Antisymmetrized Molecular Dynamics (AMD) density 9 C 14 C 10 C 15 C 11 C 16 C 12 C 17 C 13 C 18 C 19 C 20 C 22 C Yoshiko Kanada-En’yo and Hisashi Horiuchi, Progress of Theoretical Physics Supplement, 142 (2001) 205 2013 年 2 月 12 日火曜日 16

Matter radius of 9 C p ( 9 C, p ) 280-300 MeV/u 10 3 Application of our previous work 9 C H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998). 12 C 10 2 d � /d � (mb/sr) S.Terashima et al., Phys. Rev. C 77, 024317 (2008) J.Zenihiro et al.,Phys. Rev. C 82, 044611 (2010) 10 1 10 0 10 -1 We need to (1) tune the scattering amplitude 10 20 30 40 with scattering for a nearby N = Z nucleus � c.m. (deg) (2) deduce both proton and neutron density distributions 2013 年 2 月 12 日火曜日 17

(1) tune the scattering amplitude with scattering for a nearby N = Z nucleus: 12 C 10 3 Phenomenological medium modification (a) Modified MH H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998). Original MH 10 2 d � /d � (mb/sr) 10 1 g 2 j g 2 , → j ρ ( r ) 1 + a j 10 0 ρ 0 � ρ ( r ) � 10-1 1 + b j m j m j , → ρ 0 1.0 (b) 0.5 N 0 N 1 A y 0.0 m g g -0.5 12 C( p , p ) E p =300 MeV -1.0 N 0 N 1 10 20 30 40 � c.m. (deg) 2013 年 2 月 12 日火曜日 18

(2) deduce both proton and neutron density distributions Two parameter Fermi distribution N i � i (r) = 1 + exp {(r � R i )/a i } , i = p, n, 10 3 Deduced rms matter radius, 9 C best-fit χ 2 , and geometry parameters (fm) 12 C 10 2 d � /d � (mb/sr) Fit r 2 1/ 2 � 2 R p R n a p a n m 2.43 +0 .55 5.15 3.345 1.647 0.307 0.070 � 0.28 10 1 10 0 Experimental matter radii (fm) of 9 C and 9 Li. 10 -1 ( p, p ) � I � R 2.43 +0 .55 9 C a b 2.75(34), 2.71(32) c 2.42(3) � 0.28 9 Li 2.44(6) d 2.32(2) b 2.534(25) e 10 20 30 40 � c.m. (deg) a: Preset work b: A. Ozawa et al., Nucl. Phys. A 693, 32 (2001). c: R. E. Warner et al., Phys. Rev. C 74, 014605 (2006). d: A. V. Dobrovolsky et al., Nucl. Phys. A 766, 1 (2006). e: E. Liatard et al., Europhys. Lett. 13, 401 (19900. 2013 年 2 月 12 日火曜日 19

Summary ● Proton elastic scattering at 300 MeV is one method of studying nuclear radii and density density distributions. ● We have succeeded in extracting neutron density distributions of medium-heavy stable nuclei. ● We planed “Elastic Scattering of Protons with RI beams (ESPRI)” and constructed a Recoil Proton Spectrometer to measure unstable nuclei. ● We have measured following unstable nuclei: - 9,10,11 C - 66,70 Ni ● The root-mean-square matter radius of 9 C was deduced to be 2.43 (-0.28/+0.55) fm. 2013 年 2 月 12 日火曜日 20

Present work ● Measurements of neutron-rich carbon isotopes: 14,16 C @ RCNP, Osaka University Z @ RIKEN-RIBF 9 C 10 C 11 C N 2013 年 2 月 12 日火曜日 21

Present work ● Measurements of neutron-rich carbon isotopes: 14,16 C @ RCNP, Osaka University Z @ RIKEN-RIBF RCNP RIBF 9 C 10 C 11 C 14 C 16 C N 2013 年 2 月 12 日火曜日 21

Thank you for your attention Main collaborators S. Terashima (Beihang Univ.) J. Zenihiro (RIKEN) H. Sakaguchi (RCNP) H. Otsu (RIKEN) Y. Matsuda (Kyoto Univ.) RIKEN H. Takeda, K. Ozeki, K. Yoneda, K. Tanaka, T. Ichihara, T. Ohnishi Kyoto Univ. T. Murakami RCNP I. Tanihata O. H. Jin Miyazaki Univ. Y. Maeda Tohoku Univ. T. Kobayashi, T. Suda Souel Univ. Y. Sato SAGA HIMAT M. Kanazawa GSI S272 collaborators, M. Takechi 2013 年 2 月 12 日火曜日 22