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Nuclear radii and density distributions Y. Matsuda Kyoto University GCOE Symposium Feb. 12 2012 Kyoto University Clock Tower Centennial Hall International Conference Hall 2013 2 12 1 Contents Introduction Proton

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Nuclear radii and density distributions

  • Y. Matsuda

Kyoto University

GCOE Symposium

  • Feb. 12 2012 Kyoto University Clock Tower Centennial Hall International Conference Hall

1 2013年2月12日火曜日

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SLIDE 2

Contents

Introduction Proton elastic scattering from stable nuclei Elastic Scattering of Protons with RI beams Summary Present work

2 2013年2月12日火曜日

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Introduction

3 2013年2月12日火曜日

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Stable nuclei Charge radius Muonic atom Proton distribution Electron scattering Neutron distribution Proton elastic scattering By unfolding the charge distribution By using the well inferred proton distribution

Nuclear radii and density distributions

  • Fundamental properties of nuclei
  • Inputs and/or guidelines to describe the nuclear reactions and structures

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SLIDE 5

Background: http://www.nscl.msu.edu/~austin/nuclear-astrophysics.pdf

History of Universe

10-20 1 1020 1040

Time after Big Bang [seconds] Temperature [K]

Elementary particles

1020 1010 1 10-10 Hadron Light nuclei

Today

Nucleosynthesis

Big Bang

Stars Nuclear Physics

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SLIDE 6

http://www.nishina.riken.go.jp

Nuclear chart

Projectile Fragmentation In-flight U fission & P.F.

protons neutrons

stable nuclei ~300 nuclei unstable nuclei observed so far ~2700 nuclei drip-lines (limit of existence)（theoretical predictions) ~6000 nuclei magic numbers

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Introduction

Proton elastic scattering from Stable nuclei

7 2013年2月12日火曜日

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SLIDE 8

Ep=200 - 400 MeV

The longest mean free path in nuclei ( 2 fm-1)

101 102 103 10 100 1000 pp pn np

  • Elab. [MeV]

Cross section [mb]

Proton elastic scattering

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Relativistic Impulse Approximation

  • D. P. Murdock and C. J. Horowitz, Phys. Rev. C 35, 1442(1987).

F = F S + F V µ

(0) (1) µ F PV q 5 (0)

2M q 5

(1)

2M + F T µ

(0) (1) µ + F A 5 (0) µ (0) 5 (1) (1) µ

/ /

Relativistic Love-Franey model:

F L (q, E c) = i M 2 2E ckc F L

D (q) + F L X (Q)

F L

D (q)

=

j

  • L,L (j ){0 · 1}I j f j (q)

F L

X (Q)

= ( 1)T

j

B L (j ),L {0 · 1}I j f j (Q) f j (q) = g2

j

q2 + m 2

j

2

j

2

j + q2 2

i g2

j

q2 + m j 2

  • 2

j

  • 2 + q2

2

F L (pp) = F L (T = 1) F L (pn) = 1 2 F L (T = 0) + F L (T = 1)

L = S, V, PV, T, A

N 0 N 1 N 1 N 0

1 q2 + m 2

q = kc kc g 2 2 + q2L I g 2 2 + q2L I 1

kc kc kc kc

Direct

N 0 N 1 N 1 N 0 kc kc kc kc

g 2 2 + Q2 L I 1 Q = kc + kc g 2 2 + Q 2L I 1 Q 2 + m 2

Exchange

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Relativistic Impulse Approximation

Phenomenological medium modification

  • H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998).

N 0 N 1 N 1 N 0

m g g

J.Zenihiro et al.,

  • Phys. Rev. C 82, 044611 (2010)

g2

j

→ g2

j

1 + aj

ρ(r) ρ0

, mj → mj

  • 1 + bj

ρ(r) ρ0

  • ,

10 2013年2月12日火曜日

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SLIDE 11 116Sn(x104) 118Sn(x102) 120Sn(x1) 122Sn(x10-2) 124Sn(x10-4)

Trial density + medium effect Search density + medium effect

d/d (mb/sr)

c.m. (degree)

Ay(116

Sn)

Ay(118

Sn)

Ay(120

Sn)

Ay(122

Sn)

Ay(124

Sn)

c.m. (degree)

Proton elastic scattering form stable nuclei

S.Terashima et al.,

  • Phys. Rev. C 77, 024317 (2008)

J.Zenihiro et al.,

  • Phys. Rev. C 82, 044611 (2010)

Experimental data at RCNP, Osaka University

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SLIDE 12

S.Terashima et al.,

  • Phys. Rev. C 77, 024317 (2008)

J.Zenihiro et al.,

  • Phys. Rev. C 82, 044611 (2010)

Proton elastic scattering form stable nuclei

Experimental data at RCNP, Osaka University

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SLIDE 13

Introduction

Proton elastic scattering from Stable nuclei

Elastic Scattering of Protons with RI beams

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1 m RDCup pΔEup SHT NaI(Tl) RPS Beam E1 E14 E7 E8 pΔEdown RDCdown p p

Y X

Recoil Proton Spectrometer (RPS)

Solid H2 (SHT) RDC pΔE E material Para H2 Ar+C2H6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm2 440 x 440 mm2 431.8 x 45.72 mm2 thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Resolution 500 μm TOF : 0.1 nsec 0.3 %(80 MeV)

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1 m RDCup pΔEup SHT NaI(Tl) RPS Beam E1 E14 E7 E8 pΔEdown RDCdown p p

Y X

Recoil Proton Spectrometer (RPS)

Solid H2 (SHT) RDC pΔE E material Para H2 Ar+C2H6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm2 440 x 440 mm2 431.8 x 45.72 mm2 thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Resolution 500 μm TOF : 0.1 nsec 0.3 %(80 MeV)

Solid para hydrogen target φ30 mm, 1 mmt

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1 m RDCup pΔEup SHT NaI(Tl) RPS Beam E1 E14 E7 E8 pΔEdown RDCdown p p

Y X

Recoil Proton Spectrometer (RPS)

Solid H2 (SHT) RDC pΔE E material Para H2 Ar+C2H6 Plastic NaI(Tl) effective area φ 30 mm 436 x 436 mm2 440 x 440 mm2 431.8 x 45.72 mm2 thickness 1 mm 69.4 mm 2.53 / 3.09 mm 50.8 mm Resolution 500 μm TOF : 0.1 nsec 0.3 %(80 MeV)

Solid para hydrogen target φ30 mm, 1 mmt Large, thin solid hydrogen target using para-H2,

  • Y. Matsuda et al., Nucl. Instr. and Meth. A 643 6-10 (2011).

Scintillating fiber detector for momentum tagging light nuclei at intermediate energies,

  • Y. Matsuda et al., Nucl. Instr. and Meth. A 670 25-31 (2012).

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9C 10C 11C 20O 66Ni 70Ni

Z N

A drastic growth of the density distribution with an increase of the neutron number (@NIRS-HIMAC) Equation of state of asymmetric nuclear matter (@GSI)

Elastic Scattering of Protons with RI beams

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Yoshiko Kanada-En’yo and Hisashi Horiuchi, Progress of Theoretical Physics Supplement, 142 (2001) 205 9C 10C 11C 12C 13C 14C 15C 16C 17C 18C 19C 20C 22C

Antisymmetrized Molecular Dynamics (AMD) density

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10 -1 10 0 10 1 10 2 10 3 10 20 30 40

9C 12C

d/d (mb/sr) c.m. (deg)

Matter radius of 9C

Application of our previous work

  • H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998).

S.Terashima et al., Phys. Rev. C 77, 024317 (2008) J.Zenihiro et al.,Phys. Rev. C 82, 044611 (2010) We need to

(1) tune the scattering amplitude with scattering for a nearby N = Z nucleus (2) deduce both proton and neutron density distributions p(9C,p) 280-300 MeV/u

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(1) tune the scattering amplitude with scattering for a nearby N = Z nucleus: 12C

10-1 10 0 10 1 10 2 10 3

  • 1.0
  • 0.5

0.0 0.5 1.0 10 20 30 40 (a) d/d (mb/sr) Ay c.m. (deg) Original MH Modified MH (b)

Phenomenological medium modification

  • H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998).

N 0 N 1 N 1 N 0

m g g

g2

j

→ g2

j

1 + aj

ρ(r) ρ0

, mj → mj

  • 1 + bj

ρ(r) ρ0

  • ,

12C(p,p)

Ep=300 MeV

18 2013年2月12日火曜日

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SLIDE 21

i(r) = N i 1 + exp {(r R i)/a i} , i = p, n,

10 -1 10 0 10 1 10 2 10 3 10 20 30 40

9C 12C

d/d (mb/sr) c.m. (deg) Fit

(2) deduce both proton and neutron density distributions

Deduced rms matter radius, best-fit χ2, and geometry parameters (fm)

r 2

m 1/ 2

2 R p R n ap an 2.43+0 .55

0.28

5.15 3.345 1.647 0.307 0.070 (p, p) I R

9C

2.43+0 .55

0.28 a

2.42(3)

b

2.75(34), 2.71(32) c

9Li

2.44(6) d 2.32(2) b 2.534(25) e

Experimental matter radii (fm) of 9C and 9Li. Two parameter Fermi distribution

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.

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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:
  • 9,10,11C
  • 66,70Ni
  • The root-mean-square matter radius of 9C was deduced to be 2.43 (-0.28/+0.55) fm.

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Present work

9C 10C 11C

Z N

  • Measurements of neutron-rich carbon isotopes: 14,16C

@ RCNP, Osaka University @ RIKEN-RIBF

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Present work

9C 10C 11C

Z N

14C

RCNP

16C

RIBF

  • Measurements of neutron-rich carbon isotopes: 14,16C

@ RCNP, Osaka University @ RIKEN-RIBF

21 2013年2月12日火曜日

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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

22 2013年2月12日火曜日