Nuclear radii and density distributions...Nuclear radii and density distributions Y. Matsuda Kyoto University GCOE Symposium Feb. 12 2012 Kyoto University Clock Tower Centennial Hall

Nuclear radii and

density distributions

Y. Matsuda

Kyoto UniversityGCOE Symposium

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

12013年2月12日火曜日

Contents

Introduction

Proton elastic scattering from stable nuclei

Elastic Scattering of Protons with RI beams

Summary

Present work


Introduction


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


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

History of Universe

10-20 1 1020 1040

Time after Big Bang [seconds]

Tem

per

atu

re [

K]

Elementary particles

1020

1010

1

10-10

Hadron

Light nuclei

Today

Nucleosynthesis

Big Bang

Stars

Nuclear Physics


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

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

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

Nuclear chart

Projectile Fragmentation

In-flight U fission & P.F.

prot

ons

neutrons

stable nuclei ~300 nucleiunstable nuclei observed so far ~2700 nucleidrip-lines (limit of existence)（theoretical predictions) ~6000 nuclei

magic numbers




Introduction

Proton elastic scattering from Stable nuclei


Ep=200 - 400 MeV The longest mean free path in nuclei ( 2 fm-1)

101

102

103

10 100 1000

pppnnp

Elab. [MeV]

Cro

ss s

ecti

on

[m

b]

Proton elastic scattering


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) = iM 2

2EckcF LD (q) + F L

X (Q )

F LD (q) =

j

!L,L ( j ) {"0 · "1}I j f j (q)

F LX (Q ) = ( #1)T

j

B L ( j ) ,L {"0 · "1}I j f j (Q )

f j (q) =g2j

q2 + m 2j

$2j

$2j + q2

2

# ig2j

q2 + m j 2

$2

j

$2+ q2

2

F L (pp) = F L (T = 1)

F L (pn) =1

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

L = S, V, PV, T, A

N 0 N 1

N 1N 0

1

q2 + m 2

q = kc ! kc

g"2

"2 + q2#L$I0 g

"2

"2 + q2#L$I1

kc !kc

kc !kc

Direct

N 0 N 1

N 1N 0

kc !kc

kc !kc

g"2

"2 + Q2#L$I1

Q = kc + kcg

"2

"2 + Q 2#L$I0

1

Q 2 + m 2

Exchange


Relativistic Impulse Approximation

Phenomenological medium modification H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998).

N0 N1

N1N0

mg g

J.Zenihiro et al.,Phys. Rev. C 82, 044611 (2010)

g2j !

g2j

1 + aj!(r)!0

,

mj ! mj

!1 + bj

!(r)!0

",


116Sn(x10

4)

118Sn(x10

2)

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)


Experimental data at RCNP, Osaka University


S.Terashima et al.,Phys. Rev. C 77, 024317 (2008)


Proton elastic scattering form stable nucleiExperimental data at RCNP, Osaka University


Introduction

Proton elastic scattering from Stable nuclei



1 m

RDCup

p!Eup

SHT

NaI(Tl)

RPS

Beam

E1

E14

E7

E8

p!Edown

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)


1 m

RDCup

p!Eup

SHT

NaI(Tl)

RPS

Beam

E1

E14

E7

E8

p!Edown

RDCdown

p

p

Y

X







Solid para hydrogen targetφ30 mm, 1 mmt


1 m

RDCup

p!Eup

SHT

NaI(Tl)

RPS

Beam

E1

E14

E7

E8

p!Edown

RDCdown

p

p

Y

X







Solid para hydrogen targetφ30 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).


9C 10C 11C

20O

66Ni 70NiZ

N

A drastic growth of the density distributionwith an increase of the neutron number(@NIRS-HIMAC)

Equation of state ofasymmetric nuclear matter(@GSI)



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


10-1

100

101

102

103

10 20 30 40

9C12C

d!/d"

(m

b/s

r)#

c.m. (deg)

Matter radius of 9C

Application of our previous workH. 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


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

10-1

100

101

102

103

-1.0

-0.5

0.0

0.5

1.0

10 20 30 40

(a)

d!/d"

(m

b/s

r)Ay

#c.m.

(deg)

Original MH

Modified MH

(b)

Phenomenological medium modification H. Sakaguchi et al., Phys. Rev. C 57, 1749 (1998).

N0 N1

N1N0

mg g

g2j !

g2j

1 + aj!(r)!0

,

mj ! mj

!1 + bj

!(r)!0

",

12C(p,p)Ep=300 MeV


!i (r) =N i

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

10-1

100

101

102

103

10 20 30 40

9C12C

d!/d"

(m

b/s

r)

#c.m.

(deg)

Fit

(2) deduce both proton and neutron density distributions

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

r 2m1/ 2

!2 R p R n ap an

2.43+0 .55

! 0.285.15 3.345 1.647 0.307 0.070

(p, p) ! I !R9C 2.43+0 .55

! 0.28a 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 workb: 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.


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.


Present work

9C 10C 11C

Z

N

● Measurements of neutron-rich carbon isotopes: 14,16C @ RCNP, Osaka University @ RIKEN-RIBF


Present work

9C 10C 11C

Z

N14CRCNP

16CRIBF

● Measurements of neutron-rich carbon isotopes: 14,16C @ RCNP, Osaka University @ RIKEN-RIBF


Thank you for your attention

Main collaboratorsS. 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. OhnishiKyoto Univ. T. MurakamiRCNP I. Tanihata O. H. JinMiyazaki Univ. Y. MaedaTohoku Univ. T. Kobayashi, T. Suda Souel Univ. Y. SatoSAGA HIMAT M. Kanazawa GSI S272 collaborators, M. Takechi


Documents

Nuclear radii and density distributions...Nuclear radii and density distributions Y. Matsuda Kyoto University GCOE Symposium Feb. 12 2012 Kyoto University Clock Tower Centennial Hall