Proton radius of 14Be from measurementof charge changing cross sections!
S. Terashima1, I. Tanihata1,2, R. Kanungo3, A. Estradé3,4, W. Horiuchi5, F. Ameil4, J.
Atkinson2, Y. Ayyad6, D. Cortina-Gil6, I. Dillmann4, A. Evdokimov4, F. Farinon4, H.
Geissel4, G. Guastalla4, R. Janik7, M. Kimura5, R. Knoebel4, J. Kurcewicz4, Y. A. Litviinov4,M. Marta4, M. Mostazo6, I. Muhka4,T. Neff4, C. Nociforo4, H.J. Ong2, S. Pietri4, A.
Prochazka 4, R. Janik7, C. Scheidenberger4, B. Sitar7, P. Strmen7, Y. Suzuki8,9, M. Takechi4,
J.S. Tanaka2, J. Vargas6, J. Winfield4, H. Weick4!
1 School of Physics and Nuclear Energy Engineering and IRCNPC, Beihang University,
Beijing 100191, China	

2 RCNP, Osaka University, Ibaraki 567-0047, Japan	

3 Saint Mary’s University, Halifax, NS B3H 3C3, Canada	

4 GSI Helmholtz Center, 64291 Darmstadt, Germany	

5 Department of Physics, Hokkaido University, Sapporo 060-0810, Japan	

6 Universidad de Santiago de Compostela, Santiago de Compostela, Spain	

7 Comenius University, Bratislava, Slovakia	

8 Department of Physics, Niigata University, Niigata 950-2181, Japan 	

9 RIKEN Nishina Center, Wako 351-0198, Japan

Radii of nucleon distributions
in nuclei (proton, neutron, nucleon)
They provide basic information on the structure ofnuclei	In particular the difference of proton and neutronradii are important in halo and neutron skin nuclei	Decoupling of protons and neutrons in nuclei	

Movements of a core and a halo, correlation between halo neutrons,core modification, ...	

EOS of the asymmetric nuclear matter	...

Recent Developments in Proton
Radii of Light Nuclei
A great progress has been made in determination ofcharge radii of He, Li, and Be isotopes by isotope-shiftmeasurements.	

6He: L. -B. Wang et al., Phys. Rev. Letters 93 (2004) 142501.

@ANL	

8He: P. Mueller et al., Phys. Rev. Letters 99 (2007) 252501.
@GANIL with ANL group	

6,8,9Li: G. Ewald et al., Phys. Rev. Letters 93 (2004) 113002.
@ GSI	

6,8,9,11Li: R. Sánchez et al., Phys. Rev. Letters 96 (2006) 033002.
@TRIUMF with GSI group	

7,9,10,11Be: W. D. Nörtershäuser., Phys. Rev. Letters 102 (2009) 062503. @GSI	Development of atomic structure calculation up to three-electron system. 	

G. W. F. Drake Nucl. Phys. A737c, 25 (2004), Z. C. Yan et al., Phys. Rev. Letters 100 (2008) 243002.	

Proton radii measurements by charge changing crosssections (σcc)	

B-F isotopes: Chulkov et al; Nucl. Phys A674 (2000) 330.	

9,10,11Be, 14,15,16C, 16,17,18O isotopes: Phys. Rev. Lett. 107 (2011) 032502.

Proton radii of Be isotopes except 14Be has been
determined but 14Be (2-n halo nucleus) is not known!

GSI	790A MeV

Ninc= No. of the incidentnuclei
Nncc= No. of the out going
nuclei without charge change
γ=Nncc/Ninc with target	

γ0=N0ncc/N0inc without target	

C targetσcc Measurements of 7,9,10,11,12,14B

Necessary collections fordiscussion of proton radii
When 8Be is produced with only neutron removal, it isobserved as charge changing because of theimmediate decay of 8Be to 2α.	

This cross section has to be removed from theobserved charge changing cross section before theradii discussion.	

For 7Be, any removal of neutron makes the change ofproton number because it is a proton drip linenucleus. Therefore σcc = σR and proton radii can not
be determined from σcc.

Effects of 2α in ΔE spectra
9Be

ID_Z2_sub_af

ID_Z2_sub_af

1000
900

Entries

346434

Mean2.67

RMS

0.4402800

Underflow

0700

Overflow

0Integral

2.8e+049000Integral

2.629e+04

400

300

300

200

200

100

100
2.6

2.8

33.2

3.4

0
1.6

3.6
Z2cut
ID_Z2_sub_af

ID_Z2_sub_af
1000
900
800
700
600

Entries-9653566

Mean2.569

RMS
Underflow

0.45050Overflow

0Integral

2.102e+04

r 2 / ndf
Prob73.7 / 350.0001424

p0p1-553.8 ± 11.5
1738 ± 31.2

p2

117.7 ± 4.0

p32.764 ± 0.003

p40.1071 ± 0.0034

200200100

100
2.8

33.2

3.4

3.6Z2cut

2.833.201.6

1.8

3.4

0

3.6
Z2cut

ID_Z2_sub_af
Entries-9650274
Mean
2.47
RMS
0.4432
Underflow
0Overflow
0Integral
1.582e+04
r 2 / ndf
68.82 / 25Prob
5.751e-06
p0-863.4 ± 27.4
p12538 ± 69.0p212.55 ± 3.81

600

300

2.62.6700

400

2.42.4800

300

2.22.2900400221000

500

1.8

1.8

ID_Z2_sub_af

50000.444

700

500

2.42.677

RMSOverflow

400

2.2349726

MeanUnderflow

500

2Entries

800

600

1.8

ID_Z2_sub_af

1000

600

0
1.6

10Be

ID_Z2_sub_af

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6
Z2cut

757 ±4 mb

Determined σcc for Be isotopes
Measured σcc

720
710

H

Bσcc [mb]

700

B

690
B
680

B
B

670

J

660
650

J

678

9

101112A of Be isotopes

131415Glauber model for σI and σcc
Optical limit Calculationtσ R = ∫∫ [1− TR (b)] db
TR (b) = exp[i χ R (b)]2s:Transmission function( probability not to have reaction)i χ R (b) = ∫∫ ∫∫ ∑ %& ρ Pjz (s) ρTiz (t)Γ ji (b + s − t) '( dsdtPTi, j(P,T): p-p, p-n, n-p, n-n

σ cc = ∫∫ [1− Tc (b)] db
Tc (b) = exp[i χ c (b)]2zi χ c (b) = ∫∫ ∫∫ ∑ %& ρ Pp(s) ρTiz (t)Γ pi (b + s − t) '( dsdtPTbi(P,T): p-p, p-n, n-p, n-n∞

ρ Piz (s) = ∫ −∞ ρ Pi

( s + z ) dz
22' b2 *1 − iαik
Γ ik (b) =σ ik exp )− 2 ,4 πβik2( 2 βik +Comparison with models
2.8710Experimental

B

700

2.7B

690
J680

B

670

B
B

O

660

4.8 %

JJ

J

650

FO

F

640
630

F

620

OO

JO

present data
FMD
FMD scaled AMDHOO

610
600
6789101112

Mass number of Be

FMD

FAMD

B

1314

Proton Radius [fm]Charge-changing cross sections [mb]

720

2.6F
B

2.5FFFFJ

2.4B
JB
B

2.3JJJB
J

2.2
2.1

678

9 10 11 12 13 14 15Mass number of Be

σI can be reproduced by the Glauber model if we know the proton radii within 5 % discrepancies.	

All isotopes σI can be reproduced introducing one common factor ~1.05.

Proton radius of 14Be
The Glauber model provide the σcc with known
proton radii.	

Assume harmonic oscillator density distribution asmodel density.	

Fit the observed σcc by adjusting the size parameter ofthe density distribution.

14Be proton radius (Results)

Proton and nucleon radius [fm]3.1

■ Exp. proton☐ Exp. nucleon

2.9 ● FMD proton◦ FMD nucleon▲ AMD proton△ AMD nucleon

2.7
2.5BJB

2.3BJ

2.18910JBBBFJJ11 12A of Be

131415Effect of neutrons in theprojectile(P,T): p-p, p-n, n-p, n-n

σ cc = ∫∫ [1− Tc (b)] db
2T p (b) ≡ Tc (b) = exp[i χ c (b)] :Probability of protons are intact.
zi χ c (b) = ∫∫ ∫∫ ∑ %& ρ Pp(s) ρTiz (t)Γ pi (b + s − t) '( dsdtPTTn (b) = exp[i χ n (b)]i2zi χ n (b) = ∫∫ ∫∫ ∑ %& ρ Pn(s) ρTiz (t)Γ ni (b + s − t) '( dsdtPTiTI (b) = T p (b) i Tn (b)Tno (b) = [1− Tn (b)] i T p (b) :Probability hitting projectile neutron(s) without hitting proton(s)1− TI (b) = "#1− T p (b) $% +Proton removal[1− T (b)] i T (b)np“Neutron only” removal

σ ccimproved = ∫∫ #$1− T p (b) %& + α [1− Tn (b)] i T p (b)db

Alpha does not change fordifferent isotopes
Best fitting value of neutro effect alpha in Be isotopes
and 12C (plotted at A=12.5

3.1

Alpha

Proton and nucleon radius [fm]Value of correction factor (alpha)0.50.40.3
0.20.10☐ Exp. nucleon

2.9 ● FMD proton◦ FMD nucleon▲ AMD proton

91011A of Be

1213△ AMD nucleon

2.72.5BJB

2.3B
J

2.18

■ Exp. proton

8910JBBBFJJ11 12
A of Be

131415

SUMMARY
Proton radius of 14Be has been determined frommeasurement of charge changing cross sections at900A MeV	With a Glauber model analysis applying the scaling of
the cross section, <rp2>1/2 = 2.41±0.04 fm has beenobtained.	

With another Glauber model that include a influenceof neutron scatterings, <<rp2>1/2 = 2.32±0.14 has beenobtained.