Proton radius of 14 Be from measurement of charge changing cross sections

Transcription

1 Proton radius of 14 e from measurement of charge changing cross sections! S. Terashima 1, I. Tanihata 1,2, R. Kanungo 3, A. Estradé 3,4, W. Horiuchi 5, F. Ameil 4,. Atkinson 2, Y. Ayyad 6, D. Cortina-Gil 6, I. Dillmann 4, A. Evdokimov 4, F. Farinon 4, H. Geissel 4, G. Guastalla 4, R. anik 7, M. Kimura 5, R. Knoebel 4,. Kurcewicz 4, Y. A. Litviinov 4, M. Marta 4, M. Mostazo 6, I. Muhka 4,T. Neff 4, C. Nociforo 4, H.. Ong 2, S. Pietri 4, A. Prochazka 4, R. anik 7, C. Scheidenberger 4,. Sitar 7, P. Strmen 7, Y. Suzuki 8,9, M. Takechi 4,.S. Tanaka 2,. Vargas 6,. Winfield 4, H. Weick 4! 1 School of Physics and Nuclear Energy Engineering and IRCNPC, eihang University, eijing , China 2 RCNP, Osaka University, Ibaraki , apan 3 Saint Mary s University, Halifax, NS 3H 3C3, Canada 4 GSI Helmholtz Center, Darmstadt, Germany 5 Department of Physics, Hokkaido University, Sapporo , apan 6 Universidad de Santiago de Compostela, Santiago de Compostela, Spain 7 Comenius University, ratislava, Slovakia 8 Department of Physics, Niigata University, Niigata , apan 9 RIKEN Nishina Center, Wako , apan

2 Radii of nucleon distributions in nuclei (proton, neutron, nucleon) They provide basic information on the structure of nuclei In particular the difference of proton and neutron radii 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...

3 Recent Developments in Proton Radii of Light Nuclei A great progress has been made in determination of charge radii of He, Li, and e isotopes by isotope-shift measurements. 6 He: L. -. Wang et al., Phys. Rev. Letters 93 (2004) 8 He: P. Mueller et al., Phys. Rev. Letters 99 (2007) with ANL group 6,8,9 Li: G. Ewald et al., Phys. Rev. Letters 93 (2004) GSI 6,8,9,11 Li: R. Sánchez et al., Phys. Rev. Letters 96 (2006) with GSI group 7,9,10,11 e: W. D. Nörtershäuser., Phys. Rev. Letters 102 (2009) 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) Proton radii measurements by charge changing cross sections (σ cc ) -F isotopes: Chulkov et al; Nucl. Phys A674 (2000) ,10,11 e, 14,15,16 C, 16,17,18 O isotopes: Phys. Rev. Lett. 107 (2011) Proton radii of e isotopes except 14 e has been determined but 14 e (2-n halo nucleus) is not known!

4 σcc Measurements of 7,9,10,11,12,14 GSI 790A MeV C target N inc = No. of the incident nuclei Nncc= No. of the out going nuclei without charge change γ=nncc/ninc with target γ 0 =N 0ncc /N 0inc without target

5 Necessary collections for discussion of proton radii When 8 e is produced with only neutron removal, it is observed as charge changing because of the immediate decay of 8 e to 2α. This cross section has to be removed from the observed charge changing cross section before the radii discussion. For 7 e, any removal of neutron makes the change of proton number because it is a proton drip line nucleus. Therefore σcc = σr and proton radii can not be determined from σcc.

6 Effects of 2α in ΔE spectra e 10 e Entries Mean RMS Underflow Overflow Integral 2.8e Entries Mean RMS Underflow 0 Overflow 0 Integral 2.629e Z2cut Z2cut Entries Mean RMS Underflow 0 Overflow 0 Integral 2.102e+04 2 / ndf 73.7 / 35 Prob p ± 11.5 p ± 31.2 p ± 4.0 p ± p ± Entries Mean 2.47 RMS Underflow 0 Overflow 0 Integral 1.582e+04 / ndf / 25 2 Prob 5.751e-06 p ± 27.4 p ± 69.0 p ± Z2cut Z2cut

7 757 ±4 mb Determined σcc for e isotopes Measured σ cc H σcc [mb] A of e isotopes

8 Glauber model for σi and σcc Optical limit Calculation σ R = [ 1 T R (b)]db t s b T R (b) = exp[iχ R (b)] 2 :Transmission function( probability not to have reaction) iχ R (b) = P T i, j % & ρ z Pj (s)ρ z Ti (t)γ ji (b + s t) ' ( dsdt (P,T): p-p, p-n, n-p, n-n ρ Pi ( ) dz z (s) = ρ Pi s 2 + z 2 Γ ik (b) = 1 iα ik 4πβ ik 2 σ ' ik exp) b2 ( 2β ik 2 *, + σ cc = [ 1 T c (b)]db T c (b) = exp[iχ c (b)] 2 iχ c (b) = P T i z % & ρ Pp (s)ρ z Ti (t)γ pi (b + s t) ' ( dsdt (P,T): p-p, p-n, n-p, n-n

9 Comparison with models Charge-changing cross sections [mb] % 660 O 650 F O F 640 O O 630 O present data F 620 FMD O FMD scaled 610 AMD HO Mass number of e Proton Radius [fm] Experimental FMD AMD F F F F F F Mass number of e σi can be reproduced by the Glauber model if we know the proton radii within 5 % discrepancies. All isotopes σ I can be reproduced introducing one common factor ~1.05.

10 Proton radius of 14 e The Glauber model provide the σcc with known proton radii. Assume harmonic oscillator density distribution as model density. Fit the observed σcc by adjusting the size parameter of the density distribution.

11 14 e proton radius (Results) Proton and nucleon radius [fm] Exp. proton Exp. nucleon FMD proton FMD nucleon AMD proton AMD nucleon A of e F

12 Effect of neutrons in the projectile σ cc = [ 1 T c (b)]db T p (b) T c (b) = exp[iχ c (b)] 2 :Probability of protons are intact. iχ c (b) = P T i (P,T): p-p, p-n, n-p, n-n z % & ρ Pp (s)ρ z Ti (t)γ pi (b + s t) ' ( dsdt T T n (b) = exp[iχ n (b)] 2 z iχ n (b) = %& ρ Pn (s)ρ z Ti (t)γ ni (b + s t) ' ( dsdt T I (b) = T p (b)it n (b) P i T no (b) = [ 1 T n (b)]it p (b) :Probability hitting projectile neutron(s) without hitting proton(s) 1 T I (b) = " # 1 T p (b) $ % + [ 1 T n(b) ]it p (b) σ improved cc = Proton removal Neutron only removal # $ 1 T p (b)% & + α [ 1 T (b) n ]it p (b)db

13 Alpha does not change for different isotopes Value of correction factor (alpha) est fitting value of neutro effect alpha in e isotopes and 12C (plotted at A=12.5 Alpha A of e Proton and nucleon radius [fm] Exp. proton Exp. nucleon FMD proton FMD nucleon AMD proton AMD nucleon A of e F

14 SUMMARY Proton radius of 14 e has been determined from measurement of charge changing cross sections at 900A MeV With a Glauber model analysis applying the scaling of the cross section, <rp 2 > 1/2 = 2.41±0.04 fm has been obtained. With another Glauber model that include a influence of neutron scatterings, <<rp 2 > 1/2 = 2.32±0.14 has been obtained.