--- OUTLINE --- Introduction Situation @ stable nuclei How to measure radii? σ R / σ I measurements Transmission method Experimental setup Glauber model analysis Optical limit approximation Density distribution Deduced radii Isotope dependence Isobar dependence Skins & Halos Skins in Na & Ar isotopes Skins from other nuclei 2-n halo nucleus 17 B Recent results from S-250@FRS Summary Summary and future prospects 16 th Dec. 2004 / T. Suzuki German-Japanese Nuclear Structure and Astrophysics Workshop Saitama University
Nuclear r adii of unstable nuclei Nuclear radii of stable nuclei Text book says R A 1/3 Neutron radii proton radii even for 208 Pb (126-82=44 excess neutrons!) ρ Proton Neut r Same radii for mirror pairs No thick neutron skin! Diffuseness is constant. a ~ 0.6 fm How are unstable nuclei? 16 th Dec. 2004 / T. Suzuki Situation @ stable/unstable nuclei P. 1
- neutron/proton skins and halos - How to measure radii of unstable nuclei Optical isotope shift Charge radii can be measured. Only limited atomic numbers (Na, Ar, Kr, Sr, Sn, etc ). Elastic electron scattering was so far, impossible. Reaction cross-section (Interaction cross section) Matter radii can be deduced. No limitation to atomic number. 16 th Dec. 2004 / T. Suzuki How to measure radii? P. 2
- neutron/proton skins and halos - What is reaction cross- section (σ( R )? Reaction cross-section (σ R ) σ R = σ I + σ inela, σ inela : inelastic crosssection Definition of interaction crosssection (σ I ); Cross section for the change of Z and/or N in incident nucleus If σ inela is small enough, σ R σ I. At relativistic energy (~1 A GeV) 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements P. 3
- neutron/proton skins and halos - γ-ray yield (counts/channel) 10 4 1000 100 10 1 34Cl + C 34 Cl 9.1 ps 5.2 ps 32 m 1.5 s T 1/2 1 + 1 + 3 + 0 + I π 461 kev 665 kev 100 100 100 34Cl σ inela 40 mb 20 mb 10 mb 665 461 146 0 E x (kev) 0 0.2 0.4 0.6 0.8 1 Inelastic scattering Corrected E γ (MeV) σ inela 20mb Typical error for σ I 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements P. 4
- neutron/proton skins and halos - σ R radii; a simple picture Let s assume black disk nuclei! R I (P) R I (T) Target nucleus Projectile nucleus σ R = π [R I (T) + R I (P)] 2 For quantitative analysis, Glauber model is necessary. 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements P. 5
Principle of measurement Transmission method Target (thickness t) Carbon N i ( A Z) N o ( A Z) σ I = -1/t log(n o /N i ) N o *( A Z)= N o ( A Z)-N*( A Z*) σ R = -1/t log(n o */N i ) 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements p.7
Be production target Experimental setup TOF/B ρ TOF/B ρ E E F1 F3 F4 40 36 Ar/ Ar primary beam (~1A GeV) C reaction target F2 previous exp.@frs Plastic scintillators TPC Collimator MUSIC/IC NaI array (mb) 1400 A Na+C σ Ι 1200 1000 19 23 27 31 A 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements p.8
Glauber model Optical Limit σ R (r) = exp- = 2π 1 - T(r) r d 0 approximation q(r,z) dz σ - (Zero range calculations) T(r):Transmission function σ:effective NN corss-sections ρ of target ρ of projectile q(z) = dη 2π ρ T (r,z,b,η) ρ P (r,z,b,η) b db - 0 0 r 2 = r 2 Mean square radii ρ () r 4πr 2 dr P Harmonicoscillator type (p-shell) ρ P (r) = 2π -3/2 λ -3 (1-1/A) -3/2 exp(-x 2 ) (1+ (N-2) /3x 2 ) x = (r/λ) 2 16 th Dec. 2004 / T. Suzuki σ R / σ I measurements p.9
Isotope dependence of matter radii 3.4 19 C 3.2 C-isotopes RMS matter radii (fm) 3 2.8 2.6 2.4 2.2 R A 3/4 R A 1/3 2 8 10 12 14 16 18 20 22 A R A 1/3 in unstable nuclei 16 th Dec. 2004 / T. Suzuki Isotope dependence p.12
- neutron/proton skins a nd halos- A=17 system Phys. Lett. B 334 (1994) 18 R.M.S. radius (fm) 17Ne A=20 system 3.2 R.M.S. radius (fm) SIS-FRS-ESR 17N -3/2-1/2 1/2 3/2 5/2 7/2 T z (isospin) Nucl. Phys. A 603 (1996) 219 3.1 3 2.9 2.8 2.7 2.6 20 Mg 20O -2-1 0 1 2 3 4 T z (isospin ) Mirror nuclei do not have the same radii 16 th Dec. 2004 / T. Suzuki Isobar dependence p. 13
Neutron skin in Na-isotopes Definition ; n-skin = (rms-n) - (rms-p) p-skin = (rms-p) - (rms-n) Relationship Optical isotope-shift (rms-m) 2 = (Z/A) (rms-p) 2 + (N/A) (rms-n) 2 We can deduce rms-n if we know both rms-m& rms-p. 3.5 Phys. Rev. Lett. 75 (1995)3241. Neutron skin~ 0.4 fm rms radii (fm) 3 2.5 stable Neutron Proton Calculation by RMF 20 22 24 26 28 30 32 G. Lalazissis, D. Vretenar, P. Ring Eur. Phys. J. A22 (2004) 37 16 th Dec. 2004 / T. Suzuki neutron skin in Na isotopes p.15 A
0.6 Proton skin (fm) 0.5 0.4 0.3 0.2 0.1 0-0.1 Nucl. Phys. A709(2002)60 Proton skin Ar Calculation by RMF(NL3) -0.2 30 32 34 36 38 40 42 A Thick skins appear in proton-rich side too. 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16
.. Proton skin (fm) SIS-FRS-ESR 0.6 0.4 0.2 0-0.2-0.4-0.6 32 21 33 Correlation between skin and (S p -S n ) 34 22 20 38 37 36 35 40 39 23 25 26 27 29-20 -10 0 10 20 S p -S n (MeV) 28 30 31 Ar-isotopes Na-isotopes RMF(NL3) (Ar) Formation of n/p- skins is common phenomenon in unstable nuclei Skin thickness ---> Relative merits of various param. used in the RMF model. ---> EOS pressure in neutron matters ---> pygmy dipole resonance S. Yoshida & H. Sagawa PRC61 (2004) 024318 N. Tsoneva, H. Lenske, Ch Stonyanov PLB 586, (2004) 213 M. Yokoyama, T. Otsuka, N. Fukunishi, NPA599, (1996) 367 W.D. Myers & W.J. Swiatecki NPA336, (1980) 267 Droplet model,hartree-fock RPA, RMF, (R)Hartree-Bogolubov,... Another example 20 Mg, 20 N O. Bochkarev et al., Eur. Phys.J. A 1 (1998) σ R mesuremnet -> 0.56 +- 0.29 fm Neutron-rcih K & Sc N. Aissaouri et al., PRC 60(1999) 03614 40 S F. Marechal et al., PRC 60 (1999) 034615 proton scattering inverse kinematics ---> 16 th Dec. 2004 / T. Suzuki skin formation & EOS via matter radius p.17
Hadron probes suffer from the uncertainties in the reaction mechanism Table.2 summary of current values for the neutron skin thickness, S, in 208Pb Probe S (fm) Error (fm) reference 0.0 0.1 Allardyce, et al. NPA (1973) Proton (650 MeV) 0.20 0.04 Strarodubsky, et al. PRC (1994) Giant dipole resonance excitation Nucleon (40-200 MeV) Proton (0.5-1.04 GeV) Anti-protonic atoms 0.19 0.17 0.097 0.15 0.09 0.014 0.02 Krasznahorkay, et al. NPA (1994) Karataglidis, et al. PRC (2002) Clark, et al. PRC (2003) Trzci_ska, et al. PRL (2002) 0.15+-0.02 (fm) from p _ (p,n) reaction on stable 114-124 Sn using Spin Dipole Resonance A. Karsznahorkay et al. P.R.L. 82(99) 3216 (Liverpool - Surrey-GANIL - Saclay-Caen) ENAM04 N=20~ 28 systematic measurements of σ R by Villari et al. 35 Mg, 44 S (new halo candidate) 16 th Dec. 2004 / T. Suzuki Another examples p.18
What is known so far on 17 B 3.2 11 Li ~ (fm) rm 2.8 2.4 14 Be analogy 17 B 12 Be 15 B 0.1 1 S2n (MeV) 10 S2n G.Audi,O.Bersillon,J.Blachot,A.H.Wapstra, Nucl.Phys.A624(97)1 ~ r m.., Nucl.Phys.A658(99) 313 14Be dσ dω ( θ neutron ) P ( 12 Be) kinematically complete exp. Γ ~50 Γ ~88 +- +- 5MeV/c 5MeV/c σ(-2n), Invariant mass spectra K. Riisager et al., Nucl. Phys.A540 (92) 365. M.Zaharet al., Phys. Rev. C48 (93)R1484 M. Labiche etal., Phys.Rev. Lett.(00)1111 Neutronhalostructurein 14 Be in 17B? 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki 2-n halo nucleus 17 B p.19
rms matter radii for B isotopes Nucl. Phys. A658 (1999) 313. 17 B Radius of 17 B is much larger than neighbors! Necessary condition Phys. Rev. Lett. 89 (2002)012501. Narrow width in Momentum distr. Sufficient condition 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki 2-n halo nucleus 17 B p.20
Characterizing feature; core Large rms radii narrow p// ρ halo Closeness of a threshold r Small neutron separation energies Dominating cluster structure Density distribution Core + neutron(s) 10 0 10-1 10-2 Phys. Rev. C70 (2004) 05320 mixed [fm -3 ] 10-3 10-4 17 B 10-5 10-6 10-7 0 2 4 6 8 10 12 r [fm] 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki 2-n halo nucleus 17 B p.21
Proton Skin in Kr Isotope S-250 @FRS 27.10-7.11 Z / Z 0.998%(Z=31) TOF : 99.99%> is required for PID! σ 15 [ps] Analysis is in progress Analysis is in progress 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki recent results from @250@ FRS p.22
20 Nuclear determined radii R σ at from ~1 AGeV (Radius 4He of (1.47 fm) is subtract 15 Proton drip-line Z 10 Neutron drip-l 5 0.51 1.52 fm 0 0 5 10 15 20 25 N
Future plans...(eos) We want to understand the nuclear matter equation of state The energy per nucleon near the saturation point:w w = w 0 + K 0 18n 0 2 n n 0 ( ) 2 + S 0 + L ( ) 3n 0 n n 0 w 0 : the saturation energy, n 0 :the saturation density, K 0 : the incompressibility, α:neutron excess, S 0 : the density-dependent symmetry energy at n=n 0, L=3n 0 (ds/dn) n=n :the symmetry energy density-derivative coefficient 0 Y=-(K 0 S 0 )/(3n 0 L):the slope of the saturation line near α=0 α 2 roposed ccuracy 54-72 Ni isotopes Recent theoretical works show that matter radii depend strongly on L. K. Oyamatsu & K.Iida In preparation. 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki future plans p..23
Stable nuclei Summary Unstable nuclei R A 1/3 Same radii for mirror pairs No thick skin Constant diffuseness Magic number; 2, 8, 20, 28... R A 1/3 Large difference for some pairs Existence of thick skin Existence of halo tail Another magic number; 16 Nuclear structure for unstable nuclei is quite different from stable nuclei. Reaction (interaction) cross-section measurements are a very powerful tool to study nuclear structure of unstable nuclei. Future plan in 54-72 Ni isotopes Required accuracy 0.25% in σ I 0.01 fm in radius 16 th Dec. 2004 / T. Suzuki proton skin in Ar isotopes p.16 16 th Dec. 2004 / T. Suzuki Summary p.24
List of collaborators H. Geissel, K. Suemmerer, G. Muenzenberg M. Fukuda, T. Izumikawa, T. Oonishi(Tetsu)*, T. Ootsubo(Taka1), T. Suda*, A. Ozawa(Aki), T. Yamaguchi(Taka2), T. Suzuki GSI-RIKENni.Osaka - Uni. Niigata - Uni. Tsukuba - Uni. Saitama Thank you for your attention!