Polarized proton elastic scattering and Nucleon density distributions
Polarized proton elastic scattering and Nucleon density distributions Juzo Zenihiro, RIKEN Nishina Center
outline 1. 2. 3. 4. 5. 6. Nucleon density distributions Polarized proton elastic scattering How to extract Effective NN interaction Extraction of rn(r) New method of simultaneous extraction of rp(r), rn(r) 7. Summary and future perspective 2014/10/24 SPIN 2014 2
Point-nucleon density distributions Fundamental information of nuclei; rp(r), rn(r) Nuclear size & shape are helpful for comprehensive understanding of nuclear structure & reaction model, Neutron skin thickness the nuclear matter EOS 58 Ni(e, e) elastic Ø Stable nuclei • Proton density distribution rp(r) : derived from rch(r) – Charge distribution rch(r) : EM probe (simple ) – For example, rch = 208 Pb : 5. 5010(9) fm (0. 02% accuracy) • Neutron density distribution rn(r) : Our work – Hadronic probe (very complicated) – Suffering from large uncertainties Incomplete knowledge of NN interaction inside nucleus Ø Unstable nuclei • Little information about rp(r), rn(r), rch(r) ! Investigate a new method of simultaneous extraction of rp(r), rn(r) : Our work I. Sick et al, PRL 35(75)910, NPA 218(74)509 H. de Vries, et al, ADANDT 36, 495, and so on. 2014/10/24 SPIN 2014 3
Polarized proton elastic scattering ; Nuclear charge Electron scattering e- e- : well established in 1980 s g +Ze Proton scattering @ 300 Me. V P↑ ; Nuclear matter P↑ ? ? meson : our work N+Z 2014/10/24 SPIN 2014 4
Ring cyclotron facility @RCNP Experimental conditions l Scattering observables : ds/d. W, Ay, Q l Beam energy : 295 Me. V l Beam polarization : 70~80% l Energy resolution : <200 ke. V l Angular & momentum transfer range : 8~50 deg. , 0. 5~3. 5 fm-1 l Target : 40 -48 Ca, 58 Ni, 90, 92, 94 Zr, 116 -124 Sn, 204 -208 Pb GR West experimental Hall LAS l scattering chamber l VDCs & plastic scintillators 2014/10/24 l polarized proton beam l SPIN 2014 2 cyclotrons in a coupled mode : AVF (53 Me. V) and Ring (295 Me. V) cyclotron WS beam line in West Exp. Hall Vertically polarized proton beam at Ep = 295 Me. V Achromatic transport on target. Spot size : ~ 1 mm-j 5
How to extract neutron densities from proton elastic scattering? RIA (tr optical potential) C. J. Horowitz, PRC 31, 1340(1985). D. P. Murdock et al. , PRC 35, 1442(1987). Effective NN interaction Modify the RLF interaction to explain real data (58 Ni) + folding input Nucleon density distribution : rp. V(r), rn. V(r), rp. S(r), rn. S(r) output Calculation 2014/10/24 ds/d. W, Ay, Q c 2 method Fixed Ø rp. V(r) : unfolding rch(r) Ø r. S = 0. 96 r. V Free parameter Ø rn. V(r) : minimize the c 2 Experimental data ds/d. W, Ay, Q SPIN 2014 6
Effective NN interaction Medium modification of RLF NN interaction Medium effect Universal form of densitydependent terms At r=0, same as free NN interaction 2014/10/24 H. Sakaguchi et al. , PRC 57, 1749. S. Terashima et al. , PRC 77, 024317. SPIN 2014 7
Calibration of medium effect by 58 Ni l Four free parameters: aj, bj (j=s, w) l rp(r) : unfolding rch(r) l rn(r) = (N/Z)rp(r) Differential cross sections & analyzing powers of 300 Me. V polarized p-58 Ni elastic scattering minimum c 2 search c 2 min/n~10. Calibrated medium effect parameters j aj bj 2014/10/24 s w -0. 044(26) 0. 037(40) 0. 097(13) 0. 075(21) SPIN 2014 8
Extraction of neutron densities of Pb isotopes proton elastic scattering from 204, 206, 208 Pb l Fixed medium effect parameters by 58 Ni data: aj, bj (j=s, w) l rp(r) : unfolding rch(r) l rn(r) : SOG model independent function Fixed : g, Ri (same as rch(r)) Free parameters : Qi (i=1~12) minimum c 2 search reduced c 2 min ~ 4. 2014/10/24 SPIN 2014 9
Error-envelope of rn(r) l Error-envelopes due to exp. errors : c 2 ≦ c 2 min + Dc 2. ~11 l Comparison with previous rn(r) : 3 parameter-Gaussian (3 p. G) by L. Ray (Ref. [58]) 208 Pb case percent deviation 0. 06 fm (1%) rn type c 2/n (n=47) rn (fm) 3 p. G 255/47=5. 4 SOG 192/47=4. 1 5. 653(30)stat. 2014/10/24 5. 593 SPIN 2014 10
Extraction of rn(r) Polarized proton elastic scattering at 300 Me. V (Ring cyclotron facility at RCNP, Osaka University) ⇒We have succeeded in extracting neutron density distributions of Sn, Pb isotopes systematically. Stable nuclei : rp is known. Sn Drnp rn(r) ds/d. W, Ay S. Terashima et al. , Phys. Rev. C 77, 024317 (2008) Pb RIA + Medium modification Drn/rn < 0. 5% J. Zenihiro et al. , Phys. Rev. C 82, 044611 (2010) 2014/10/24 SPIN 2014 11
Simultaneous extraction from twoenergy p-elastic data For stable nuclei ; Nuclear charge Electron scattering e- e- : well established in 1980 s g +Ze Proton scattering @ 300 Me. V p ; Nuclear matter p meson : our work N+Z 2014/3/5 WS @ kyushu-u 12
Simultaneous extraction from twoenergy p-elastic data For unstable nuclei Proton scattering @200 Me. V p p meson N+Z Proton scattering @ 300 Me. V p p meson N+Z 2014/10/24 SPIN 2014 13
Energy dependence of NN interaction and Nuclear potential Expecting… 1. pp & pn interactions are different and have different energydependences from each other. 2. Central part (Vc) of optical potentials Central part of nuclear optical potential changes shallow attractive to shallow repulsive from 200 to 300 Me. V (-5 ~ 10 Me. V), while the nuclear Coulomb potential does not change and relatively large (> 10 Me. V) Scattering observables are really sensitive to both densities? 2014/10/24 SPIN 2014 14
Test experiment at RCNP (E 366) Obtained data of 90 Zr, 58 Ni @ 200, 300 Me. V Blue : original RIA Red : RIA with realistic rp & rn =rp *N/Z Calibrate effective NN interaction @ 200 Me. V For 300 Me. V already calibrated by previous work ↓ 2014/10/24 SPIN 2014 J. Zenihiro et al. , Phys. Rev. C 82, 044611 (2010) 15
Some results Fitting results for 90 Zr @ 200 & 300 Me. V Extracted densities of 90 Zr Simultaneous search of Neutron & Proton Pr ary in lim e r P y r a in m i el From 300 & 200 Me. V data rn rp 4. 300(17) 4. 210(20) 2014/10/24 SPIN 2014 Drnp 0. 090(26) 16
Summary • For stable nuclei – We developed a new description of effective interaction in the framework of RIA, and which is very successful. – Proton density distributions can be derived from nuclear charge distributions – We succeeded in extracting rn(r) of Pb, Sn isotopes from polarized proton elastic scattering • For unstable nuclei – New method has been developed to extract both rp(r), rn(r) from two-energy proton elastic scattering data. – Feasibility test experiment has been done and the preliminary result shows that this method works very well! 2014/10/24 SPIN 2014 17
Ongoing & future • ESPRI project (Elastic Scattering of Protons with RI beam) has been already launched. – Detector development and test using RI beam has been done at HIMAC, Chiba and GSI, Germany. – 1 mm-t & 30 mm-f p. SHT [Y. Matsuda, et al. , NIMA 643, 6(2011)] – Excitation energy resolution ~ 500 ke. V(s) • ESPRI experiments @RIBF, RIKEN, Japan – NP 0709 -RIBF 40 : 16 C at 300 Me. V/u (light unstable nuclei) Successfully done in FY 2013! – NP 1112 -RIBF 79 : 132 Sn at 200&300 Me. V/u Approved. • Experiment will be performed in FY 2015 • The new method will be adopted. • neutron skin thickness of 132 Sn will constrains the symmetry energy. 2014/10/24 SPIN 2014 18
4. ESPRI detectors Recoil Proton Spectrometer (RPS) Solid hydrogen target 1 m L〜 Drift Chamber θlab = 66° - 80°, Ep=20 -120 Me. V, ΔΩ〜 10 msr/deg. q=1 -2. 2 fm-1, ΔEx = 400 -500 ke. V Recoil drift chamber Plastic scintillator Na. I(Tl) calorimeter 2014/3/5 1 mmt φ30 mm 436 x 436 mm 2 (x-y-x’-y’-x’-y) 440 x 440 mm 2 x 2 mmt 431. 8 x 45. 72 mm 2 x 50. 8 mmt WS @ kyushu-u 19
Elastic Scattering of Protons with RI beams (ESPRI) project Collaborators S. Terashima (Beihang Univ. ) Y. Matsuda (RCNP) H. Sakaguchi (RCNP) H. Otsu (RIKEN) T. Baba (Kyoto Univ. ) RIKEN H. Takeda K. Ozeki K. Yoneda Tohoku Univ. T. Kobayashi 2014/10/24 Kyoto Univ. T. Kawabata T. Murakami M. Tsumura T. Furuno Miyazaki Univ. Y. Maeda SPIN 2014 RCNP I. Tanihata H. Jin Ong GSI S 272 collaborators NIRS E. Takada M. Kanazawa 20
Thank you! 2014/10/24 SPIN 2014 21
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protons & neutrons in a nucleus Nucleus is finite quantum many-body system made from 2 different fermions, p & n. How are nucleons (p, n) distributed in a nucleus? : rp, rn fundamental and direct information to constrain nuclear structure or reaction models Shell structure Saturation property Halo, skin structure nuclear matter EOS with isospin asymmetry Neutron skin thickness vs. Symmetry energy 2014/10/24 SPIN 2014 24
300 Me. V proton Good probe to extract interior information of nucleus pp total cross section – Interact with both neutrons and protons – long mean free path (~2 fm) interior structure ( surface structure) np total cross section – one-step reaction is dominant simple description ; successful Relativistic Impulse Approximation (RIA) 2014/10/24 SPIN 2014 25
RIA framework • Dirac tr-optical potential : single folding of NN amplitude (t) & densities (r) – NN amplitude; 10 mesons’ coupling including both direct & exchange terms are tuned by free NN phase shift analysis(RLF model by C. J. Horowitz) – For spin-0 nucleus only Scalar & Vector component remain Relatively good agreement with p-A scattering data, particularly, analyzing powers above 100 Me. V • Not enough to extract densities Need effective NN interaction inside nuclear medium 2014/10/24 SPIN 2014 D. P. Murdock and C. J. Horowitz, PRC 35, 1442. C. J. Horowitz and B. D. Serot, NPA 368, 503. H. Sakaguchi et al. , PRC 57, 1749. 26
Calibration of medium effect by 58 Ni Various experimental & theoretical results say : 58 Ni 2014/10/24 SPIN 2014 27
rp rn Drnp DME+D 1 3. 68 3. 67 -0. 01 PRC 21, 1568(1980) HF-BCS+SIII 3. 738 3. 732 -0. 006 NPA 603, 23(1996) HF-BCS+Sk. M* 3. 722 3. 720 -0. 002 PRC 33, 335(1986) HF-BCS+SGII 3. 719 3. 697 -0. 012 PRC 72, 044307(05) RMF+NL 3 3. 652 3. 691 0. 040 ADNDT 71, 1(1999) RMH+RH 3. 652 3. 691 0. 039 NPA 368, 503(1981) Glauber 3. 763(50) 3. 72(5) -0. 043(70) PLB 67, 402(1977) Glauber 3. 67(5) 3. 60(5) -0. 07(7) PLB 72, 33(1977) Glauber 3. 763(50) 3. 75(10) -0. 01(7) NPA 360, 233(1981) 1 st KMT 3. 688 3. 652(74) -0. 035(74) PRC 18, 2641(1978) 2 nd KMT 3. 686 3. 700(50) 0. 014(50) PRC 19, 1855(1979) p atom - - -0. 09+0. 09 -0. 16 PRL 87, 082501(01) 3. 680 0. 000 58 Ni This work 2014/10/24 SPIN 2014 Ref. 28
Estimation of error-envelopes of rn(r) l c 2 min/n ~ 4 : incompleteness of theoretical model as well as unknown experimental systematics l Error-envelopes due to model uncertainties : S realizes c 2 min/n = 1. Total error-envelope 2014/10/24 SPIN 2014 29
Neutron root-mean-square radii l 2 types of errors of rn : due to experimental errors only (drnstd) ~ 0. 5 % total errors including model & unknown systematic uncertainties (drnmdl) ~1 % Extracted rn, drn (all in fm) rch rn 204 Pb 5. 479(2) 5. 420(2) 5. 598 206 Pb 5. 490(2) 5. 433(2) 5. 613 208 Pb 2014/10/24 rpunfold 5. 503(2) 5. 442(2) SPIN 2014 5. 653 drnstd drnmdl +0. 029 +0. 047 -0. 020 -0. 059 +0. 026 +0. 048 -0. 026 -0. 064 +0. 026 +0. 054 -0. 029 -0. 063 30
The symmetry energy coefficients deduced from Drnp for 204, 206, 208 Pb l Deduced region of the symmetry energy coefficients : weighted average S(rsat) = 33. 0± 1. 1 Me. V L = 67. 0± 12. 1 Me. V comparable with previous studies but still large !!Note that 3 ranges in plot are due to experimental errors only!! 2014/10/24 SPIN 2014 31
Simulation results of simultaneous extraction of rp(r), rn(r) Simulation results from pseudo-data (ds/d. W, Ay) of 208 Pb, 14 C(p, p) at 200, 300 Me. V with ~5% experimental errors. dr/r ~ 0. 35% dr/r ~ 0. 8% 208 Pb 14 C Z=82 Z=6 Best fit (solid) Input (dashed) Error envelope from 5% exp. errors proton neutron Fixed : g, Ri (same as rch(r)) Free parameters : Qi (i=1~12) 2014/10/24 SPIN 2014 32
The case of unstable nucleus; 132 Sn u Test of simultaneous extraction of rp(r), rn(r) of 132 Sn from pseudodata of differential cross sections u Using RIA and relativistic-Hartree g. s. (input) g. s. (extracted) calculations as nucleon density rn 4. 916 4. 907(23) distributions. r 4. 650 4. 612(49) p Drnp 0. 266 0. 295(54) dr/r 0. 46% 1. 0% -- 132 Sn 2014/10/24 SPIN 2014 33
Extraction of densities of 90 Zr Very preliminary !! Fitting results for Search rn of 90 Zr Comparison of 3 ways Neutron & Proton li re p y Neutron Ø Ø Ø 300 Me. V 200 Me. V both Proton y From 200 Me. V r Ve From 300 & 200 Me. V data 2014/10/24 only From 300 Me. V Simultaneous search of ar n i m 90 Zr SPIN 2014 Radius (fm) 34
Extracted radii and skin of 90 Zr Very preliminary !! c 2/n rn rp Type III 262/45 218/53 488/98 4. 285(16) 4. 300(22) 4. 200 Drnp 0. 085(16) 0. 100(22) 4. 300(17) 4. 21(2) 0. 090(26) (all in fm) Type I : 300 Me. V data only Type II : 200 Me. V data only Type III : 200 & 300 Me. V data * Errors are experimental only! 2014/10/24 SPIN 2014 35
Recoil proton spectrometer (RPS) RI 2014/10/24 SPIN 2014 36
ESPRI measurement for 16 C Kinematical correlation plot beam profile on SHT e n i l On [Photo] [Data] Plastic (pd. E) QDC Clear identification of recoil protons d. E-TOF d. E-E e n i l n O Recoil proton energy [Me. V] SH(16 C, p)*C e n i l n O inelastic Recoil proton angle [degree] Analysis is ongoing. Plastic TDC 2014/10/24 Na. I(Tl) ADC SPIN 2014 37
Summary 1. ESPRI @ HIMAC, Chiba and GSI, Germany. Successfully done! ü HIMAC-P 179&P 213 : 9 C, 10, 11 C, 20 O (FY 2007 -2009) [Y. Matsuda, et al. , Phys. Rev. C 87, 034614(2013)] ü GSI-S 272 : 66, 70 Ni (FY 2009 -2010) 1 mm-t & 30 mm-f p. SHT [Y. Matsuda, et al. , NIMA 643, 6(2011)], energy resolution of ~500 ke. V(s) still large experimental errors due to low statistics 2. Test of the simultaneous extraction of rp(r) & rn(r) from proton elastic scattering data at 200, 300 Me. V/u ü two-energy analysis method is now being developed with stable nuclei. ü RCNP-E 366 : 90, 92, 94 Zr (FY 2012) p RCNP-E 375 : 12, 13, 14 C (FY 2013 -2014) feasibility test experiment (E 366) shows good results. 3. ESPRI @ RIBF with high-intensity RI beam ü NP 0709 -RIBF 40 : 16 C at 300 Me. V/u (light unstable nuclei; successfully done in April 2013!) p NP 1112 -RIBF 79 : 132 Sn at 200&300 Me. V/u (heavy unstable nuclei; approved by 2011 NP-PAC) p Detectors are now being developed. p Will be performed in 2015 (14 days). 4. Stable nuclei ü p 5. Neutron densities of Sn & Pb isotopes, neutron skin of 208 Pb Neutron skin of 48 Ca, 90 Zr Future work? p 2014/10/24 HI+HI elastic scattering r~ 2 r 0 : T. Furumoto, et. al, . PRC 85, 044607(2012) SPIN 2014 38
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