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1. Bulk Properties of Nuclear Mass Formulae 2. R-Process Nucleosynthesis (3

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1. Bulk Properties of Nuclear Mass Formulae 2. R-Process Nucleosynthesis (3 New Era of Nuclear Physics in the Cosmos -the r-process nucleosynthesis, RIKEN, Sep. 25, 25, 2008 核物理から見た宇宙 -rプロセス研究の新時代に向かって 理研2008年9月25-26日 原子核質量公式とr-過程元素合成 Nuclear mass formulae and the r-process nucleosynthesis Hiroyuki KOURA Japan Atomic Energy Agency (JAEA) 1. Bulk properties of nuclear mass formulae 2. r-process nucleosynthesis (3. Effect of β-delayed fission to r-process abundance) 1 Z=114 100 Known nuclides Z Z=82 80 60 Z=50 -1984(2204 nucl.) 40 -1992(2523 nucl.) Z=28 -2000(2817 nucl.) Proton (Atomic) number 20 -2004(2915 nucl.) stable N=28 N=50 N=82 N=126 0 0 20 40 60 80 100 120 140 160 Neutron number N 2 Z=114 100 Known nuclides SHE Z Z=82 80 60 r-process Z=50 -1984(2204 nucl.) 40 -1992(2523 nucl.) Z=28 -2000(2817 nucl.) Proton (Atomic) number 20 -2004(2915 nucl.) stable N=28 N=50 N=82 N=126 Known nuclides: taken from Chart of 0 the nuclides by JAERI 0 20 40 60 80 100 120 140 160 Neutron number N SHE r-process 2 Importance of nuclear masses for the r-process nucleosynthesis Neutron-rich nuclei(A>~ 80)=>quite difficult to measure so far. Q , S , ...=>require to estimate λ ,λn, ... • β n β • Estimations of decay modes of α,βand SF =>important in the SHE region • Nuclear structure (magicity, isomer)=>gives abundance pattern • mass curvature=> reach 3rd peak (+U,Th) or not ．．． • 3 II. Phenomenological Mass Formulas • First-principle calculation Theoretical approaches on nuclear masses (calculation from the realistic nuclear force) first principle第一原理 To treat nuclear masses with the first principle is not appropriate approxi- 現象論system- way from consideration on 近似 mation システマティックスatics properties of nuclear force, many- body force, computational time, modelモデル and accuracy for the present and WB in the near future. Nuclear masses are estimated from various viewpoints for various purposes. 4 Systematics・Phenomenology Z ・Garvey-Kelson-like mass systematics focusing on relation between mass values and Z, N − + + + Comay-Kelson-Zidon, Jänecke-Masson (1988) ≈ 0 + − N ・Empirical shell term focusing on Bulk part (WB-like)+deviation（Shell term） Tachibana-Uno-Yamada-Yamada (1988) ・Phenomenological shell model calculation Polynomials of particle and hole numbers, 100 obliged to assume magic numbers in advance. Liran-Zeldes (1976) 50 ・... 0 0 50 100 150 Properties ・Good reproduction of masses for known nuclei + good prediction for unknown nuclei (quite) near mass-measured nuclides. (300-600 keV) ・No predictable power for superheavy nuclei (next magic number, etc.) ・No deformation is obtained. 5 Hilf-Groote-Takahashi(HGT,1976) Macroscopic part: deformed liquid-drop (Myers-Swiatecki-type) Microscopic part 6 S systematics 50 2n 50 N=20 N=8 Exp.(AW95) TUYY 40 N=20 40 N=28 N=28 N=50 N=82 30 30 N=50 N=126 N=82 N=126 (MeV) (MeV) 20 2n 20 2n S S 10 10 0 0 20 40 60 80 100 20 40 60 80 100 Proton number Z Proton number Z 50 N=20 N=50 GHT 40 N=28 N=82 30 N=126 (MeV) 20 2n S 10 0 20 40 60 80 100 Proton number Z 7 Mass Model, Approximation Recent mass formulas: ・ 310 are designed for nuclei with Z, N=8 to [126]184 or more ・have the RMS dev. from exp. masses. of 600-800 keV ・give deformation parameters β2, β4... and fission barriers ・Density functional theory <- recent project by M.Stoitsov, etc. ・Hartree-Fock method with Skyrme force micro Strong short-range force => δ-function => HF calc. (-like) ETFSI (1995), HFBCS (2001), HFB (2002-) ・Liquid-drop model by S.Goriely Deformed liquid-drop part+Micro. (folded Yukawa) macro+ FRDM (1995), FRLDM (2002), micro ・Mass formula with spherical-basis shell term by P.Möller Phenom. gross (WB-like)+spherical-basis shell part KUTY (2000), KTUY (2005) Koura, Uno, Tachibana, Yamada phenom. 8 (Koura, Uno, Tachibana, Yamada, NPA674, 2000) III. KTUY (KUTY) mass formula (Koura, Tachibana, Uno, Yamada, PTP113, 2005) M(Z, N)=M (Z, N)+M (Z, N)+M (Z, N) gross eo shell M (Z, N): gross term gross 2 2.39 M gross(Z,N)=M HZ+M n N+a(A)A+b(A) N–Z +c( A)(N–Z) / A + EC(Z,N) – k el Z 1/3 2/3 1 a(A)=a1 + a2A− + a3A− + a4(A + αa)− Volume, Surface, etc... 1/3 2/3 1 b(A)=b1 + b2A− + b3A− + b4(A + αb)− Wigner term 1/3 2/3 1 c(A)=c1 + c2A− + c3A− + c4(A + αc)− Asymmetry term Z2 1 E = a (Z, N) 1 0.76C C C A1/3 − x Z2/3 Coulomb with an exchange term ! " M (Z, N): shell term shell Spherical nuclei Calculated from Spherical single-particle potential for any nuclei (includes the BCS paring, reduction) Deformed nuclei (Spherical-basis condieration) Obtained by an appropriate mixture of the above spherical shell energies + liquid-drop deform. energies 9 RMS dev. of masses and separation energies from Exp. Neutron sep. Proton sep. Mass formula Masses Sn S2n Sp S2p Z, N≥2 (2219 nuclei) (2054 nuclei) (1997 nuclei) (2016 nuclei) (1897 nuclei) KTUY03(05) 666.7 keV 352.9 keV 442.0 keV 389.9 keV 532.2 keV KUTY(00) 689.8 keV 389.1 keV 462.4 keV 473.6 keV 558.2 keV Z, N≥8 (2149 nuclei) (1988 nuclei) (1937 nuclei) (1948 nuclei) (1835 nuclei) KTUY03(05) 652.8 keV 316.2 keV 379.1 keV 353.0 keV 490.1 keV KUTY(00) 670.7 keV 339.5 keV 386.5 keV 379.2 keV 499.7 keV FRDM(95) 655.5 keV 399.3 keV 511.7 keV 395.2 keV 493.6 keV HFBCS-1(01) 770.7 keV 451.8 keV 477.3 keV 496.5 keV 603.8 keV 1000 652.8 keV KTUY05 KUTY00 800 379.1 keV FRDM95 HFBCS01 600 316.2 keV 400 200 RMS deviation (keV) 0 Mass S1n S2n S1p S2p 10 S systematics 2n 50 50 N=20 Exp.(AWT03) KUTY02KTUY03KTUY05 N=28 N=50 40 N=8 (even-N) 40 N=20 N=82 30 N=28 N=50 30 N=126 N=126 N=82 (MeV) (MeV) 2n 20 20 2n S S 10 10 0 0 20 40 60 80 100 Proton number Z 20 40 60 80 100 Proton number Z 50 50 N=20 FRDM N=20 N=28 HFBCS 40 N=28 40 N=50 N=82 N=50 N=82 30 N=126 30 N=126 (MeV) 20 (MeV) 20 2n 2n S S 10 10 0 0 20 40 60 80 100 20 40 60 80 100 Proton number Z 11 Proton number Z S systematics 2n 50 50 N=20 Exp.(AWT03) KUTY02KTUY03KTUY05 N=28 N=50 40 N=8 (even-N) 40 N=20 N=82 30 N=28 N=50 30 N=126 N=126 N=82 (MeV) (MeV) 2n 20 20 2n S S 10 10 0 0 Smoothness 20 40 60 80 100 Proton number Z 20 40 60 80 100 Proton number Z 50 50 N=20 FRDM N=20 N=28 HFBCS 40 N=28 40 N=50 N=82 N=50 N=82 30 N=126 30 N=126 (MeV) 20 (MeV) 20 2n 2n S S 10 10 Anomalous 0 Kink 0 Zigzag N=22,30 line 20 40 60 80 100 20 40 60 80 100 Proton number Z N=20,28 gap Proton number Z ->crossing 11->already weak S systematics 2n 50 50 N=20 Exp.(AWT03) KUTY02KTUY03KTUY05 N=28 N=50 40 N=8 (even-N) 40 N=20 N=82 30 N=28 N=50 30 N=126 N=126 N=82 (MeV) (MeV) 2n 20 20 2n S S 10 10 0 0 20 40 60 80 100 Proton number Z 20 40 60 80 100 Proton number Z 50 50 N=20 FRDM N=20 N=28 HFBCS 40 N=28 40 N=50 N=82 N=50 N=82 30 N=126 30 N=126 (MeV) 20 (MeV) 20 2n 2n S S 10 10 0 0 20 40 60 80 100 20 40 60 80 100 Proton number Z 11 Proton number Z S systematics 2n 50 50 N=20 Exp.(AWT03) KUTY02KTUY03KTUY05 N=28 N=50 40 N=8 (even-N) 40 N=20 N=82 30 N=28 N=50 30 N=126 N=126 N=82 (MeV) (MeV) 2n 20 20 2n S S 10 10 0 0 20 40 60 80 100 Proton number Z 20 40 60 80 100 Proton number Z 50 50 30 KTUY03 N=28 N=20 FRDM N=20 N=28 HFBCS 40 N=28 40 20 N=50 N=82 N=50 N=82 N=50 30 N=126 30 (MeV) 10 N=126 2n S (MeV) 20 (MeV) 20 2n 2n 0 S S 10 10N=8 4 8 12 16 20 24 28 (N=16) N=20 (N=32) (N=58) 0 0 N=14,20,28,50 gap 20 40 60 80 100 20 40 60 80 100 Proton number Z 11 ->decreasingProton number Z Light neutron-drip line 16 KTUY05 known RMS dev. : 0.35MeV for Sn nuclides(-2000) 0.44MeV for S2n 12 Notani (02) Z Baumann (07) 42Al 8 S =−0.05 31 n 26O F 4 S =+0.21 Fail to predict 8 nuclei whether bound/unbound 2n S2n=−0.47 22 0 C 31 All the n-sep. energy of these nuclei are within 1.5 19 Ne Proton number C S = 0.31 2n − times of RMS dev.
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