Properties of Nuclei deduced from the Nuclear Mass

Transcription

1 Properties of Nuclei deduced from the Nuclear Mass -the 2nd March 16-20, 2015 Yoshitaka Fujita Osaka University Image of Nuclei Our simple image for Nuclei!? Nuclear Physics by Bohr and Mottelson Cover page (1969) 1

2 Mass Parabola (for A=106 Nuclei) unstable stable odd-odd & even-even: energies (masses) are different by 2 odd-odd Pairing Int. is Important! even-even Z mass represents the overview! E = mc 2 2

3 Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! Nuclear Binding Energy (per nucleon) Fe,Ni Sn Energy Pb U, Th, Energy Energy release light nuclei: by Fusion heavy nuclei: by Fission 3

4 Volume Surface Radius Nuclear Volume : proportional to mass A Surface : A 2/3 Radius : A 1/3 Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! 4

5 Coulomb Force: Combination of Protons Permutation & Combination The number of combination r = 2 n C 2 = (1/2) n(n-1) Coulomb int.: Think of Coulomb Interaction among Protons *Coulomb Interaction: two-body interaction a long range force *- sign: repulsive Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! 5

6 Saturation of Nucleon Density in Nuclei Net density: (r) = A/Z ch (r ) R=r 0 A 1/3 *Charge Density can be easily studied by (e,e ) due to the short range nature of nuclear interaction due to the intermediate mass of pion (~135 MeV) therefore, the two-body Nucleon-Nucleon int. is dominant! therefore, the mass term is proportional to mass number A Nuclear Chart Most stable Z as a function of A Z becomes smaller than (1/2)A as A increases! 6

7 Nuclear Binding Energy -Overview- Fe,Ni Sn Pb U, Th, Why smaller B.E.? mainly due to the repulsive Coulomb Energy Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! 7

8 Nuclear Binding Energy -Surface Energy- Sn U, Th, Pb Fe,Ni Smaller B.E. due to the Surface Energy! round shape is preferred! is tightly bound cluster structure! Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! 8

9 Symmetry Energy Symmetry Energy prefers N=Z! proton, neutron: both are Fermions! 40 Ca is the last stable nucleus with N=Z Filling of Shells Additional neutrons would occupy higher-energy shells! Protons Neutrons 9

10 Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Binding energy =N - Z *mass term surface term Coulomb term **symmetry term pairing term (even-odd term) * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! Mass Parabola (for A=106 Nuclei) unstable stable odd-odd & even-even: energies (masses) are different by 2 odd-odd Pairing Int. is Important! even-even Z 10

11 Nuclear Chart rare! stable odd-odd 10 B, 14 N A=5, 8 are missing! Only 3 He is above the N=Z line Z for each A only one nucleus is stable even Z or N are favored at most N Terms in Mass Formula and Interactions (Correlations) in Nuclei Mass Surface Coulomb Symmetry Pairing Main part of the Nuclear Interaction is short range! Coulomb Interaction is Strongly p-n Interaction is Important. p-p, n-n Interactions are Important. Main part of the NI is Attractive Coulomb force is Repulsive. p-n int. is Attractive p-p, n-n int. is Attractive 11

12 Contribution of Various Terms Relative weight in the BE Symmetry energy/nucleon Coulomb energy/nucleon Surface energy/nucleon Remaining BE/nucleon mass A Good correspondence of shapes! Nuclear Binding Energy -Shell Effect- Fe,Ni Sn Pb U, Th, Zigzag of the B.E. Nuclear Shell effect 12

13 ABUNDANCE (Si = 10 6 ) H, He C, O Solar Abundance Fe,Ni solar abundance distribution MASS NUMBER Ba Pb Mass Parabola (for A=106 Nuclei) unstable stable odd-odd & even-even: energies (masses) are different by 2 Pairing Int. is Important! odd-odd 106 Cd: -nucleus even-even Z 13

14 Mass Relationship in -decay Nuclei A mass A system Requirements for -decay system *initial & final: even-even ( so-called stable ) *intermediate: odd-odd ( -unstable) There are 35 candidates! Mass Relationship in -decay Nuclei 14

15 Candidates of -decay Nuclei List of Good -decay nuclei by K. Zuber Larger Q value (phase space) is needed! 15

16 Candidates of -decay Nuclei -modes (A,Z) (A,Z-2) + 2 e + (+2 e ) Q - 4m e c 2 16

17 Binding Energy (A: log scale) Binding Energy/ Nucleon 4 He has a large B.E.! Mass Number -particle: Component of Cluster States in Nuclei -decay : 2 protons, 2 neutrons J = 0 + follow the Bosonic statistics is a good cluster component a heavy nucleus 17

18 Role of Hoyle state in the formation of 12 C Hoyle state: dilute cluster gas Mass and Binding Energy of Nuclei Nuclear mass Bethe-Weizsäcker mass formula Strong Int. Binding energy EM Int. Strong Int. =N - Z *mass term surface term Coulomb term **symmetry term pairing term There is no term from the Weak Interaction (even-odd! term) The contribution is small. However, it has the function to change the charge of nucleons. proton neutron. * mass term shows that the nuclear force is short range! **symmetry term originates from the Pauli exclusion principle for fermions! 18

19 proton =uud Importance of field (potential E): nucleon mass vs. quark mass neutron =udd ~10-15 m nucleon mass : ~940 MeV pion mass: ~140 MeV u-quark mass: 3 MeV d-quark mass: 6 MeV The quark mass is only ~1% of the nucleon mass! Where is the other part of the mass (energy)? (E = mc 2 ) Ans: Potential Field The field of the strong interaction (gluon field)carries the main part of the energy! Nucleon mass = kinetic energy of quarks + potential energy (gluon cloud) + (small)quark mass (quark size < m) Nucleons are almost empty! Matter is made by quarks and electrons! To which extent a human being is quark? Quark mass: <1% Volume: <10-36 The Mass and the Volume is carried by the field (interaction)! Matter is almost empty! 19