Quantum tunnel effect and alpha-decay of nuclei

1. Quantum tunnel effect and alpha-decay of nuclei • Zhongzhou REN • Department of Physics, Nanjing University, Nanjing, China • Center of Theoretical Nuclear Physics, • National Laboratory of Heavy-Ion Accelerator, Lanzhou, China

2. Outline • Introduction • Microscopic calculations on superheavy nuclei • Spherical generalized density-dependent cluster model • Deformed generalized density-dependent cluster model • Summary

3. Alpha of nuclear physics: 1896-1930 • Discovery of radioactivity: Becquere. • Identify Po and Ra by Curies. 1903…年。 • Alpha, Beta, gamma rays: Rutherford. • Existence of nucleus by alpha scattering • The size of nucleus by alpha scattering • Quantum mechanics for alpha decay: Gamow, 前苏联—丹麦---美国

4. Introduction The study on α decay dates back to the early days of nuclear physics. It, although one of the oldest objects of study in nuclear physics, remains an attractive decay mode. Proton radioactivity (Z≥51) Alpha decay (Z≥52) Cluster radioactivity (Z≥87) Spontaneous fission (Z ≥90)

5. There are more than 400 nuclei in the periodic table that exhibit the alpha-decay phenomenon.

6. It has been used as a reliable way to identify new synthesized elements and isomeric states.

7. It provides new information on the variety of shapes (i.e., shape coexistence).

8. Talk toady: 2 students. • Begin researches in 4th year (undergraduate) • Then become graduate student in my group • One: 3.5 year for Ph. D. Then assoc. Prof. in 2008 (Chang XU). • Another: second year (Dongdong Ni) .

9. List of Publications (Second:1+1) • D. Ni, Z. Ren et al.Phys. Rev. C 78, 044310 (2008). • (2) D. Ni and Z. Ren Eur. Phys. J. A 38, 251 (2008). • (3) D. Ni, L. Wei, Z. Ren Commun. Theor. Phys. 51, 713 (2009). • (4) D. Ni and Z. Ren Nucl. Phys. A 825, 145 (2009). • (5) D. Ni and Z. Ren Nucl. Phys. A 828, 348 (2009). • (6) D. Ni and Z. Ren Phys. Rev. C 80, 014314 (2009). • (7) D. Ni and Z. Ren Phys. Rev. C 80, 051303(R) (2009).

10. Nuclear physics: bright future • First student: strong with other field. • Second student: also strong • Third: 澳门科技大学, 因我推荐核物理. • assistant professor, high salary. • Tiekuang Dong • All in Nanjing now( Texas, Macao,圣诞)

11. Quantum theory for alpha decay • Gamow: qualitative quantum tunnel effect • Explain the Geiger-Nuttall law • Quantative calculation of half-lives: • 1. Buck et al, 1990s • 2. Royer et al, 2000s…. • semi-classical, quasi-classical Quantiza.

12. V(r) Q 0 r Rt RC V0 理论计算alpha衰变寿命 1. 唯象模型: (1) Geiger-Nuttall 规律 (2) Viola-Seaborg 公式 …… 2. 理论近似 (半经典): (1) 结团模型 (2) ……

13. WKB way of density-dependent cluster model The depth of the nuclear potential is determined by applying the Bohr-Sommerfeld quantization condition. The polar-angle dependent penetration probability of alpha-decay is evaluated in terms of the WKB semiclassical approximation

14. New way for calculations of half-lives The α-decay process is described by the quantum transition of an alpha cluster from an isolated quasibound state to a scattering state.

15. To solve S-equation for Q-B state • Quantum mechanics: 源atomic physics • Hydrogen-atom: bound (B) state and scattering (S) • Real: quasi-bound state, finite lifetime • Nuclei: 4He, 16O, 208Pb, g.s., bound. • 238U, 235U, quasi-bound state • 多数量子力学书不讲 : ( Q-B) state.

16. (I) Heavy and superheavy nuclei (Woods-Saxon shape potential) (II) Medium mass nuclei and N=126 closed-shell region nuclei (spherical generalized density-dependent cluster model) (III) Systematic deformed calculations (deformed generalized density-dependent cluster model) Research objects: 3 steps

17. Heavy and superheavy nucleiNPA 825 145-158 (2009)

18. Woods-Saxon shape nuclear potentials V0 is determined by the characteristic of the alpha-cluster quasibound state.

19. The number of internal nodes is determined by the Wildermuth condition Behaving like the irregular Coulomb wave function

21. Comparison of experimental alpha-decay half-lives and theoretical ones for even-even nuclei with N>126 log10(Tcal/Texp): 0.3, 0.4, and 0.5 Tcal/Texp: 2.0, 2.5, and 3.2

22. Superheavy nuclei with Z=106-118 (e-e)

23. Five recently studied decay chains (o)

24. Generalized density-dependent cluster model GDDCM is a new model of alpha decay: • 1) effective potential based on the Reid potential • 2) low density behavior included • 3) exchange included • 4) microscopic calculation of decay widths • 5) agreement within a factor of three

25. Spherical GDDCM The effective potential between alpha clusters and daughter nuclei is obtained from well-established double folding model. The effectiveM3Ynucleon-nucleon interaction is used in the generalized density-dependent cluster model

26. The density distribution of the spherical alpha-particle is The density distributions of the spherical core has a Fermi form is fixed by integrating the density distribution equivalent to mass number of nucleus.

27. Comparison of experimental alpha-decay half-lives and theoretical ones for medium mass nuclei

28. N=126 closed-shell region nucleiPRC 80 014314 (2009)

30. 形变核alpha衰变示意图 6+ E6 Jπ= 0+ 4+ E4 Q0 2+ E2 0+

31. 推广的密度依赖集团模型 真实的M3Y-Reid核子相互作用 ——推广的密度依赖集团模型(GDDCM) （1）纯量子模型（用直接求解Schrödinger方程的方法代替WKB半经典近似） （2）考虑了原子核在表面区域的弥散行为 （3）Pauli不相容原理

33. Ground-state-to-ground-state transitions

34. Survey of the observed alpha transitions to both ground states and excited states around the N=126 shell gap

35. Ground-state-to-excited-state transitions

36. Deformed GDDCM In the generalized density-dependent cluster model, we consider a spherical alpha-particle interacts with a deformed daughter nucleus which has an axially symmetric nuclear shape. The decay process is described by the tunneling of the α particle through a deformed potential barrier.

37. The microscopic deformed potential is numerically constructed in the double folding model by the multipole expansion method. The matter or charge density distributions of the deformed core has a Fermi form

38. It is worth noting that the parameter values describing the matter or charge density distributions of nuclei do not change with the transition from the spherical case to a deformed one. The double folding model involves a complex six-dimensional integral which cannot be reduced to fewer dimensions by the common Fourier transformation technique. In this case, the multipole expansion method is used, where a large number of numerical computation and complicated derivations are involved.

39. In the multipole expansion, the density distribution of the axial-symmetric daughter nucleus is expanded as The corresponding intrinsic form factor has the form Then the double folding potential can be evaluated as the sum of different multipole components

40. The multipole components are written as For the Coulomb potential, the renormalized factor λis taken to be λ=1, and the density distribution of daughter nuclei is their charge density distribution rather than their matter density distribution.

41. 耦合Schrödinger方程

42. GDDCM 我们用双折叠模型计算alpha粒子与子核之间的相互作用势,其中核子-核子相互作用势采用M3Y-Reid形式 M3Y-Reid有效核子核子相互作用

43. 微观形变势 对于Alpha粒子的密度分布，我们采用标准的高斯形式 对于形变子核，它的质量（或电荷）密度分布具有各向异性，我们在费米分布的基础上，引进了对形变和空间角度的依赖。

44. Partial decay width At large distances R Half-life Branching ratio

45. Schematic plot of two-channel wave functions in the emitter 242Cm

46. Branching ratios for transitions from g.s. to g.s.

47. Schematic diagram of different terms in the alpha decay of the nucleus 242Cm

48. The relation between nuclear deformations and partial α-decay half-lives 174Os β2= 0.226 β4 = -0.006 254Fm β2= 0.245 β4 = 0.026 Möller et al.,s calculationCorrespond to the daughter nucleus

49. Comparison of calculated half-lives with the experimental data

50. Comparison of experimental alpha-decay half-lives and theoretical ones for even-even nuclei (Z= 52−104)