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## Quantum tunnel effect and alpha-decay of nuclei

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**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**Outline**• Introduction • Microscopic calculations on superheavy nuclei • Spherical generalized density-dependent cluster model • Deformed generalized density-dependent cluster model • Summary**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**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)**There are more than 400 nuclei in the periodic table that**exhibit the alpha-decay phenomenon.**It has been used as a reliable way to identify new**synthesized elements and isomeric states.**It provides new information on the variety of shapes (i.e.,**shape coexistence).**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) .**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).**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)**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.**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) ……**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**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.**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.**(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**Woods-Saxon shape nuclear potentials**V0 is determined by the characteristic of the alpha-cluster quasibound state.**The number of internal nodes is determined**by the Wildermuth condition Behaving like the irregular Coulomb wave function**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**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**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**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.**Comparison of experimental alpha-decay half-lives and**theoretical ones for medium mass nuclei**形变核alpha衰变示意图**6+ E6 Jπ= 0+ 4+ E4 Q0 2+ E2 0+**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**Survey of the observed alpha transitions to both ground**states and excited states around the N=126 shell gap**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.**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**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.**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**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.**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**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。**Partial decay width**At large distances R Half-life Branching ratio**Schematic plot of two-channel wave**functions in the emitter 242Cm**Branching ratios for transitions**from g.s. to g.s.**Schematic diagram of different terms in the alpha decay of**the nucleus 242Cm**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**Comparison of calculated half-lives**with the experimental data**Comparison of experimental alpha-decay half-lives and**theoretical ones for even-even nuclei (Z= 52−104)