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
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
理论计算 alpha衰变寿命 1.唯象模型: (1) Geiger-Nuttall 规律 (2)Viola-Seaborg 公式 ●●●●●● uIM 2理论近似(半经 r(fm 典) ()结团模型 2 rR ●●。● P=e×P(hR ∫v2A()-gdh 12
12 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) …… 2 1 2 exp 2 [ ( ) ] R R P V r Q dr = − − Rt RC 0V(r) V0 Q r
WKB way of density-dependent cluster model The depth of the nuclear potential is determined by applying the Bohr-Sommerfeld quantization condition 丌PR lO-VTotal(R, B)]sin Bd RdB 0 JRI(B) (G-L+1) The polar-angle dependent penetration probability of alpha-decay is evaluated in terms of the WKB semiclassical approximation R3(B) B=exp-2 2 -VTotal(R, B)dr R2(B) 13
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
New way for calculations of half- lives The a-decay process is described by the quantum transition of an alpha cluster from an isolated quasibound state to a scattering state. T=2rkYV;-VrIap)2 m(7)=6( 9(r)= 丌h2k Vi(r)=VN(r)+vc(r)+ C(C+1)b2 V()=V(r)+ +1)b2 2 14
14 New way for calculations of halflives 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: R atomic physics Hydrogen-atom: bound (B)state and scattering (s) Real: quasi-bound state, finite lifetime Nuclei: 4He, 160, 208Pb, g.s., bound 238U, 235U, quasi-bound state 多数量子力学书不讲:(QB) state 15
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