Description of α-decay of heavy and superheavy nuclei
A. Sobiczewski and A. Parkhomenko
Sołtan Institute for Nuclear Studies, Warsaw
XII Nuclear Physics WorkshopKazimierz Dolny, Sept. 21-25, 2005
Program
1. Introduction 2. Description of Qα
3. Formula for Tα
4. Description of Tα
5. Conclusions
122 124 126 128 130 132 134 136 138 140 142 144 146 148 150
-0,50,00,5
-0,50,00,5
-0,50,00,5
N
Po
-0,50,00,5
At
-0,50,00,5
Rn
-0,50,00,5
Fr
Qth-Q
exp (MeV) Ra
-0,50,00,5
Ac
-0,50,00,5
Th
-0,50,00,5
Pa
U
-0,50,00,5
122 124 126 128 130 132 134 136 138 140 142 144 146 148 150
Np
134 136 138 140 142 144 146 148 150 152 154 156 158
-0,50,00,5
-0,50,00,5
-0,50,00,5
Pu
N
-0,50,00,5
Am
-0,50,00,5
Cm
-0,50,00,5
Bk
Qth-Q
exp (MeV)
Cf
-0,50,00,5
Es
-0,50,00,5
Fm
-0,50,00,5
Md
No
-0,50,00,5
134 136 138 140 142 144 146 148 150 152 154 156 158
Lr
150 152 154 156 158 160 162 164 166 168 170 172 174 176 178
-0,50,00,5
-0,50,00,5
-0,50,00,5
Rf
N
-0,50,00,5
Db
-0,50,00,5
Sg
-0,50,00,5
Bh
Qth-Q
exp (MeV)
Hs
-0,50,00,5
Mt
-0,50,00,5
Ds
-0,50,00,5
112
114
-0,50,00,5
150 152 154 156 158 160 162 164 166 168 170 172 174 176 178
116
Nuclei N
MeV
rms MeV
e-e 61 0.19 0.27
o-e 45 0.27 0.36
e-o 55 0.26 0.36
o-o 40 0.33 0.43
Table 1 exp QQth
Z = 84 -111 N = 128 -161 (201 nuclei)
Phenomenological formula for Tα
log10Tα(Z,N) = a Z (Qα - E)-1/2
+ b Z + c
a = 1.5372 b = 0.1607 c = 36.573
Nuclei n rms np
e-e 61 0.13 0.16 1.3 3 0
o-e 45 0.32 0.41 2.1 1 0.113
e-o 55 0.51 0.60 3.2 1 0.171
o-o 40 0.60 0.72 4.0 0 0.284
]/)(log[ expexp TQT ph
Table 2
Z = 84 -111 N = 128 -161
f E
(201 nuclei)
Nuclei n rms np
e-e 61 0.71 0.95 5.1 3 0
o-e 45 1.09 1.43 12.3 1 0.113
e-o 55 1.04 1.35 11.0 1 0.171
o-o 40 1.24 1.57 17.4 0 0.284
]/)(log[ exp TQT thph
Table 3
Z = 84 -111 N = 128 -161
f E
(201 nuclei)
122 124 126 128 130 132 134 136 138 140 142 144 146 148 150
-2-1012
-2-1012
-2-1012
N
Po
-2-1012
At
-2-1012
Rn
-2-1012
Fr
Ra
-2-1012
Ac
-2-1012
Th
-2-1012
Pa
U
-2-1012
122 124 126 128 130 132 134 136 138 140 142 144 146 148 150
log[Tph(Q
exp)/Texp]
Np
134 136 138 140 142 144 146 148 150 152 154 156 158
-2-1012
-2-1012
-2-1012
Pu
N
-2-1012
Am
-2-1012
Cm -2-1012
log[Tph(Q
exp)/Texp]
Bk Cf
-2-1012
Es
-2-1012
Fm
-2-1012
Md
No
-2-1012
134 136 138 140 142 144 146 148 150 152 154 156 158
Lr
150 152 154 156 158 160 162 164 166 168 170 172 174 176 178
-2-1012
-2-1012
-2-1012
Rf
N
-2-1012
Db
-2-1012
Sg
-2-1012
log[Tph(Q
exp)/Texp]
Bh Hs
-2-1012
Mt
-2-1012
Ds
-2-1012
112
-2-1012
150 152 154 156 158 160 162 164 166 168 170 172 174 176 178
114
116
135 140 145 150 155 160 165 170 175 180 185 190 195
0123456789
1011121314151617
135 140 145 150 155 160 165 170 175 180 185 190 195
Z
1021009896
94104106
108
110112
114
116118120
Qth
(M
eV)
N
130 135 140 145 150 155 160 165 170 175 180 185 190 195-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12130 135 140 145 150 155 160 165 170 175 180 185 190 195
1 y
1 h
1s
1s
Z
114
120
118
114
108
110
108
104100
9694
lo
g(T
ph(Q
th))
/s)
N
5. Conclusions1) Macro-micro calculations describe Qα of heaviest nuclei with an
average accuracy of about 200 keV (e-e nuclei) to 300 keV (o-o nuclei).
2) With a simple (5-parameter) phenomenological formula, one can reasonably desribe Tα of heavy and superheavy nuclei (within approximately a factor of 1.3, 2, 3 and 4 for e-e, o-e, e-o and o-o, respectively).
3) To the total inaccuracy of calculated Tα, the inaccuracy Qα contributes importantly. Due to this, the above factor increases to about 5, 12, 11 and 17, respectively, i.e. by about a factor of 4 to 5.
4) Effects of shell structure of nuclei on Tα are large and well seen in its systematics, for both deformed and spherical nuclei.