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.