Superdeformed oblate superheavy nuclei - mean field results

1. Introduction – some features of exotic shapes

2. Decay modes & possibility of K-isomers

3. Selfconsistent results

4. Conclusions & possible other exotic SHs

work done with Piotr Jachimowicz and Michał Kowal [PRC 83 (2011) 054302]and with Michał Warda.

136 144 152 160 168 176 184 192

98100102104106108110112114116118120122124126 min

20

-0.50-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.0500.050.100.150.200.250.30

N

Z

SDO

OBLATE

PROLATE

SPHERICAL

1 .0 0 .5 0 .5 1 .0Y

0 .6

0 .4

0 .2

0 .2

0 .4

0 .6

Z

Ground state shapes

20

:

0.5

3.

2

SDO

Axis ratio

SDO minima

-3.5-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0

-1.0

0

-1.5

0.50.5

-2.0

-2.5

1.0

1.0

-4.0

1.5

-3.0-4.5 -3.5

0.5

1.0

-1.5

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2 cos ( )

2 s

in ( )

116166

-3.5

-3.5-3.0

-2.5-2.0

-1.5-1.0

-1.0

-0.5

0

-0.5

-1.0

0

-1.5

-2.0

0.5

-2.5

0.5

-3.0

1.0

1.0

1.5

-4.0

0.5

1.0

-2.0

1.5

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2 cos ( )

2 s

in ( )

118166

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

-1.5

-1.0

-0.5

-0.5

-1.0

0

-1.5

-2.0

0.5

-2.5

-3.0

1.0

0.5

-3.5

1.5

0

0.5

-2.0

1.0

-2.5

1.5

-3.0

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2cos ( )

2 s

in ( )

120166

-2.5-2.0

-1.5

-1.0-0.5

0

-1.0

-0.5

-0.5-1.5

-1.0

0

-1.5

-2.0

0.5

-2.5

-3.0

1.0-2.5

-3.5

0

1.5

0.5 1.0

-3.0

1.5

-3.5

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2 cos ()

2 s

in ()

122166

-1.5

-1.0

-0.5

0-1.0

-0.5-1.0

-1.50

-1.5

-2.0

-2.0

0.5

-2.5

-2.5

1.0

-3.5

-3.0

-0.5

0.5

-2.0

1.0

-2.5

-3.5

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2 cos ( )

2 s

in ( )

124166

-1.0

-0.5

-1.5

-1.5

0

-0.5

0

-2.0

-2.0

-2.5

0.5

-2.5

-3.0

-1.5

-3.5

-3.0

1.0

-1.0

-1.0

0.5

-1.5

1.0

-2.0

-3.5

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

0.4

min. in: (aaa,a

2 cos ( )

2 s

in ( )

126166

0.00.1

0.20.3

0.40.5

0.0

0.1

0.2

0.3

0.4

-5-4-3-2-1012

288122

sin ()

cos ()E

(MeV

)

-5.5

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.52.0

SDOMINIMUM

OBLATEMINIMUM

SP III

SP II

SP I

Fission

0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0288122

E (

Me

V)

Path length

min. in: (ccc,c

SDO (g.s)

SADLE POINT

EXIT

Tsf~10-5s

-2.5

-2.0

-1.5

-1.5

-1.0 -0.5

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

-3.5

-1.0-0.5

-1.5

0

-2.0

-4.0

0.5 0-2.5

1.0

-4.5

1.5

-5.0

-3.0

0

0.5

-2.5

1.0

-3.0

1.5

-3.5

-3.0

0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.1

0.2

0.3

0.4

min. in: (ccc,c

288122

cos ()

sin

()

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-4

-3

-2

-1

0

min (3,

4,

5,

6,

7,

8)

288122166

E(M

eV)

20

Tsf~1012

Alpha decay

• Formula a’laViola Seaborg from Royer

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4-5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.0

Q=15.2 MeV

Log(T[s]) =-9.1

E(M

eV)

2

Z=118, N=164 Z=120, N=166

Q=13.2 MeV

Log(T[s]) = -5.5

Alpha decay of Z=120 isotopes

156 158 160 162 164 16612.5

13.0

13.5

14.0

14.5

15.0

15.5

Q(

MeV

)

N

GS(SDO) -> GS(PROLATE) GS(SDO) -> EX(SDO)

Z=120

156 158 160 162 164 166-9.5

-9.0

-8.5

-8.0

-7.5

-7.0

-6.5

-6.0

-5.5

-5.0

GS(SDO) -> GS(PROLATE) GS(SDO) -> EX(SDO)

Z=120lo

g10

[T 1/

2 (s

)]

N

One proton emission half livesapprox. from Nucl. Phys. A 611(1996) 211

Beta decay2 2

2 2 2 2 4233

2

2.42 ( ) .( )

mcF

e

m ce

GM mc E E m c EdE

c

, , 1( ),

e A Z A ZQ m m m m m

* 3

2

2 2 5

( ) ( )

1

0.1 10

n p

e

F

M r r d r

For Q m c

M G Q

and M

T s

Since for high-K isomers |M| is reduced, their beta+ decay is even slower.

A fascinating possibility for their longer life-times is related to K-isomerism, high-K configurations at the SDO shape are

very likely.

-15/2 -9/2 -3/2 3/2 9/2 15/2

-12

-10

-8

-6

-4

-2 SDO-MIN 286120

NEUTRONS

n(M

eV)

Fermi level

-15/2 -9/2 -3/2 3/2 9/2 15/2

-4

-2

0

2

4

6

8

PROTONS SDO-MIN 286120

p(M

eV)

Fermi level

(13/2-)+(7/2+)=>10-(15/2+)+(9/2-)=>12-

OPTIMAL CONFIGURATION:

K=22+

• Probable configurations in neighbouring nuclei (A,Z):

• 285,119 : 13/2-• 285,120 : 15/2+• 284,119 : 14-

Gallagher rule for the low-lying state: sigma_1 + sigma_2 =0.

Check for the chosen configuration: sigma_1 sigma_2 sumNeutrons: 15/2+ 0.44 ; 9/2- -0.44; 0Protons: 13/2- 0.10 ; 7/2+ -0.16; -0.06.

Effects of the K-isomerism

FISSION HINDRANCE:• T_{sf} for odd and odd-odd heavy and superheavy nuclei

are by 3-5 orders longer than for their even-even neighbours.

• An increase was found for high-K isomers, with respect to (prolate) shape isomers on which they are built, in even 240-244Cm.

For SDO superheavy K-isomers two factors combine to increase fission half-life:

A) the axial fission path is closed by the conservation of the K quantum number.

B) triaxial barriers increase due to a decrease in pairing caused by the blocking of two neutrons or protons.

Additional hindrance of fission is expected for configurations involving blocked high-Omega intruder states.

ALPHA DECAY HINDRANCE:

High-K isomer in 270Ds has longer (partial) half-live T_{alpha}= 6.0 ms than the g.s., T_{alpha}(g.s.)=100 microsec.

For SDO nuclei, an additional hindrance may result from

• a difference between the parent and daughter high-K configuration,

• an extra excitation in the daughter, leading to a smaller Q_{alpha}.

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=156 N=158 N=160

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV

)

2

N=162 N=164 N=166

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=168 N=170 N=172

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=174 N=176 N=178

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

20

N=180 N=182 N=184

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

20

N=186 N=188 N=190

Z=120

YpE

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=156 N=158 N=160

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=162 N=164 N=166

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=168 N=170 N=172

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

2

N=174 N=176 N=178

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

20

N=180 N=182 N=184

Z=120

-0.6 -0.4 -0.2 0.0 0.2 0.4-6-5-4-3-2-1012

E(M

eV)

20

N=186 N=188 N=190

Z=120

LSD•LSD 1 MeV deeper minima!

NP A 611

Nature

SLy6

Gogny D1

Comparison of self-consistent calculations

-80 -60 -40 -20 0 20 40 60 80

0

2

4

6

8

10

E [M

eV]

Q[b]

N=162 N=164 N=166Sly6

Z=120

-80-60-40-20 0 20 40 60 80

0

2

4

6

8

10

Gogny

Z=120 N=162 N=164 N=166

E[M

eV]

Q[b]

Conclusion

Selfconsistent results confirm the superdeformed

oblate minima in a number of Z>=120, N>=160 nuclei.

If a K-isomer with sufficient EM half-life exists & its alpha-decay is delayed, it may live longer than 10^-5 s, i.e. can be experimentally detected.

Geometrically, SDO states look like equilibria that are transitional between normal oblate configurations and tight toroids – oblate shapes with a sizable central density depression - for even larger Z (and N). Such toroids may be a next possibility for SHN.