ON E0 TRANSITIONS IN HEAVY EVEN – EVEN NUCLEI VLADIMIR GARISTOV, A. GEORGIEVA* Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, [email protected]

ON E0 TRANSITIONS IN HEAVY EVEN – EVEN NUCLEI

VLADIMIR GARISTOV, A. GEORGIEVA*Institute for Nuclear Research and Nuclear Energy,

Sofia, Bulgaria, [email protected]*Institute of Solid Physics, Sofia, Bulgaria

Sofia 2015

This work was partially supported by the Bulgarian NationalFoundation for Scientific Research under Grant Number

№ ДФНИ-Е02/6

Scenario: To make You familiar with our

approaches for the classification of the excited states energies with J = 0+ in the same

nucleus

Parabolic distribution

and classification of the excited states within the Interacting Vector Bosons

Model (IVBM) : energies with the same set of model

parameters and also the estimation of the E0

transition probabilities in this two approaches.

Sofia 2015

Sofia 2015

E [ Me

V ] o

f 0+

excite

d state

s

0 2 4 6 8 10 12 14 16 18 20

Number of Monopole Bosons ( n )

Distribution function

n

Редкоземельные элементы:

58 Ce 60Nd 62Sm 64Gd 66Dy 68Er 70Yb

Актиниды:

90Th 92U 94Pu 96Cm 98Cf 100Fm 102No

Exploration of the energy distributions of excited states with arbitrary J in

the same nucleus

Parabolic distributionEn = a n – b n2 +C

In the case of J = 0+

C = 0

0 5 1 0 1 5 2 0 2 5

0 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

n

0E

ner

gies

MeV

164

162

160

158

156

154

152

Dy isotopes

En = a n – b n2

0 5 1 0 1 5 2 00 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

3 .5

n

MeV 114Cd

0 5 1 0 1 5 2 00

1

2

3

4

5

n

MeV

118Sn

0 5 1 0 1 5

0

1

2

3

4

n

MeV 132Ba

0 5 1 0 1 50 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

n

MeV

156Gd

0 5 10 15 20 25 30

0

1

2

3

4

2.9460 0(+),1,2,3+

3.1789 0(+),1,2,3(+)

3.2120 0(+),1,2,3+

3.3476 0(+),1,2,3+

3.5050 0(+),1,2,3+

3.5425 (0+),1,2,3,4(+)

3.5590 0(+),1,2,3(+)

3.5795 0+,1,2,3,4+

3.6500 (0+),1,2,3,4(+)

3.6985 (0+),1,2,3,4(+)

3.8485 0(+),1,2,3+

3.8595 0(+),1,2,3(+)

3.99254 0(+),1,2,3+

4.0086 0(+),1,2,3(+)

136Ba

= 1.46471 KeV

0.47749630 n 0.014296738486862 n2

0+ ??

Ambiguous spins data

We also had a chance to drag into this affair the experimentalists from

JINR - Dubna: Adam J, Solnyshkin A.A. Islamov T.A.

and ITEP – Moscow:Bogachenko D.D., Egorov O.K. ,

Kolesnikov V.V.,Silaev V.I..

As a result – trusting in our predictions the two new 0+ states

in 160Dy has been observed.

Time to blow ones own trumpet

0.00+

2+

0+

0+

0+

0+

0+

0+

2+

2+ 2503.8

2297.51952.3

1708.2

1456.7

1280.0703.0681.3

86.8

K12

71.0

I K=

0.02

4

159

4.5

I=

0.8182

2.5

I=

0.24

594.5

616.2

K68

1.3

I K=

0.02

4

K70

3I K

=0.

086

160Dy

Observed transitions in 160Dy

Sofia 2015

Adam J et.al. (2014) Bulg. J. Phys.} 41, 10–23.

Why did we impose the restrictions - positive and integer

classification parameter?

the application of the group theory in nuclear physics

To draw attention of theoreticians that work with

Sofia 2015

Ana Georgieva, Michael Ivanov, Svetla Drenska, Nikolay Minkov, Huben Ganev, Kalin Drumev

We found a suitable approach -Interacting Vector Bosons Model (IVBM)

Philosophy of this approachGeorgieva A I, Raychev P and Roussev R, (1982)J. Phys. G: Nucl. Phys., 8, 1377.

Ganev H G, Garistov V P, Georgieva A I and Draayer J P, (2004), Phys. Rev., C70, 054317.

Solnyshkin A A, Garistov V P, Georgieva A, Ganev H and Burov V V (2005) Phys. Rev., C72, 064321.

Georgieva, A.I., Ganev, H.G., Draayer, J.P and Garistov V.P., Physics of Elementary Particles and Atomic Nuclei, 40, 461 (2009).

Garistov V P, Georgieva A I and Shneidman T M, (2013), Bulg. J. Phys., 40, 1–16

Adam J et.al. (2014) Bulg. J. Phys.} 41, 10–23.

Interacting Vector Bosons Model (IVBM)

Peter Raychev, Roussy Roussev, Ana Georgieva

FML,

k,mC1k1mLM uk

um GML,

k,mC1k1mLM ukum

AML,

k,mC1k1mLM uk

um

um, un , n,m

um umum um

sp(4,R) and su(3) algebras are related through the u(2)su(2)u(1) algebra of the pseudo spin T, which is the same in both chains.

λ=2T μ=N/2 -T

To make the analysis of the structureof low lying excited states we need the description of several rotational bands.

Classification of the excited states energies with arbitrary J within the same set of model parameters and also theestimation of the transition probabilities

IVBM confirmed it’s advantages in description of the rotational bands

energies.To bind our new clssification to the

predetermined parameters obtained from the description of rotational bands’ energies

Band’s energies

Here K and N0 marks the belonging to rotational band type

Band’s heads energies

Here N0 specifies the correspondingrotational band head’s type

β - type band’s heads energies

Here N0 specifies the position of rotational band head

N0 = 2 ,4, 6,8, …

Rotational β - band energies

0 5 1 0 1 5 2 0 2 5 3 0

2

4

6

8

1 0

L

MeV

b a n d G d 156

0 5 10 15 20 25 300

1

2

3

4

5

N 0

MeV

D y 156 0

IVBM

IVBM

Band’s head energy

0 10 20 30 400

1

2

3

4

N 0

MeV

G d 158 0

Garistov’s approach

IVBM

0 5 1 0 1 5 2 0 2 50

1

2

3

4

5

L

MeV

160 G d


0 5 1 0 1 5 2 0 2 5 3 00 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

N 0

MeV

160Gd

From band

IVBM 0+ states energies

0 5 1 0 1 50 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

3 .5

n

MeV

160 G d

0 6 12 18 24 30 36 42 480

2

4

6

8

10

12

14

16

18

Ener

gy

MeV

L

150Dy

152Dy

154Dy

156Dy

158Dy

160Dy

162Dy

164Dy

bands in Dy isotopes


Here N0 specifies the corresponding

rotational band head’s type and for J

N0 = 2 ,4, 6,8, …

IVBM

Parabola

0 5 1 0 1 5 2 0 2 50

1

2

3

4

5

L

MeV

160 G d


Here N0 specifies the corresponding

rotational band head’s type and for J

N0 = 2 ,4, 6,8, …

0 5 1 0 1 5 2 0 2 5 3 00 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

N 0

MeV

160Gd

From band


0 5 1 0 1 50 .0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

3 .5

n

MeV

160 G d


0 1 0 2 0 3 0 4 00

2

4

6

8

1 0

1 2

1 4

L

MeV

168Yb

0 5 1 0 1 5

0 .0

0 .5

1 .0

1 .5

2 .0

C la ssific a tio n p a r a m e te r n

MeV

168Yb

a = 0.485916b = 0.0275156=0.002 MeV

0+

E0+ = a n – b n2

0 5 1 0 1 5 2 0 2 5 3 00 .0

0 .5

1 .0

1 .5

2 .0

T

MeV

168 Y b

IVBM 0+ states energydistribution

2 4 6 8 1 00 .0 0 0

0 .0 0 2

0 .0 0 4

0 .0 0 6

0 .0 0 8

0 .0 1 0

0 .0 1 2

0 .0 1 4

n N0

2 n,N 0P arabo la n 0

IVBM N0 0

4 6 8 1 0 1 20 .0 0 0

0 .0 0 5

0 .0 1 0

0 .0 1 5

0 .0 2 0

0 .0 2 5

0 .0 3 0

n N0

2 n,N 0P arabo la n 2

IVBM N0 2

6 8 1 0 1 2 1 4 1 60 .0 0

0 .0 1

0 .0 2

0 .0 3

0 .0 4

0 .0 5

0 .0 6

0 .0 7

n N0

2n,N 0

P arabo la n 4

IVBM N0 4

Thank You !

0 10 20 30 40 50 600

5

10

15

20

25

30

L

MeV

b a n d s D y 156

Band’s heads energies

Here N0 specifies the correspondingrotational band head’s type

2 4 6 8 1 00 .0 0 0

0 .0 0 5

0 .0 1 0

0 .0 1 5

0 .0 2 0

n T

2n,T

P arabo la n 1

IVBM T 1

3 4 5 6 7 8 9 1 00 .0 0 0

0 .0 0 5

0 .0 1 0

0 .0 1 5

0 .0 2 0

0 .0 2 5

0 .0 3 0

n T

2n,T

P arabo la n 2

IVBM T 2

4 5 6 7 8 9 1 00 .0 0

0 .0 1

0 .0 2

0 .0 3

0 .0 4

0 .0 5

n T

2 n,TP arabo la n 3

IVBM T 3

beta 2+beta 2+

gamma 2+1-

3-

5 10 15 20 25

1.0

1.5

2.0

2.5

3.0

3.5

N 0

MeV

D y 160 b e ta 0 a n d 2

2 4 6 8 10 12 14

2.0

2.5

3.0

L

MeV

O c tu p o le b a n d E r 166

beta 2+beta 2+

gamma 2+

5 1 0 1 5 2 0 2 5

0

1

2

3

4

n

2E

ner

gies

MeV

166

164

162

160

158

156

154

152

150

Dy isotopes

En = a n – b n2 +c

0 5 1 0 1 5 2 0 2 5 3 0

1 .0

1 .5

2 .0

2 .5

3 .0

N 0

MeV

160Gd

From band

From band


0 5 1 0 1 5 2 0 2 5 3 0

1

2

3

4

N 0

2st

ates

ener

gies

MeV156Gd

From band

From band


5 1 0 1 5 2 0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

n

MeV

152Gd

2+ states

gamma

beta

2→0

4→0

6→0

8→02→0

4→2

6→4

N=N

2+ gamma

2+ beta

5 10 15 20 25 30200

400

600

800

1000

1200

1400

1600

L

Wu

B E 2 U 236

5 10 15 20 25 30

250

300

350

400

450

L

Wu

B E 2 L L 2 U 236

IVBM

Rig id ro to r

5 10 15 20 25

200

250

300

350

L

Wu

B E 2 L L 2 D y 160

experimen t

IVBM

Rig id ro to r

5 10 15 20 25 30

200

250

300

L

Wu

B E 2 L L 2 G d 156

experimen t

IVBM

Rig id ro to r

5 10 15 20 25 30

0

100

200

300

400

500

L

W.u

.

B E 2 L L 2 W 170

expRig id ro to rIVBMIBM

5 10 15 20 25 30

100

200

300

400

500

L

W.u

.

B E 2 L L 2 W 170

expIVBM N 0 10IVBM N 0 4IVBM N 0 0

N0=10N0=4

N0=0

0 5 1 0 1 50 .0

0 .5

1 .0

1 .5

2 .0

2 .5


MeV

E2+ = a n – b n2 + c

168Yb

a = 0.55132b = 0.0266917c = - 0.450742 = 0.002 MeV

2+

AmbiguousSpin Data

beta 2+beta 2+

gamma 2+

beta 2+beta 2+

gamma 2+1-

3-

0 5 1 0 1 5 2 0 2 5 3 0

0 .5

1 .0

1 .5

2 .0

2 .5

3 .0

3 .5

N 0

MeV

168Yb

type 2+ states

type 2+ states

Ground band 2+ state

0 5 1 0 1 50 .0

0 .5

1 .0

1 .5

2 .0

2 .5


MeV

E2+ = a n – b n2 + c

168Yb

a = 0.55132b = 0.0266917c = - 0.450742 = 0.002 MeV

2+

AmbiguousSpin Data

sp(12,R) sp(4,R) so(3) ∩ u(6) u(2) su(3)

sp(4,R) and su(3) algebras are related through the u(2)su(2)u(1) algebra of the pseudo spin T, which is the same in both chains.

This permits an investigation of the behavior of low lying collective states with the same angular momentum L in respect to the number of excitations N that build these states.

mutual complementarity of sp(4,R) with the so(3)

Documents

ON E0 TRANSITIONS IN HEAVY EVEN – EVEN NUCLEI VLADIMIR GARISTOV, A. GEORGIEVA* Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, [email protected]