Документ взят из кэша поисковой машины. Адрес оригинального документа : http://qfthep.sinp.msu.ru/talks2015/imasheva_QFTHEP.pdf
Дата изменения: Sat Jun 27 08:44:30 2015
Дата индексирования: Sat Apr 9 23:16:48 2016
Кодировка:

The XXII International Workshop High Energy Physics and Quantum Field Theory June 24 July 1, 2015 Samara, Russia

Nucleon pairing in N=126 isotones

L. T. Imasheva1, B. S. Ishkhanov1,2, M. E. Stepanov
1 2

1,2a,

T. Yu. Tretyakova

2

Faculty of Physics, Moscow State University, Moscow 119991, Russia Skobeltsyn Institute Of Nuclear Physics, Moscow State University, Moscow 119991, Russia E-mail: astepanov@depni.sinp.msu.ru

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 2

Structure of this work
· · · · · Introduction Basic definitions and formalism Results of calculations for isotones N = 126 Formation of a multiplet on excited state Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 3

Shell model
· Non-interacting particles · Residual interaction · Magic core
pp
p p

n
126 1i 126

p
1h
9/2

92 82

13/2

1h

11/2

N, Z (N, Z) = (126, 82)
Heavy nuclei

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 4

Pairing effect
10 8 6 4 2 0 80 82 84 86 88 90 92

Sp, MeV N = 126

Proton separation energy on the proton number Sp(Z) in isotones N = 126
Sp(N, Z) = M(N, Z1) + mp M(N, Z) = = Ebind (N, Z) Ebind (N, Z1)

Z

pp(N,Z) = Spp(N,Z) - 2·Sp(N,Z-1) = = Ebind(N,Z) - 2·Ebind(N,Z-1) + Ebind(N, Z - 2) = = Sp(N,Z) -Sp(N, Z-1).

pp(N,Z) = Sp(N,Z) - Ѕ[Sp(N, Z-1)+Sp(N, Z+1)].
Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 5

Residual interaction
· Ground State Multiplet (GSM) J = 0, 2, 4,...Jmax , Jmax = 2j 1. · Delta-interaction V (r1 , r2 ) V0 (r1 r2 )
E J E0 T 1, S j j 1 1 2 2 0, even J (2 j 1) 0 J [1].
2

EJ /E0
0

J
8
8 6 4 2

NN
1

0
NN

( J )

E J 1 E 0

[1] I. Talmi, Simple Models of Complex Nuclei, Harwood Ac. Publ., Chur, 1993.

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 6

Seniority scheme
number of unpaired nucleons n number of identical nucleons in j subshell
J = 2,4,5,8 J = 2, 4, 6
NN =4 =2

J = 0,2,3,4 ,5,6 ,7,8,9,10,12 =4 J = 2, 4, 6, 8
NN =2

2

2

J=0

J=0

n=0

2

4

0

2

4

j = 7/2

j = 9/2

Jmax = (2j + 1)/2

n=2n=3n=4...
Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 7

Results. Seniority = 2
11-

E , MeV
1,5 8 6 4 2 1,0
+ + +

*

1h9/2
8 6 4 2
+ + + +

2

E , MeV
2,0 (8+) 8+ 6+ 4+ 31,5 2+

*

1h9/2

-2

8+ 6+ 4+ 2+

+

1,0

0,5
0,5

exp calc
pp

0,0

0

+

0

+

0,0

0+

0+

210 84

Po

216
126

90

Th

126

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 8

Results. Seniority = 3
E , MeV
1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 9/2
_

*

1h
(21/2) _ (17/2)_ (15/2) _ (11/2) _ (3/2) _ (13/2) _ (5/2) _ (7/2)
_

3 9/2

21/2 _ 17/2_ 15/2 _ 3/2 _ 11/2_ 13/2 _ 5/2 _ 7/2

_

9/2

_

exp calc
pp

211 85

At

126

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 9

Results. Seniority = 3
E , MeV
2,0
*

1h9/2

5

1h9/2
(21/2-) (17/2-) 21/217/215/2(13/2-) 3/211/213/25/27/2-

-3

1,5

21/217/213/2(13/2)+

21/217/215/23/211/213/25/27/2-

1,0

0,5

(7/2-)

exp calc
9/29/29/2-

0,0

9/2-

pp

213 87

Fr

215 126 89

Ac

126

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 10

Results. Seniority = 4
E*, MeV
(10 ) + (8 ) + 2+ (8 ) ++ 42 5+ + 6+ 2 + 3 ,4 + 6 + 4 2
+ +

3,5 3,0 2,5 2,0

1h
(12 ) (12_ ) (11+) (10 ) (8 )
+ + + +

4 9/2

12 10 + 8 8+ 6+ 4+ 2
+

+

14 + 12+ 12 + 10 11
_

+

1h

-4 9/2
12 10 8
+ +

+

+

6 4 1,5 2 1,0 0,5

+ + +

(8 ) + (6) + 4+ 2

8+ 8+ 6+ 4 + 2

+

8+ 6+ 4+ 2

+

exp calc
+

0

+

0,0 0

0

+

0

+

0

+

0

+

pp

212 86

Rn

126

214 88

Ra126

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 11

Multiplet on excited state
E , MeV
pp
p
*
*

p

E*

3,2 3,1

p

(17/2) + (13/2) + (9/2) 5/2
+

+

1h9/2
17/2 13/2 + 9/2+ 5/2

+ +

N, Z 1

N, Z 2

3,0 2,9

exp calc
pp
*

1/2

+

1/2

+

pp* (N,Z) = pp (N,Z) - - (2E*(N,Z- 1) - E*(N,Z))

2,8 2,7 2,6 2,5

1h9/23s1/2
209 83

2

-

Bi

126

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones, p. 12

Conclusions
The systematics of the GSM for N = 126 isotones is considered in this work . 1. Multiplets with value of a seniority = 2, 3, 4 have been clearly marked in the considered nuclei. There are multiplets on the excited states here too. Therefore, the excited states in even-even and even-odd nuclei can be interpreted using this model. 2. Values of multiplet splitting correspond to pairing energy, which can be defined from the mass of nuclei. 3. Comparison of the pairing energy NN and the excitation energy for maximum angular momentum E*(Jmax) gives information about the level excitement mechanism.

Introduction Formalism Results GSM on ex.st. Conclusions

Imasheva Lilya

Nucleon pairing in N=126 isotones

Imasheva Lilya

Nucleon pairing in N=126 isotones

Imasheva Lilya

Nucleon pairing in N=126 isotones

E ,MeV
0,75
_ _

*

2f

7/2

1g

7/2

2g
6 4
_ _

9/2

1h

9/2

(6 ) (4 ) 0,50 (5 ) (3 ) _ (2 ) _ (7 )
_ _

_ 25 _ 3

_

7 1

_

8 6 4

_ _ _ _

6_ 4 _ 7_3_5 2 9 1
_ _

_

8

_

_

l1 l2
0,25

_ 75

_

3 2 _ 9

_

_

0,00 (0_(1 ) )

_

exp

134 51

calc

0

_

0 1

_ _

0

_

exp

calc

Sb

210 83

83
Backup slides

Bi

127

np