Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA H.Shimoyama, M.Matsuo Niigata University 1 Dynamics and Correlations.

Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes

studied with continuum QRPA

H.Shimoyama, 　 M.MatsuoNiigata University

1

Dynamics and Correlations in Exotic Nuclei (DCEN2011)Yukawa Institute for Theoretical Physics

One-day workshop IV Oct. 24

Outline Outline

Anomalous pairing vibration state in neutron-rich 132-140Sn

・ Introduction

・ Framework

・ Results

Skyrme Hartree-Fock-Bogoliubov mean-field + continuum Quasiparticle Random Phase Approximation

Giant pairing vibration in stable Sn isotopes

Pairing vibration in Ni isotopes

・ Conclusion

(Monopole pair transfer in Sn and Ni isotopes )

Pairing vibration in Sn isotopes

2

relation to the anomalous pairing vibration state beyond N=82

weak-binding feature

Outline Outline


・ Introduction

・ Framework

・ Results




・ Conclusion



3



2n-addition2n-removal

A → A+2

2-neutron transfer2-neutron transfer

11Li + p → 9Li + tExample ）

03+

02+

A A + 2A - 2

energy

+ 2n- 2n

0gs+

0+gs

03+

02+

0gs+

A → A-2

( t , p )( p , t )

4

D. R. Bes , et. al, NP(1966) R. A. Broglia , at. Al, NP(1973)

Pairing vibration

Re⊿

Im⊿

superfluid phase open-shell nuclei

E

Pairing rotation

02+

02+ 02

+

0gs+

0gs+ 0gs

+

Pairing vibration Pairing vibration

A + 2A - 2A

Pairing rotation Pairing rotation

weak weak

strong strong

Collective two-neutron transfers in surperfulid nucleiCollective two-neutron transfers in surperfulid nuclei

This is a standard picture of the two-neutron transfer modes.

5

Δ F/e F

Lombardo et. al, (2001)Margueron et. al, PRC (2008)M.Matsuo PRC73 (2006)

E. Khan et. al, PRC69 (2004); ibid PRC80 (2009)Recent studyB. Avez, et. al, PRC78 (2008)M. Matsuo, Y.Serizawa (2010)

neutron-rich O, Sn

r [fm]

protonneutron

dens

ity

neutron-skin

Two-neutron transfer in neutron-rich nucleiTwo-neutron transfer in neutron-rich nuclei

～ for unstable nuclei ～

I. Tanihata et al. PRL 100, (2008)11L + p → 9L +tExperiments

The neutron-rich nuclei often accompany low density distributions of neutrons surrounding the nucleus. 　

The pairing in low-density neutron matter is predicted to be stronger.

ρ/ρ0

If the neutron pairing becomes strong around the surface, we can expect a large probability for a neutron pair to be added or removed from a nucleusby a transfer process.

10010-110-210-310-4

30Mg + t → 32Mg + p K. Wimmer et al. PRL 105,(2010)6

),(),(),,(),( 03

rrrrRrdr ext

Linear response equation

particle-hole densitypair -addition density)()(),(~* rrtr †† )()(),(~ rrtr

pair -removal densityThe densities describing the pair transfer is provided:

・ Skyrme interaction parameter ： SLy4

・ Pairing interaction parameter ：　 Density Dependent Delta Interaction

（ ph channel of cQRPA → Landau-Migdal approximation ）　

Two-neutron transfer in QRPATwo-neutron transfer in QRPA

)()(),( rrtr †

59.00 )8.0(71.01],[ npnnV

The parameter set reproduces the scattering length of the nn-interaction


DDDI-bare (surface type)

ann=-18.5 fm strong @ outside

weak @ inside7

)()(0000 rrYdrP )()(0000 rrYdrP

Pair-removal operatorPair-addition operator

strength function

transition density

NPNirP rmadi ;02;)( )(

00)/(

0†

Monopole pair transfer modeMonopole pair transfer mode

),(~ Im1)0Pad/rm(

00

rYdrd

dB

2)(

00 0);0Pad/rm( gsPiigsB †

QRPA calc. of excitation modes

Hartree-Fock-Bogoliubov mean-field calc.

drrrPNPNB HFBHFBgsgs2)(

00)(

00 )(~400;02;0)gsgs0; Pad/rm(††

ground–ground pair transfer

Pair transfer to excited 0+ states

strength

strength

8

Outline Outline


・ Introduction

・ Framework

・ Results




・ Conclusion



9

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 0

5

10

15

20

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 0

5

10

15

20

Monopole neutron pair transferMonopole neutron pair transfer

addition

removal

stre

ngth

The pair addition strength to the pair vibration 0+ state in 134Sn is large.

The pair vibrational state of 134Sn is a narrow resonance though it is located above the one-neutron separation energy.

stre

ngth

addition

removal

E ( MeV)

Strength function for the pair transfer

As we explain below, this pairing vibrational mode in 134Sn is quite anomalous.

E ( MeV)

02

A-2 A A+2

02

0gs0gs0gs

10

0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150 0

1

2

3

4

5

100 110 120 130 140 150

Sn isotopes

Pair addition strength of pairing vibrational mode

0gs0gs

02 022n-add

A A+2gs-gs

Ratio ( 02+ vs gs )

60-90 ％

A A

Large strength twice or more 　

str

engt

h

AnomalousAnomalous Pairing Vibration Pairing Vibration

11

gsgsPB ad ;0

PVgsPB ad ;0ratio

less than 10 % in stable nucleiR. A. Broglia, O. Hansen, and C. Riedel (1973)

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16

Transition density of pairing vibrational mode

120-130Sn132-140Sn

r [fm]

r2 P(a

d)00

(r)

[

fm-1

]AnomalousAnomalous Pairing Vibration Pairing Vibration

0

-5

-2.14

-0.36(0.27)(0.66)

-7.68

es.p.

The transition densities to the pair vibrational mode of 132-140Sn have a long tail.

By adding two-neutrons in the weakly bound p orbits, we can have a long tail.

Very long tail r ～ 15 fm

The weakly bound p orbits play an important role !!

2N-add

f7/2

p3/2

p1/2

h11/2

Hartree-Fock single-particle energy in 134Sn

N= ８２

[MeV]

12

0

5

10

15

20

25

100 110 120 130 140 150 0

5

10

15

20

25

100 110 120 130 140 150

Strength of ground state transfer

Pair

add

ition

str

engt

hRelation to the ground state transferRelation to the ground state transfer

A

p orbits occupied in excited states p orbits occupied

in ground states

Sn isotopes

0gs0gs

02 022n-add

A A+2gs-gs

13

drrrrdrrYB gsgs2

00 )(~40)()(0)0P(

0

-5

-0.84-0.23

(0.01)

-7.68

es.p. 2N-add

N=82

f7/2

p3/2

p1/2

h11/2

[MeV]

-2.62

Hartree-Fock single-particle energyin 142Sn

The anomalous pairing vibration in 132-140Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

Outline Outline ・ Introduction

・ Framework

・ Results




・ Conclusion


14



2 4 6 8 10 12 14 16 18

2 4 6 8 10 12 14 16 18

2 4 6 8 10 12 14 16 18

2 4 6 8 10 12 14 16 18

2 4 6 8 10 12 14 16 18

Low-lyingPairing Vibration

Giant Pairing Vivration

Pair addition strength function

2nd-GPV

1st-GPV

Giant Pairing Vibration (GPV) in stable Sn isotopesGiant Pairing Vibration (GPV) in stable Sn isotopes

E [MeV]

2nd-GPV

Gs-gs transferPairing Vibration


0

-5

-0.84-0.23

(0.01)

-7.68

es.p. 2N-add

N=82

f7/2

h11/2

[MeV]

-2.62

p3/2

p1/2

15

0 2 4 6 8 10 12 14 16 18

0 2 4 6 8 10 12 14 16 18

E [MeV]

E [MeV]


2nd- GPV

Anomalous pairing vibration

0 2 4 6 8 10 12 14 16 18

0 2 4 6 8 10 12 14 16 18

E [MeV]

E [MeV]

Giant Pairing Vibration (GPV) in stable Sn isotopesGiant Pairing Vibration (GPV) in stable Sn isotopesPair addition transition density

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16

r2 P(a

d)00

(r)

[

fm-1

]

2nd- GPV in 122-130Sn

Anomalous pairing vibration in 132-140Sn

The transition densities of 2nd-GPV have a long tail.

However the collectivity of the anomalous pairing vibration is much stronger.

122Sn

Same character of the anomalous pairing vibration.

r [fm]


2nd- GPV


16

Outline Outline ・ Introduction

・ Framework

・ Results




・ Conclusion


17



0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

)()(2

000 ii

iadd EEPES †Pair addition strength function

Pairing vibration in neutron-rich Ni isotopesPairing vibration in neutron-rich Ni isotopes

E [MeV]

The pairing vibration appears both isotopes, but the strength in 80Ni is not large.

E [MeV]

Pair

add

ition

str

engt

h

Pair

add

ition

str

engt

h

18

0

0.2

0.4

0.6

0.8

1

55 60 65 70 75 80 85


Strength of pair addition transfer to pairing vibration and ground state transfer

gsgsPB ad ;0

PVgsPB ad ;0ratio

10-20 ％

A A

Ni isotopes

Pair

add

ition

str

engt

h

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

pair addition strength function

Pair

- add

str

engt

h

E (MeV)

GPV

The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region.

19

0

1

2

3

4

5

6

55 60 65 70 75 80 85 0

1

2

3

4

5

6

55 60 65 70 75 80 85

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16


0

-5

-1.36

-0.28

es.p.

g9/2

d5/2

s1/2

N=50

[MeV]

(0.27) d3/2

-5.60

The transition densities of neutron-rich 78-84Ni have a long tail ( r ～　15fm )because the relevant weakly bound orbit is an s orbit.

The collectivity is small.

2n-add

Hartree-Fock single-particle energyin 80Ni

78-84Ni

58-66Ni

Pair addition transition density

f [fm]

20

80NiPair

add

ition

str

engt

h

132Sn 134Sn 136Sn 138Sn 140Sn100-130Sn

0gs

0gs 0gs 0gs 0gs 0gs0gs

02 02 02 02 02

02

142-150Sn

strong strong strong strong very strong

strong

strong

strong

strongweak

strong

weakweak

strong

The neutron-rich 132-140Sn have the anomalous pair vibrational state.

　～ as same value as the ground state transfer 　～・ the pair addition strength is very large,

・ the transition density has a long tail extending to the outside, 　～ weakly bound p orbits play an important role ～

ConclusionConclusion

The ground state transfers is significantly enhanced beyond A=140,due to the weakly bound p orbits occupied in ground state. The anomalous pairing vibration is a precursor of this strong transfer.

We found the pairing vibration beyond 78Ni. They have a weak-bound feature because the relevant weakly bound orbit is an s orbit. However the collectivity is smaller.

It is also related to the giant pairing vibration in stable Sn isotopes.

21

( t , p ) ( t , p ) ( t , p ) ( t , p ) ( t , p )

22

23

)(],[),( rrVrrV pnnpair

DDDI mix 　

DDDI volume

DDDI bare’ 　

Density Dependent Delta type Interaction

10 )16.0(5.01],[ pnpnnV

59.00 )8.0(71.01][ nnnV

0],[ pnnVNo dependent on the density >

Density Dependent delta Interaction parameter Density Dependent delta Interaction parameter

Acts by a low density strong >

0

1

2

3

4

5

100 110 120 130 140 150 0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150 0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150 0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150

24

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0gs+―0gs

+

r2 P(a

d)gs

(r)

　 [

fm-1

]

0

-5

-0.84-0.23

(0.01)

-7.68

es.p. 2n-add

N=82

f7/2

p3/2

p1/2

h11/2

[MeV]

-2.62


ｒ　　 [fm]

120-130Sn132-140Sn

142-150Sn

Relation to the ground state transferRelation to the ground state transfer

Strength of ground state transfer

)(~0)()(0 rrr HFBHFB

NrrN gsgs ,0)()(2,0

The anomalous pairing vibration in 132-140Sn appears as a precursor of large enhancement of the ground state transfer beyond A=140.

0

-5

-2.14

-0.36(0.27)(0.66)

es.p.2n-add

f7/2

p3/2p1/2

N= ８２

[MeV]

0

-5

-1.58

-0.43

es.p.2n-add

g9/2

d5/2s1/2

N=50

[MeV]

0

-5-5.73

-3.56

-1.60

es.p.2n-add

p3/2

p1/2

f5/2

[MeV]

(0.43) d3/2

-6.02N=2

８

Not weakly bound

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

r2P(ad) gs(r)　　

[fm

-1]

48-54Ca

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

42-46Ca-GPV134-140Sn 80-84Ni

58-64Ni120-130Sn

[ ｆｍ ] [ ｆｍ ] [ ｆｍ ]

Weak-bound featurWeak-bound featur

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16

0 2 4 6 8 10 12 14 16 18

0 2 4 6 8 10 12 14 16 18

E [MeV]

E [MeV]

Giant Pairing Vibration (GPV) in stable Sn isotopesGiant Pairing Vibration (GPV) in stable Sn isotopesPair addition transition density

r2 P(a

d)00

(r)

[

fm-1

]

1st- GPV in 122-130Sn

ground state transfer in 132-140Sn

122Sn

Same character of the ground state transfer of neutron-rich Sn isotopes.

r [fm]


1st- GPV

ground state transfer

26

27


0

-5

es.p. 2n-add

f7/2

p3/2

p1/2

h11/2

Pairing Vibration0

-5

es.p. 2n-add

f7/2

p3/2

p1/2

2nd-GPV

1st-GPV

h11/2

g.s. transfer

g.s. transfer

Pairing Vibration

Neutron-rich 132-140SnStable area 120-130Sn

Hartree-Fock single-particle energy

N=82 N=82

28

0

1

2

3

4

5

6

100 110 120 130 140 150 0

1

2

3

4

5

6

100 110 120 130 140 150 0

1

2

3

4

5

6

100 110 120 130 140 150

GPV

stre

ngth

Sn isotopes

0

1

2

3

4

5

6

55 60 65 70 75 80 85 0

1

2

3

4

5

6

55 60 65 70 75 80 85 0

1

2

3

4

5

6

55 60 65 70 75 80 85

29

Ni isotopes

GPVstre

ngth

30

0

1

2

3

4

5

6

35 40 45 50 55

stre

ngth

Ca isotopes

GPV

0

1

2

3

4

5

6

35 40 45 50 55 0

1

2

3

4

5

6

35 40 45 50 55

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10

31

82Ni

r2 P(a

d)gs

(r)

　 [

fm-1

] Pair addition strength function

0

0.2

0.4

0.6

0.8

1

55 60 65 70 75 80 85 0

1

2

3

4

5

6

55 60 65 70 75 80 85 0

1

2

3

4

5

6

55 60 65 70 75 80 85


Strength of pair addition transfer to pairing vibration and ground state transfer

gsgsPB ad ;0

PVgsPB ad ;0ratio

A A

Ni isotopes

Pair

add

ition

str

engt

h

The pairing vibrational states which are as large as ground state transfer are not appeared in neutron-rich region.

32

0

5

10

15

20

25

30

100 110 120 130 140 150 0

1

2

3

4

5

6

100 110 120 130 140 150

Strength of the ground state transfer [Pairing gap]2

GRPUND STATE PROPERTIES AND THE PARING ROTATIONGRPUND STATE PROPERTIES AND THE PARING ROTATION

DDDI-bare’　mixvolume　


33

A A

stre

ngth

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

Transition density of the ground state transfer

120-130Sn132-140Sn142-150Sn

GRPUND STATE PROPERTIES AND THE PARING ROTATIONGRPUND STATE PROPERTIES AND THE PARING ROTATION

r2 P(a

d/rm

) gs(r

) 　　　　[

fm-1

]

f [fm]34

0

5

10

15

20

25

2 4 6 8 0

5

10

15

20

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 0

5

10

15

20

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 0

5

10

15

20

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 0

5

10

15

20

102Sn102Sn 120Sn120Sn

134Sn134Sn 142Sn142Sn

Pair addition

Pair removal

stre

ngth

st

reng

th

stre

ngth

st

reng

th

E [MeV] E [MeV]

E [MeV] E [MeV]

PAIRING VIBRATION ( strength function )PAIRING VIBRATION ( strength function )

35

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

102Sn102Sn 120Sn120Sn

134Sn134Sn 142Sn142Sn

Pair addition

Normal NPair removal

Pair addition


Pair addition


Pair addition


(Tra

nsiti

on d

ensi

ty)×

r2(T

rans

ition

den

sity

)×r2

(Tra

nsiti

on d

ensi

ty)×

r2(T

rans

ition

den

sity

)×r2

f [fm] r [fm]

f [fm] r [fm]

PAIRING VIBRATION ( transition density )PAIRING VIBRATION ( transition density )

36

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14

134Sn134Sn 142Sn142Snpairing vibration[f7/2]2

[p3/2]2

pairing vibration[f7/2]2

[p3/2]2

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Pair addition Pair removal

full QRPAunperturbed

full QRPAunperturbed

134Sn134Sn 142Sn142Sn

PAIRING VIBRATION ( Microscopic origin )PAIRING VIBRATION ( Microscopic origin )st

reng

th

stre

ngth

(Tra

nsiti

on d

ensi

ty)×

r2

(Tra

nsiti

on d

ensi

ty)×

r2

f [fm] f [fm]

E [MeV] E [MeV]

37

0

5

10

15

20

100 110 120 130 140 150 0

1

2

3

4

5

100 110 120 130 140 150

Pair addition mode

Excitation energy Strength

E [M

eV]

A A

stre

ngth



PAIRING VIBRATION ( systematics )PAIRING VIBRATION ( systematics )

38

0

5

10

15

20

100 110 120 130 140 150 0

1

2

3

4

5

100 110 120 130 140 150

Pair removal mode

Excitation energy StrengthDDDI-bare’　

mixvolume　

PAIRING VIBRATION ( systematics )PAIRING VIBRATION ( systematics )E

[MeV

]

stre

ngth


39

A A

0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150 0

0.2

0.4

0.6

0.8

1

100 110 120 130 140 150

Ratio Pair addition Pair removal

PAIRING VIBRATION ( comparison with the ground state transfer )PAIRING VIBRATION ( comparison with the ground state transfer )

40

A A

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 0

5

10

15

20

25

3 3.5 4 4.5 5

DDDI-bare’　mix

volume　

134Sn134Sn

SENSITIVITY TO DENSITY-DEPENDENT PARINGSENSITIVITY TO DENSITY-DEPENDENT PARING

41

E [MeV]

stre

ngth

42

0

5

10

15

20

25

30

100 110 120 130 140 150 0

1

2

3

4

5

100 110 120 130 140 150

B(Pad0)Ground state trensfer

0gs+

2n-add

A A+2gs-gs

0gs+

02+

21+

A A

stre

ngth

stre

ngth

02+0gs

+

21+

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0.9

1.2

0 2 4 6 8 10 12 14 16

21+

02+0gs

+

43

0gs+

2n-add

A A+2gs-gs

0gs+

02+

21+

r2 P(a

d)00

(r) 　

[fm

-1]

r2 P(a

d)gs

(r) 　

[fm

-1]

Transition density of pair vibration mode

120-130Sn132-140Sn142-150Sn

PAIRING VIBRATION ( systematics )PAIRING VIBRATION ( systematics )

r2 P(a

d)00

(r) 　

[fm-1

]

f [fm]44

0

0.3

0.6

0 2 4 6 8 10 12 14 16

0

0.3

0.6

0 2 4 6 8 10 12 14 16

45

)()(0000 rrYdrP )()(0000 rrYdrP

Pair-removal operatorPair-addition operator

strength function

transition density

NPNirP rmadi ;02;)( )(

00)/(

0†

Monopole pair transfer modeMonopole pair transfer mode

),(~ Im1)0Pad/rm(

00

rYdrd

dB

2)(

00 0);0Pad/rm( gsPiigsB †

QRPA calc. of excitation modes

Hartree-Fock-Bogoliubov mean-field calc.

drrrrdrrYB gsgs2)()(

00 )(~40)()(0)gsgs0; Pad/rm( ††

ground–ground pair transfer

Pair transfer to excited 0+ states

strength

strength

)(~0)()(0,0)()(2,0)/(0 rrrNrrNP HFBHFBgsgsrmad

gs

transition density

47

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16[ fm ]

r2 P(a

d)(r

) 　

[f

m-1

]

2nd-GPV in 122-130 Sn


1st-GPV in 122-130Sn

0 2 4 6 8 10 12 14 16 18

0 2 4 6 8 10 12 14 16 18

r2 P(a

d)(r

) 　

[f

m-1

]

[ fm ]

g.s. transfer in 132-140Sn


in 132-140 Sn


E [MeV]

E [MeV]

Transition densities have a same character.

Transition densities of 2nd-GPV have a long tail ( r ~ 15fm ).


0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

-5

-1.36

-0.28

es.p.

g9/2

d5/2

s1/2

N=50

[MeV]

(0.27) d3/2

-5.60

The transition densities of neutron-rich 78-84Ni have a long tail ( r ～　15fm )because the relevant weakly bound orbit is an s orbit.

The collectivity is small.

2n-add

Hartree-Fock single-particle energyin 80Ni

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

0

0.1

0.2

0.3

0.4

0.5

0 2 4 6 8 10 12 14 16

78-84Ni

58-66Ni


f [fm]

48

49

Anomalous two-neutron transfer in neutron-rich Ni and Sn isotopes studied with continuum QRPA H.Shimoyama, M.Matsuo Niigata University 1 Dynamics and Correlations.

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