NITheP WITS node seminar: Prof. V. Yu. Ponomarev (Technical University of Darmstadt, Germany) TITLE:...

Pygmy dipole resonance in atomic nuclei

V.Yu. Ponomarev

Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany

V.Yu. Ponomarev (TU Darmstadt) 13.05.2014 1 / 31

Outline

IntroductionQuasiparticle-phonon modelBasic of pygmy resonanceLow lying E1 strength in Ni, Sn, N=82 isotones, and PbExcitation of pygmy in (α, α′) reactionExcitation of pygmy in (p,p′) reaction1− states in (e,e′) scattering


P H OTO —F I SSI ON I N HEAVY ELEMENTS

evaluating f, the range of an electron has beentaken proportional to its energy.

We now assume that all electrons from thewall which enter the thimble produce an equalaverage ionization, 8, of 60 ion pairs per cen-timeter. The specific ionization of electrons isnearly independent of energy for electron ener-gies above 300 kev, amounting for air to 76 ionpairs per centimeter at 300 kev, decreasing to53 at 2 Mev, then rising slowly to 70 ion pairsper centimeter at 100 Mev. Low energy electronswhich ionize appreciably higher than this arealso highly scattered and are contributed fromvery thin layers of the wall; th'erefore, the errorintroduced by neglecting their higher ionizingpower is not serious. The eSect of multiple scat-tering and of the initial angular distribution ofproduced secondaries is somewhat reduced byhaving the thimble surrounded by the lead onall sides.

The integration of (4) wa, s carried out graphi-cally. For 8= 10 Mev, the number of secondariescontributed from all three absorption processeswas calculated. To this were added the pairs andrecoils resulting from absorption of quanta above10 Mev for a sequence of values of 8 up to 100Mev, the x-ray spectrum in each case having theform assumed above and with the constant Zadjusted to unity. The result of this calculationis given in Fig. 6. Absolute accuracy cannot beclaimed for it, but it is believed that its trendwith energy closely parallels the actual variationof sensitivity of the r-thimble.

The reading of the r'-meter can then be written

r(E) =s 8 ~(E) Z=2.9X10 'r(E) It e.s.u. (5)

It follows that. to produce a reading of 1 roentgenunit (i.e. , one e.s.u. of charge per cubic cen-timeter) in the r-meter when the thimble isirradiated with 100-Mev x-rays and surroundedwith 8" of lead, there must be approximately2.5X10"/e quanta of energy e per unit energyinterval per square centimeter.

Analysis of the Excitation Curves

The "x-ray fission yield" is the quotient

C'(E) = ~(E)/r(E) (6)

where Ii(E) and r(E) are given by (1) and (5).

From them it follows that the fission crosssection is

2.9X10 'E d(Cv)0E =NA dE

Figure 7 shows the analysis of the data foruranium. It is evident that the cross section forphoto-fission must be extremely small forquantum energies above 30 Mev. The resultingcurve of 0 (E) vs. E is given in Fig. 8 for uranium.

0'a to "cM',

7

0 20

E, Msv

30

FrG. 8. Cross section for photo-fission of uranium.Because of approximations made in the analysis anduncertainty of the experimental data for low x-ray energies,this curve must be considered of only qualitative sig-nificance.

The determination of the cross section in-volves first drawing a smooth curve through theexperimental points, multiplying the ordinatesof this curve by a function known only roughly, ,

and then differentiating the product; It is evidentthat the given data are not sufficiently preciseto determine the cross section as a function ofenergy, even if the calculation of r(E) wereexact, since in this case the portion of the yieldcurve which is most significant to the deter-mination of the cross section is that below 30Mev. The experimental points in this region aresubject to considerable Huctuation, and the trueyield curve may be appreciably different fromthat shown in Fig. 3. It is also true that theeffects of the approximations made in calculatingr(E) are more serious at low energies. Therefore,it must be stressed that no significance can beattributed to the shape of the curve of 0 vs. 8nor to the absolute values of the cross sectiongiven on the scale of ordinates. The curve of

G.C. Baldwin and G.S. Klaiber,Phys. Rev. 71 (1947) 3

EGDR ∝ 80 · A−1/3 MeV


R. M. Laszewski and P. Axel


Cologne, Darmstadt, Gent


QPM Hamiltonian : H = Hs.p. + Hpair + Hres

Hs.p. − Woods− Saxon,

Hpair = −G0

∑jj′mm′

a†jma†j−maj′−m′aj′m′

Hres = −∑λµ

(κis + κivτ1τ2)M†λµMλµ;

M†λµ =∑

jj′mm′〈jm|iλRλ(r)Yλµ|j ′m′〉a†jmaj′m′


I. BCS: a†jm → α†jm

α†jm = uja†jm + vjajm αjm|〉g.s = 0

II. QRPA: [α†jmα†j′m′ ]λµ → Q†λµ

Q†λµi =

N,Z∑jj′

Xλi

jj′ [α†jmα†j′m′ ]λµ + Yλi

jj′ [αjmαj′m′ ]λµ

Qλµi |〉g.s = 0

III. Coupling to complex configurations:

|ΨνJ 〉 =

[∑Ji

RνJiQ†Ji +

∑12

Pν12[Q†1Q†2]J +

∑123

T ν123[Q†1Q†2Q†3]J

]|〉g.s

1 (2,3) = λi


Q+

Q+Q

+Q+

Q+Q

+ Q

+Q

+Q

+

Q+Q

+

Q+ Q

+Q

+

Q+ Q

+ Q

+

Q+ Q

+ Q

+

Q+Q

+

0

0ν ν

1ν2

ν

νν1

ν2

ν1

ν2

ν3

ν4

ν5

ν1

ν2

ν1

ν2

ν3

ν1

ν2

ν3

ν4

ν5

Pauli principle corrections: exact [Q+λ1µ1 i1 ,Qλ2µ2 i2 ]

Large s.p. basis, easy control of truncations


0

5

10

15

0 5 10 15 20 25E

x (MeV)

0

5

10B(E

1)

(e

2 fm

2)

136Xe

mean field+ BCS

QRPA


-0.1

0

0.1PDR

neutronprotons

-15 -10 -5 0 5 10 15Axial distance (fm)

-0.5

0

0.5

r2(r

) (

e f

m-1

)

GDR

208Pb


B(E1,Ex ) ∼

∣∣∣∣∣∣(Ejj′≤Ex )∑

jj′(Xjj′ + Yjj′)〈j ′||E1||j〉

∣∣∣∣∣∣2

Ejj′ = εj + εj′

10 20 30Ex (MeV)

0

10

20

B(E

1) (

e2 fm2 )

GDR

PDR

non-collective

124Sn


B(E1,Ex ) ∼

∣∣∣∣∣∣(Ejj′≤Ex )∑

jj′(Xjj′ + Yjj′)〈j ′||E1||j〉

∣∣∣∣∣∣2

Ejj′ = εj + εj′ 0

2

4

B(E

1) (

e2 fm2 )

10 20 30Ex (MeV)

0

10

20 GDR

PDR

non-collective

124Sn


B(E1,Ex ) ∼

∣∣∣∣∣∣(Ejj′≤Ex )∑

jj′(Xjj′ + Yjj′)〈j ′||E1||j〉

∣∣∣∣∣∣2

Ejj′ = εj + εj′

0

0.2

0.4

0

2

4

B(E

1) (

e2 fm2 )

10 20 30Ex (MeV)

0

10

20 GDR

PDR

non-collective

124Sn


0

0.2

0.4

a)136

XeΣ B(E1) =0.84e2fm

2

0

0.03

0.06B

(E1)

[e2 fm

2 ] b)Σ B(E1) =0.90e2fm

2

4 5 6 7 8Energy [MeV]

0

0.02

0.04 c) B(E1) =0.90e2fm

2Σ


0

0.01

0.02

0.03

0.04

B(E

1 )

(e2 fm

2 )

4 6 8

Ex (MeV)

0

0.5

1

B(M

1 )

(µ2 N

)

60Ni

1-

1+

60Ni 1

-

68Ni


0

0.01

0.02

0.03

0.04

B(E

1 )

(e2 fm

2 )

4 6 8 10 12 14

Ex (MeV)

0

0.5

1

B(M

1 )

(µ2 N

)

60Ni

1-

1+

60Ni 1

-

68Ni


0

0.01

0.02

0.03

0.04

B(E

1 )

(e2 fm

2 )

4 6 8 10 12 14

Ex (MeV)

0

0.5

1

B(M

1 )

(µ2 N

)

60Ni

1-

1+

5 10 15 20Ex (MeV)

0

0.1

0.2

0.3

0.4

B(E

1 )

(e2 fm

2 )

60Ni 1

-

68Ni


0

0.05

0.1

4 6 8 10 12 14

Ex (MeV)

0

0.05

0.1

B(E

1

) (

e2fm

2)

60Ni 1

-

68Ni


0

20

40

60

Experiment136

Xe

0

20

40

60

138Ba

0

20

40

60

B(E

1)[10-3e2fm

2]

140Ce

0

20

40

60

142Nd

0

20

40

60

2000 4000 6000 8000

E [keV]

144Sm

QPM136

Xe

138Ba

140Ce

142Nd

2000 4000 6000 8000 10000

E [keV]

144Sm


0.0

0.2

0.4

0.6

0.8

1.0

1.2

B(E1)[e

2fm

2]

1.521.461.411.371.32

N/Z

136Xe

138Ba

140Ce

142Nd

144Sm

.....

.Experiment

QPM

QPML

EX < 8.02 MeV

0

10

20

30

40

B(E1)[10-3e2fm

2] Exp.a)

0

10

20

30

40

B(E1)[10-3e2fm

2]

2000 3000 4000 5000 6000 7000 8000 9000

Energy [keV]

2000 3000 4000 5000 6000 7000 8000 9000

QPMa)

Sn


0

40

80

120 136Xe

ExperimentQPM

0

40

80

120 138Ba

0

40

80

120

B(E1)[10-3e2fm

2]

140Ce

0

40

80

120 142Nd

0

40

80

120

0 10 20 30 40 50 60

B(E1)[10-3e2fm

2]

144Sm


140Ce


0

0.01

0.02

0.03

0.04B

em(E

1) (

e2 fm2 ) 124

Snelectromagnetic

3 4 5 6 7 8 9Ex (MeV)

0

500

1000

1500

Bis(E

1) (

e2 fm6 )

isoscalar

0

0.02

0.04

0.06

0.08

Bem

(E1)

(e2 fm

2 )4 5 6 7 8

Ex (MeV)

0

500

1000

1500

Bis(E

1) (

e2 fm6 )

140Ce

electromagnetic

isoscalar

electromagnetic: eN = −Z/A, eZ = N/A

isoscalar: eN = eZ = 1


I1(r) =

∫ r

0ρem

1−i(r)r3dr I3(r) =

∫ r

0ρis

1−i(r)r5dr

-0.4

-0.2

0

0.2

I 1(r)

[e fm

]

neutronsprotons

0 5 10

r [fm]

0

20

40

I 3 (r)

[e

fm3 ]

0 5 10 15

Ex = 7.133 MeV Ex = 8.580 MeV


P. PapakonstantinouV.Yu. Ponomarev (TU Darmstadt) 13.05.2014 29 / 31

20 40 60 80 100E

e [MeV]

10-7

10-6

10-5

10-4

dσ

/dΩ

[fm

2/s

tr]

1- (pygmy)

1+

iv

1+

is

[email protected]

[email protected]

208Pb(e,e’), θ = 175

o


0

2

4

6

8

Γ g.s. (

eV)

5 6 7 8Ex (MeV)

0

2

Γ 2+1 (

eV)

140Ce (1

- states)

0

10

20

30

40

Γ g.s. (

eV)

8 10 12 14Ex (MeV)

0

10

Γ 2+1 (

eV)

60Ni (1

- states)

1−i → 2+1 , [1−i ⊗ 2+

1 ]1− → 2+1 , [λπ1

1i ⊗ λπ22j ]1− → 2+

1


NITheP WITS node seminar: Prof. V. Yu. Ponomarev (Technical University of Darmstadt, Germany) TITLE:...

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