Standard Model goes pear-shaped in CERN experimentThe Register

Physicists get a good look at pear-shaped atomic nucleiThe Los Angeles Times

Exotic atoms could explain why Big Bang created more matterNewstrack India

The lopsided nuclei, described today (May 8) in the journal Nature, could be good candidates for researchers looking for new types of physics beyond the reigning explanation for the bits of matter that make up the universe (called the Standard Model), said study author Peter Butler, a physicist at the University of Liverpool in the United Kingdom.

The findings could help scientists search for physics beyond the Standard model, said Witold Nazarewicz. An electric dipole moment would provide a way to test extension theories to the Standard Model, such as supersymmetry, which could help explain why there is more matter than antimatter in the universe.

Until now, only one pear-shaped nucleus had been found experimentally: radium 226, whose shape was sketched out back in 1993.

H.J. Wollersheim, H. Emling, H. Grein, R. Kulessa, R.S. Simon, C. Fleischmann, J. de Boer, E. Hauber, C. Lauterbach, C. Schandera, P.A. Butler, T. Czosnyka; Nucl. Phys. A 556, 261 (1993).

„If equal amounts of matter and antimatter were created at the Big Bang, everything would have been annihilated, and there would be no galaxies, stars, planets or people“ (Tim Chupp Univ. Michigan)

The Standard Model describes four fundamental forces or interactions

Qu

ark

sL

epto

ns

For

ce C

arri

ers

I II IIIThree Generations of Matter

Gau

ge b

oson

s

Elementary Particles

Shape parameterization

00 ,1,

YRR

axially symmetric quadrupole axially symmetric octupole

=220≠0, 2±1= 2±2= 0

=330≠0, 3±1,2,3 = 020≠0, 2±1,2 = 0

Octupole collectivity

R.H. Spear At. Data and Nucl. Data Tables 42 (1989), 55

232

62

16

930;3

RZEB

Y30 coupling

Δℓ=3 Δj=3

some subshells interact via the r3Y30 operator

e.g. in light actinide nuclei one has an interaction between j15/2 and g9/2 neutron orbitals i13/2 and f7/2 proton orbitals

13822688 Ra

(W.u.)

Octupole collectivity

Octupole correlations enhanced at the magic numbers: 34, 56, 88, 134

Microscopically …

Intruder orbitals of opposite parity and ΔJ, ΔL = 3 close to Fermi level

226Ra close to Z=88 N=134

2/152/92/132/7 jgif

226Ra

+++++

---

--

226Ra

In an octupole deformed nucleus the center of mass and center of charge tend to separate, creating a non-zero electric dipole moment.

Octupole collectivity

The double oscillator

Ea

a

V

BH

2

320

23

22

2

-a a

V

V0

0202

2

1

2

1 V

eveneven eV

E

0202

2

1

2

1 V

oddodd eV

E

Merzbacher ‘Quantum Mechanics’

octupole deformed

β3 β3

octupole vibrational

Coulomb excitation

scattering angle

impact parameter

cm

Ruthfi

cm

fi

d

dP

d

d

bdfIIEBEZ

A

A

Ad EfiMeVE ,;21819.4 22

2

1

2

2

12

3- 4+

2+

0+

channel number

coun

ts

Scattered α-spectrum of 226Ra (t1/2= 1600 yr)

4He → 226Ra Eα = 16 MeV θlab = 1450

λ βλ (exp) βλ (theo)

2 2.27 (3) 0.165 (2) 0.164

3 1.05 (5) 0.104 (5) 0.112

4 1.04 (7) 0.123 (8) 0.096

2/0 ebEM

beam direction226Ra-target

Si-detector

Ruth

fi

el

fifi d

d

d

dP

226Ra: t1/2= 1600 yr

3- 4+

2+

0+

channel number

coun

ts

Scattered α-spectrum of 226Ra

4He → 226Ra Eα = 16 MeV θlab = 1450

beam direction226Ra-target

Si-detector

In

Ii

If

0+

4+

2+

E2

E2

E4

λ βλ (exp) βλ (theo)

2 2.27 (3) 0.165 (2) 0.164

3 1.05 (5) 0.104 (5) 0.112

4 1.04 (7) 0.123 (8) 0.096

2/0 ebEM

226Ra

PPAC ring counter150≤ΘL≤450, 00≤φL≤3600

4 PPAC counter530≤ΘL≤900, 00≤φL≤840

208 Pb beam

Ge 1

Ge 2

Ge

3

Ge 4

Ge 7

Ge 6

Ge

5

Ge8

Experimental set-up

226RaBr2 (400 μg/cm2) on C-backing (50 μg/cm2) and covered by Be (40 μg/cm2)

Coulomb excitation of 226Ra

γ-ray spectrum of 226Ra

energy [keV]

cou

nts

208Pb → 226Ra Elab = 4.7 AMeV

150 ≤ θlab ≤ 450

00 ≤ φlab ≤ 3600

γ-ray spectrum of 224Ra

224Ra → 60Ni / 120Sn Elab = 2.83 AMeV

Signature of an octupole deformed nucleus

4043032020 1 YYYRR

Ra22688

β2= 0.16β3=-0.11β4= 0.10

E2 E1

Single rotational band with spin sequence:I = 0+, 1-, 2+, 3-, …excitation energy E ~ I·(I+1)

competition between intraband E2 and interband E1 transitions

E1 transition strength 10-2 W.u.

π: +

π: -

Signature of an octupole deformed nucleus

E2 E1

π: +

π: -

224RaObservation of unexpectedly small E1 moments in 224Ra, R.J. Poynter, P.A. Butler et al., Phys. Lett. B232 (1989), 447

Signature of an octupole deformed nucleus

2

11

IEIEIEIE

Energy displacement δE between the positive- and negative-parity states if they form a single rotational band

rotorrigidfor

2

2

W. Nazarewicz et al.; Nucl. Phys. A441 (1985) 420

Electric transition quadrupole moments in 226Ra

eQ

I

IIIEMI

212

1

32

1522

negative parity statespositive parity states

W. Nazarewicz et al.; Nucl. Phys. A467 (1987) 437

rigid rotor model:

liquid drop:

22

20

25

3fm

RZQ

Q2(exp) = 750 fm2

Q2(theo) = 680 fm2

β2 = 0.21

H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

4224

23

22 967.0328.0336.0360.0

Static quadrupole moments in 226Ra

110 022

2

32121

12

EM

IEMI

III

II

Q

IQS

H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

negative parity statespositive parity states

rigid rotor model:

rigid triaxial rotor model:

Davydov and Filippov, Nucl. Phys. 8, 237 (1958)

3sin897

3cos622

0

1

Q

Qs

Electric transition octupole moments in 226Ra

33

30

37

3fm

RZQ

β3

0.18

0.12

0.06

W. Nazarewicz et al.; Nucl. Phys. A467 (1987) 437

7I

13I

13I

15I

MeV10.0

MeV15.0- 0.1

0.1

0.1

- 0.1

0

0

0.16

β3

β2

β3

H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

eQ

II

IIIIEMI

33232

21

32

3533

eQ

II

IIIIEMI

33232

11

32

2131

liquid drop:

4332 769.0841.0

Electric transition octupole moments in 224Ra

Intrinsic electric dipole moments in 226Ra

liquid-drop contribution:

rigid rotor model:

43321 458.1 ZACQ LDLD

fmCwith LD4102.5

eQIIEMI 14

311

G. Leander et al.; Nucl. Phys. A453 (1986) 58H.J. Wollersheim et al.; Nucl. Phys. A556 (1993) 261

Intrinsic electric dipole moments in 226Ra

liquid-drop contribution:

43321 458.1 ZACQ LDLD

fmCwith LD4102.5

G. Leander et al.; Nucl. Phys. A453 (1986) 58

224Ra: Q1 (e fm)

Iπ 1989 2013

3- 0.027(3) 0.031(6)

5- 0.040(10) 0.028(9)

7- < 0.05 < 0.08

Collective parameters

In general,

,1, *

0 YRR

forbidden – density change!

forbidden – CM moves!

OK...

λ=0

λ=1

λ=2

λ=3

time

Center of mass conservation

dr

dz

dy

dx

o

0

0

0

0 The coordinates (x, y, z) can be expressed by

12

3

03

2

1

,1

miyx

mzYr m

dYdrrdYr 103

100 ,3

40

dYYYYR

m mmmmmmmm 10

***40

11 2211

221122111111641

40

0

1

000

1 2121

21

2/1

21***10 4

31212640

22

2211

11 mmmmm

m

0

1

000

1 2121

21

2/1

21***10 4

31212

2

322

2211

11 mmmmm

m

The dipole coordinate is not an independent quantity. It is non-zero for nuclear shapes with both quadrupole and octupole degrees of freedom.

2332

22/1

1

32

4

375

2

3

000

1

32135

9

4

3

35

332

000

1

4363

12

4

3

Intrinsic electric dipole moment

dYdrredzeQ pprotonLD ,

3

410

31

The local volume polarization of electric charge can be derived from the requirement of a minimum in the energy functional. (Myers Ann. of Phys. (1971))

rVeC C

LDneutronproton

neutronproton

4

1

where ρp and ρn are the proton and neutron densities, CLD is the volume symmetry energy coefficient of the liquid drop model and VC is the Coulomb potential generated by ρp inside the nucleus (r < R0)

01

00

2

0 12

3

2

1

2

3

R

ZeY

R

r

R

rrVC

nCLD

p rVeC

4

0np 0

rVe

C CLD

p 4

11

20

Keeping the center of gravity fixed, the integral dYdrr 103

00 32135

9

4

3

0

303

3

0202

2

0101

0

2

0 7

3

5

3

2

1

2

3

R

ZeY

R

rY

R

rY

R

r

R

rrVC

Intrinsic electric dipole moment

dYdrrrVe

CeQ C

LD

LD ,

4

11

23

410

301

dYdrrYR

rY

R

rY

R

r

R

r

R

Z

CR

AeQ

LD

LD10

3303

3

0202

2

0101

0

2

0030

31 7

3

5

3

2

1

2

3

4

1

8

3

3

4

dYYYYYYR

dYYYYYYR

dYYYYYYR

dYYYYYYYR

dYYYYYYYR

R

Z

CR

AeQ

LD

LD

10303303202101303

40

10202303202101202

40

10101303202101101

40

102

303202101303202101

40

102

303202101303202101

40

030

31

777

3

665

3

55

156162

1

64142

3

4

1

8

3

3

4

dYYYR

dYYYYYR

dYYYR

dYYYYYR

dYYYYYR

R

Z

CR

AeQ

LD

LD

10302032

40

10302032201021

40

102010211

40

103020322010211

40

103020322010211

40

030

31

777

3

665

3

55

2215662

1

226442

3

4

1

8

3

3

4

Intrinsic electric dipole moment

32

32

1

321

321

31

35

3

4

3

7

335

3

4

3

5

35

135

3

4

3

2

5

2

135

3

4

3

2

9

2

3

32

3

3

4

LD

LD

C

ZAeQ

35

3

4

3

000

132

4

3752

103020

dYYY

323

13535

60

32

3

LD

LD

C

ZAeQ

fmC

ZAeQ

LD

LD321 01245.0

CLD ≈ 20 MeV

Summary

single rotational band for no backbending observed β2, β3, β4 deformation parameters are in excellent agreement with calculated values octupole deformation is three times larger than in octupole- vibrational nuclei equal transition quadrupole moments for positive- and negative- parity states static quadrupole moments are in excellent agreement with an axially symmetric shape electric dipole moments are close to liquid-drop value ( )

octupole deformation seems to be stabilized with increasing rotational frequency

10I

10I

Coulomb excitation of 226Ra

226Ra target broken after 8 hours Christoph Fleischmann