Standard Model goes pear-shaped in CERN experiment The Register
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Transcript of Standard Model goes pear-shaped in CERN experiment The Register
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