Slides - 11th International Spring Seminar on Nuclear Physics

Report
Isospin symmetry and
independence in analogue
excited states
11th INTERNATIONAL
SPRING SEMINAR
ON NUCLEAR PHYSICS
Mirror Symmetry
Silvia M. Lenzi
Dipartimento di Fisica e Astronomia“Galileo Galilei”
Università
Silvia
Lenzidi Padova and INFN
University of Padova and INFN
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Neutron-proton exchange symmetry
Charge symmetry : Vpp = Vnn
p
n
Charge independence: (Vpp + Vnn)/2= Vnp
Deviations are small
Electromagnetic interactions lift the degeneracy
of the analogue states, but do not generally affect
the underlying symmetry.
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Analogue states in the A=22, T=1 triplet
MeV
5
T=1
MeV
T=1
T=0 and T=1
5
4
4
4+
3
4+
4+
2
3
2
1
2+
0
0+
22
12 Mg 10
0.693
4+
1++
3
22
11 Na 11
2+
2+ 1
0+
0+ 0
22
10 Ne 12
LARGE differences in mass/binding energy mainly due to Coulomb effects
SMALL differences in excitation energy
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Differences in analogue excited states
Z
Mirror Energy Differences (MED)
MED
N
J
 E x J ,T z   T  E x J ,T z   T
Test the charge symmetry of the interaction
Triplet Energy Differences (TED)
TED
J
 E x J ,T z   T  E x J ,T z   T  2 E x J ,T z  0
Test the charge independency of the interaction
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Mirror symmetry is (slightly) broken
Isospin symmetry breakdown, mainly due to the Coulomb field, manifests when
comparing mirror nuclei. This constitutes an efficient observatory for a direct
insight
nuclear
properties.
th Int. Spring
Silvia
Lenzi – 11into
Seminarstructure
on Nuclear Physics,
Ischia, May 12-16, 2014
Measuring MED and TED
Can we reproduce such small energy differences?
What can we learn from them?
They contain a richness of information
about spin-dependent structural phenomena
We measure nuclear structure features:
How the nucleus generates its angular momentum
Evolution of radii (deformation) along a rotational band
Learn about the configuration of the states
Isospin non-conserving terms of the interaction
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED and nucleon spatial correlations
probability distribution for the
relative distance of two like
particles in the f7/2 shell
J
8
J
8
courtesy P. Van Isacker
j
6
j
6
neutron 4
align.
proton
align.
4
2
0
2
0
j
A(N,Z)
A(Z,N)
I=8
angular momentum
j
J=0
j
j
7
MED
j
j
ΔEC
Shifts between the excitation energies
of the mirror pair at the backbending
indicate the type of nucleons that are
aligning
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
100
MED and nucleon alignment
50
Energy 51Fe
-150
(MeV)
6 -200
5
7
51Mn
Experiment
11 13 15 17 19 21 23 25 27
-100
Experiment
D.D. Warner, M.A. Bentley and P. Van Isacker,
Nature Physics 2 (2006) 311
-50
fp-shell Model
0
fp-shell
Model
Shell
Model
9
25
+ Coulomb
11 13 15 17 19 21 23 25 27
MED
21
Alignment
17
2J
3
13
7
9
9
-200
MED (keV)
-150
-100
-100
-50
0
0
100
50
5
5
100
0
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Including monopole Coulomb effects
Can we do better?
When we “normalize” to the g.s. energy, large Coulomb
effects vanish, however…
a small but important effect remains as a function of the
angular momentum, and it is related to changes of the
nuclear radius, or deformation and to single-particle effects.
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
9
Improving the description of Coulomb effects
V C  V CM  V Cm
VCM Multipole part
of the Coulomb
energy:
Between valence
protons only
3 e Z ( Z  1)
2
E Cr 
VCm Monopole
part of the
Coulomb
energy:
5
R
radial effect:
radius changes with J
L2 term to account for shell effects
 4 . 5 Z cs
13 / 12
E Cll 
A
[ 2 l ( l  1)  N ( N  3 )]
1/ 3
( N  3 / 2)
electromagnetic LS term
E Cls  ( g s  g l )
keV
change the
single-particle
energies
 1 dV C 

 l.s
2 2
4 m N c  r dr 
1
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
The radial term
The difference between the Coulomb energy of the ground states (CDE):
 E C  J  0   E C Z    E C Z   
3 n  2 Z   n e
2
5 RC
Tz  
If RC changes as a function of the angular momentum…
 E Cr  J    E C  J    E C 0   nC   R C  J
n
2
J

In f7/2 nuclei the radial contribution can be calculated from the relative p3/2
occupation number along the yrast band in the shell model framework
Δ V Cr  J  na m  m p 3 / 2  J  na m
z p3 / 2  n p3 / 2
2
J
z and n are the number of protons
and neutrons in the p3/2 orbit,
relative to the g.s. (J=0)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
The electromagnetic spin-orbit term
Analogous to the atomic case, the nuclear
electromagnetic spin-orbit coupling has relativistic origin.
V Cls
 1 dV C   
 g s  g l 
 l s
2 2 
2 m N c  r dr 
1
s
ℓ
f7/2
 
l  s  l  j  l  s
 
l s  l 1 j  l  s
ΔEp ~ 220 keV
j=l+½
ℓ s d3/2
j=l-½
f7/2
j=l+½
d3/2
j=l-½
π
ν
Its contribution to the MED becomes significant for configurations with a pure single-nucleon
excitation to the f7/2 shell: a proton excitation in one nucleus and a neutron excitation in its mirror
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Are Coulomb corrections enough?
49
25
Mn
VCM+VCm
 24 Cr 25
24
49
VCM
Exp
VCm
Another isospin symmetry breaking (ISB) term is needed and it has to be big!
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Looking for an empirical interaction
In the single f7/2 shell, an interaction V can be defined by two-body matrix elements
written in the proton-neutron formalism :
V

,V


,V
We can recast them in terms of isoscalar, isovector and isotensor contributions
ππ
πν
U
νν
U
U
Mirrors
Triplet
MED
V

V

(1)
V

V

(2)
V

V

V

 2V

( Ti- We
Ca )assume
 U f 7 / 2 , J that
 V C the
 Vconfigurations
,J
B ,J
Isovector
42
J
(0)
42
(1 )
(1 )
(1 )
of these states are pure (f7/2)2
42
42
42
(2)
(2)
(2)
TED J ( Ti  Ca - 2  Sc )  U f , J  V C , J  V B , J Isotensor
7/2
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Looking for an empirical interaction
VC is calculated for every J state in the f7/2 shell
and then subtracted to MED and TED to estimate VB
MED
81
VC
MED-VC= V(1)B
5
J=2
24
93
J=4
6
5
-11
-48
J
42
Ca )  V C , J  V B , J
(1 )
(1 )
150
J=6
Energy (keV)
J=0
42
( Ti-
100
Coul
MED-Coul
50
0
-50
0
2
4
-100
TED-VC=V(2)B
117
81
3
-42
spin
This suggests that the role of the isospin non conserving nuclear force is at
least as important as the Coulomb potential in the observed MED
A. P. Zuker et al., PRL 89, 142502 (2002)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
6
The “J=2 anomaly”
Coulomb matrix elements (MeV)
Is this just a Coulomb two-body effect?
Spatial correlation probability for two nuclons in f7/2
Calculation (using Harmonic
Oscillator
w.f)
Two
possibilities:
1) Increase the J=2 term
2) Decrease the J=0 term
We choose 1) but there is not
much difference
See talk by M. Bentley
Angular momentum J
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Looking for an empirical interaction
From the yrast spectra of the T=1 triplet 42Ti, 42Sc, 42Ca we deduce the interaction
J=0
J=2
J=4
J=6
81
24
6
-11
MED-VC
5
93
5
-48
TED-VC
117
81
3
-42
VC
Calculated
estimate VBf7/2 (1)
estimate VBf7/2 (2)
Simple ansatz for the application to
nuclei in the pf shell:
V Bpf ( ( f 7 / 2 ) J  2 )   100 keV
(1 )
2
V Bpf ( ( f 7 / 2 ) J  0 )   100 keV
(2)
2
A. P. Zuker et al., PRL 89, 142502 (2002)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Calculating MED and TED
We rely on isospin-conserving shell model wave functions and obtain the
energy differences in first order perturbation theory as sum of expectation
values of the Coulomb (VC) and isospin-breaking (VB) interactions
exp
J
MED
MED
TED
theo
J
exp
J
 E J Z    E J Z  
*
*
  M V Cm  J   M V CM  J   M V B  J
(1 )
 E J Z    E J Z    2 E J  N  Z 
TED
*
Theo
J
*
*
  T V CM  J   T V B  J
(2)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Calculating the MED with SM
MED
theo
J
  M V Cm  J   M V CM  J   M V B  J
(1 )
Theo
VCM: gives information on the
nucleon alignment or recoupling
49Mn-49Cr
VCM
Exp
VCm: gives information on
changes in the nuclear radius
VCm
Important contribution from the
ISB VB term:
of the same order as the
Coulomb contributions
VB
A. P. Zuker et al., PRL 89, 142502 (2002)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED in T=1/2 states
Very good quantitative description of data without free parameters
A = 45
45
23
V 22  22 Ti
45
A = 47
23
A = 49
A = 51
51
26
Fe 25  25 Mn
49
25
Mn
47
24
Cr 23  23 V 24
47
 24 Cr 25
49
24
51
26
53
27
Co 26  26 Fe 27
A = 53
M.A. Bentley and S.M.L.,
Prog. Part. Nucl. Phys. 59,
497-561 (2007)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
53
MED in T=1 states
A = 42
42
22
Ti
 20 Ca
20
42
A = 46
22
A = 48
50
26
48
25
Mn
46
24
Cr 22  22 Ti 24
46
 23 V 25
48
23
Fe 24  24 Cr 26
50
A = 50
140
120
A = 54
100
M.A. Bentley and SML,
Prog. Part. Nucl. Phys. 59,
497-561 (2007)
Same parameterization
for the whole f7/2 shell!
54
28
Ni 26  26 Fe 28
54
80
60
40
20
0
-20
-40
0
2
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
4
6
Some illustrative
examples
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
22
Evidence of the monopole radial effect
Multipole (alignment) effects
are cancelled out
48
25
Mn
3
48
23
23
 f7 / 2  f7 / 2
3
V 25
3
 f7 / 2  f7 / 2
3
radial term
Most important contribution
M.A. Bentley et al.,
PRL 97, 132501 (2006)
The nucleus changes shape
towards band termination
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
The electromagnetic spin-orbit effect:
disentangling configurations
35Ar
23/2-
35Cl
23/2-
19/2-
19/215/2-1
11/2-1
15/2-2
11/2-2
15/2-1
15/2-2
11/2-2
11/2-1
Negative parity
11/2-1
MED > 300 keV
11/2-2
From the MED experimental values
we can identify those states with
configurations of pure proton (neutron)
excitation to the f7/2 shell.
F. Della Vedova et al.,
Phys.Rev. C 75, 034317 (2007)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
T=1 A=54/42 MED: the VB term
A=54
A=42
no collectivity: only multipole effects:
smooth recoupling and J=2 anomaly
2 particles / holes
A=54
A=42
A.Gadea et al., PRL 97, 152501 (2006)
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
TED (keV)
TED (keV)
TED (keV)
TED (keV)
TED in the f7/2shell
Only multipole effects are relevant.
The ISB term VB is of the same magnitude of the Multipole Coulomb term
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Some questions arise…
What happens farther from stability
or at larger T in the f7/2 shell?
The same prescription applies (see M. Bentley’s talk)
Can we understand the origin of this term?
Work in progress with A. Zuker
Is the ISB term confined to the f7/2 shell
or is a general feature?
If so the same prescription should work
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Looking for a systematic ISB term
Necessary conditions for such studies:
• good and enough available data
• good shell model description of the structure
Ideal case: the sd shell
But…few data at high spin and
no indications of J=2 anomaly in A=18
28
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
A systematic analysis
of MED and TED
in the sd shell
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
29
The method
We apply the same method as in the f7/2 shell
However, here the three orbitals, d5/2, s1/2 and d3/2 play an important role
MED
theo
J
  M V Cr  ll  ls  J   M V CM  J   M V B  J
(1 )
VCr (radial term): looks at changes in occupation of the s1/2
V Bpf ( ( d 5 / 2 ) J  2 ,  ( d 3 / 2 ) J  2 )   100 keV
(1 )
2
TED
Theo
J
2
  T V CM  J   T V B  J
(2)
V Bpf ( ( d 5 / 2 ) J  0 ,  ( d 3 / 2 ) J  0 ,  ( s1 / 2 ) J  0 )   100 keV
(2)
2
2
2
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED: different contributions
A=29
T=1/2
T=1/2
A=26
T=1
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED (keV)
MED in the sd shell
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
TED (keV)
TED in the sd shell
The prescription applies successfully also in the sd shell!
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
What about other mass regions?
The next mass region is the upper pf and fpg shells
but…
not much data to perform a systematic analysis
The shell model description is not that good.
The development of deformation and
shape coexistence enter into play
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED and TED in the
upper pf shell
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
35
The method
We apply the same method as in the f7/2 shell
However, here the three orbitals, p3/2, f5/2 and p1/2 play an important role
MED
theo
J
  M V Cr  ll  ls  J   M V CM  J   M V B  J
(1 )
VCr (radial term): looks at changes in occupation of both p orbits
V Bpf ( ( f 7 / 2 , p 3 / 2 , p 1 / 2 , f 5 / 2 ) J  0 )   100 keV
(1 )
TED
2
Theo
J
2
2
2
  T V CM  J   T V B  J
(2)
V Bpf ( ( f 7 / 2 , p 3 / 2 , p 1 / 2 , f 5 / 2 ) J  0 )   100 keV
(2)
2
2
2
2
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
MED (keV)
MED in the upper pf shell
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
TED in the upper pf and fpg shells
TED
Theo
J
  T V CM  J   T V B  J
V Bpf ( ( f 7 / 2 , p 3 / 2 , f 5 / 2 , p 1 / 2 ) J  0 )   100 keV
(2)
2
2
2
2
(2)
V Bfpg ( ( p 3 / 2 , f 5 / 2 , p 1 / 2 , g 9 / 2 ) J  0 )   100 keV
(2)
2
2
2
2
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
N~Z nuclei in the A~68-84 region
Around N=Z quadrupole correlations are dominant.
Prolate and oblate shapes coexist.
The fpg space is not able to reproduce this behaviour, the fpgds space is needed.
s1/2
d5/2
g9/2
f5/2
p
quasi
SU3
40
pseudo
SU3
MED are sensitive to
shape changes and
therefore a full
calculation is needed,
which is not always
achievable with large
scale SM calculations
A.P. Zuker, A. Poves, F. Nowacki and SML, arXiv:1404.0224
Experimentally it is not clear if what we measure are energy
differences between analogue states, as ISB effects may
exchange the order of nearby states of the same J
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
Conclusions
Z
N~Z nuclei present several interesting properties and
phenomena that can give information on specific terms
of the nuclear interaction.
N
The investigation of MED and TED allows to have
an insight on nuclear structural properties and their
evolution as a function of angular momentum such
as: alignments, changes of deformation, particular
s.p. configurations.
The need of including an additional ISB term VB shows up not only
in the f7/2 shell but also in other mass regions (sd, upper pf and fpg).
Investigation of its origin is in progress.
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014
In collaboration with
Mike Bentley
Rita Lau
Andres Zuker
Silvia Lenzi – 11th Int. Spring Seminar on Nuclear Physics, Ischia, May 12-16, 2014

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