Ground-state nucleon occupancies of 0ν2β
candidate systems
D. K. Sharp
The University of Manchester, UK
MEDEX’15
Prague 9th-12th July 2015
Brief Overview
•  Brief introduction to importance of nuclear structure observables to nuclear
matrix elements for 0ν2β.
•  General approach to measurement of ground-state nucleon occupancies.
•  Summary of previous 76Geà76Se measurements (B. P. Kay).
•
130Teà130Xe
neutron occupancies (B. P. Kay).
•  Some results for 100Moà100Ru system
•  Present neutron and proton occupancies.
•  Reminder of pairing results.
•
Preliminary results for 150Ndà150Sm system.
•  Neutron occupancies.
Nuclear Matrix Elements
For neutrinoless double beta decay mediated by a light massive neutrino
0 ν −1
= (Matrix Element) x (Phase space factor) x
1/2
!"T #$
mν
2
Observation of decay and measurement of decay rate provides fundamental information
on the neutrino:
•  Evidence that neutrino is a Majorana particle.
•  Access to absolute neutrino mass scale .
Nuclear Matrix Elements
For neutrinoless double beta decay mediated by a light massive neutrino
0 ν −1
= (Matrix Element) x (Phase space factor) x
1/2
!"T #$
mν
2
Relies on calculations of the nuclear
matrix element.
Several theoretical approaches
(QRPA, ISM, IBM……)
Calculations agree to a factor of
2-3. Even if they agree, does not
necessarily mean they are all
correct.
How does one test the validity of
NME calculations?
Iachello, NEUTEL 2015.
Neutrinoless double beta decay
0νββ distinctly different from 2νββ
2 neutrino case proceeds via
intermediate nucleus.
1+
0+ ias
T=6
0+
T=5 das
1+
states in the
gs
0+gs
Neutrinoless case involves excitations up to 10s
of MeV are accessible with angular momentum
up to ~5-6 ħ.
T=6
76As
T=6
T=5
76Ge
0+gs
76Se
T=4
There is more available nuclear structure
information for the 2νββ case. Details of
intermediate nucleus matters less to the 0νββ
as long as closure approximation is valid.
No other process samples the same matrix
element as 0νββ.
How do we benchmark the models used to
calculate nuclear matrix elements?
What can we measure?
What aspects of the nuclear physics of the decay process are important and what other
nuclear properties indicate important influences on the matrix elements?
Measure these properties and use results to gauge to what extent they can be reproduced
by the models used to calculate matrix elements.
Ground state occupancies:
Details of the valence single-particle occupancies before and after decay have important
consequencesà Any rearrangement of nucleons is likely to hinder the decay rate.
(Single-nucleon transfer).
A change in deformation during the decay can drive such rearrangements.
Pairing:
Decay involves conversion of two neutrons to two protons, so naively expect pairing
correlations to be important – as they are in pair-adding and –removing reactions. More
than a naive assumption as importance of J=0 contributions to NME are known.
See recent review article S. J. Freeman and J. P. Schiffer, J. Phys.G: Nucl Part. Phys. 39 124004 (2012).
Single nucleon transfer reactions
Measure:
Yield à Cross section
Momentum à Energy
Experimental conditions
arranged to favour
single-step transfer of a
nucleon to/from target
Angular momentum, ℓ𝓁,
from angular distributions
d
d
= Slj
d⌦ exp
d⌦ DWBA
Spectroscopic factor: Measure
of the overlap between the final
and initial state
Single nucleon transfer reactions
Due to correlations between nucleons, strength
of an independent-particle model (IPM) orbit
can be spread over many states.
Spectroscopic factor: Measure of the overlap
between the final and initial state.
Extracted from experiment by comparison of
measured cross sections with reaction models
assuming an IPM state.
SF =
D
MB
JB |A[
SF =
JA
exp
dwba
Essentially reduced cross sections.
Proportional to emptiness or fullness of a
particular orbital.
Vacancy =
X
j
2
(2j + 1)C SF+
Occupancy =
X
j
C 2 SF
MB
j ]JB
E
2
Generalisation of experimental methods
Light-ion induced reactions with beam
energies of 10-20 MeV/u – direct
mechanism dominates.
Where possible use two sets of reactions to
meet matching conditions for low- and high𝓵 transfer.
High-Q valueàhigh-𝓵 transfer.
Low-Q valueàlow-𝓵 transfer.
12
Counts / BIC (x10 )
0.8
L=2
0.6
L=4
L=5
102
L=0
Ru
(p,d)
( He, )
3
L=5
0.4
L=0
0.2
0.0
0
500
1000
Excitation Energy (keV)
1500
Generalisation of experimental methods
Light-ion induced reactions with beam
energies of 10-20 MeV/u – direct
mechanism dominates.
Where possible use two sets of reactions to
meet conditions for low and high 𝓵 transfer.
Use magnetic spectrograph to momentum
separate outgoing ions and identify using
energy loss characteristics in focal plane
detector.
Generalisation of experimental methods
Light-ion induced reactions with beam
energies of 10-20 MeV/u – direct
mechanism dominates.
(d,p)
0.1
Measure cross sections at peaks of
distributions where assumptions in DWBA
are best met.
3038
l=1
0
290
l=2
0.4
Ensure consistency in both experimental
approach and reaction modelling.
0.01
( He, )
0
0.4
0
2067
l=3
0.1
0.1
1423
l=0
2
0
1102
l=1
0.04
0.02
0
0.08
0
885
l=2
0.2
0.1
0
0.01
0
0.08
1680
l=3
393
l=3
0.04
0
0.02
0
0.04
0.01
702
l=4
0
0
0.02
10 20 30
0.1
724
l=5
0
0
697
l=4
0
0
20
40
683
l=5
0
0
20
1468
l=4
0.2
0.1
0
1726
l=2
1732
l=2
0.05
0
2466
l=1
0.04
0.02
Angular distributions allow 𝓵 identification
1237
l=0
0.2
0.02
Cross Section (mb/sr)
Use magnetic spectrograph to momentum
separate outgoing ions and identify using
energy loss characteristics in focal plane
detector.
0
0.04
3
( He,d)
4
1196
l=0
0.05
Where possible use two sets of reactions to
meet conditions for low and high 𝓵 transfer.
3
(p,d)
40
Laboratory Angle (degrees)
0 10 20 30
Reaction normalisation
Measure absolute cross sections and deduce spectroscopic factor – reduced cross section.
S ' = σ exp / σ DWBA
Need to normalise reaction model, remove some uncertainty on absolute numbers due to choices
in calculations.
Can normalise observed strength to expected total number of valence nucleons (removing
reactions) or holes (adding reactions) outside closed shell (need to be confident total strength has
been observed).
More robust to use Macfarlane and French some rules if both adding and removal reactions are
available.
N j = S '/ S = (ΣG+ S 'adding + ΣG− S 'removing ) / (2 j +1)
Normalisation deduced for each orbital and we use an average across a number of isotopes then
occupancy for each orbital deduced using common normalisation.
Consistency of normalisations over a range of isotopes gives confidence in methodology.
M. H. Macfarlane and J. B French, Rev. Mod. Phys. 32, 567 (1960)
Quenching of cross sections
Required normalisation found to be consistent across a range of reactions, mass,
transferred momentum or type of nucleon – lends confidence to adopted method.
Cross sections found to quenched to 50-60%. Consistent with proton knockout
reactions from 1980s.
Appears to be uniform property thought to be associated in part due to the effects of
short-range correlations (SRC).
This indicates that this methodology is robust
B. P. Kay et al., Phys. Rev. Lett. 111, 042502, (2013)
Candidate decays
150Nd➝150Sm
136Xe➝136Ba
N = 126
130Te➝130Xe
116Cd➝116Sn
Decay
100Mo➝100Ru
96Zr➝96Mo
82Se➝82Kr
76Ge➝76Se
N = 82
48Ca➝48Ti
Q (MeV)
N = 28
N = 20
N=8
% Abundance
Decay
150Ndà150Sm
3.37
Q (MeV)
63.03
Abd. 5.6
(%)
136Xeà136Ba
2.48
14.58
8.9
130Teà130Xe
2.53
14.22
34.5
9.04
5.6
16.70
7.5
3.03
15.92
9.6
96Zrà96Mo
3.35
20.58
2.8
82Seà82Kr
2.99
10.16
9.2
76Geà76Se
2.04
2.36
7.8
48Caà48Ti
4.27
24.81
0.187
α
2.23
β–
116Cdà116Sn
EC, β+ 2.80
100
100 stable
124Snà124Te
N = 50
G0ν
Moà
Ru
Slide courtesy of B. P. Kay
The Ge System: Impact on the NME’s?
A=76 decay: NME’s
before (black) and after (red) enforcing Schiffer’s occupancies
7
QRPA(Tu)
RQRPA(Tu)
QRPA(Jy)
ISM
Magnitude of NME
6
5
~40%
~50%
4
~70%
3
QRPA (Tu)
RQRPA (Tu)
QRPA (Jy)
ISM
2
Figure 3. The evolution of the NME’s of the A=76 decay when the ISM and QRPA calculations
Yes, some. Though much discussed, a 40-70% reduction in the well-known “gap” between
are modified so as to reproduce the experimental occupancies
QRPA and the ISM, resulted.
Modified figure from Menéndez, Poves, Caurier, Nowacki, J. Phys.: Conf. Ser. 312, 072005 (2011)
43
Slide courtesy of B. P. Kay
Change in Vacancy/Occupancy: A = 76
Neutron vancancy (76Se–76Ge)
Neutrons
Theory–experiment
2
1
0
–1
Protons
Theory–experiment
2
A
B
C
Proton occupancy (76Se–76Ge)
–2
1
0
–1
–2
A
B
C
EXP
A
B
C
0g9/2
1p
2
2
2
2
1
1
1
1
0
0
0
0
EXP
A
B
0f5/2
C
2
2
2
2
1
1
1
1
0
0
0
0
EXP — J. P. Schiffer et al., Phys. Rev. Lett. 100, 112501 (2008); BPK et al., Phys. Rev. C 79, 021301(R) (2009)
A — QRPA by Rodin et al., priv. com., Nucl .Phys. A 766, 107 (2006)
B — QRPA by Suhonen et al., priv. com., Phys. Lett. B 668, 277 (2008)
C — ISM by Caurier et al., priv. com., Phys. Rev. Lett. 100, 052503 (2008)
44
Slide courtesy of B. P. Kay
ew
N
The A = 130 Summary
Can the 0g7/2 be “turned off”?
Beyond this, the main discrepancies between theory and calculations are the 1d, the
vacancy changing too little, and the 0h11/2, the vacancy changing too much.
Neutron vancancy (130Te–130Xe)
Neutrons
Theory–experiment
2
1
0
–1
–2
A
B
C
D
EXP
A
B
C
D
2
2
2
2
2
1
1
1
1
1
0
0
0
0
0
0h11/2
2s1/2
1d
0g7/2
There must be a quantitative impact on the NMEs were the calculations to be modified to
reproduce the experimental data.
EXP — BPK et al., Phys. Rev. C 87, 011302(R) (2013)
A,B — J. Suhonen and O. Civitarese, Nucl. Phys. A 847, 207 (2010)
C — A. Neacsu, priv. com.; A. Neascu and M. Horoi, Phys. Rev. C 91, 024309 (2015)
D — J. Menéndez, priv. com.; J. Menéndez, A. Poves, E. Caurier, and F. Nowacki, Nucl. Phys. A 818, 139 (2009)
45
100Moà100Ru
system – previous measurements
Previous neutron data incomplete or inconsistent –
measured at a range of energies, facilities, using a
range of reaction modeling.
ββ
Very little in the way of proton data.
Necessary to make consistent measurements over
isotopes of interest.
98Mo
(p,d)
100Mo
✓ (38.6, 52 MeV) ✓ (21, 40, 52 MeV)
100Ru
102Ru
✗
✓ (26.3 MeV)
(d,p)
✓ (10,12 MeV)
✓ (3.75, 12 MeV)
(3He,α)
✗
✓ (18 MeV)
✗
✗
✓ (18 MeV)
✗
✗
✗
✗
✗
(3He,d) ✓ (18, 33.3 MeV)
(α,t)
✗
✓ (11.5, 12 MeV) ✓ (12,14,15, 45 MeV)
100Moà100Ru
system – what have we measured?
Neutron- and proton- adding and
removal reactions on 98,100Mo and
100,102Ru targets.
Neutron Fermi surfaces in shell that
includes: 0g7/2 , 1d5/2 , 1d3/2 , 2s1/2 and
0h11/2 .
Proton Fermi surfaces in shell that
includes: 1p3/2 , 0f5/2 , 1p1/2 and 0g9/2.
Neutron pair transfer, (p,t) reaction.
ββ
100Moà100Ru
system – extracted occupancies
Neutron occupancies for lowℓ𝓁 states deduced using
MacFarlane and French sum
rules.
Proton occupancies inferred
from deduced vacancies.
Strength observed in protonremoval reactions normalised
to total number of nucleon
holes.
Nucleon Occupancy
High-ℓ𝓁 strength normalised to
the remaining number of
nucleons.
NEUTRONS
PROTONS
8
16
7 1h
11/2
14
6
12
10
5
4
1g7/2
8
3
6
2 1d
4
1
2
0
1g9/2
2s1/2
1f5/2
1p
0
102
Ru
100
Ru
100
98
Mo Mo
102
Ru
100
Ru
100
98
Mo Mo
system – change in occupancies
Occupancy measurements
indicate that the 0h11/2 and 1d
neutrons participate
significantly in a double β decay
process.
Smaller contributions from 2s1/2
and 0g7/2.
Increase in number of protons
in during decay mainly in the
0g9/2 orbital with 1p protons
playing a lesser role.
NEUTRONS
Difference in Occupancy
100Moà100Ru
3
100
Mo-Ru
3
1d
2
PROTONS
100
Ru-Mo
2
0g9/2
1
1
2s1/2
0
EXP
-1
0h11/2
0g7/2
0
EXP
-1
THEORY
-2
0f5/2
1p
THEORY
-2
system – change in occupancies
Instructive to compare measured
occupancies with those extracted
from theoretical studies of nuclear
matrix elements.
Quantitative occupancies not always
given in theoretical publications.
Comparison with one calculation
shows some broad similarities (loss
of neutrons in 1d orbitals and gain in
protons in 0g9/2 orbital).
However, calculation predicts more
complex rearrangement of nucleons
than has been observed
experimentally.
NEUTRONS
Difference in Occupancy
100Moà100Ru
3
100
Mo-Ru
3
1d
2
PROTONS
100
Ru-Mo
2
0g9/2
1
1
2s1/2
0
EXP
-1
0h11/2
0g7/2
0
EXP
-1
THEORY
-2
0f5/2
1p
THEORY
-2
Theory: J. Suhonen, O. Civitarese., Nucl. Phys. A. 924, 1, (2014)
100Moà100Ru
system – change in occupancies
Majority of difference appears to come
from 100Mo neutron occupancies.
Though still room for improvement in
100Ru as well.
Neutrons
Exp.
8
Protons
20
Theory
Exp. Theory
Proton occupancies in good
agreement.
BCS approximation used. Not at
QRPA level. What effect does this
have?
Nucleon Occupancy
1h11/2
Exp.
Theory
15
Exp. Theory
6
1g7/2
1g9/2
10
4
1f5/2
1d
5
2
Larger effect on high-ℓ𝓁 orbitals.
1p
0
2s1/2
100
0
Mo
100
Mo
100
Ru
100
Ru
100
Mo
100
Mo
100
Ru
100
Ru
Theory: J. Suhonen, O. Civitarese., Nucl. Phys. A. 924, 1, (2014)
M. A. RAHMAN AND M. S. CHOWDHURY
100Moà100Ru
PHYSICAL REVIEW C 73, 054311 (200
neutron pairing
its spin orbit partner 1g7/2 orbital [9,10]. The deformati
parameter β2 increases with neutron number. It is 0.175
98
Mo, 0.217 for 100 Mo, 0.311
for 102 Mo, and1000.33 for 104 M
100
Neutron pair transfer measurements show 95% of[2,23].
ℓ𝓁=0(p,t)
=0(p,t)
strength in Ru g.s. For Mo
It may therefore be noted that the 102 Mo nucleus exi
~20% in an excited state.
at the edge of a region of well-deformed shape.
Neutron-pairing vibrations due to shape coexisting states. Transitional region with onset
later in Ru than Mo à well known in this region of the nuclear chart.V. CONCLUSIONS
Total pair strength consistent to 10%.
The nuclear properties of the levels in 102 Mo have be
studied with the 100 Mo(t, p)102 Mo reaction. A number of n
energy levels have been found, and spin assignments we
made for many of them. The present results are in go
agreement with the previous results. The systematics of t
first 2+ , 0+ , and 3− states in Fig. 3 and the appearan
of the low-lying 0+ state as the bandhead of a deform
band that becomes the ground state in the heavier 104,106 M
nuclei suggest that the 102 Mo nucleus exists at the end of t
transitional region. Theoretical calculation of the level schem
of 102 Mo60 is not yet available. It will be useful to have furth
experimental and theoretical investigations of 102 Mo.
ACKNOWLEDGMENTS
The authors would like to thank the operating staff
the tandem accelerator at AWRE, Aldermaston, for th
+
+
−
cooperation and Professor P. D. Kunz, University of Colorad
FIG. 3. Systematics of the low-lying first 2 , 0 , and 3 states.
The
0 Thomas,
transition et
strength
has86,
been
normalized
for sending us the DWUCK4 program. One of the authors (MS
(p,t)LJ.=S.
al., PRC
047304
(2012)to 100 units for
100
Mo.
the
transitions
of
grateful to the University of Bradford for financial supp
(t,p) M. A. Rahman and M. S. Chowdhury, Phys. Rev. C 73, 054311 is
(2012)
and to Professor G. Brown and Dr. W. Booth, University
150Ndà150Sm
system
Deformed system - change in deformation between initial and final state.
Change of deformation may hinder the decay and impacts on calculation of NMEs.
Active valence neutron orbitals are
3p1/2,3/2, 2f5/2,7/2, 1h9/2 and 1i13/2.
Location of fermi surface can vary from
calculation to calculation and may be
different for 150Nd and 150Sm due to
differing deformation.
J. M. Yao et al., Phys. Rev. C 91 023316 (2015)
150Ndà150Sm
system
Have made high resolution measurements of
(d,p) and (p,d) reactions at Munich as well as
(3He,α) reaction.
148
Nd
Measurements on 148Nd, 152Sm and 154Sm
provide consistency checks of the sum rules.
Yield/BIC (arb. units)
150
Sm
152
Sm
154
150
Sm
Nd
0
1
Excitatin energy (MeV)
2
150Ndà150Sm
system
Preliminary differences between 150Nd and 150Sm occupancies suggest that majority is
due to 1h9/2 and 1i13/2 orbitals. There is also some increase in the occupancy of the 2f
orbital – more complex rearrangement.
Likely impacted by change in deformation in decay.
Need (α,3He) reaction in order to more
confidently describe the l=5 and 6
occupancies using the sum rules.
Proposal accepted to measure this
reaction.
Current data is preliminary.
Predictions from theoretical studies of
nuclear matrix elements…..
Summary
We have made quantitive measurements of the ground-state occupancies of the A=76,
100, 130 and A=150 0υ2β candidate systems.
A=76 system provided benchmark for calculations and subsequent improved agreement
between differing calculations.
Change A=130 occupancies shows disparity with theoretical calculations.
Neutron and proton occupancies for 100Mo and 100Ru appear at odds with theoretical
predictions from one set of calculations.
Interesting to see impact of these measurements on NME calculations.
Previously looked at pairing in A=100 system. Significant strength found in excited 0+ state
in 100Mo due to transitional nature of this region. How does this impact?
Preliminary results for A=150 system suggest that majority of the change in neutron
occupancy between 150Nd and 150Sm is in the h9/2 and i13/2 orbitals. Further measurements
required to more reliably extract information on the high-l orbitals.
Possibility of extracting proton occupancies?
Collaborators
D. K. Sharp, S. J. Freeman, S. D. Blot, T. E. Cocolios, J. P.
Entwilse, A. M. Howard, S. A. McAllister, A. J. Mitchell, S. V.
Szwec and J. S. Thomas
The University of Manchester, UK
B. P. Kay, J. P. Schiffer, J. A. Clark, C. M. Deibel and C. R.
Hoffman
Argonne National Laboratory, USA
T. Faestermann, R. Hertenberger and H-. F. Wirth
Maier-Leibnitz-Laboratorium der Münchner Universitäten,
Germany
Slide courtesy of B. P. Kay
DNP 2015!
!
Fall Meeting of the
Division of Nuclear Physics of the
American Physical Society!
Local Organizing Committee :!
Convention Center, Santa Fe, NM !
Joe Carlson!
October 28-31, 2015!
Vincenzo Cirigliano!
Steven Clayton!
Stefano Gandolfi!
Marian Jandel!
Christopher Lee!
Hye Young Lee!
Susan Seestrom!
Cesar da Silva!
Richard Van de Water!
Ivan Vitev!
W. Scott Wilburn (chair)!
!
There will be a dedicated
symposium on Nuclear
Matrix Elements for
Neutrinoless Double Beta
Decay.
We would welcome the
submission of abstracts
and look forward to
making this an exciting
session.
The deadline is July 1st.
Information can be found
at:
www.lanl.gov/dnp/2015
46