$^{48}$Ca, the lightest double beta decay candidate, is the only one simple
enough to be treated exactly in the nuclear shell model. Thus, the
$\beta\beta(2\nu)$ half-life measurement, reported here, provides a unique test
of the nuclear physics involved in the $\beta\beta$ matrix element calculation.
Enriched $^{48}$Ca sources of two different thicknesses have been exposed in a
time projection chamber, and yield T$_{1/2}^{2\nu} = (4.3^{+2.4}_{-1.1} [{\rm
stat.}] \pm 1.4 [{\rm syst.}]) \times 10^{19}$ years, compatible with the shell
model calculations.Comment: 4 pages, LaTex, 3 figures imbedded, PRL forma

Balysh, A.

De Silva, A.

Lebedev, V. I.

Lou, K.

Moe, M. K.

Nelson, M. A.

Piepke, A.

Pronskiy, A.

Vient, M. A.

Vogel, P.

English

arXiv

48Ca, the lightest experimentally accessible double beta decay candidate, is the only one simple enough to be treated exactly in the nuclear shell model. Thus the ββ2ν half-life measurement, reported here, provides a unique test of the nuclear physics involved in the ββ matrix element calculation. Enriched 48Ca sources of two different thicknesses have been exposed in a time projection chamber. We observe a half-life of T1/22ν = (4.3-1.1+2.4[stat]±1.4[syst])×101^9 yr, consistent with shell model calculations

Caltech Authors - Main

VOLUME 77, NUMBER 26 P HY S I CA L REV I EW LE T T ER S 23 DECEMBER 1996
5186Double Beta Decay of 48Ca
A. Balysh,1 A. De Silva,2 V. I. Lebedev,1 K. Lou,3 M.K. Moe,2 M.A. Nelson,2 A. Piepke,3
A. Pronskiy,1 M.A. Vient,2 and P. Vogel3
1Kurchatov Institute, Kurchatov Square, 123182 Moscow, Russia
2Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697
3Physics Department, California Institute of Technology, Pasadena, California 91125
(Received 2 August 1996)
48Ca, the lightest experimentally accessible double beta decay candidate, is the only one simple
enough to be treated exactly in the nuclear shell model. Thus the bb2n half-life measurement, reported
here, provides a unique test of the nuclear physics involved in the bb matrix element calculation.
Enriched 48Ca sources of two different thicknesses have been exposed in a time projection chamber.
We observe a half-life of T2n1y2 ­ s4.312.421.1fstatg 6 1.4fsystgd 3 1019 yr, consistent with shell model
calculations. [S0031-9007(96)01989-8]
PACS numbers: 23.40.Hc, 21.10.Tg, 21.60.Cs, 27.40.+zNeutrinoless double beta decay (bb0n) is the most
sensitive known test for Majorana neutrino mass. The
unfolding of a mass value (or limit) from measured decay
rates relies on complicated nuclear structure calculations
[1]. Comparison of theoretical and experimental rates
for the standard bb2n mode is an important test for the
validity of these calculations.
Among all realistically measurable candidates for bb
decay, 48Ca ! 48Ti is unique since it is the only one
which can be treated “exactly” in the nuclear shell model
by solving the problem of eight nucleons distributed
within the fp shell without truncation. Consequently,
this decay has been a favored testing ground of nuclear
theories [2]. However, until now only a lower limit of
the bb2n decay half-life, T2n1y2 . 3.6 3 1019 yr, has been
determined experimentally [3].
The nuclear shell model, constrained by the require-
ment that it describe well the spectroscopy of the A ­
48 nuclei, restricts the corresponding half-life also from
above, T2n1y2 # 1020 yr [4]. Therefore the experimental
observation of the decay acquires added significance; if it
turns out that the shell model cannot predict this theoreti-
cally tractable rate, we have to wonder about our ability to
describe the nuclear matrix elements in the more complex
nuclei. Here we present the result from a new experiment
using a time projection chamber (TPC).
The search for bb decay of 48Ca was among the first
to be attempted in live-time experiments beginning in
the early fifties (for an extensive chronology see [1]).
With the largest energy release of all bb candidates,
48Ca (Qbb ­ 4.271 6 0.004 MeV [5]) has a bb2n sum-
energy spectrum that extends to higher energies than most
radioactive backgrounds. Yet calcium has a tendency to
harbor chemically similar radio-impurities such as 90Sr
and 226Ra, which do intrude on a major fraction of the
48Ca spectral range.
When the two b particles are tracked in a TPC they
are seen to both carry negative charge, originate from a0031-9007y96y77(26)y5186(4)$10.00common point, and have separately measured energies.
Although this distinctive visualization eliminates the bulk
of unrelated activity, there remain several well-known
mechanisms for production of negative electron pairs that
constitute background for bb decay. The most serious
of these are Möller scattering of single b particles and
b-g cascades in which a g ray internally converts or
Compton scatters. These processes are fed principally
by the primordial decay chains, but also by cosmogenic
and man-made radionuclides. Decay-chain induced back-
ground events can often be tagged by a or b particles
from neighboring links if the source is thin enough to al-
low the tagging particles escape into the TPC gas.
The miniscule 0.187% natural abundance of 48Ca
makes enrichment both necessary and expensive. Poten-
tial loss of costly isotope is a deterrent to chemical pu-
rification or conversion to the lightest stable compound.
The material used was supplied by the Kurchatov Institute
as finely powdered CaCO3 enriched to 73% in 48Ca, and
relatively free of U and Th (,0.8 ppb by mass spectro-
scopic analysis). The CaCO3 powder was injected into
a large glass box in bursts of compressed Ar, allowed to
settle uniformly onto a 4 mm Mylar substrate, then fixed
with a mist of Formvar. Two such deposits, face-to-face,
formed the first bb source, with a total of 42.2 g of
CaCO3 (18.5 mgycm2 total thickness with substrate and
binder).
The shielded UC Irvine TPC [6,7] containing the bb
source as the central electrode in a magnetic field was
located in a tunnel at the Hoover Dam under a minimum
of 72 m of rock. Data were recorded on magnetic tape,
and subsequently passed through stripping software to
select clean 1e2 and 2e2 events. The 2e2 events were
individually scanned. All unambiguous negative pairs
emitted from opposite sides of the source with a common
point of origin were fitted with helices, and the parameters
written to a bb candidate file or a 214Bi file, depending
on whether a 214Po a particle appeared at the vertex© 1996 The American Physical Society
VOLUME 77, NUMBER 26 P HY S I CA L REV I EW LE T T ER S 23 DECEMBER 1996within the following millisecond. The far more numerous
1e2 events were fitted automatically by software and also
written to a parameter file.
The lone electron (1e2) spectrum plotted against kinetic
energy sKd in Fig. 1 represents the total beta activity
of source contaminants, and can be broken down into
the contributions from individual radionuclides by a least
squares fit. 90Sr (2250 mBqyg), 226Ra (530 mBqyg), and
their daughters account for the bulk of the spectrum.
Contributions from 137Cs (940 mBqyg) and daughters of
228Ra ( 90 mBqyg) are also present. The two Ra activities,
being much larger than the mass spectroscopic limits on
U and Th, indicate severe breaking of equilibrium in the
respective series. Single b decay of 48Ca is allowed, with
a half-life in excess of 6 3 1018 yr [8] corresponding to a
specific activity of less than 15 mBqyg. Any background
from b decay of 48Ca or its daughter 48Sc through the
above-mentioned processes is insignificant. The daughters
of greatest concern (Qb . 2 MeV) are 90Y, 214Bi, 228Ac,
212Bi, and 208Tl. As a check of the fitting procedure, the
energy spectrum of electrons tagged by 214Po a particles
was noted to closely match the fitted 214Bi component
when adjusted for the a escape probability (Pa ­ 0.24 6
0.01 from an independent measurement).
The activities determined from the lone electron spec-
trum were used as input to a Monte Carlo calculation of
the 2e2 background. 90Sr and its daughter 90Y are essen-
tially pure b emitters and contribute only through Möller
scattering. The other high Qb nuclei have complex de-
cay schemes with multiple gamma rays [9], all of which
were included in the Monte Carlo with their correspond-
ing conversion coefficients. Most of these simulated 2e2
backgrounds were directly testable against TPC measure-
ments, with good agreement: The measured 214Bi compo-
FIG. 1. The lone electron spectrum for the thick source, and
the most important of the fitted components. From top to
bottom at low energy are the total spectrum, 90Sr, 226Ra,
and 228Ra. Daughters are assumed in equilibrium, with the
exception of 210Pb. Its daughter 210Bi was fitted separately,
then included in the 226Ra curve.nent was simply the 2e2 data subset tagged by the 214Po
a and corrected for the a escape probability. The 90Y
2e2 measurement was provided by a drop of 90Sr solu-
tion applied to a natural isotopic replica of the 48Ca source
and placed in the TPC. The 212Bi and 208Tl 2e2 measure-
ments were scaled from those produced after an injection
of 220Rn, by comparing observed rates of the rapid 212Bi-
212Po, b-a sequence.
Since the Monte Carlo 2e2 rates were derived from
intrinsic activity levels in mBqyg, their agreement with
direct measurements also confirms the Monte Carlo pre-
dicted 2e2 efficiency of the TPC. A Monte Carlo genera-
ted background spectrum was essential only for 228Ac
where we have no TPC measurement, but in our 2e2
background model we elected to use the smoother, better-
statistics Monte Carlo spectra for the other contributions
as well.
An alternative determination of 2e2 background was
carried out by a separate subgroup of the collaboration
and included independent Monte Carlo calculations and
a greater reliance on the above-mentioned TPC mea-
surements as opposed to lone-electron fits. We refer to
this direct measurement method as analysis “A,” and the
lone-electron based method as analysis “B.” To eliminate
events with the poorest energy resolution, analysis B in-
cluded a cut on electrons making the smallest angles with
the magnetic field (j cossud j , 0.9).
The 2e2 sum spectrum from the 48Ca source, after
event-by-event removal of the a-tagged 214Bi, is shown in
Fig. 2(a) with a singles threshold of 400 keV. The vari-
ous remaining background spectra as determined by analy-
sis A are superimposed. The residual spectrum following
background subtraction appears in Fig. 2(b). Comparison
of the residual spectrum with the theoretical bb shape re-
sults in a x2yDF ­ 0.9 (analysis interval 0.8–3.2 MeV).
FIG. 2. (a) The measured 2e2 sum-energy spectrum and
background spectra for the thick source with a 400 keV singles
threshold. From top to bottom at low energy are the total
measured spectrum, Möller events, 214Bi, and daughters of
228Ra. (b) Residual bb candidates and Monte Carlo Primakoff-
Rosen bb spectrum at the corresponding T2n1y2 ­ 4.1 3 1019 yr
obtained at this threshold (dashed line).5187
VOLUME 77, NUMBER 26 P HY S I CA L REV I EW LE T T ER S 23 DECEMBER 1996The above procedure was repeated for a series of
singles thresholds and one relatively high sum threshold,
with consistent results. The corresponding half-lives were
calculated in each case, as shown for two of the threshold
combinations in Table I. The 2 MeV sum threshold was
accompanied by an additional singles spectrum cut on the
strong 214Bi conversion line at 1.3 MeV. Quoted errors
in the table are statistical. The calculated half-life is
independent of threshold and of analysis A or B within
errors.
Since the half-life precision was degraded by the unex-
pectedly large Ra and Sr contamination, the 42.2 g source
was replaced after 2440 hours exposure with one contain-
ing only 10.3 g of enriched CaCO3 and total thickness
5.4 mgycm2. The thinner source was exposed 4001 hours,
and these results are also included in Table I. The 214Bi
rejection improved greatly as a result of an increase in Pa
from 0.24 to 0.69, and the 90Y component was weakened
by the large reduction in target mass for Möller scatter-
ing. The thin-source analog of Fig. 2(b) yields x2yDF ­
1.0. It is encouraging that despite different dependence on
source mass for the 48Ca signal and the background rates
(particularly 214Bi) the half-lives derived from thick and
thin sources agree within statistics.
The thick and thin source residual spectra were each
corrected for energy loss and efficiency distortion, then
combined for the Kurie plot shown in Fig. 3(a). Including
the singles threshold (e) and using the Primakoff-Rosen
approximation [10] for the Coulomb effect leads to the5188Kurie plot formula
ssdNydKdyhsK 2 2ed ff0sKd 1 fesKdgjd1y5 ~ sQbb 2 Kd ;
f0sKd ­ K4y30 1 K3my3 1 4K2m2y3 1 2Km3 1 m4,
fesKd ­ esK 2 ed fK2y15 1 2Kmy3
1 2m2y3 1 esK 2 edy5g ,
with electron mass (m) and the sum kinetic energy
(K). (The approximation produces ,1% distortion over
the plotted range.) The Kurie plot energy intercept at
4.2 6 0.1 MeV is consistent with the 48Ca Qbb value
of 4.27 MeV. The small error bars resulting from the
Kurie transformation have been omitted in the figure. By
comparison, in Fig. 3(b) the a-tagged 214Bi 2e2 events
produce an intercept of 3.8 6 0.1 MeV, and in Fig. 3(c)
the plot for measured 208Tl (Qb ­ 5.0 MeV) events is
grossly nonlinear.
Since the thick and thin sources were exposed sepa-
rately, corresponding pairs of columns in the table
can be combined as independent measurements. For
example, combining thick and thin bb events for
0.400y0.800 MeV singlesysum thresholds, analysis A,
yields T2n1y2 ­ s4.3
12.4
21.1d 3 1019 yr. Either of the other
two thick-thin pairs would combine to give an equally
valid result. However, since the other two results wouldTABLE I. Breakdown of counts from the two sources for two energy thresholds.
Thick source (0.0775 mol-y) Thin source (0.0310 mol-y)
Singles threshold (MeV) 0.400 0.200 0.400 0.200
Sum threshold (MeV) 0.800 2.000 0.800 2.000
214Bi 1.3 MeV line cut No Yes No Yes
Analysis A Analysis B Analysis A Analysis B
Small polar angles cut No Yes No No Yes No
Counts
With a tag 55 50 6.8 6 1.4a 79 72 8.0 6 1.6a
Without a tag 500 472 72 142 134 21
Backgrounds
Untagged 214Bi 189.1 6 25.5 186.3 6 35.7 23.4 6 4.9 40.2 6 4.5 36.4 6 8.9 4.1 6 0.8
Möller eventsb 191.5 6 4.6 163.4 6 5.6 3.2 6 0.6 53.7 6 1.7 46.1 6 2.1 1.5 6 0.3
228Ac, 212Bi, 208Tlc 42.8 6 7.5 29.4 6 5.6 4.0 6 0.8 19.8 6 3.5 13.3 6 2.1 1.4 6 0.3
Total background 423.3 6 27.0 379.1 6 36.6 30.7 6 5.0 113.7 6 6.0 95.8 6 9.4 7.0 6 0.9
bb events 76.7 6 35.0 92.9 6 42.5 41.3 6 9.8 28.3 6 13.3 38.2 6 14.9 14.0 6 4.7
Statistical significance 2.2s 2.2s 4.2s 2.1s 2.6s 3.0s
Efficiencyd 0.097 0.090 0.041 0.105 0.097 0.047
T2n1y2 s1019 yd 4.1
13.5
21.3 3.1
12.7
21.0 3.2
11.0
20.6 4.8
14.2
21.5 3.3
12.1
20.9 4.3
12.2
21.1
SignalyBackground 0.18 0.25 1.35 0.25 0.40 2.04
Kurie plot intercept (MeV) 4.1 6 0.1 4.4 6 0.1
aScaled from counts at lower threshold by the ratio observed in a larger 214Bi data set.
bExclusive of 214Bi which is included in the row above.
cExclusive of Möller, which is included in the row above.
dFrom Monte Carlo simulation.
VOLUME 77, NUMBER 26 P HY S I CA L REV I EW LE T T ER S 23 DECEMBER 1996FIG. 3. (a) High-energy portion of the Kurie plot for residual
bb candidates combined from thick and thin sources at a
singles threshold of 400 keV. (b) Tagged 214Bi fit over the
same range, 1.6–3.6 MeV. (c) 208Tl from 220Rn injection.
sFsK , ed ­ sK 2 2ed f f0sKd 1 fesKdg. See text.d
not be statistically independent from the first, we do not
attempt a grand average. Rather, we choose the above
half-life value for the following reasons. The lower
threshold includes a broader range of the spectrum than
the 2 MeV sum threshold, and the 2e2 TPC background
measurements in analysis A are more direct than back-
ground levels inferred from the lone-electron spectrum, as
in analysis B. We include the A-B analysis difference in
the systematic error. The remainder of the systematic er-
ror is largely in the detector efficiency. Thus we quote a
final result of T2n1y2 ­ s4.3
12.4
21.1fstatg 6 1.4fsystgd 3 1019
yr. This observation is consistent with the spectroscopy-
constrained shell model of Ref. [4].
The high energy threshold cuts (columns 4 and 7 of
Table I) contain little spectral shape information. How-
ever, we could alternatively select these results because of
their high combined statistical significance of 5.0s. The
combined half-life in this case is T2n1y2 ­ s3.5
10.9
20.6fstatg 6
0.5fsystgd 3 1019 yr, statistically consistent with the low
threshold analysis.Although the 48Ca-enriched sample contained traces of
radium and strontium activity, backgrounds were well de-
fined by associated alpha particles and the lone electron
spectrum. The residual data give half-life values that are
consistent between two bb sources of different thickness
and among various energy thresholds. The correspond-
ing Kurie plots form straight lines which intercept the
energy axis near the 48Ca Qbb value, unlike plots made
from measured samples of the various backgrounds. We
believe these results constitute strong evidence for 48Ca
double beta decay at a half-life supporting the relatively
rigid shell model calculations for this light double beta
decay nucleus.
We gratefully acknowledge the hospitality of Blaine
Hamann and William Sharp at the Hoover Dam. We
thank Felix Boehm for his advice and support, and
one of us (A. P.) wishes to acknowledge the support of
the Alexander von Humboldt Foundation. This work
was funded by the U.S. Department of Energy under
Contracts No. DE-FG03-01ER40679 and No. DE-FG03-
88ER40397.
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(1959).5189


Double Beta Decay of 48Ca

A. Balysh

A. De Silva

V. I. Lebedev

K. Lou

M. K. Moe

M. A. Nelson

A. Piepke

A. Pronskiy

M. A. Vient

P. Vogel

Crossref

Physical Review Letters

Double Beta Decay of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow /><mml:mrow><mml:mn>48</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi>Ca</mml:mi></mml:math>

https://authors.library.caltech.edu/3349/1/BALprl96.pdf

Double beta decay of $^{48}$Ca

Double beta decay of $^{48}$ Ca

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Double beta decay of 48^{48}48Ca

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Double beta decay of $^{48}$ Ca