Gamow-Teller strengths in the A = 14 multiplet: a challenge to the shell model.
ABSTRACT A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the beta decay of the A=14 multiplet is presented. The GT strength distributions to excited states in 14C and 14O were studied in high-resolution (d,2He) and (3He,t) charge-exchange reactions on 14N. No-core shell-model calculations capable of reproducing the suppression of the beta decays predict a selective excitation of Jpi=2+ states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the 14N ground state wave function. However, the fragmentation of the GT strength over three 2+ final states remains a fundamental issue not explained by the present no-core shell model using a 6homega model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way.
- Physical Review C 02/1992; 45(1):473-476. · 3.72 Impact Factor
Article: p-shell nuclei in a (0+2)Physical Review C 12/1990; 42(5):2062-2078. · 3.72 Impact Factor
Article: Equilateral-triangular shape in 14C.[show abstract] [hide abstract]
ABSTRACT: An equilateral-triangular shape of three alpha clusters surrounded by excess neutrons is suggested for 14C, based on the molecular-orbit model. It is found that the attractive interaction between an excess neutron and an alpha particle stabilizes the K(pi)=0(+) and 3(-) rotational bands, which demonstrates an equilateral-triangular symmetry. This K(pi)=3(-) band at 3 MeV below the 10Be+alpha threshold energy corresponds to the experimentally observed band built on top of the second 3(-) state. A positive-parity rotational band (0(+), 2(+), 4(+)) arises similarly. These two bands suggest a molecular 3-alpha structure stabilized by the excess neutrons and can be viewed as a realization of the alpha crystallization in the dilute nuclear medium.Physical Review Letters 05/2004; 92(14):142501. · 7.94 Impact Factor
Gamow-Teller Strengths in the A ? 14 Multiplet: AChallenge to the Shell Model
A. Negret,1,*T. Adachi,2B.R. Barrett,3C. Ba ¨umer,4A.M. van den Berg,5G.P.A. Berg,5P. von Brentano,6D. Frekers,4
D. De Frenne,1H. Fujita,7K. Fujita,7Y. Fujita,2E.-W. Grewe,4P. Haefner,4M.N. Harakeh,5K. Hatanaka,7K. Heyde,1
M. Hunyadi,5E. Jacobs,1Y. Kalmykov,8A. Korff,4K. Nakanishi,7P. Navra ´til,9P. von Neumann-Cosel,8L. Popescu,1,*
S. Rakers,4A. Richter,8N. Ryezayeva,8Y. Sakemi,7A. Shevchenko,8Y. Shimbara,2Y. Shimizu,7Y. Tameshige,2
A. Tamii,10M. Uchida,10J. Vary,11H.J. Wo ¨rtche,5M. Yosoi,10and L. Zamick12
1Vakgroep Subatomaire en Stralingsfysica, Universiteit Gent, Proeftuinstraat 86, 9000 Gent, Belgium
2Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
3Department of Physics, University of Arizona, Tuscon, Arizona 85721, USA
4Institut fu ¨r Kernphysik, Westfa ¨lische Wilhelms-Universita ¨t Mu ¨nster, D-48149 Mu ¨nster, Germany
5Kernfysisch Versneller Instituut, University of Groningen, 9747 AA Groningen, The Netherlands
6Institut fu ¨r Kernphysik, Universita ¨t zu Ko ¨ln, 50937 Ko ¨ln, Germany
7Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
8Institut fu ¨r Kernphysik, Technische Universita ¨t Darmstadt, D-64289 Darmstadt, Germany
9Lawrence Livermore National Laboratory, Livermore, California 94551, USA
10Department of Physics, Kyoto University, Sakyo, Kyoto 606-8224, Japan
11Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
12Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855, USA
(Received 7 April 2006; published 7 August 2006)
A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT)
transitions in the ? decay of the A ? 14 multiplet is presented. The GT strength distributions to excited
states in14C and14O were studied in high-resolution ?d;2He? and ?3He;t? charge-exchange reactions on
14N. No-core shell-model calculations capable of reproducing the suppression of the ? decays predict a
selective excitation of J?? 2?states. The experimental confirmation represents a validation of the
assumptions about the underlying structure of the
fragmentation of the GT strength over three 2?final states remains a fundamental issue not explained
by the present no-core shell model using a 6@! model space, suggesting possibly the need to include
cluster structure in these light nuclei in a consistent way.
14N ground state wave function. However, the
DOI: 10.1103/PhysRevLett.97.062502PACS numbers: 27.20.+n, 21.60.Cs, 21.60.Gx, 25.45.Kk
The anomalously slow ? decay in the A ? 14 multiplet
represents a very old, persistent puzzle. The ground state
(g.s.) of the stable N ? Z nucleus14N is characterized by
J?? 1?and T ? 0, while the unstable mirror nuclei14C
and14O both have g.s.’s with J?? 0?, T ? 1, suggesting
that the g:s: ! g:s: ? decays can proceed through allowed
transitions of the Gamow-Teller (GT) type. However, the
measured lifetimes are several orders of magnitude longer
than expected . This anomaly has been known for many
years, and the resulting long lifetime of14C enables dating
Numerous theoretical attempts were made to explain
this anomaly in the framework of the shell model based
on a special structure of the wave function of the14N g.s.
[2–5]. In the simplest picture, the g.s.’s of the three nuclei
are described as two holes in the 1p shell. It was empha-
sized that the suppressionofthe transitions can becorrectly
reproduced in an LS coupling scheme if the two holes
would carry almost exclusively angular momentum L ?
2 in the14N g.s. and L ? 0 and 1 in the g.s.’s of14C and
14O. In this case, the g:s: ! g:s: transitions are suppressed
because the GToperator does not change L. It was pointed
out that this suppression could not be explained using only
central and spin-orbit two-body interactions: Jancovich
and Talmi  were the first to show that a reasonable
tensor interaction could explain the suppression. Such a
picture is supported, e.g., by a study of the12C?3He;p?
reaction, where the angular distributions for transitions to
the g.s. and the 3.95 MeV state of14N were characterized
by angular momentum transfers ?L ? 2 and 0, respec-
tively . This idea was also investigated extensively by
Genz et al. , who extracted phenomenological wave
functions which were capable of describing many (but
not all) features of the A ? 14 multiplet simultaneously.
Garcı ´a and Brown  found that by mixing the two lowest
1?states and adding 2@! contributions they could repro-
duce the strength of the M1 transitions in14N and fit the
14N?e;e0? data but could not account for the large asym-
metry in the logft values. Starting from the same shell-
model calculations, but introducing renormalized axial-
current operators, Towner and Hardy  were able to
account for the ?-decay data in the A ? 14 nuclei.
Atpresent, there isnotheoretical frameworkinwhichall
relevant spectroscopic information is consistently de-
scribed. The strong retardation of the ? decay makes con-
tributions from the tensor part of the effective nucleon-
PRL 97, 062502 (2006)
11 AUGUST 2006
© 2006 The American Physical Society
nucleon interaction relevant [10,11], as well as processes
such as meson-exchange currents, core polarization, or
relativistic effects, usually neglected in calculations of
GT transitions. New information is highly desirable, in
particular, on the properties of the GT strengths and nu-
clear structure in the mass-14 system.
Here we try to shed light on this long-standing problem
by studying GT transitions from the14N g.s. to excited
states of14C and14O. Such information can be obtained
from charge-exchange reactions on
100–400 MeV=nucleon, since at these energies the excita-
tions are mediated at small momentum transfers by the
spin-isospin term of the nucleon-nucleon interaction .
While such experiments cannot provide new insight into
the suppressed g.s. transitions because of the complexity of
the reaction mechanism (see, e.g.,  and references
therein), for strong GT transitions good agreement is found
with ? decay if the measured charge-exchange reaction
cross sections are extrapolated to zero-momentum transfer
. The present work is also motivated by a recent no-
core shell-model (NCSM)calculation of the GT strength in
the mass-14 multiplet, which predicts a dominant excita-
tion of J?? 2?final states .
close to 0?are presented. Both reactions have been devel-
oped in recent years as high-resolution spectroscopic tools
for the determination of B?GT??and B?GT??strengths,
respectively [15,16]. The good energy resolution in both
reactions allows one to resolve the GT strength distribution
to individual excited states in the final nuclei. The
14N?3He;t?14O reaction was already studied at 45 MeV
3He beam energy , but at this energy no GT informa-
tion could be extracted.
Kernfysisch Versneller Instituut (KVI), Groningen. A deu-
teron beam was accelerated to 172 MeV by the
Accelerateur Groningen-Orsay cyclotron. The outgoing
particles were momentum analyzed and detected with the
Big Bite Spectrometer  and the EuroSuperNova detec-
tion system . The reaction product2He is an unbound
system of two protons in a relative1S0state. These were
detected in coincidence. The limited momentum accep-
tance of the spectrometer restricts the relative energy of the
two protons to ? < 1 MeV, which guarantees that the two
protons are in an
targets of 4.5 and 9 mg=cm2thickness were used. Data
were taken for angle settings ? ? 0?, 3?, 5?, and 7.8?. An
energy resolution of ?E ’ 170 keV [full width at half
maximum (FWHM)] was achieved.
The14N?3He;t?14O reaction was measured at the West-
South beam line and the Grand Raiden spectrometer of the
Ring cyclotron at the Research Center for Nuclear Physics
(RCNP), Osaka, using a 420 MeV
Scattering angles were very accurately determined, and a
resolution of ?E ? 33 keV (FWHM) was obtained at very
forward angles, as described in Ref. .
14N at energies of
14N?3He;t?14O reactions measured
14N?d;2He?14C reaction has been measured at
1S0state . Melamine (C3H3N6)
3He beam .
The B(GT) values were determined following a standard
procedure (see, e.g., [23,24]). For this purpose, the cross
sections deduced from spectra from Fig. 1 were extrapo-
lated to zero-momentum transfer using distorted-wave
Although not essential for most of our arguments below
[that address mainly the B(GT) distribution], the absolute
B(GT) values were evaluated starting from the assumption
that the extrapolated cross sections are proportional to the
B(GT) values . We considered that the proportionality
factor for14N and12C (12C was observed as an impurity in
our spectra) remains the same within ?30% [13,24].
The angular distributions of transitions to excited states
in14C and14O are presented in Fig. 2. They are used only
to identify the ?L ? 0 transitions, which are characterized
by cross sections decreasing rapidly with increasing angle.
The g:s: ! g:s: transitions display an anomalous behavior,
in particular, in the14N?3He;t?14O reaction. The B(GT) de-
termination itself is independent from any fit to the experi-
mental distributions, but, due to the rather poor agreement
between the DWBA calculations and experimental results,
the ?L ? 2 contribution could not be reliably evaluated.
However, all transitions to J?? 0?;1?;2?excited states
in both final nuclei are dominated by a ?L ? 0 shape, and,
therefore, we considered them all as pure GT transitions. A
detailed description of the techniques and analysis proce-
dures for both experiments can be found in Ref. .
In Fig. 3, we present the extracted B(GT) distributions
and compare them with the predictions of Ref. . The
comparison points towards the presence of a mirror asym-
metry not accounted for in the present calculations. Results
of detailed studies, using more general potentials, will be
discussed in a forthcoming paper. Also, the B(M1) tran-
targets at very forward scattering angles.
The ?d;2He? and ?2He;t? spectra of the melamine
PRL 97, 062502 (2006)
11 AUGUST 2006
sition strength to the 1?isobaric analog state at Ex?
13:75 MeV in14N has been obtained in high-resolution
electron scattering . Assuminga pure spin nature of the
transition, the corresponding strength B?GT? ? 0:078?20?
agrees with both values found in this work [0.072(27) for
14C and 0.051(15) for14O]. The major part of the GT
strength is clearly concentrated in transitions to the J??
2?final states in agreement with the shell-model result
, which attributes this strength essentially to a single
states with D-wave character independently confirms the
arguments about a dominant D-wave component of the
J?? 1? 14N g.s. wave function discussed above.
On the other hand, the elaborated NCSM calculations do
not reproduce the observed fragmentation of the GT
strength over three J?? 2?final states or the first excited
0?state, even using a 6@! model space. The existence of
at least two 2?states in the low-excitation region of14O
was already known . It is interesting to note that
simplified calculations using either a weak-coupling model
 or considering the lowest 2 particle–4 hole configu-
3=2) transition. The preferential population of
rations in14C made of a12C ? 2n configuration, with the
two neutrons in the 1d5=2and 2s1=2orbitals  or, more
generally, considering a full 0 ? 2@! shell-model space
 seem to be able to reproduce the experimental finding
of a further 0?state and three 2?states in the excitation
region of interest. However, these early studies were very
phenomenological in scope (see also Ref. ), contrary to
the shell-model calculations of Ref. . On the other
hand, Itagaki et al. , using cluster calculations, suc-
ceeded in producing three J?? 2?states in the low-
excitation region. There exists indeed recent experimental
evidence for alpha-clustering effects in14C [34,35], but
previous experiments indicated that these effects appear
only at higher excitation energies, namely, above 15 MeV.
Von Oertzen et al.  argue that two kinds of alpha
clustering are possible in14C: a prolate shape, where the
three clusters are aligned, and an oblate shape, where they
form an equilateral triangle. This second possibility was
investigated in Ref. , where a rather good description
of the 0?
structure characteristic for a triangular shape is obtained.
There appears, however, a serious problem with the exci-
tation energy of the first 2?state, which exhibits mainly a
2n hole character of the ?1p?1
One notices that the calculated GT strength to the 2?
statesPB?GT? ? 2:61  is significantly larger than the
and 0.81(36) (14O). This is most probably due to the fact
that the structure of the 2?states is far too complex to be
well reproduced even in a 6@! NCSM calculation and
using the bare GT operator. Also, three-body forces may
be necessary to obtain better results. The better agreement
between theory and experiment for B(GT) strength to 1?
states is probably somewhat accidental, since the summed
1?strength doubles in going from a 4@! to a 6@! space,
indicating lack of convergence. The important point is that
the NCSM calculations correctly predict a strong summed
B(GT)strength forthe2?states versusaweakvalue forthe
1?states, a direct consequence of the nature of the
nucleon-nucleon interaction. It is interesting to note that
2, and 4?
1states forming a rotational band
experimentally found values:PB?GT? ? 0:92?33? (14C)
theoretical result of Aroua et al. , where the B(GT) to the
2?state was scaled down by a factor of 3.
Experimental B(GT) distributions, compared to the
14N?d;2He?14C and14N?3He;t?14O reactions. The vertical error
bars include only statistical contributions. The horizontal bars
indicate merely the considered angular intervals. The dashed
lines represent the DWBA calculations (0@!) used for the
extrapolation to zero-momentum transfer.
(color online). Angulardistributionsfor the
PRL 97, 062502 (2006)
11 AUGUST 2006
the early p-shell calculations of Cohen and Kurath 
produced similar B(GT) values as the present noncon-
verged 6@! NCSM calculations.
In conclusion, we have reported high-resolution studies
of the14N?d;2He? and14N?3He;t? reactions, exploring the
GT distributions in the14O and14C final nuclei. In both
cases, J?? 2?final states are predominantly populated, a
selectivity which independently confirms the peculiar
D-wave nature of the two-hole pair of the J?? 1? 14N
ground state in a shell-model picture put forward as a
possible explanation of the anomalous ? decay in the
mass-14 multiplet. However, neither a reproduction of
the total experimental B(GT) strength nor a detailed de-
scription of fragmentation into three final 2?states is
possible with NCSM, even using very large (6@!) model
spaces. Cluster model calculations invoking specific con-
figurations seem to be able to reproduce several of the 0?
and 2?states below 12 MeV missing in the NCSM results.
However, no B(GT) values have at present been calculated
using cluster models.
This situation calls for a unified description combining
typical shell-model and cluster-type configurations. At
present, Green-function Monte Carlo calculations have
gone up to A ? 12, but no results for heavier masses are
expected in the near future . Another approach that
might shed light on this problem uses fermionic molecular
dynamics to generate correlated wave functions starting
from realistic nucleon-nucleon potentials . The experi-
mental B(GT) distributions presented here might further-
more provide stringent tests of the mixing between the
shell-model and cluster configurations.
The authors are grateful to the accelerator groupsof KVI
and RCNP for providing high-quality beams and to
N. Smirnova, J. Heyse, M. Hagemann, C. Borcea, and
I. Stetcu for very useful discussions. This work was per-
formed as part of the research program of the Fund for
Scientific Research-Flanders. L.P. and A.N. acknowledge
support for the 21st Century COE program ‘‘Toward a new
basic science’’ of the Graduate School of Science, Osaka
University. G.P.A.B. acknowledges support from JSPS.
This work was supported by the EU under EURONS
within the 6th framework under Contract No. RII3-CT-
2005-506065, by Monbukagakusho, Japan, under Grant
No. 15540274, and by DFG, Germany, under Contracts
No. SFB 634 and No. Br799-12-1. This work was partly
performed under the auspices of the U.S. DOE by the
University of California, Lawrence Livermore National
Laboratory under Contract No. W-7405-Eng-48.
*Permanent address: NIPNE-HH, Strada Atomis ¸tilor,
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