VOLUME 88, NUMBER 4 PHYSICAL REVIEW LETTERS 28 JANUARY 2002
Two-Proton Widths of
12
O,
16
Ne, and Three-Body Mechanism of Thomas-Ehrman Shift
L. V. Grigorenko,
1,2
I. G. Mukha,
3,2
I. J. Thompson,
1
and M.V. Zhukov
4
1
Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
2
Russian Research Center, “The Kurchatov Institute,” 123182 Moscow, Russia
3
Gesellschaft für Schwerionenforschung mbH, Planckstrasse 1, D-64291 Darmstadt, Germany
4
Department of Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden
(Received 3 May 2001; published 11 January 2002)
Two-proton decays of
12
O and
16
Ne ground states are studied in a three-body model. We have found
that the two-proton widths for the states should be much less than the existing experimental values (about
10 times for
12
O and about 100 times for
16
Ne). We also have found that the structure of these states
differs significantly from the mirror isobaric analog states (IAS): breaking of isobaric symmetry is at the
level of tens of percents. Together with a corresponding decrease ofthe Coulomb energy, this effect can
be considered as a three-body mechanism of the Thomas-Ehrman shift.
DOI: 10.1103/PhysRevLett.88.042502 PACS numbers: 23.50.+z, 21.10.Sf, 21.45.+v, 21.60.Gx
Although predicted many years ago [1], two-proton
radioactivity is still a complicated and controversial
problem from both experimental and theoretical sides. A
novel theoretical approach to the two-proton radioactivity
problem has been developed in [2]. Together with
6
Be,
the
12
O and
16
Ne nuclei are the only known light two-
proton emitters and they have methodological importance
for understanding this phenomenon in general. We are
going to demonstrate that these nuclei deserve also special
attention as representing an interesting form of nuclear
dynamics. In some approximations these nuclei, as well
as the mirror
6
He,
12
Be, and
16
C nuclei, can be considered
in a three-body core 1 N 1 N model.
The properties of the
12
O ground state (g.s.) are E
T
1.8212 MeV, G 400250 keV [3] or E
T
1.794 MeV, G 580200 keV [4] (E
T
is the en-
ergy above two-proton threshold). There is a controversy
about the widths [5 –8]. For example, Barker insists that
an upper limit for the width of
12
O g.s. is about 100 keV
[6] and for diproton emission the upper limit is only 5 keV
[8]. Our calculations correspond well to these estimates.
The situation in
16
Ne is very similar to that in
12
O, but
as yet it has attracted only a little attention [9]. The experi-
mental data is E
T
1.358 MeV, G 200100 keV [3]
or E
T
1.402 MeV, G 11040 keV [10]. Just these
values are enough to raise some questions: the corre-
sponding characteristics of the well studied
6
Be g.s. E
T
1.37 MeV and G 92 keV are very close to them, but the
Coulomb interaction of protons with
14
O core is 4 times
stronger in
16
Ne. The exponential character of penetra-
bility dependence implies a very rough estimate G
16
Ne
G
4
6
Be
2g
2
WL
3
0.02 3 eV if we assume that the re-
duced width in
6
Be is close to the Wigner limit g
2
WL
.A
solution of this paradox was suggested in the qualitative
discussion in [9], where the experimental widths of
6
Be and
16
Ne were used to infer a considerable difference in their
structures. In our studies, based on firm three-body calcu-
lations of
6
Be and
16
Ne, we derive the width which is larger
than in the simple estimate above, but still much lower than
the experimental value.
We find that the peculiar nuclear dynamics in
12
O
and
16
Ne leads to a strong (tens of percents) breaking of
isobaric symmetry. This can be considered as a three-body
mechanism for the Thomas-Ehrman shift (TES). The
original idea of TES [11] applies to core 1 N mirror
nuclei. When the proton drip line is approached, the wave
function (WF) of the nucleon in the last shell becomes
wider due to larger penetration to the classically forbid-
den region, and correspondingly the Coulomb energy
decreases. This decrease is most pronounced for the
s-wave states, which leads to a relative shift of levels
in the mirror partners. The recent papers [12,13] give a
more general view of TES. Paper [12] speculates about
the possible “indirect” mechanism of the TES due to
a modification of the residual nuclear interaction, and
considers also core 1 N 1 N systems. The definition of
the TES in [13] as the difference between perturbative and
actual Coulomb shifts for the isobaric analog states (IAS)
in mirror nuclei is physically close to the original and is
applicable not only to core 1 N systems.
Studying
12
O and
16
Ne nuclei, we have found that not
only has the WF expanded, but also the structure of the
states has changed significantly compared to isobaric states
in
12
Be and
16
C. While
12
Be and
16
C have a strong s, p, d
configuration mixing for the valence nucleons, the s-wave
components of their proton-rich analogs have markedly
increased. The qualitative reasons for that are clear, as
the variational WF benefits most from the decrease of the
Coulomb energy in the channels where the barriers are
lowest, and the WF has the best opportunity for radial
expansion. This mechanism differs significantly from the
ordinary perception of TES as a purely “geometric” effect,
connected only with shape of the WF.
The large isobaric symmetry breaking and a novel
mechanism of TES which we have found are not restricted
to just these two systems. The effects could be expected
in heavier, even Z , systems as well. The combination of
042502-1 0031-9007 02 88(4) 042502(4)$20.00 © 2002 The American Physical Society 042502-1