Particle Unstable Light Nuclei
Michael Thoennessen
National Superconducting Cyclotron Laboratory and
Department of Physics & Astronomy
Michigan State University, East Lansing, MI 48824
Abstract. Exotic nuclei produced in fragmentation reactions can be used to study nuclei beyond the drip lines. The level
structure of these nuclei yields information about disappearing, shifting and emerging shells along the driplines. Light
nuclei beyond the neutron dripline (for example 9He, 10Li, and 13Be) and the proton dripline (for example 11N and 15F)
are used to establish the vanishing of the N = 8 and Z = 8 shell closures close to the neutron and proton dripline,
respectively.
of a new shell. In the present work the evolution of the
N = 8 and Z = 8 shells towards and beyond the
driplines is studied.
INTRODUCTION
The availability of fast radioactive beams has
opened up the possibility for detailed studies of nuclei
along and even beyond the drip lines. The extreme
short lifetimes (up to ~10-21s) of these nuclei make it
difficult and for heavy nuclei essentially impossible to
study with traditional methods. The strong forward
focusing of the reaction products following the
production via stripping or transfer reactions from fast
radioactive beams allows the detection of these
fragments with large efficiency. From the angle and
energy determination the invariant mass of these
unbound nuclei can be reconstructed. The structure of
these nuclei can help to follow systematic trends even
beyond particle stable nuclei.
N = 8 SHELL
The first indication of the disappearance of the N =
8 shell closure was the observation of the shell
inversion of the s- and p-shell in 11Be [3]. Bohr and
Mottelson demonstrated this disappearance in a plot of
the single neutron separation energies [1]. The
emergence or disappearance of a shell closure in such
a plot is most obvious when other systematic trends
like pairing are separated. Thus, in order to study the
N = 8 shell the one neutron separation energy is
plotted only for odd neutron nuclei below and above N
= 8. In addition, the odd and even Z nuclei are plotted
separately. Figure 1 shows the chart of nuclei for the
light mass region around N = 8. The short-dashed lines
indicate the odd-N even-Z nuclei crossing the N = 8
line, and the long-dashed lines indicate the odd-N oddZ nuclei across the N = 8 line. The corresponding
single neutron separation energies are shown in Figure
2 for the even-Z (top) and the odd-Z (bottom) nuclei.
The black circles show the known separation energies
of particle-bound nuclei. The 11Be to 15C (N = 7, N =
9, top) crossing is the only one showing the
disappearance of the N = 8 shell. In order to determine
if this is an anomaly or if it persists for other neutron
rich nuclei, it is necessary to extend the systematics to
unbound nuclei.
It has been known for a long time that single
particle separation energies are valuable tools to
extract systematic trends over the chart of nuclei [1].
These separation energies typically increase
monotonically with increasing Z (or N) for a given N
(Z). However, just beyond a shell closure there is a
dramatic drop in separation energy.
Recently these systematic studies for the neutron
separation energies were extended towards the neutron
dripline [2]. The disappearance of the characteristic
drop of the separation energy towards the neutron
dripline across the N = 20 shell clearly confirmed the
disappearance of this shell. At the same time the
separation energy exhibited a reduction for N = 16
very close the dripline, thus indicating the emergence
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
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FIGURE 1. Relevant part of the chart of nuclei for light
isotopes. The short dashed (long dashed) lines connect
even-Z (odd-Z) odd-N nuclei of constant isospin. The
solid vertical line indicates the N = 8 shell closure.The
black squares are stable nuclei and the grey squares are
particle bound nuclei. Particle-unstable nuclei included
in the present systematics are labeled beyond the neutron
dripline.
The squares in Figure 2 represent 13Be (N = 9, top),
He (N = 7, top) and 10Li (N = 7, bottom). In all three
cases the ground-state corresponds to s-wave
resonances, which were analyzed in terms of the
scattering lengths. Due to the experimental resolution
only a lower limit of the scattering length can be
extracted. For 10Li the scattering length is more
negative than -25 fm corresponding to an excitation
energy of less than 50 keV for the virtual state [4].
13
Be [5] and 9He [6] have scattering lengths of < -10
fm or excitation energies of < 200 keV. The
experiments on 9He and 10Li confirmed the predictions
that the level inversion observed in 11Be is not an
isolated occurrence but continues to exist in the
lightest nuclei of the N = 7 isotone chain. It is thus not
surprising that the single neutron separation energy
systematics also confirms the disappearance of the N =
8 shell for these isotopes.
9
FIGURE 2. Neutron separation energies (circles) for
odd-N-even-Z nuclei (top, short-dashed lines of
Figure 1) and odd-N-odd-Z nuclei (bottom, longdashed lines of Figure 2). The location of the Z=8
shell is indicated by the vertical line. The squares are
the separation energies of the unbound nuclei 9He,
13
Be (top) and 10Li (bottom).
Z = 8 SHELL
the relevant part of the chart of nuclei for the Z = 8
shell. Only the odd-Z, even-N nuclei below and above
the Z = 8 shell are indicated. In contrast to the N = 8
shell the separation energies of particle unbound nuclei
(5Li and 9B) have to be included already for nuclei
very close to the line of stability. Figure 4 shows the
corresponding single proton separation energies. The Z
= 8 shell closure indicated by the vertical line is
clearly visible as a sharp drop between two adjacent
nuclei (13N, Z = 7 and 17F, Z = 9) close to stability.
Even for nuclei beyond the dripline (11N and 15F) the
discontinuity seems to be still present which would
indicate the continuation of the Z = 8 shell.
Similar to the single neutron separation energy
systematics, single proton separation energies can be
used to study proton shell structures. Figure 3 shows
However, 11N is the mirror of 11Be where the level
inversion of the p1/2 and the s1/2 shows the break-down
of the N = 8 shell. The mass of 11N has recently been
294
FIGURE 4. Proton separation energies for odd-Zeven-N nuclei. The location of the Z = 8 shell is
indicated by the vertical line. The vanishing of the Z =
8 shell closure suggests a smaller value (open circle)
of the proton separation energy for 15F.
FIGURE 3. Relevant part of the chart of nuclei for light
nuclei. The short dashed lines connect odd-Z even-N
nuclei of constant isospin. The solid horizontal line
indicates the Z = 8 shell closure. The black squares are
stable nuclei and the grey squares are particle bound
nuclei. Particle-unstable nuclei included in the present
systematics are labeled beyond the proton dripline.
ACKNOWLEDGMENTS
This work was supported by the National Science
Foundation under grant PHY-0110253.
measured by several groups [7-9] and the same level
inversion as in 11Be has been determined for the Z = 8
shell. Thus, the increase in proton separation should
not be present. A potential explanation is the large
uncertainty of the mass of 15F which is unbound by
1.48(13) MeV [10]. Based on the presence of the level
inversion in 11N and the single proton separation
energy systematics, 15F has been predicted to be less
unbound with a separation energy of ~1 MeV [11].
The open circle in Figure 4 indicates the predicted
proton separation energy of 15F. A recent measurement
of the mass of 15F seems to confirm this prediction
[12]. However, if the original mass measurement of
15
F is confirmed it seems to support the largest value
for the mass of 11N [9].
REFERENCES
1. A. Bohr and B.R. Mottelson, Nuclear Structure Vol. 1,
W.A. Benjamin, (New York, Amsterdam, 1969), p. 193
2. A. Ozawa et al., Phys. Rev. Lett. 84, 5493 (2000).
3. I. Talmi and I. Unna, Phys. Rev. Lett. 4, 469 (1960).
4. M. Thoennessen et al., Phys. Rev. C59, 111 (1999),
5. M. Thoennessen et al., Phys. Rev. C63, 014308 (2000).
6. L. Chen et al., Phys. Lett. B505, 21 (2001).
7. L. Axelsson et al., Phys. Rev. C54, R1511 (1996),
K. Markenroth et al., Phys. Rev. C62, 034308 (2000).
8. A. Azhari et al., Phys. Rev. C57, 628 (1998).
CONCLUSIONS
9. J. M. Oliviera et al., Phys. Rev. Lett. 84, 628 (2000).
Systematics of neutron and proton separation
energies can be powerful tools to study the nuclear
structure at and even beyond the driplines. It can be
used to predict masses and separation energies of
nuclei beyond the neutron and proton driplines.
10. G. J. Kekelis et al., Phys Rev. C17, 1929 (1978).
11. M. Thoennessen, RIKEN Review 39, 68 (2001).
12. M. T. Zerguerras et al., subm. to Phys. Lett. B (2002).
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