Fig.1: The knowledge of the even-even stable and neutron-rich nuclei in the N=20-28, Z<20 region till late 1995. The magic and semi-magic nuclei are marked by lines.
2. Experiment
The experiment was performed in late 1995 at GSI by the
CB-
LAND-
FRS-Collaboration from GSI,
Darmstadt and
MPI-K,
Heidelberg.
After the fragmentation reaction of 50Ti on 9Be at 330 AMeV,
about 50 nuclear species (in which more than 30 were beta-unstable neutron-rich isotopes)
with Z = 4-20, A/Z around 2.1-2.5 and
energies in the range of 210-280 AMeV (v/c about 0.58-0.64) were selected simultaneously by
the FRagment Separator FRS at GSI, Darmstadt.
This secondary RIB which was transferred to the target area had
an intensity of around 10^4 pps (particles per second) for the full composition of nuclear
species i.e. on the average about 200 pps for each nuclear species.
Secondary peripheral reactions of the RIB with a 0.94 g/cm^2 Pb and a 0.54 g/cm^2 C target
were employed to populate the excited states.
The mass number A1 of each nuclear species in the RIB was identified by time of flight;
A2 after the secondary reactions was obtained by the dE-Brho-TOF method employing the dipole
magnet ALADIN;
the charge numbers Z1 and Z2 were determined by two dE counters.
Two experimental particularities are related to the high beam energy. An average Doppler broadening of 15% is expected for in-beam gamma-spectra detected by a common gamma-detector with an opening angle of 18 degrees (fig.2); the cross section of atomic background is at least three orders of magnitude larger than typical Coulomb excitation cross sections (fig.3). The Darmstadt-Heidelberg Crystal Ball (CB) consisting of 162 individual NaI crystals with an intrinsic energy resolution of 8% is therefore well suited; moreover, its 4pi solid angle and large full energy efficiency (70% at 1.3 MeV) compensate for the low beam intensity. To suppress atomic background, a 2 mm thick Pb tube was installed between the CB and the secondary target which was placed at the center of the CB, and a threshold of 500 keV was set to the CB trigger. In addition, the scattering angle theta was measured in order to suppress those events being composed of only atomic background and distributing at theta around 0 degree. Another goal to measure theta is to try to distinguish Coulomb and nuclear excitation which dominate at different impact parameter regions.
Fig.2: (a) Doppler shift, (b) Doppler broadening assuming an opening angle of 18 degrees for one detector element (the 7% intrinsic energy resolution of the CB is marked by the dashed line), (c) angular distribution of gamma-rays in the rest system and (d) in the lab system (after the Lorentz transformation). The angular distribution of gamma-rays in the lab system is peaked at forward angles where Doppler broadening is rather severe.
Fig.3: Angle-integrated cross section of the atomic background from 43Ar on the Pb (solid line) and C target (dashed line) at 222 AMeV. The 500 keV detection threshold of the NaIs of the CB used in the experiment is marked.
In order to measure the neutrons evaporated from giant resonances which is expected to be populated in relativistic Coulomb excitation, the neutron detector LAND was employed.
Fig.4: The experimental set-up in the target area Cave B (another scheme where detector positions are indicated is also available).
The scattering angle theta was determined with an efficiency of 30%.
With an intrinsic resolution of 5 mrad and the atomic angular straggling of 6 and 2 mrad
for the Pb and C target, the combined resolution was not sufficient to distinguish Coulomb
and nuclear excitation but helpful to suppress atomic background in the gamma-spectra.
3. Analysis
Z1 and Z2 were measured with a resolution of 0.5 mass units and an efficiency of nearly 100%,
while A1 was measured with a resolution 0.3 to 0.6 mass units (better for lighter isotopes) and
an efficiency of 80%.
The resolution of A2 for heavy nuclei like Ar was 0.8 mass units with an efficiency of 30%;
for light nuclei like Mg, A2 could be derived by the standard mode with 0.8 mass units resolution
and 55% efficiency and another mode with a better resolution of 0.6 mass units but only 10%
efficiency. See fig.5 and fig.6. 
Fig.5:
The charge and mass distribution of the RIBs
produced from the fragmentation of the 330 AMeV 50Ti primary beam on a 4 g/cm^2 9Be
primary target with FRS setting optimized to 38S.
The borderline between stable and neutron-rich
nuclei is marked. On the top-left the Z1 distribution is shown;
on the bottom-right, as examples, the A1 distributions of Mg and Ar are shown.
Fig.6:
The charge and mass distribution behind the Pb (left) and C (right) target requiring
incoming 28Mg.
The top panels show the Z2 charge distributions.
The middle and bottom panels display the A2 mass distributions derived by different modes
requiring Z2 = 12.
There is contribution from atomic background in the Z2=Z1 and A2=A1 peak
because no condition on the CB is required.
