Model independent analysis

==Introduction==

The motivation for development of Gosia was to
implement the capability to extract measured
<math>E\lambda</math>
matrix elements model-independently from Coulomb excitation data. The first
major task required to achieve this goal was to design experiments covering a
wide dynamic range of Coulomb excitation strength that provide sufficient
experimental data to overdetermine the many unknown matrix elements.
Experimental techniques were developed to achieve this requirement in the
1980's and primarily involved Coulomb excitation measurements over a wide
range of both scattering angle and unexcited nucleus
<math>Z</math> value. The second major task was the development of Gosia to
model-independently extract the matrix elements via a least-squares search of
the data. During the 1980's and early 1990's the ready availability of beam
time at heavy-ion accelerator facilities, the availability of high-efficiency
<math>p-\gamma</math> detector facilities, and access to fast computer systems needed for the Gosia
least-squares searches, enabled the first model-independent extraction of
<math>E\lambda</math>
matrix elements from multiple Coulomb excitation data. These fairly complete
sets of E2 matrix elements made it possible to exploit the rotational invariants
technique to extract the underlying quadrupole collective degrees of freedom
directly from the Coulomb excitation data. Note that it is not viable to
perform a completely model-independent analysis in that models extrapolate
from the set of measured
<math>E\lambda</math>
matrix elements to estimate other matrix elements that are insensitive to the
data set but play a weak role in the Coulomb excitation process, for example
the influence of virtual excitation of the highest spin states or of
excited-state static electric quadrupole moments.