Experiment planning

The GOSIA suite of codes are ideally suited to the design and planning of
low-energy heavy-ion induced Coulomb excitation experiments as well as the subsequent
analysis. Coulomb excitation experiments can seem deceptively simple,
especially for few-state problems, leading some experimenters to fall into 
analysis traps or collecting data that have less than optimal sensitivity to
the goals of the experiment. The [[experiment_planning | Experiment planning]] page identifies a few potential pitfalls
in the design and analysis of Coulomb excitation experiments. Additional
insight can be obtained from study of prior publications and review articles
on heavy-ion induced Coulomb excitation.<ref>K. Alder and A. Winther, ''Electromagnetic Excitation: Theory of Coulomb Excitation with Heavy Ions,'' North Holland, Amsterdam (1975).</ref><ref>D. Cline, Ann. Rev. Nucl. Part. Sci. 36:683 (1986).</ref>

==Experimental parameter considerations==

===Safe bombarding energy===

The basic assumption of Coulomb excitation is that the interaction between the
scattering ions is purely electromagnetic in origin. This situation
applies when the range of nuclear forces for both interacting
nuclei are completely separated in space. Coulomb excitation
cross sections are maximized by using the highest safe bombarding energy for
which the interaction is purely electromagnetic resulting in a sensitive
balance between maximizing the cross sections and minimizing the influence of 
nuclear excitation. The optimal value depends on the goals of the planned
experiment. Experimental data on the influence of Coulomb-nuclear
interference on the second-order reorientation effect in Coulomb
excitation<ref>D. Cline, H.S. Gertzman, H.E. Gove, P.M.S. Lesser and J.J. Schwartz, Nucl. Phys. A133,445 (1969)</ref><ref>P.M.S. Lesser, D. Cline, P. Goode and R. Horoshko, Nucl. Phys. 28,368 (1972).</ref> was used to estimate the maximum bombarding energy at which the influence of nuclear
excitation can be neglected for second-order processes. Near the barrier the
Coulomb-nuclear interference is destructive which reduces the inelastic
scattering cross sections at large scattering angles in a manner that mimics
the reorientation effect corresponding to a negative static quadrupole moment.

Chapter 2 of the Gosia manual discusses the issue of safe bombarding energy in detail.

===The semiclassical approximation===

The long range of the Coulomb interaction, coupled with the small integrationstep size necessitated by the short wavelength, and the large number of
partial waves that make significant contributions, conspire to make it
impractical to use fully quantal codes with current computers that are capable
of handling the large number of coupled channels important to heavy-ion
induced Coulomb excitation. Fortunately a considerable simplification
can be achieved by assuming a semiclassical treatment of two-body
kinematics as pioneered by Alder and Winther.<ref>K. Alder, A. Winther, K. Dan. Vidensk et al., Mat. Fys. Medd. 32, Number 8 (1960).</ref>
The semiclassical picture exploits the fact that the monopole-monopole Coulombinteraction <math>Z_1 Z_2 e^2/r</math> 
dominates and determines the relative motion of the two colliding nuclei.
The semiclassical picture assumes that the size of the
incoming projectile wavepacket is small compared to the
dimensions of the classical hyperbolic trajectory which is
expressed in terms of the [[Sommerfeld_parameter | Sommerfeld parameter]].

==Simulation==

Gosia can be used to estimate the sensitivity to a particular matrix element or set of matrix elements that will be obtained in a planned experiment and to optimize the experiment for a desired measurement.  Refer to the [[Simulation_(experiment_planning) | Simulation]] page for more detail.


==Planning tools==

While Gosia is the obvious tool for planning low-energy Coulomb excitation experiments, the [[Rachel,_a_GUI_for_Gosia | GUI]] for Gosia can offer much greater speed and automation in the planning process, including predicting the measurable count rate and estimating the expected errors in the planned experiment.

==Notes==

<references/>