coulomb excitation data analysis codes; gosia 2007 - Physics and ...

1 INTRODUCTION1.1 Gosia suite of Coulomb excitation codesCoulomb excitation, which is excitation of nuclear states caused solely by the electromagnetic field actingbetween the colliding nuclei, is a powerful probe of collective nuclear structure [ALD56, ALD66, ALD75].The main advantage of Coulomb excitation lies in the fact that, unlike nuclear reactions, the interaction canbe described by the well-established theory of the electromagnetic interaction allowing nuclear structure tobe studied in a model-independent way. Excitation via the short-ranged nuclear interaction is negligible forbombarding energies well below the Coulomb barrier, whereas the long-ranged electromagnetic interactionstill gives rise to a considerable Coulomb excitation. Coulomb excitation is the preeminent probe of collectivedegrees of freedom in nuclear structure in that it selectively populates collective states with cross sectionsthat are a direct measure of the electromagnetic matrix elements.The recognition of Coulomb excitation as a method of studying collective motion in nuclei dates backto the early 1950’s [ALD56]. Coulomb excitation with light-ion beams has been exploited extensively tomeasure the reduced excitation probabilities and quadrupole moments of the lowest excited states. Experimentsperformed using light-ion beams can be interpreted relatively easily because first- and second orderperturbation theory are applicable since only one and two step excitation processes need to be taken intoaccount (see e.g. the extensive discussion of the perturbation approach in [ALD75] ). The situation changesdramatically for multiple Coulomb excitation that results when heavy-ion beams are employed. MultipleCoulomb excitation populates many excited states (up to spin, 40~ in strongly deformed nuclei) providingsensitivity to a large body of electromagnetic matrix elements but unfortunately perturbation methods areno longer viable. Review papers by Cline [CLI86] and de Boer[BOE84] contain a short summaries of theearly multiple Coulomb excitation work, complete with a extensive lists of references.A semiclassical theory of multiple Coulomb excitation was developed in 1956[ALD56]. The first semiclassicalmultiple Coulomb excitation computer program COULEX was developed by Winther and de Boerin 1965[WIN65]. The code COULEX provided the first opportunity to calculate quantitatively multipleCoulomb excitation amplitudes using an assumed set of the reduced electromagnetic matrix elements. Thiscode greatly expanded the exploitation of the powerful Coulomb excitation technique to determine electromagneticmatrix elements in nuclear structure. However, the ultimate goal of a model-independent extractionof the electromagnetic structure parameters (reduced matrix elements) from the heavy-ion experiments wasnot viable until development, in 1980, of the code GOSIA described in this manual. The main difficultyfor making a model-independent analysis lies in the large number of reduced matrix elements influencingheavy-ion excitation. More than a hundred matrix elements can contribute significantly to Coulomb excitationwhen using heavy beams to excite strongly deformed nuclei. There are two major tasks to makinga model-independent analysis of multiple Coulomb excitation data. The first task is to overdetermine theproblem by collecting enough experimental data, this requires measurements for a wide dynamic range ofCoulomb excitation strength. The second task is to extract the many unknown matrix elements from thisoverdetermined data set.The need to collect Coulomb excitation data for a wide dynamic range of Coulomb excitation interactionstrength, has led to development of experimental methods to record deexcitation γ-rays in coincidence withscattered ions over a wide range of particle scattering angle. The efficiency of data collection has been verymuch enhanced by the development of 4π arrays of Compton-suppressed Ge detectors, such as Gammasphere,and large solid-angle, position-sensitive, parallel-plate avalanche detectors that provide mass and scatteringangle resolution for detection of both scattered ions in kinematic coincidence. The particle detector allowsevent-by-event kinematic reconstruction to correct the considerable Doppler shifts of observed γ-ray energies,dramatically improving the quality of the γ-ray spectra. Ref. [SIM97] gives technical details of the Rochesterdesigned charged particle detection CHICO, that has been used extensively with Gammasphere for Coulombexcitation studies since 1995.Initially multiple Coulomb excitation data were analysed by comparing the data with the predictionsobtained using the code COULEX coupled to a program like CEGRY[CLI74] to evaluate the γ-deexcitation.The sets of matrix elements required as input data to COULEX were taken from model predictions andthe conclusions were drawn based on the quality of the agreement obtained. However, the results of such amodel-dependent analyses were not conclusive, primarily due to the unknown sensitivity of the experimental6