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

11.3.2 Fitting Matrix Elements to Gamma-Ray Yield DataThis section describes the use of a series of sample inputs to fit matrix elements to experimental data. Thesimplest possible case is examined: fitting one parameter (two E2 reduced matrix elements coupled as oneparameter) to a few experimental gamma-ray yields (from the lowest 4 excited states in a fictitious nucleus).The level scheme is the same as the one in the previous demonstration, that is Fig 13, but in this case,matrix elements 3 and 5 will be adjusted to find the chi-squared minimum in the calculated yields.This “toy” problem can be used as a model for the basic procedure used to analyze real data, eventhough a real problem might involve more sophistication, such as, axially asymmetric particle detectors (ofarbitrary shape), data from user-defined Ge detector “clusters,” choices regarding the normalization of onedata subset to another, data from multiple beam and target combinations, data from unresolved doublets,inverse scattering kinematics, etc. A flowchart of the general procedure to define the germanium detector(s),fit matrix elements to the data and estimate the errors in the fitted matrix elements is given in Fig 15 plus16.The demonstration is run using a set of inputs and related files in the toyfit.tar archive on the Gosiawebsite. Each step of the demonstration is run with a different *.inp file. In practice it is probably betterto use the same input file for all or most steps to prevent accidental inconsistencies between steps. The filesshould be modified for each step in a text editor such as emacs or vi, paying attention to delimiters, spacingand capitalization. The second fitting demonstration (section 11.4) uses this method of editing one inputfile between steps and fits more matrix elements. However, the present demonstration can be run withoutany modification to each input file.Eachstepintheprocedureisexecutedbytypinggosia < *.inpAt each step, the relevant portion of the input is described, but the novice user should refer to the manualentry in Chapter 5 for complete details of the records and fields required for a particular Gosia option, e.g.OP,GOSI or OP,INTG etc. This demonstration includes two iterations of the fitting procedure to makesure that the correction factors for the point approximations used in the fit weresufficiently accurate at thestarting point in the chi-squared surface (steps 5 - 7).A set of simulated gamma-ray yield data is provided for the user in the file ge-data.yld. In practice, thisfile would be typed by the user according to the format in section 5.31.1. Define the Ge detector(s) (1-make-detector.inp)In Gosia, detectors are considered to be “physically different” if they have different geometry (crystal length,crystal radius, etc.), if they are placed at different distances from the target position, or if they are fittedwith different absorbers. Two identical Ge detectors placed at different distances from the target would needto be defined separately, but two identical detectors that only differ by their angular position in space (andtheir efficiencies) should be defined as the same “type.” In this demonstration, one detector type is definedand named type “1.”Refer to the file “1-make-detector.inp”. In OP,FILE the three necessary files for OP,GDET are defined.The general output will be written to 1-make-detector.out, but the coefficients for the angular attenuation(Sections 5.10 and 2.2.3) will be written to “det.gdt” for use by Gosia in steps 2 - 10.OP,GDET has three lines. The first line is the detector type, 1. The second line0.1,2.5,10.,15.defines a Ge crystal with an inactive core of radius 0.1 cm, outer radius of 2.5 cm and length 10. cm, placed15. cm from the target. The angular position(s) in space of all detectors of this type will be definedinthenext step.To execute the input, issue the commandgosia < 1-make-detector.inpThe output file 1-make-detector.out contains verbose output, some of which is selected by the user in thesub-option PRT of CONT. Error messages will also be written to file 22 (*.out in this demonstration). TheGe detector file det.gdt is created with the following records.160