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

ME =< INDEX2||E(M)λ||INDEX1 > The multipole matrix element defined by equation 2.16. Itis given in units of e.barns 1/2 for Eλ matrix elements and μ N .barns (1−1)/2 for Mλ matrix elements.The sign assigned INDEX2 plays no role in the definition of the matrix element. A negative signsignifies coupled matrix elements as discussed below.The lower and upper limits,respectively, between which the given matrix element ME is allowedto vary. Obviously R 2 >R 1 . Equality of R 1 and R 2 implies that this given matrix element is kept fixed atthe value ME. Note that in this case, i.e.,R 1 = R 2 , R1 need not be equal to the ME. For example record1, 2, 0.5, 2, 2 is equivalent to 1, 2, 0.5, 0.5, 0.5Fixing matrix elements as in the first example is recommended because of two features of the code. First,when an OP,RE command is used the limits of fixed matrix elements are set as R 2 = |R 2 | and R 1 = −|R 1 |.If fixing is done as in the second example the matrix element will be allowed to vary only in one direction,i.e., between ±0.5. Secondly, when fitting the q-parameters, the ζ-ranges are set according to the actuallimits R 1 ,R 2 .Iffixed matrix elements are released at a later stage during the analysis, then there is less riskof incorrect extrapolation if the approach used in the first example is employed rather than later extendingthe limits without recalculating the q-parameter maps. Note that neither R 1 nor R 2 should be exactly zero,use a small number instead.A negative sign assigned to INDEX2 specifies that the matrix element defined by the pair of indicesINDEX1, INDEX2 is not a free variable but is a coupled one. In this case R 1 and R 2 are no longer upperand lower limits but the pair of indices of the matrix element to which this matrix element is coupled. Thecode automatically assigns upper and lower limits to the coupled matrix elements using the upper and lowerlimits given to the one to which it is coupled while preserving the ratio of the initial values of the coupledmatrix elements. These upper and lower limits calculated by the code are used by the code if this couplingis subsequently released. The ratio of coupled matrix elements set by the initial values is preserved in theleast squares search if the coupling is not released.]As an example consider the pair of matrix elements:1, 2, 2.0, −4, 42, −3, 1., 1, 2The second statement signifies that the matrix element connecting state 2 to 3 is coupled to the matrixelement connecting states 1 and 2 in the ratio:M(2 + 3)M(1 + 2) =+0.5This ratio will be preserved in the least squares search if this coupling is not released. Limits (R 1 ,R 2 )of−2, +2 will be assigned by the code to the matrix element connecting states 2 and 3. These limits are usefulif the coupling of these matrix elements is subsequently released.The convention of coupling matrix elements already described is valid only within a single multipolarity.The coupling of matrix elements belonging to different multipolarities is performed by using 100λ +R 2 asinput for the index R 2 of the “slave“ matrix element where λ is the multipolarity of the master matrixelement. The convention that λ= 7for M1 and λ= 8for M2 is still valid.An important restriction is that there can be only one “master“ matrix element with a number of slavescoupled to it if a group of matrix elements are specified to be mutually related. For example, a valid sequenceis1, 2, 2., −4, 4 E2 set of matrix elements2, −3, 2., 1, 2·2, −3, 0.5, 1, 202 M1 set of matrix elements91