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

Note that the definition of reduced matrix element does not include the i λ term for the Eλ matrixelements used in the original Winther-deBoer semiclassical Coulomb excitation code (WI66). The Eλ matrixelements are given in units of e.barns λ/2 i.e., e (10 −28 m 2 ) λ/2 .TheMλ matrix elements are given in units ofμ n barns (λ−1)/2 . Within a given multipolarity, only matrix elements in the upper triangle, i.e. INDEX2 ≥INDEX1, should be given. Matrix elements in the lower triangle are set by the program. Within a givenmultipolarity both INDEX1 and INDEX2 columns must appear in increasing order (odometer ordering).The header of the next multipolarity ends input for a given multipolarity. A single record of 3 zeros endsthe input to ME.RESTRICTIONS:Note that the sequence of matrix elements is uniquely set by the input conventions. An error messagewill be printed and the job aborted if any of the following restrictions are violated.a. Multipolariaties must appear in order from lowest to highest starting with Eλ and then Mλ.b. Matrix elements must belong to the upper triangle, i.e., INDEX2 ≥ INDEX1.c. INDEX values must be in increasing order, i.e. odometer order.MATRIX ELEMENT PHASES:Note that the phase of a wavefunction is arbitrary. However, to facilitate comparison with models itis best to fix the relative phases of states. Choosing one matrix element between two states to be positivecouples the relative phases of the wavefunctions of these two states to be the same. Then the phases of anyother matrix elements coupling these two states, relative to the phase of the positive one, are observables.Consequently for typical collective bands it is convenient to choose the primary ∆I =2,E2 transitions inthe band to have a positive phase locking the state wavefunctions of the band to have the same phase. Inaddition the phase of one strong matrix element connecting two separate collective bands locks the relativephase between these collective bands.When entering matrix elements in the upper triangle be careful to enter the correct phase rememberingthat time reversal invariance relates the time-reversed matrix elements by=(−) J1−J2−λ Thus the phase of the matrix elements in the lower triangle is related to the upper triangle phase bythe (−) J 1−J 2 −λ phase term. Similar care must be taken comparing the observed relative phases with modelpredictions.88