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

Figure 11: Distribution plot of the parameters Q 2 and δ required to define the E2 properties in the intrinsicframe for a state S. All possible E2 moments are defined by the region Q ≥ 0 and 0 ≤ δ ≤ 60 ◦ .states are measured with large errors, unless some additional data, most important the branching ratios, areavailable.Restricting ourselves to J =0, 2 and 4 couplings we have from 6.17 and 6.18:andQ 6 cos 2 3δ(0) = 352 P 6 1 (0) = 35 2 P 6 2 (0) (6.21)Q 6 cos 2 3δ(J) J=2,4 = 35(P 6 1,2(4) −√54 P 6 1,2(2)) (6.22)with P1 6 5(2J +1)1/2 X(J) = M su M ut M tr M rv M vw M ws2I s +1rutvw½ ¾½ ¾½ ¾½ ¾2 2 J 2 2 2 2 2 J 2 2 2•(−1)I s I r I t I s I t I u I s I r I w I w I r I 2Is+It+Iw (6.23)vwith P2 6 5(2J +1)1/2 X(J) = M su M ut M tr M rv M rw M ws2I s +1rutvw½ ¾½ ¾½ ¾½ ¾2 2 J 2 2 2 2 2 J 2 2 2•(−1)I s I r I t I s I t I u I s I r I v I s I v I Is+Ir+It+Iw (6.24)w6.21 through 6.24 define three independent estimates of Q 6 cos 2 3δ - one involving the J =0 coupling,identical for both P1 6 and P 26 and two involving the J =2and J =4couplings for P1 6 and P 2 6 , respectively.Using the value of Q 6 (6.19) the expectation from 6.22, which, combined with the expectation value of cos3δcan be obtained which defines the softness in δ as being given by the square root of the cos3δ variance:v 2 (cos 3δ) =< cos 2 3δ>− < cos 3δ > 2 (6.25)122