Notes:

• Inclusion of $I\rightarrow I'$ transition in the table of couplings, does not include automatically $I'\rightarrow I$. We then need two &step/ namelist in order both couplings are considered.
• The values of M(Ek) must be entered in units of $e\, fm^{\lambda}$. This means that the reduced transition probabilities, $B(E\lambda)$ are in units of $e^{2}\, fm^{2\lambda}$. Notice that some databases use different units. For instance, the ENSDF database at NNDC [] uses for the transition probabilities the units $e^{2}b^{\lambda}$. Frequently, transition probabilities are given in Weisskopf units, which are estimates of transition strengths for a single proton in a uniform charge distribution 2.
  

  Table 2: Transition probabilities T(sec-1) expressed by B(EL) in $e^{2}fm^{2\lambda }$ and B(ML) in $(\frac{e\hbar}{2mc})^{2}fm^{2\lambda-2}$. E= Gamma-ray energy, measured in MeV.

  Transition rate

  Weisskopf estimate T(E1)=1.587 1015E3  B(E1)

  
  

• The transition probability for an electric radiation is roughly two orders of magnitude larger than for an equivalent magnetic transition, meaning electric transitions are favored, $\frac{\lambda(M1)}{\lambda(E1)}<<1$. The probability is also inversely proportional to the multipolarity meaning higher multipolarities are slower, $\frac{\lambda(l+1)}{\lambda(l)}<<1$ . The effect of this is that while an E2 transition can compete with an M1, the M3 and higher orders are negligible. Also, an M2 cannot compete with an E1, which is therefore generally described as a `pure' dipole.
• Fresco gives also the possibility of defining the couplings to excited states through the &coupling/ and &inel/ namelists. As an example, consider the reaction ⁸Li+²⁰⁸Pb in a two state model of ⁸Li, including the g.s. (2⁺) and its excited state ( 1⁺). Using the values $B(E2;2^{+}\rightarrow1^{+})=30\,\mathrm{e^{2}fm^{4}}$ and the deformation length $\delta=1.75\,\mathrm{fm}$ from the literature the fresco input looks like:

8Li+208Pb quasielastic
NAMELIST
 &FRESCO hcm=0.1 rmatch=100 rintp=0.5 hnl=0.033 
	 rnl=3.00 centre=0.00 jtmax=100 absend=0.001 dry=F 
	 jump(1:6:1)=0 0 0 0 0 0 jbord(1:6)=0 0 0 0 0.0 0.0 
	 thmin=2.00 thmax=-180.00 thinc=2.00 ips=0.01 iblock=2 
	 pralpha=F pade=1 nnu=24 chans=1 smats=2  xstabl=1 
	 pel=1 exl=1 lab=1 lin=1 lex=1 elab=34.404 
	 nlab(1:3)=0 0 0 fatal=F nosol=F psiren=T 
	 unitmass=1.000 finec=137.03599d0  /

 &PARTITION namep='Li-8' massp=8 zp=3 namet='Pb-208' 
	 masst=207.977 zt=82 qval=0.0000 pwf=T nex=2  /
 &STATES jp=2.0 bandp=1 ep=0.000 kkp=1 cpot=1 
	 jt=0.0 bandt=1 et=0.000 fexch=F  /
 &STATES jp=1.0 bandp=1 ep=0.981 kkp=1 cpot=1 
	 jt=0.0 copyt=1 bandt=1 et=0.000 fexch=F  /

 &partition /
 
 &POT kp=1 itt=F ap=8 at=208 rc=1.200  /
 &POT kp=1 type=12 shape=10 itt=F p1=0.000 p2=10. 
	 p3=0.000 p4=0.000 p5=0.000 p6=0.000  /
 &STEP ib=2 ia=1 k=2 str=12.24  /
 &STEP ib=1 ia=2 k=2 str=12.24  /
 &STEP ib=1 ia=1 k=2 str=-5.976  /
 &STEP ib=2 ia=2 k=2 str=5.477  /
 &step / 
 
 &POT kp=1 type=1 itt=F p1=60 p2=1.3 p3=0.65 
	 p4=150 p5=1.3 p6=0.60  /
 &POT kp=1 type=12 shape=10 itt=F p1=0.000 p2=1.75 
	 p3=0.000 p4=0.000 p5=0.000 p6=0.000  /
 &STEP ib=2 ia=1 k=2 str=2.1433  /
 &STEP ib=1 ia=2 k=2 str=2.1433  /
 &STEP ib=1 ia=1 k=2 str=-1.0458  /
 &STEP ib=2 ia=2 k=2 str=0.9585  /
 &step / 
 
 &pot / 
 
 &overlap / 
 
 &coupling / 
 
Output code for fresco input written by xfresco v.1.0
 at Mon Sep 23 16:03:22 2002
 

Alternatively, we can define a &coupling/ namelist with kind=1 (excitations of projectile):

\&COUPLING icto=1 icfrom=1 kind=1 ip1=8 /

Here, icto=icfrom indicates the partition where excitations are defined. Then, a &inel/ namelist is included for each coupling. For instance,

 &INEL ib=2 ia=1 k=2 no=2 kp=1 a=12.24 /

indicates that state ia=1 (i.e., the g.s.) is coupled to state ib=2 (the excited state) with multipolarity k=2. The coupling will be generated using the component no=2 of potential kp=1 (which corresponds to a deformed coulomb potential). Note that this amplitude a is to be multiplied to the value of p(k) in the deformed potential. The product of both quantities is supposed to give the reduced matrix element $M(Ek;\, I\rightarrow I')$ (for Coulomb couplings) or $RDEF(k;I\rightarrow I')$ (for nuclear couplings)

8Li+208Pb quasielastic
NAMELIST
 &FRESCO hcm=0.1 rmatch=100 rintp=0.5 hnl=0.033 
	 rnl=3.00 centre=0.00 jtmax=100 absend=0.001 dry=F 
	 jump(1:6:1)=0 0 0 0 0 0 jbord(1:6)=0 0 0 0 0.0 0.0 
	 thmin=2.00 thmax=-180.00 thinc=2.00 ips=0.01 iblock=2 
	 pralpha=F pade=1 nnu=24 chans=1 smats=2  xstabl=1 
	 pel=1 exl=1 lab=1 lin=1 lex=1 elab=34.404 
	 nlab(1:3)=0 0 0 fatal=F nosol=F psiren=F 
	 unitmass=1.000 finec=137.03599d0  /

 &PARTITION namep='Li-8' massp=8 zp=3 namet='Pb-208' 
	 masst=207.977 zt=82 qval=0.0000 pwf=T nex=2  /
 &STATES jp=2.0 bandp=1 ep=0.000 kkp=1 cpot=1 
	 jt=0.0 bandt=1 et=0.000 fexch=F  /
 &STATES jp=1.0 bandp=1 ep=0.981 kkp=1 cpot=1 
	 jt=0.0 copyt=1 bandt=1 et=0.000 fexch=F  /

 &partition /
 
 &POT kp=1 itt=F ap=8 at=208 rc=1.200  /
 &POT kp=1 type=12 shape=10 itt=F p2=1  /
 &step / 
 
 &POT kp=1 type=1 itt=F p1=60 p2=1.3 p3=0.65 
	 p4=150 p5=1.3 p6=0.60  /
 &POT kp=1 type=12 shape=10 itt=F p2=1  /
 &step / 
 
 &POT kp=2 itt=F ap=8 at=208 rc=1.200  /
 &POT kp=2 type=1 itt=F p1=60 p2=1.3 p3=0.65 
	 p4=150 p5=1.3 p6=0.60  /
 &POT kp=2 type=12 shape=10 itt=F p2=1  /
 &step / 
 
 &pot / 
 
 &overlap / 
 
 &COUPLING icto=1 icfrom=1 kind=1 ip1=8  /
 &INEL ib=2 ia=1 k=2 no=2 kp=1 a=12.24  /
 &INEL ib=1 ia=2 k=2 no=2 kp=1 a=12.24  /
 &INEL ib=1 ia=1 k=2 no=2 kp=1 a=-5.976  /
 &INEL ib=2 ia=2 k=2 no=2 kp=1 a=5.477  /
 &INEL ib=2 ia=1 k=2 no=3 kp=2 a=2.1433  /
 &INEL ib=1 ia=2 k=2 no=3 kp=2 a=2.1433  /
 &INEL ib=1 ia=1 k=2 no=3 kp=2 a=-1.0458  /
 &INEL ib=2 ia=2 k=2 no=3 kp=2 a=0.9585  /
 &INEL/ 
 
 &coupling / 
 
Output code for fresco input written by xfresco v.1.0
 at Mon Sep 23 16:16:16 2002