I'm afraid this problem will more challenge your computer skills than your skills as a quantum mechanic.

Aim: fit and plot (cross-section vs. k) and (phase shift vs k) data to the Breit-Wigner formalism

The data consists of the actual U=30 resonance near k=1.47 due to delta3

Theoretical delta function (but see below!)
delta=ArcCot[(k2-x)/k1]
Theoretical sigma function
sigma=k4+k3/((k2-x)^2+k1^2)

where k2 is the resonance location, k1 (called Gamma/2 in class) determines
the resonance width, k3 determines the peak value (relates to (2L+1)4 pi/k^2), and k4
represents the contributions of the other partial waves.

ArcCot proves to be a problem (getting the right branch of the inverse function)
and so it is never used in the above form.

OPTION 1: go with Mathematica...
Your final work product will be a pair of graphs like math/class34.pdf along with
the numerical values for the fit parameters.

here is the data in Mathematica form:

delta3={{1.35, 0.10253225166633644}, {1.36, 0.11709300222014721}, 
 {1.37, 0.13481163723025624}, {1.38, 0.15675052971036327}, 
 {1.39, 0.1844940466509399}, {1.4,   0.22050258303555526}, 
 {1.41, 0.2687842111588437},  {1.42, 0.33624341021558796}, 
 {1.43, 0.43552883091509803}, {1.435, 0.5040119992500022}, 
 {1.44, 0.591054908802321}, {1.445, 0.7032460906999967}, 
 {1.45, 0.8487508759425039}, {1.455, 1.0352224064040147}, 
 {1.46, 1.2635918830960984}, {1.465, 1.51908729200725}, 
 {1.47, 1.7714867497887987}, {1.475, 1.9925440520752802}, 
 {1.48, 2.170922453572415}, {1.485, 2.309504357961785}, 
 {1.49, 2.4163610927135655}, {1.495, 2.499435016117197}, 
 {1.5, 2.564972933856243}, {1.51, 2.660353196501439}, 
 {1.52, 2.725431984358919}, {1.53, 2.772129836056384}, 
 {1.54, 2.8069915029358095}, {1.55, 2.8338374048766117}, 
 {1.56, 2.8550240964046907}, {1.57, 2.872075304583604}, 
 {1.58, 2.8860162908695046}, {1.59, 2.8975605934387727}, 
 {1.6, 2.9072193058892193}}

sigma={{1.35, 7.953352539070761}, {1.36, 8.011110144071242}, 
 {1.37, 8.123599378929775}, {1.38, 8.318265721886887}, 
 {1.39, 8.641082527811756}, {1.4, 9.172865114412495}, 
 {1.41, 10.063822134893922},  {1.42, 11.61098148375059}, 
 {1.43, 14.437523755134773}, {1.435, 16.703859641140856}, 
 {1.44, 19.873065947101296}, {1.445, 24.279566376253623}, 
 {1.45, 30.18370512939687}, {1.455, 37.31111770058124}, 
 {1.46, 44.0357423015019}, {1.465, 47.379474842854876}, 
 {1.47, 45.55400694837987}, {1.475, 40.08212914440045}, 
 {1.48, 33.737756976127976}, {1.485, 28.15281634419416}, 
 {1.49, 23.743066839836807}, {1.495, 20.390132303197195}, 
 {1.5, 17.854923201141542}, {1.51, 14.425066746928962}, 
 {1.52, 12.306721871785923}, {1.53, 10.911339688517446}, 
 {1.54, 9.93813777384912}, {1.55, 9.225736536071333}, 
 {1.56, 8.682605768624551}, {1.57, 8.254086553550458}, 
 {1.58, 7.906025206807025}, {1.59, 7.6162264114979985}, 
 {1.6, 7.3697681574628175}}

Instead of ArcCot use:
ArcTan[(k2-x),k1]
ArcTan[a,b] is a 4-quadrant, two-argument version of inverse tangent

Note: FindFit can fit, ListPlot can plot the data, and you can combine
separate function and data plots with Show.

OPTION 2: go with linux fit/plot
Your final work product will be a pair of graphs like 
class34_delta.pdf class34_sigma.pdf along with
the numerical values for the fit parameters.

fit/plot want data with errors; find this data (with errors):
delta3.dat
sigma.dat

Instead of ArcCot we must use atan, but kick it into the proper quadrant, Do:
set f(x)=atan(k1/(k2-x))+pi*w(x-k2) B=10

your fit session will look something like:
bethe 104% fit
* set file=delta3.dat
* read
 k	delta3	error
 READ Done.
* set f(x)=atan(k1/(k2-x))+pi*w(x-k2), B=10
* set k1 yourguess k2 yourguess
* fit
Enter list of Ks to vary, e.g. K1-K3,K5 k1,k2
 FIT finished with change in Ks implying 3 significant figures
   4 iterations used
 REDUCED chi-squared=   1.379910      chi-squared=   42.77719