Implementing a modified harmonic potential using pair_style lepton/sphere

Dear all,
I am trying to implement the modified version of harmonic potential to implement AQS as described in the paper “Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow10.1103/PhysRevLett.93.016001)”.
I am using lammps-stable_2Aug2023 version of lammps.
To prepare the initial configuration of a bidisperse system with packing fraction 1.0, this is the input code I am using

units           si  # lj or real or metal or si or cgs or electron or micro or nano (unitless
atom_style      sphere
dimension       2

region          box prism 0.0 200.0 0 200.0 -0.5 0.5  0.0 0.0 0.0
region          particle prism 0.0 200.0 0.0 200.0 -0.5 0.5  0.0 0.0 0.0


create_box      2 box
create_atoms 1 random 37968 3000 particle units box
create_atoms 2 random 46932 4000 particle units box





set type 1 diameter 1.0
set type 2 diameter 0.5257
set type 1 mass 1.0
set type 2 mass 1.0



pair_style lepton/sphere 1.0
pair_coeff 1 1 "(k*((1-d)^2)*step(1-d)); k=1.0; d=r/r0; r0=radi+radj"
pair_coeff 2 2 "(k*((1-d)^2)*step(1-d)); k=1.0; d=r/r0; r0=radi+radj"
pair_coeff 1 2 "(k*((1-d)^2)*step(1-d)); k=1.0; d=r/r0; r0=radi+radj"

compute fcl all property/local patom1 patom2
compute fc all pair/local dist force
compute peratom all stress/atom NULL pair
compute p all reduce sum c_peratom[1] c_peratom[2] c_peratom[3] c_peratom[4]
variable press equal -(c_p[1]+c_p[2])/(2*vol)
variable sigmaxy equal c_p[4]/vol



fix             2 all enforce2d
thermo 100
thermo_style custom step ke pe v_press v_sigmaxy
dump            mydump all atom 1 energyscale_1.dump
dump             1 all custom 100 *.data id type diameter mass x y z vx vy fx fy
dump    pairf all local 100 *.pairf c_fcl[1] c_fcl[2]  c_fc[1] c_fc[2]
dump_modify  1 sort id
min_style cg
restart 100 restart.*.energyscale_1
minimize     0.0 1.0e-08 1000000 10000000 

Now while applying the formula of potential used in the paper, which will be the right way to use pair_style lepton.

**pair_style lepton/sphere 1.0**
**pair_coeff 1 1 "(k*((1-d)^2)*step(1-d)); k=1.0; d=r/r0; r0=radi+radj"**

OR

**pair_style lepton/sphere 1.0**
**pair_coeff 1 1 "(0.5*k*((1-d)^2)*step(1-d)); k=1.0; d=r/r0; r0=radi+radj"**

As mentioned in the lammps manual the usual 1/2 factor is included in k.
Any suggestion is appreciated