COLOSS: Complex-scaled Optical and couLOmb Scattering Solver is a program designed to address the scattering problem using a bound-state technique known as complex scaling. In this method, the oscillatory boundary conditions of the wave function are transformed into exponentially decaying ones, accommodating the long-range Coulomb interaction. This program implements the general local optical model potential and the Perey-Buck nonlocal optical potential, with all parameters included in a well-designed input format for ease of use. This design offers users straightforward access to compute S-matrices and cross-sections of the scattering process.
The program employs Lagrange-Laguerre functions as the basis functions and provides two methods to perform numerical integration: one based on the approximation of Lagrange functions, and the other using direct Gauss-Legendre quadrature. Additionally, COLOSS incorporates two distinct rotation methods, making it adaptable to potentials without analytical expressions.
For those interested in the theoretical foundations and implementation details of COLOSS, a comprehensive published paper is available at https://www.sciencedirect.com/science/article/abs/pii/S0010465525000712?via%3Dihub. Furthermore, to facilitate the preparation of input files, which are crucial for defining the parameters of the scattering problem, a user-friendly UI interface input file generator named coloss-input-generator.html is provided. This tool enables users to generate the necessary input files with ease, ensuring a smooth start to their computational tasks.
COLOSS utilizes the FORTRAN namelist to construct a user-friendly input format.
General namelist: nr, alpha, Rmax, ctheta, matguass, bguass, numgauss, rmaxgauss, method,backrot, cwftype, thetah, thetamax
- nr(integer*4): number of the Lagrange-Laguerre basis/ order of the generalized Laguerre polynomial in the calculation
- alpha(real*8): parameter of the generalized Laguerre polynomial
- Rmax(real*8): maximum value of the points in the scaled Lagrange-Laguerre mesh
- ctheta(real*8): rotation angle for complex scaling in degrees
- matgauss(logical): determines whether to use the Gauss-Legendre quadrature to evaluate the matrix elements of the Hamiltonian
- bgauss(logical): determines whether to use the Gauss-Legendre quadrature to evaluate the inhomogeneous terms in the linear equation
- numgauss(integer*4): number of Gauss-Legendre mesh points
- rmaxgauss(real*8): maximum radius of the Gauss-Legendre mesh points
- method(integer*4): options for 2 different method to calculate the scattering amplitude, set it as 1 for linear equation method, and 2 for the Green's function method
- backrot(logical): determines whether to rotate the basis backward or to rotate the potential directly in the calculation
- cwftype(integer*4): options for 2 different subroutines to calculate Coulomb wave functions. Set it as 1 to call COULCC, and 2 to call cwfcomplex
- thetah(real*8): step size for the angle in the output differential cross section
- thetamax(real*8): maximum angle in the output differential cross section
- readinpot(logical): determines whether to import the potential from external file 'pot.dat', please set backrot as t when using this option
- zp, zt(real*8): charge number of the projectile and the target
- massp, masst(real*8): mass number of the projectile and the traget
- namep, namet(character): name of the projectile and the target
- jmin, jmax(integer*4): minimum/maximum total angular momentum of the reaction system considered in the calculation
- sp(real*8): spin of the projectile
- elab(real*8): incident kinetic energy of the projectile in the laboratory frame
Pot namelist: vv, rv, av, wv, rw, aw, vs, rvs, avs, ws, rws, aws, vsov, rsov, asov, vsow, rsow, asow, rc
- vv, rv, av(real*8): depth, radius, and width parameters of the real volume term in OMP
- wv, rw, aw(real*8): depth, radius, and width parameters of the imaginary volume term in OMP
- vs, rvs, avs(real*8): depth, radius, and width parameters of the real surface term in OMP
- ws, rws, aws(real*8): depth, radius, and width parameters of the imaginary surface term in OMP
- vsov, rsov, asov(real*8): depth, radius, and width parameters of the real spin-orbit coupling term in OMP
- vsow, rsow, asow(real*8): depth, radius, and width parameters of the imaginary spin-orbit coupling term in OMP
- rc(real*8): charge radius for Coulomb interaction in OMP
- nonlocal(logical): determines whether to use a nonlocal form of OMP proposed by F. PEREY and B. BUCK(Nuclear Physics,32,353-380)
- nlbeta(real*8): beta parameter in F. PEREY and B. BUCK's nonlocal form of OMP
- fort.1: The local copy of the input file
- fort.2: The table of all the angular momentum channles consided in the calculation.
- fort.10: The scaled Lagrange-Laguerre mesh points and weights
- fort.60: The S-matrices for different angular momentum channels
- fort.61: The nuclear scattering amplitudes for different angular momentum channels
- fort.67: The angular distribution of the differential cross section
In COLOSS, we use GNU Compiler Collection(GCC). Make sure you have installed GCC. For linear algebra subroutines, we use LAPACK package. To complie the program:
- Edit the Makefile and specify your path of the LAPACK package on your machine.
- Use the provided Makefile to compile all the source code.
prompt> make - Transfer the executable program, COLOSS, to the test directory, and initiate program execution through standard input:
prompt> ./COLOSS < inpufile
&general
nr=60 alpha=0 Rmax=40 ctheta=7
matgauss=f bgauss=f method=1
thetah=1.0 thetamax=180 /
&system
zp=0 massp=1 namep='n'
zt=20 masst=40 namet='40Ca'
jmin=0 jmax=10 elab=20 sp=0.5/
&pot
vv=46.553 rv=1.185 av=0.672
wv=1.777 rw=1.185 aw=0.672
vs=0 rvs=0 avs=0
ws=7.182 rws=1.288 aws=0.538
vsov=5.343 rsov=0.996 asov=0.590
vsow=-0.110 rsow=0.996 asow=0.590
rc=1.698 /
&nonlocalpot
nonlocal=f nlbeta=0.0 /
************************************************************
* COLOSS: Complex-scaled *
* Optical and couLOmb Scattering Solver *
************************************************************
Rotation Angle for Complex Scaling: 7.00 degrees
Rotation Operation: Applied to Potential
-------------------Reaction system-------------------
Projectile: n (A: 1.00 Z: 0.00)
Target: 40Ca (A: 40.00 Z: 20.00)
Lab Frame Energy: 20.00 MeV
C.M. Frame Energy: 19.51 MeV
Generating the channel index
There are 20 different channels
Total J Range: 0.0 <= J <= 10.0
-------------- Lagrange-Laguerre Mesh --------------
Laguerre Polynomial Order: 60
Laguerre Mesh Max Value: Scaled from 219.3181 to 40.0000
Scaling Factor: 0.1824 (fm)
------------- Optical Model Potential -------------
Optical Potential for A = 40.0 Z = 20.0 at 20.000 MeV rc = 1.698
Vv rvv avv Wv rw aw
46.553 1.185 0.672 1.777 1.185 0.672
Vs rvs avs Ws rws aws
0.000 0.000 0.000 7.182 1.288 0.538
Vsov rsov asov vsow rsow asow
5.343 0.996 0.590 -0.110 0.996 0.590
------------------------------------------------
Initializing Complex Coulomb Function
Sommerfeld Parameter: 0.0000
Generating Rotated Coulomb Wave Function on Laguerre Mesh
(CPU time = 0.00025700 seconds)
Using Linear Equation Method to Solve
L S J | (Real(Smat), Imag(Smat)) | Partial Wave Reac_Xsec (mb)
----------------------------------------------------------------------------
0 0.5 0.5 | ( 0.349804, 0.223235) | 28.5534
1 0.5 0.5 | ( 0.508537, 0.041797) | 25.5125
1 0.5 1.5 | ( 0.479616, 0.195699) | 50.4749
2 0.5 1.5 | ( 0.321689, -0.152658) | 60.2393
2 0.5 2.5 | ( 0.392012, 0.086108) | 86.8096
3 0.5 2.5 | ( -0.032075, -0.496351) | 77.8789
3 0.5 3.5 | ( 0.317075, -0.310480) | 110.8004
4 0.5 3.5 | ( -0.134338, -0.189716) | 130.5159
4 0.5 4.5 | ( 0.171986, -0.508775) | 122.7206
5 0.5 4.5 | ( 0.448912, 0.217764) | 129.5308
5 0.5 5.5 | ( 0.219593, 0.066785) | 196.0549
6 0.5 5.5 | ( 0.878907, 0.126747) | 43.7629
6 0.5 6.5 | ( 0.839528, 0.167094) | 64.5332
7 0.5 6.5 | ( 0.977509, 0.037757) | 10.3944
7 0.5 7.5 | ( 0.975107, 0.047042) | 12.9563
8 0.5 7.5 | ( 0.995748, 0.009952) | 2.3144
8 0.5 8.5 | ( 0.995614, 0.011765) | 2.6742
9 0.5 8.5 | ( 0.999183, 0.002546) | 0.5053
9 0.5 9.5 | ( 0.999178, 0.002913) | 0.5636
10 0.5 9.5 | ( 0.999841, 0.000644) | 0.1093
----------------------------------------------------------------------------
(CPU time = 0.003733 seconds)
----------------- Files Created -----------------
1: local copy of input.
2: list of channel index.
10: scaled Laguerre mesh points and weights.
60: S matrix LSJ distribution.
61: scat amplitude LSJ distribution.
67: cross section angular distribution.
Total CPU time = 0.029168 seconds
***************** CONSTANTS **********************
* hbarc=197.32697 MeV.fm e^2= 1.43997 MeV.fm *
* so, alpha= 1/137.03547 amu=931.4943 MeV *
**************************************************