Procedures

Add a trailing character trail to the character chr if it is not already the last character

Compare two a and b and see if the magnitude of their difference is smaller than a tolerance, taking machine epsilon*max(|a|,|b|) for their precision as the default value

Return the phase of a complex number in (-π,π]

Using the eigenvectors and energies from a diagonalized rotational Hamiltonian, determine which projection is maximal. The eigenvectors can be in the Ka or Kc basis. This routine will return the array Kvals which indicats the absolute value of the projection that contributes the most to a particular eigenvector

Returns the Clebsch-Gordan coefficient $C^{jm}_{j_1m_1,j_2m_2} \equiv \left\langle j_1m_1,j_2_m2|jm \right\rangle$ by using its relation to the Wigner 3j symbol

Combine Coulomb-Born and S-matrix cross sections to be on the same electron energy grid. In general, a different number of transitions will exist for the Coulomb-Born cross sections and for the S-matrix cross sections. This routine matches the transitions, interpolates the CB cross sections to the total energy grid used by the S-matrix routines, and adds them together: σ(tot) = σ(S-mat) + σ(TCB) - σ(PCB)

Convert the supplied array of multipole moments from cartesian, obtained as typical output from quantum chemistry codes, to spherical multipole moments $Q_{\lambda,\mu} = \int d\vec{r} \rho(\vec{r}) Y_lambda^\mu(\hat{r})$

Return the Kronecker delta function $\delta_{m,n}$

Detects the type of the operating system. As far as system calls and directory structure go, this basically resolved to Windows or not Windows.

Build the rigid-rotor hamiltonian for each N and diagonalize it. Keep eigenenergies and eigenvectors, stored in the eigenH type of n_states !!!!!!!!!!!!!!!!!!!!!!! nonlinear rotors !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!! linear rotors !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Takes an integer dJ and results the character representing half of it. dJ2char(2) -> "1" dJ2char(3) -> "3/2"

Use the Coulomb-Born approximation to get scattering cross sections for e⁻ + target. Also determines Einstein A coefficients and excited state average lifetimes within !! the radiative dipole/multipole approximation. The target charge Z is supplied and used by the routine that are called here, so various target charges can be used, including Z = 0 (neutral targets). This routine loops over the different pairs Nτ —→ N'τ'

Read K-matrices from an electron-molecule scattering calculation, get S-matrices, add the rotation via the rotational frame transformation for asymmetric tops, then use the MQDT channel elimination to get electron-impact excitation cross sections entirely from the K-matrix scattering data.

Print error messages to the screen without the WARNING prompt. This will typically precede a call to DIE

Return an n x n identity matrix

Returns one of the following transforms 1. ₂F₁(a,b;c;x) = (1-x)^{-b} ₂F₁(b,c-a;c;x/(x-1)) 2. ₂F₁(a,b;c;x) = (1-x)^{-a} ₂F₁(a,c-b;c;x/(x-1)) 3. ₂F₁(a,b;c;x) = (1-x)^{-a} Γ(c)Γ(b-a)/(Γ(b)Γ(c-a)) ₂F₁(a,c-b;a-b+1;1/(1-x)) + (1-x)^{-b} Γ(c)Γ(a-b)/(Γ(a)Γ(c-b)) ₂F₁(b,c-a;b-a+1;1/(1-x)) 4. ₂F₁(a,b;c;x) = Γ(c)Γ(c-a-b)/Γ(c-a)Γ(c-b) ₂F₁(c-a, c-b, c-a-b+1, 1-x) + (1-x)^(c-a-b) Γ(c)Γ(a+b-c)/Γ(a)Γ(b) ₂F₁(c-a,c-b;c-a-b+1;1-x) Regions of validity: 1. |a| < |b|, -1 ≤ x < 0 2. |a| > |b|, -1 ≤ x < 0 3. -∞ < x < -1 4. ½ < x < 1

Checks if x is indeed in (0,1/2), and then makes a choice of evaluating the ODE (large a,b,c) or defaulting to the usual Taylor series

Returns the Gauss hypergeometric function ₂F₁(a,b,;c;z) via a Taylor series method, with quad precision

!n

Find the indices for each element in targs that map to the elements in search. Return 0 if there is no such mapping.

Calculate the excitation and de-excitation cross sections (xs) for an asymmetric top up. The sum over partial waves is either truncated to $l_\text{max}$ or determined analytically. The summation over the angular momentum components, multipole terms, and partial waves are separable for each value of λ as summation = (sum over angular momentum and multipole moments) $\times$ (sum overpartial waves).

Read a file from the CDMS search to get Einstein A coefficients that will be used in determining Coulomb-Born cross sections.

Given the quantum numbers of a rotational transition, find the matching CDMS transition and get the corresponding Einstein A coefficient

Update the energy of our rotational states with those from the CDMS

Return the first index i where channel .eq. channels(i) is .true., or the last index is reverse is .true.

Calculate only the Einstein A coefficeints for a transition

Given the point group, output an array containing the names of the irreps in the supplied point_group. Only Abelian point groups are considered. Irreps in the code will be referred to by their indicies

Given a rotationally resolved S-matrix, calculate rotational (de-)excitation cross section probabilities for the supplied transitions.

Return the number of elements in point_group

Construct the $2N + 1 \times 2N + 1$ symmetric top rigid-rotor Hamiltonian $H = Bx N_x^2 + By N_y^2 + Bz N_z^2$

Interpolate f(xold) -> f(xnew). Only consider xnew values that are contained within xold for now. Xnew returns untouched, but fx is overwritten with interpolated values on the grid xnew(idxx)

Compute 1/z

Given an irrep index in point_group, return the name of the corresponding irrep

Determine whether a matrix is symmetric

Determine whether a matrix is unitary w.r.t the Frobenius norm

Test whether x is in the interval spanned by x1,x2 l/rclosed if true include xl and xr, respectively. They are true by default

Check if a real/complex number is an integer

Check if a real/complex number is a natrual number

returns whether the arguments satisfy the triangle inequality, assuming that they're positive quantities

ln(!n)

returns a lower case character

Calculates the integral $M^\lambda_{l+λ,l}$ via the expression given in "Electromagnetic Excitation: Theory of Coulomb Excitation with Heavy Ions " by Kurt Alder and Aage Winther, Chapter IX, section 2, page 244, equation 14. for λ = 1, where $-4M^\lambda_{l+λ,l} = I^λ_{l+λ, l}$. There is an expression for λ = 2 in "Study of Nuclear Structure by Electromagnetic Excitation with Accelerated Ions" by K. Alder, A. Bohr, T. Huus, B. Mottelson, and A. Winther, but only the dipole is used (at least for now).

Make a segmented grid starting at E0 Example with num_segments = 3, grid_segments = [1e-3, 1e-2, 1e-1, 1], nelemnts_per_seg = [1000,1000, 100] E0+1e-3 E0+1e-2 E0+1e-1 E0+1.0 !------------------!-------------------!- - - - - - - - -! 1000 energies 1000 energies 100 energies

Makes the directory "directory" and checks that it exists and is writeable

Returns number of characters an integer will occupy

Returns the integer $(-1)^{i)$}

Returns an array of possible spin symmetry values

Print the dipole components in the determined ABC frame

Print the dipole components in the determined ABC frame

Reads num_read lines from unit read_unit, not storing any information. If num_read is not supplied, read one line.

Reads in a K-matrix from a file with a very particular file format given by kmat_output_type

Reads user parameters and puts them into the config derived type Contains parameters and values that are necessary to run the program

Remove all instances of the value val from the array arr

Build the electronic S-matrix from the electronic K-matrix, then perform the rotational frame transformation on the S-matrix

Returns X = AB⁻¹ without evaluating B⁻¹

Rotate the rigid rotor eigenvectors from one of the principal axes A,B,C to another principal axis A,B,C using the Wigner D-matrix

convert seconds to hours, minutes, seconds

Bubble sort the array of channels such that the channel energies are in ascending order

Sort the array vals and return the permutation indices

Returns the spin symmetry of the current N, Ka, Kc state

Returns the subscript version of the integer x

Returns the superscript version of the integer x

converts a character to lower case

converts a character to upper case

Given a rotational channel with the l quantum number, return the equvalent channel without the l quantum number

Returns the unique elements of arr

Return the unitary defect with respect to the Frobenius norm $rF = ||A^{\dagger}A-I||_F / sqrt{n}$

returns an upper case character

returns the Wigner 3j symbol via explicit calculation. These should probably be precomputed, but this works for now. The WignerSymbol-f repo seems like a good implementation. The wigner repo by ogorton takes up way too much memory for the high partial waves because it tries to allocate (2N+1)^6 doubles. NOTE: for the high partial wave, we know that we'll only need values with m1 = m2 = m3 = 0, so take advantage of this ?

Writes a Coulomb-Born cross section to a file whos name and file header carry information about the state symmetry

Write rotational channel info to file

Writes the states involved in the excitation and their lifetimes

Writes an S-matrix (+CB) cross section to a file whos name and file header carry information about the state symmetry

Write the total cross-sections (S-matrix + CB correction) to disk for a single transition

Extrapolate an excitation/de-excitation cross section to its excitation threshold. Use a power law scaling by fitting the first 2 points. Re-allocates Eel and xs to contain the extrapolated values