(** Set of Gaussians with a given {!AngularMomentum.t}

{% \\[
g(r) = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} \exp \left( -\alpha |r-R_A|^2 \right)
   \\] %}

where:

- {% $n_x + n_y + n_z = l$ %}, the total angular momentum

- {% $\alpha$ %} is the exponent

*)

type t 

val to_string : t -> string
(** Pretty-printing of the primitive shell in a string. *)

val make : AngularMomentum.t -> Coordinate.t -> float -> t
(** Creates a primitive shell from the total angular momentum, the coordinates of the
    center and the exponent. *)

val expo : t -> float 
(** Returns the exponent {% $\alpha$ %}. *)

val center : t -> Coordinate.t
(** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *)

val totAngMom : t -> AngularMomentum.t
(** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *)

val norm_coef : t -> float 
(** Normalization coefficient of the shell:

    {% \\[
    \mathcal{N} = \sqrt{\iiint \left[ (x-X_A)^{l}
                  \exp (-\alpha |r-R_A|^2) \right]^2 \, dx\, dy\, dz}
      \\] %}
*)

val norm_coef_scale : t -> float array
(** Scaling factors adjusting the normalization coefficient for the.
  particular powers of {% $x,y,z$ %}.  They are given in the same order as
  [AngularMomentum.zkey_array totAngMom]: 

  {% \\[
  f = \frac{1}{\mathcal{N}} \sqrt{\iiint [g(r)]^2 \, d^3r}
    \\] %}
*)

val size_of_shell : t -> int
(** Number of functions in the shell. *)