The following quantities are defined for LAW=1:

LANG

indicator that selects the angular representation to be used:
LANG=1, Legendre coefficients are used;
LANG=2, Kalbach systematics is used;
LANG=11-15, a tabulated angular distribution is given using NA/2 cosines and the interpolation scheme specified by LANG-10 (for example, LANG=12 selects linear-linear interpolation).

LEP

interpolation scheme for secondary energy:
LEP=1, histogram;
LEP=2, linear-linear, etc.

NR,NE,EINT

standard TAB2 parameters.
INT=1 is allowed (the upper limit is implied by File 3), INT=12-15 is allowed for corresponding-point interpolation, INT=22-25 is allowed for unit-base interpolation,

NW

total number of words in the LIST record: NW=NEP*(NA+2).

NEP

number of secondary energy points in the distribution.

ND

number of discrete energies given. The first ND entries in the list of NEP energies are discrete, and the remaining NEP-ND entries are to be used with LEP to describe a continuous distribution. Discrete primary photons should be flagged with negative energies. ND can be zero, and it must be less than or equal to NEP.

NA

number of angular parameters:
use NA=0 for isotropic distributions (note that all options are identical if NA=0);
use NA=1 with LANG=2 (Kalbach).

The structure of a subsection is

where NA is the number of angular parameters, i denotes the product being described, E is the incident energy, E' is the energy of the product emitted with cosine μ, f_i is the normalized distribution with units (eV-unit cosine)^-1, f_l(E,E') are the Legendre coefficients, and P_l(μ) are the Legendre polynomials. Note that these coefficients are not normalized like those for discrete two-body scattering (LAW=2); instead, f₀(E,E') gives the total probability of scattering from E to E' integrated over all angles. This is just the function g(E,E') normally given in File 5.

The Legendre coefficients are stored with f₀ in B0, f₁ in B1, etc. Therefore, an isotropic distribution would go like this

    EP1, f0(E,EP1), EP2, f0(E,EP2), EP3, f0(E,EP3),
    EP4, f0(E,EP4), ...,

   EP1, f0(E,EP1), f1(E,EP1), EP2, f0(E,EP2), f1(E,EP2),
   EP3, ...,

A + a -> C -> B + b

where

A

is the target,

a

is the incident particle,

C

is the compound system,

b

is the emitted particle, and

B

is the residual nucleus.

E_a

energy of the incident projectile a in the laboratory system (normally called E),

eps_a

entrance channel energy, the sum of the kinetic energy of the incident projectile a and the target particle A in the center-of-mass system,

eps_b

emission channel energy, the sum of the kinetic energy of the emitted particle b and the residual nucleus B in the center-of-mass system,

E_b

energy of the emitted particle in the center-of-mass system (normally called E'), and

μ_b

cosine of the emission angle of particle b in the center-of-mass system.

These energies are related as follows:

It is required that LCT=2 with LANG=2.

The Kalbach distribution is represented by

where r(E_a,E_b) is the pre-compound fraction as given by the evaluator and a(E_a,E_b) is a simple parameterized function that depends mostly on the center-of-mass emission energy E_b, but also depends slightly on particle type and the incident energy at higher values of E_a (see below).

The center-of-mass energies and angles E_b and μ_b are transformed into the laboratory system using the expressions

The pre-compound fraction r, where r goes from 0.0 to 1.0, is usually computed by a model code, although it can be chosen to fit experimental data.

The formula for calculating the Kalbach slope parameter, a(E_a,E_b), is

where

The quantities S_a and S_b are the separation energies for the incident and emitted particles, respectively, neglecting pairing and other effects. The formulas for the separation energies are:

where S_a and S_b are the separation energies in MeV; the subscripts A, B, and C refer to the target nucleus, the residual nucleus, and the compound nucleus as before; the quantities N, Z, and A are the neutron, proton, and mass numbers of the nuclei; and I_a and I_b are the energies required to break the incident and emitted particles into their constituent nucleons as taken from the following table:

The parameter f₀(E_a,E_b) has the same meaning as f₀ in the first equation of this page; that is, the total emission probability for this E_a and E_b. The number of angular parameters (NA) is always 1 for LANG=2, and the f₀ and r are stored in the positions of B0 and B1, respectively. Therefore, a particular distribution goes as follows:

   EP1, f0(E,EP1), r(E,EP1), EP2, f0(E,EP2), r(E,EP2),
   EP3, ...,

This formulation uses a single-particle-emission concept; it is assumed that each and every secondary particle is emitted from the original compound nucleus C. When the incident projectile a and the emitted particle b are the same, S_a = S_b, regardless of the reaction. For incident projectile z, if neutrons emitted from the compound nucleus C are detected, the same S_b would be used for all reactions, for example both (z,n') and (z,2n).

In order to make things line up neatly, the preferred values for NA are 4, 10, 16, 22, etc. As an example, a simple distribution with NA=4 might look like this:

   EP1, f0(E,EP1), -1.0, 0.5, 1.0, 0.5,
   EP2, f0(E,EP2), -1.0, 0.4, 1.0, 0.6,
   EP3, ....

In order to provide a good representation of sharp peaks, LAW=1 allows for a superposition of a continuum and a set of delta functions. These discrete lines could be used to represent particle excitations in the CM frame, because the method of corresponding points can be used to supply the correct energy dependence. However, the use of LAW=2 together with MT=50-90, 600-650, etc., is preferred. This option is also useful when photon production is given in File 6.