Kalbach Distributions

File 6 with LAW=1 provides for an especially elegant and compact representation of coupled energy-angle distributions for neutrons and charged particles developed by Kalbach based on systematics. The general shape of the function was later shown to come directly out of preequilibrium theory by Chadwick. The Kalbach distribution for a reaction of the form

A + a -> C -> B + b can represented by

where r(E_a,E_b) is the precompound fraction as given by the evaluator, and a(E_a, E_b) is a simple parameterized function that depends on emission energy, incident energy, and particle type.

Note that if r and a are small, the distributions are basically isotropic. This corresponds to emission from a well equilibrated compound system. As r increases, the distribution becomes more forward peaked. Because r tends to increase with the emission energy, we see forward peaking for high particle energies and isotropy for low particle energies. This is the effect that cannot be represented using the combination of File 4 and File 5.

The following is an example taken from the ENDF/B-VI evaluation for ²⁷Al. It shows the (n,2n) neutron emission distribution for an incident energy of 40 MeV. Each line contains two triplets: E', f(E,E'), and r(E,E'). Note the increase in r with increasing E'.

     0.000000+0 4.000000+7          0          1        198         661325 6 16
     0.000000+0 1.463653-8 2.774204-4 3.609812+4 2.663865-8 2.908748-41325 6 16
     7.219623+4 3.562323-8 3.043292-4 1.203271+5 4.369308-8 3.222684-41325 6 16
     1.684579+5 5.047795-8 3.402077-4 2.165887+5 5.644923-8 3.581469-41325 6 16
     ...
     4.091120+6 5.029411-8 8.229791-3 4.572428+6 4.580329-8 1.160481-21325 6 16
     5.053736+6 4.182685-8 1.619895-2 5.535044+6 3.824886-8 2.245802-21325 6 16
     6.016353+6 3.515369-8 3.071985-2 6.497661+6 3.237198-8 4.158862-21325 6 16
     6.978969+6 2.981761-8 5.597233-2 7.460277+6 2.765722-8 7.438953-21325 6 16
     7.941585+6 2.592982-8 9.753015-2 8.422894+6 2.461467-8 1.260132-11325 6 16
     8.904202+6 2.364081-8 1.603900-1 9.385510+6 2.298213-8 2.006077-11325 6 16
     9.866818+6 2.272568-8 2.456513-1 1.034813+7 2.276480-8 2.963706-11325 6 16
     1.082943+7 2.312538-8 3.510374-1 1.131074+7 2.376400-8 4.081861-11325 6 16
     1.179205+7 2.465185-8 4.658113-1 1.227336+7 2.581909-8 5.226821-11325 6 16
     1.275467+7 2.726533-8 5.776199-1 1.323598+7 2.899395-8 6.296106-11325 6 16
     1.371728+7 3.098722-8 6.779314-1 1.419859+7 3.324436-8 7.218539-11325 6 16
     1.467990+7 3.557207-8 7.621944-1 1.516121+7 3.833738-8 7.979111-11325 6 16
     ...
     2.430606+7 1.964407-9 9.958412-1 2.478737+7 0.000000+0 0.000000+01325 6 16

The Kalbach representation is used in many of the Los Alamos evaluations in ENDF/B-VI, and it is an important factor in the new high-energy libraries to 150 MeV now being constructed for accelerator applications at several laboratories in the world.

INDEX

15 December 2012

T-2 Nuclear Information Service

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