Kinematics with Fortran

View files


CINE.for is a FORTRAN program to calculate the kinematics of a nuclear reaction.

To compile:

$ g77 CINE.for -o CINE

To run:

$ ./CINE

CINE requires an input file "" with data about the reaction in the following format:

proyectile(target,recoil)scattered @ Energy MeV
projectile target diff recoil Q exc-recoil exc-pro
initialEnergy finalEnergy increment
initialAngle  finalAngle  increment

For example:

78Ni(p,p)78Ni @ 7800 MeV
78. 1. 78. 1.  0.  0.  0.
7800.  7800.  1.
0. 180.  .1

The output of CINE are the energies and angles of the incident and scattered nucleus of a nuclear reaction. Visualize the results with read.C. This results can be used as input in the simulation mentioned in Bragg curves. See an example in kine simulation.

The physics

Direct reactions

Direct reactions are fast reactions (10−21 seconds) where the projectile and the target hit each other and the recoils emerge. The angular distribution is highly forward peaked, as opposed to a compound nucleus, where it is isotropic because the reaction is slow and the entrance channel is forgotten. They happen mostly at high projectile energies, while compound nuclei usually form at low energies.

Inverse kinematics

A typical way to study an unknown nucleus is to force a nuclear reaction by shooting a beam of stable particles to a target made of that nucleus. This is called "direct kinematics". However, to study unstable nuclei, where a target can not be produced because it will dissapear decay after decay, "inverse kinematics" are used. A stable target is then shot with radioactive nuclei.

Direct reactions in Inverse kinematics

This repo contains two reactions of this type:

Elastic scattering

The nuclei are dispersed with no changes in their internal structure. Elastic scattering reactions allow to accurately determine the nuclear matter radii, and the radial shape of the nuclear matter distributions.

Some examples of phenomena that can be studied with these reactions are:

Halo nuclei

In stable nuclei, protons and neutrons are distributed uniformly, and the radio is proportional to the total number of nucleons, A. However, exotic nuclei near the drip line of protons or neutrons, show some loosely bound nucleons orbiting a core. As a result, the spatial distribution (the aparent radius) is that of a heavy nucleus, however the density is much smaller.

Borromean nuclei

A Borromean nucleus is an atomic nucleus that has a nuclear halo containing two neutrons. Such a nucleus breaks into three components and never two when disrupted, in analogy to Borromean rings. One example is 6He, which you can find in the repo.

Borromean rings Helium 6 The figures above show examples of the Borromean rings and 6He, formed by an alpha particle plus two halo neutrons.

Double magic nuclei

These nuclei have both the neutron and the proton shells closed, i.e., they are filled and can not accept more nucleons. As a result, they are very stable. In exotic nuclei, the shells are organized in a different way, and the magic numbers can change. 78Ni for example, is one of the bounded nucleus with a bigger unbalance between the number of neutrons and protons (28 p + 50 n). 78Ni is key in the syntesis of elements beyond iron in supernovas, but because it is double magic, the reactions can be delayed. 78Ni is simulated in the repo.

Transfer reactions

Reactions where the projectile and the scattered nuclei exchange nucleons. They are great for the study of mono-particle properties, like single-particle states, angular moments, closure of shells, neutron capture cross-sections in astrophysics, etc. There are two types:


The projectile transfers one or more nucleons to the target.


The projectile "steals" one or more nucleons from the target.

The reactions

Reactions in the repo:

Published: 2006-05-23 19:30