# Classical Scattering with a Penetrable Square-Well Potential

Classical Scattering with a Penetrable Square-Well Potential

The penetrable square-well (PSW) interaction potential is defined by a repulsive energy barrier of height and range , surrounded by an attractive well of depth and width . The PSW interaction model includes the square-well potential and the penetrable-sphere potential (0 or ) as particular cases.

ϵ

r

σ

ϵ

a

λ-σ

(∞)

ϵ

r

ϵ

a

λ-σ0

A classical projectile particle of mass moving with speed and impact parameter is scattered an angle by a fixed target that interacts with the projectile via the PSW potential, analogously to the classical Rutherford scattering problem. Three types of collisions are possible:

μ

g

b

χ(b,g)

A. the particle penetrates into the inner repulsive core;

B. the particle is reflected by the core; and

C. the particle misses the core.

Events of type A occur if and , while events of type C take place if and ; otherwise, the collision is of type B.

μ2>

2

g

ϵ

r

b<

1-2/μ

σϵ

r

2

g

μ>/2>-1

2

g

ϵ

a

2

λ

2

σ

λ>b>

1-2/μ

σϵ

a

2

g

This Demonstration plots versus for different possible values of the potential parameters and of the particle speed. The control panel also includes the PSW potential as a visual aid in the identification of the control variables.

cosχ

2

(b/λ)