Chapter 7
Nuclear Physics – I
7.1 Basic Concepts and Formulae
Solid angle
In two dimensions the angle in radians is defined as the ratio of the arc of the circle
and the radius, that is θ = s/r . In three dimensions, the element of solid angle dΩ
is defined as the elementary area A at a distance d from a point, perpendicular to
the line joining the point and the area, divided by the square of the distance, that is
d Ω = ΔA/d
2 . For a ring of radii r and r + dr , located on the surface of a sphere of
radius R, the element of solid angle in polar coordinates is subtended at the centre
O is given by (Fig. 7.1)
d Ω = 2 π sin θ dθ
(7.1)
We assume an azimuthal symmetry, that is scattering is independent of the
azimuthal angle β.
Fig. 7.1 Concept of solid
angle
369
Nuclear Physics – I
7.1 Basic Concepts and Formulae
Solid angle
In two dimensions the angle in radians is defined as the ratio of the arc of the circle
and the radius, that is θ = s/r . In three dimensions, the element of solid angle dΩ
is defined as the elementary area A at a distance d from a point, perpendicular to
the line joining the point and the area, divided by the square of the distance, that is
d Ω = ΔA/d
2 . For a ring of radii r and r + dr , located on the surface of a sphere of
radius R, the element of solid angle in polar coordinates is subtended at the centre
O is given by (Fig. 7.1)
d Ω = 2 π sin θ dθ
(7.1)
We assume an azimuthal symmetry, that is scattering is independent of the
azimuthal angle β.
Fig. 7.1 Concept of solid
angle
369