Scatter vector

The scattering vector is in the waves - Physics of that vector , the at scattering results in a wave to an object as the difference between run-in wave vector and leaking wave vector : ${\ displaystyle {\ vec {q}}}$ ${\ displaystyle {\ vec {k}} _ {1}}$ ${\ displaystyle {\ vec {k}} _ {2}}$

{\ displaystyle {\ vec {q}} = {\ vec {k}} _ {1} - {\ vec {k}} _ {2}}

It is used to simplify some expressions that occur when considering scattered waves (e.g. the phase change or the Doppler shift ).

With elastic scattering (incoming and outgoing waves have the same wavelength , that is ), the amount of the scattering vector is given by ${\ displaystyle \ lambda}$ ${\ displaystyle | {\ vec {k}} _ {1} | = | {\ vec {k}} _ {2} | = \ textstyle {\ frac {2 \ pi} {\ lambda}}}$

{\ displaystyle | {\ vec {q}} | = {\ frac {4 \ pi} {\ lambda}} \ sin {\ frac {\ theta} {2}},}

where is the scattering angle (angle between and ). ${\ displaystyle \ theta}$ ${\ displaystyle {\ vec {k}} _ {1}}$ ${\ displaystyle {\ vec {k}} _ {2}}$

If one considers the scattering of waves in a medium , then the wavelength is in the corresponding medium. For electromagnetic waves, the difference between the wavelength in the medium and the wavelength in a vacuum is described using the refractive index : ${\ displaystyle \ lambda}$ ${\ displaystyle \ lambda _ {0}}$ ${\ displaystyle n}$

{\ displaystyle \ lambda = {\ frac {\ lambda _ {0}} {n}}}

If, instead of using the wavelength in a vacuum , all wave vectors and the scatter vector must be multiplied by the factor . ${\ displaystyle \ lambda}$ ${\ displaystyle \ lambda _ {0}}$ ${\ displaystyle n}$

literature

BH Bransden, CJ Joachain: Physics of Atoms and Molecules . 2nd Edition. Prentice Hall, Essex 2003, ISBN 978-0-582-35692-4 , pp. 623 .

Web links

Scattering vector . ( Memento from April 24, 2015 in the Internet Archive ) There, however, the scatter vector is defined the other way round, note the sign!