Hi,

I enrolled in a course about astronomical spectroscopy in my
university. The lecturer made a remark which I don't fully understand
and I'd appreciate your comments. We were discussing how electronic
transitions produce specific absorption or emission lines. At some
point he said that this was true for bound electrons but that not for
unbound electrons, which wouldn't produce either absorption or
emission, and that this was explained by both relativity and quantum
mechanics. I can see that it should not be possible for an unbound
electron to produce an absorption or emission line because an unbound
electron can have any energy value, but then, shouldn't a cloud of
unbound electrons be able to produce a continuous absorption from a
source in the background? It is less clear to me whether the same
cloud would be able to produce continuous emission because I don't see
why they would spontaneously decelerate and emit photons.

Also, which may be the relativistic and quantum mechanical reasons for
these processes being forbidden?

Many thanks in advance.

Vivianne

On Jun 26, 10:58 am, wrote:
Hi,

I enrolled in a course about astronomical spectroscopy in my
university. The lecturer made a remark which I don't fully understand
and I'd appreciate your comments. We were discussing how electronic
transitions produce specific absorption or emission lines. At some
point he said that this was true for bound electrons but that not for
unbound electrons, which wouldn't produce either absorption or
emission, and that this was explained by both relativity and quantum
mechanics. I can see that it should not be possible for an unbound
electron to produce an absorption or emission line because an unbound
electron can have any energy value, but then, shouldn't a cloud of
unbound electrons be able to produce a continuous absorption from a
source in the background? It is less clear to me whether the same
cloud would be able to produce continuous emission because I don't see
why they would spontaneously decelerate and emit photons.

Also, which may be the relativistic and quantum mechanical reasons for
these processes being forbidden?

Many thanks in advance.

Vivianne

It's not that unbound electrons cannot emit or absorb photons. It's
that they do not display a discrete spectrum and can emit and absorb
all frequencies and wavelengths, so their spectrum is continuous.
Bound electrons in atoms only emit and absorb energies at certain
values corresponding to differences in their shell energies, which are
dependent on quantum numbers, and hence are discretely arranged. Free
electrons are without such restrictions. The main difference is due
to the presence of a potential energy in the Schrodinger equation for
the bound electrons which is not there for the unbound.

wrote:

Hi,

I enrolled in a course about astronomical spectroscopy in my
university. The lecturer made a remark which I don't fully understand
and I'd appreciate your comments. We were discussing how electronic
transitions produce specific absorption or emission lines. At some
point he said that this was true for bound electrons but that not for
unbound electrons, which wouldn't produce either absorption or
emission, and that this was explained by both relativity and quantum
mechanics. I can see that it should not be possible for an unbound
electron to produce an absorption or emission line because an unbound
electron can have any energy value, but then, shouldn't a cloud of
unbound electrons be able to produce a continuous absorption from a
source in the background? It is less clear to me whether the same
cloud would be able to produce continuous emission because I don't see
why they would spontaneously decelerate and emit photons.

Also, which may be the relativistic and quantum mechanical reasons for
these processes being forbidden?

Many thanks in advance.

Vivianne

In the absence of a background potential there is no transition for a
single particle. What would separate energy states? Free electron
lasers have magnetic background, Cerenkov radiation requires a
medium. You could spin-flip... but spin-flip vs. what, absent a
background? Spin direction is undefined in vacuum free space.

If you have even two electrons, you have singlet and triplet states.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

On Jun 26, 7:58 am, wrote:

We were discussing how electronic
transitions produce specific absorption or emission lines. At some
point he said that this was true for bound electrons but that not for
unbound electrons, which wouldn't produce either absorption or
emission, and that this was explained by both relativity and quantum
mechanics. [...]

Also, which may be the relativistic and quantum mechanical reasons for
these processes being forbidden?

A free electron cannot emit photons. This is forbidden by the laws of
conservation of momentum and energy.

Suppose that in the initial state you have one free electron at rest.
It's mass is m, its momentum is zero, and its energy is E=mc^2.
Suppose that this electron emits a photon with momentum k. In the
final state you have two particles: a photon with momentum k and
energy c|k| and an electron with momentum -k (from the momentum
conservation law) and energy E= sqrt(m^2c^4 + k^2c^2). The energy
conservation law now reads

mc^2 = c|k| + sqrt(m^2c^4 + k^2c^2)

You can now see that this equation can be true only if k=0. But there
are no photons with zero momentum and energy. So, the emission is
impossible.

Eugene.

On Jun 26, 12:50 pm, Sam Wormley wrote:

A free [unbound] electron cannot emit photons. This is forbidden by the laws of
conservation of momentum and energy.

Synchrotron Radiation
http://hyperphysics.phy-astr.gsu.edu...nchrotron.html


Electrons emitting synchrotron radiation are not free in my
definition. There is a (magnetic) force acting on them. So, my
analysis does not apply to this situation.
I was talking about electrons moving freely in empty space.

Eugene.

On Jun 26, 9:44 pm, Sam Wormley wrote:
wrote:
Hi,

I enrolled in a course about astronomical spectroscopy in my
university. The lecturer made a remark which I don't fully understand
and I'd appreciate your comments. We were discussing how electronic
transitions produce specific absorption or emission lines. At some
point he said that this was true for bound electrons but that not for
unbound electrons, which wouldn't produce either absorption or
emission, and that this was explained by both relativity and quantum
mechanics. I can see that it should not be possible for an unbound
electron to produce an absorption or emission line because an unbound
electron can have any energy value, but then, shouldn't a cloud of
unbound electrons be able to produce a continuous absorption from a
source in the background? It is less clear to me whether the same
cloud would be able to produce continuous emission because I don't see
why they would spontaneously decelerate and emit photons.

Also, which may be the relativistic and quantum mechanical reasons for
these processes being forbidden?

Many thanks in advance.

Vivianne

An electron doesn't need to be bound to a nucleus to absorb or emit
photons. In the early universe up till about 380,000 years all the
electrons were unbound and absorbing (and re-emitting) light. Consider
the interior of stars--photons being absorbed and emitted by all those
charged particles.



More than just true. Electrons only emit and receive photons all the
time. If you think about it its all hanging around the same basic idea
again and again - every twist and turn, bending and fields created
inside... Some of those spectrums are quantum and others are super :-))