Is degenerate matter transparent?
Matt Kennel
white dwarf stuff?
I wonder if it would be, because if a photon tried to interact with
a electron it would have to push the electron up to a different state,
but they're all full.
Suppose you had some degenerate matter made out of atoms whose
nuclei were bosons.
Does that mean you would get stuck at some point when squeezing
the electrons, but you could somehow keep on going with the bosons?
--
-Matt Kennel m...@inls1.ucsd.edu
-Institute for Nonlinear Science, University of California, San Diego
-*** AD: Archive for nonlinear dynamics papers & programs: FTP to
-*** lyapunov.ucsd.edu, username "anonymous".
Eugen Raicu
: Is Fermi degnerate matter transparent? Say a macroscopic amount of
: white dwarf stuff?
:
: I wonder if it would be, because if a photon tried to interact with
: a electron it would have to push the electron up to a different state,
: but they're all full.
There are always more available states, it just takes extra energy to
put the electrons into them. The energy can no longer be supplied by
gravitational attraction but it can be supplied by the photon which is
absorbed.
:
: Suppose you had some degenerate matter made out of atoms whose
: nuclei were bosons.
:
: Does that mean you would get stuck at some point when squeezing
: the electrons, but you could somehow keep on going with the bosons?
The nuclei would probably not be squeezed due to COulomb repulsion,
which is no longer screened by the more dilute electrons.
:
: --
: -Matt Kennel m...@inls1.ucsd.edu
: -Institute for Nonlinear Science, University of California, San Diego
: -*** AD: Archive for nonlinear dynamics papers & programs: FTP to
: -*** lyapunov.ucsd.edu, username "anonymous".
--
Eugen Raicu
ra...@netcom.com
1912 Addison Street Apt. 15, Berkeley, CA 94704-1128
(510) 644 3204
SCOTT I CHASE
>Matt Kennel (m...@poincare.ucsd.edu) wrote:
>: Is Fermi degnerate matter transparent? Say a macroscopic amount of
>: white dwarf stuff?
>:
>: I wonder if it would be, because if a photon tried to interact with
>: a electron it would have to push the electron up to a different state,
>: but they're all full.
>
>There are always more available states, it just takes extra energy to
>put the electrons into them. The energy can no longer be supplied by
>gravitational attraction but it can be supplied by the photon which is
>absorbed.
Not necessarily. The phenomeon which Matt has described is call "Pauli
blocking" in particle/nuclear physics. If the final state is already
occupied by a particle of the same type, then the scattering is not
allowed by the exclusion principle. This lowers the total scattering
cross section, in proportion to amount of the final phase space which
is filled prior to the scattering event.
In some cases, for example if the photon hasn't got enough energy to
bump the electron up to any open state, then the cross-section will
vanish.
I suspect that Matt is more or less correct, and that pure dense nuclear
matter is more transparent to photons in the middle of the lump than one
would expect in the absence of Pauli blocking.. However, in practice, such
as in a neutron star, there is a shell of low-pressure matter on the
surface (as there must be, since the pressure of empty space is zero.) In
the case of a neutron star, there is is a huge surface magnetic field, which
creates a surface which might be described as a superconducting electron gas.
I have been told by neutron star experts that this surface will be metallic
in appearance, i.e., silvery.
-Scott
--------------------
Scott I. Chase "It is not a simple life to be a single cell,
SIC...@CSA2.LBL.GOV although I have no right to say so, having
been a single cell so long ago myself that I
have no memory at all of that stage of my
life." - Lewis Thomas
John C. Baez
>Is Fermi degnerate matter transparent? Say a macroscopic amount of
>white dwarf stuff?
>
>I wonder if it would be, because if a photon tried to interact with
>a electron it would have to push the electron up to a different state,
>but they're all full.
No, all the states below the Fermi energy are full, but not ALL states
are full - none above the Fermi energy are full! I would be shocked if
charged Fermi degenerate matter was transparent. As for neutronium,
maybe - but I bet in reality there are still plenty of ways for photons
to interact with the stuff, since I think one should pretend there are
lots of virtual electron-proton pairs around.
David M. Palmer
>In article <1jdp6n...@network.ucsd.edu> m...@poincare.ucsd.edu (Matt Kennel) writes:
>>Is Fermi degnerate matter transparent? Say a macroscopic amount of
>>white dwarf stuff?
>As for neutronium,
>maybe - but I bet in reality there are still plenty of ways for photons
>to interact with the stuff, since I think one should pretend there are
>lots of virtual electron-proton pairs around.
Neutronium has some protons and electrons in equilibrium with the
neutrons. (Somewhere between 1% and 1% of 1% as I recall. Don't
quote me. Lokk in Shapiro and Teukolsky 'Black holes, white dwarfs
and neutron stars')
--
David Palmer pal...@alumni.caltech.edu
Douglas S. Miller
>Is Fermi degnerate matter transparent? Say a macroscopic amount of
>white dwarf stuff?
Funny you should ask---this question just came up at our department
pizza party. The considered opinion of a big group of semi-drunken pizza
chomping physicists is that neutron stars will have an atmosphere that
will be just about a perfect reflector in the visible range because it
will have a sky high plasma frequency. White dwarfs should be much the
same. It is worth noting that we sort of side-stepped the issue; we
figure the degenerate matter must be shielded by a layer of more or less
normal hot plasma sitting on top of it.
Matt Kennel
: In article <1993Jan18.1...@netcom.com>, ra...@netcom.com (Eugen Raicu) writes...
Okay. I was thinking about not quite "neutronic" degenerate matter, but just
ordinary electron degnerate matter. I'm wondering if there are any strange
quantum-mechanical consequences for inertially confined fusion setups,
because in those cases, the fuel is compressed to just about Fermi
degnerate density.
:
: -Scott
: --------------------
: Scott I. Chase "It is not a simple life to be a single cell,
: SIC...@CSA2.LBL.GOV although I have no right to say so, having
: been a single cell so long ago myself that I
: have no memory at all of that stage of my
: life." - Lewis Thomas
--
Eugen Raicu
: In article <1993Jan18.1...@netcom.com>, ra...@netcom.com (Eugen Raicu) writes...
: >Matt Kennel (m...@poincare.ucsd.edu) wrote:
: >: Is Fermi degnerate matter transparent? Say a macroscopic amount of
: >: white dwarf stuff?
: >:
: >: I wonder if it would be, because if a photon tried to interact with
: >: a electron it would have to push the electron up to a different state,
: >: but they're all full.
: >
: >There are always more available states, it just takes extra energy to
: >put the electrons into them. The energy can no longer be supplied by
: >gravitational attraction but it can be supplied by the photon which is
: >absorbed.
:
: Not necessarily. The phenomeon which Matt has described is call "Pauli
: blocking" in particle/nuclear physics. If the final state is already
: occupied by a particle of the same type, then the scattering is not
: allowed by the exclusion principle. This lowers the total scattering
: cross section, in proportion to amount of the final phase space which
: is filled prior to the scattering event.
:
: In some cases, for example if the photon hasn't got enough energy to
: bump the electron up to any open state, then the cross-section will
: vanish.
I thought this was a white dwarf, not a neutron star, in which the electrons
form a fermi gas and there is a continuum of EMPTY electron states
immediately above the fermi energy.
:
: I suspect that Matt is more or less correct, and that pure dense nuclear
: matter is more transparent to photons in the middle of the lump than one
: would expect in the absence of Pauli blocking.. However, in practice, such
: as in a neutron star, there is a shell of low-pressure matter on the
: surface (as there must be, since the pressure of empty space is zero.) In
: the case of a neutron star, there is is a huge surface magnetic field, which
: creates a surface which might be described as a superconducting electron gas.
: I have been told by neutron star experts that this surface will be metallic
: in appearance, i.e., silvery.
:
: -Scott
: --------------------
: Scott I. Chase "It is not a simple life to be a single cell,
: SIC...@CSA2.LBL.GOV although I have no right to say so, having
: been a single cell so long ago myself that I
: have no memory at all of that stage of my
: life." - Lewis Thomas
Blair P. Houghton
>Funny you should ask---this question just came up at our department
>figure the degenerate matter must be shielded by a layer of more or less
>normal hot plasma sitting on top of it.
It seems to be mozarella.
Perhaps you should keep the lab cleaner...
--Blair
"I'd like a red giant with
double pepperoni and extra
cheese, please..."
Jim Carr
>white dwarf stuff?
These are two different questions. One normally talks about infinite
fermi matter (such as infinite nuclear matter or an infinite sea of
electrons) because of the simplifications that occur. One can also
talk about semi-infinite fermi matter to look at surface effects.
A clump (say a sphere) of a fermi liquid or gas is more like the
latter, where I have limited expertise, but my quess is that transparency
would be dictated by surface effects. In a real star-sized object held
together by gravity (as opposed to some ideal thing with a sharp
surface), the fall-off in density at the surface will complicate any
simple analysis based on the infinite case.
>I wonder if it would be, because if a photon tried to interact with
>a electron it would have to push the electron up to a different state,
>but they're all full.
They are not *all* full. An infinite fermi gas fills space but does
not fill all of phase space. If you look at it in momentum space
rather than coordinate space, you see that all states below a critical
momentum (the Fermi momentum, k_F) are full. So you can kick a particle
from below the Fermi surface to above it an absorb the photon.
This can happen for very low photon energies if you are close enough to
the Fermi surface, but the number of available initial states is now
small and serves to limit the probability. (Now the astute reader will
note that in infinite matter, any probability means total absorption over
the extent of space, but one works with prob. densities to avoid this.)
>Suppose you had some degenerate matter made out of atoms whose
>nuclei were bosons.
>
>Does that mean you would get stuck at some point when squeezing
>the electrons, but you could somehow keep on going with the bosons?
Normally one speaks of a Fermi gas made up of a single species. But
if you were to start with an atom as you propose, at some point you
would start to see the behavior expected of a bose gas. But, since
the nuclei are made up of fermions (and they are made up of fermions
too), at some point you would see a transition back to fermi gas
behavior. Indeed, in a simplified view, the Relativistic Heavy Ion
Collider (RHIC) is looking for a phase transition from a nucleon
dominated to a quark dominated phase.
--
J. A. Carr | "The New Frontier of which I
j...@gw.scri.fsu.edu | speak is not a set of promises
Florida State University B-186 | -- it is a set of challenges."
Supercomputer Computations Research Institute | John F. Kennedy (15 July 60)