[math-fun] Neutron stars as atoms
Whitfield Diffie I recall reading the intreaguing observation that stable neutron structures run up to around atomic wieght 300 and then their is a long gap before you get to the neutron stars with atomic weights around 10^50. Perhaps we should regard the neutron stars as isotopes of very heavy elements. The atomic numbers would be miniscule by comparison with the atomic weights but a mildely positively charged neutron star doesn't seem impossible: would adding a billion protons make a difference? --WDS: A better way to view this is: replace the word "stable" with "stable under pressure." See, I would claim that it is an illusion that there is no stable nucleus with atomic weight 1000. Actually, if you put it under enough pressure, then it would presumably become stable. The only problem is humans have no hope of sustaining pressures that large and the only known way to reach them is inside a neutron star. Anyhow, with suitable pressure ramp up, probably there is no "gap" at all, and practically the full range of atomic weights become reachable with stability. Another thing is: the usual nuclei generally are in the ground state. Excited states that last long, are rare for nuclei. But for a neutron star, it presumably never reaches ground, there are too many excited states it gets trapped in for long periods. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
A better way to view this is: replace the word "stable" with "stable under pressure."
That just seems to me to diddling the rules; a neutron star isn't under external pressure; it is in free space. The important point is that a nucleus has to become quite large before the gravitational force begins to play a role in its stability.
Another thing is: the usual nuclei generally are in the ground state. Excited states that last long, are rare for nuclei. But for a neutron star, it presumably never reaches ground, there are too many excited states it gets trapped in for long periods.
That and related things do seem to be major differences between `small' and `large' nuclei. A neutron start presumably changes both atomic number and atomic weight quite freely, so you could reasonably argue with its being stable. Whit
On 6/25/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
A better way to view this is: replace the word "stable" with "stable under pressure."
That just seems to me to diddling the rules; a neutron star isn't under external pressure; it is in free space. The important point is that a nucleus has to become quite large before the gravitational force begins to play a role in its stability.
--The pressure is created by gravity & the weight of the matter on top of it. A "true" neutron star in free space. i.e. composed entirely of neutrons, likely could not exist. In order for a neutron star to exist it presumably must have "normal" matter in the outer layers, neutrons being unstable if not under pressure. As we go inward, larger and larger nuclei will be able to exist until eventually we reach a region which could be regarded as "one big nucleus." Now if somehow enormous pressure were externally exerted by nongravitational means, then "neutronium" presumably could stably exist in much smaller chunks than a neutron star. Incidentally, in certain sci-fi stories by Larry Niven, he has chunks of neutronium the mass of, e.g. the Moon, or less, sitting around being used for various purposes. That was bullshit, any such chunk should experience an enormous explosion immediately.
The Wikipedia article about neutron stars says that the outer crust is a weird high-pressure allotrope of iron, and that inside there are several phase changes between higher and higher pressure forms of exotic matter, many of these hypothetical. A "neutron superfluid" is one of them. On Wed, Jun 25, 2014 at 3:18 PM, Warren D Smith <warren.wds@gmail.com> wrote:
On 6/25/14, Whitfield Diffie <whitfield.diffie@gmail.com> wrote:
A better way to view this is: replace the word "stable" with "stable under pressure."
That just seems to me to diddling the rules; a neutron star isn't under external pressure; it is in free space. The important point is that a nucleus has to become quite large before the gravitational force begins to play a role in its stability.
--The pressure is created by gravity & the weight of the matter on top of it. A "true" neutron star in free space. i.e. composed entirely of neutrons, likely could not exist. In order for a neutron star to exist it presumably must have "normal" matter in the outer layers, neutrons being unstable if not under pressure. As we go inward, larger and larger nuclei will be able to exist until eventually we reach a region which could be regarded as "one big nucleus."
Now if somehow enormous pressure were externally exerted by nongravitational means, then "neutronium" presumably could stably exist in much smaller chunks than a neutron star.
Incidentally, in certain sci-fi stories by Larry Niven, he has chunks of neutronium the mass of, e.g. the Moon, or less, sitting around being used for various purposes. That was bullshit, any such chunk should experience an enormous explosion immediately.
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I would suppose that a neutron star would continually have neutrons undergo beta decay, producing a proton and electron which are captured by gravity and a neutrino which isn't. Brent Meeker On 6/25/2014 10:29 AM, Warren D Smith wrote:
Whitfield Diffie I recall reading the intreaguing observation that stable neutron structures run up to around atomic wieght 300 and then their is a long gap before you get to the neutron stars with atomic weights around 10^50. Perhaps we should regard the neutron stars as isotopes of very heavy elements. The atomic numbers would be miniscule by comparison with the atomic weights but a mildely positively charged neutron star doesn't seem impossible: would adding a billion protons make a difference?
--WDS: A better way to view this is: replace the word "stable" with "stable under pressure." See, I would claim that it is an illusion that there is no stable nucleus with atomic weight 1000. Actually, if you put it under enough pressure, then it would presumably become stable. The only problem is humans have no hope of sustaining pressures that large and the only known way to reach them is inside a neutron star. Anyhow, with suitable pressure ramp up, probably there is no "gap" at all, and practically the full range of atomic weights become reachable with stability.
Another thing is: the usual nuclei generally are in the ground state. Excited states that last long, are rare for nuclei. But for a neutron star, it presumably never reaches ground, there are too many excited states it gets trapped in for long periods.
One would expect an equilibrium between neutrons and protons plus electrons. The equilibrium position depends critically on temperature and pressure, which is why the equilibrium would favor neutrons inside a neutron star, but not elsewhere. On Wed, Jun 25, 2014 at 4:49 PM, meekerdb <meekerdb@verizon.net> wrote:
I would suppose that a neutron star would continually have neutrons undergo beta decay, producing a proton and electron which are captured by gravity and a neutrino which isn't.
Brent Meeker
On 6/25/2014 10:29 AM, Warren D Smith wrote:
Whitfield Diffie I recall reading the intreaguing observation that stable neutron structures run up to around atomic wieght 300 and then their is a long gap before you get to the neutron stars with atomic weights around 10^50. Perhaps we should regard the neutron stars as isotopes of very heavy elements. The atomic numbers would be miniscule by comparison with the atomic weights but a mildely positively charged neutron star doesn't seem impossible: would adding a billion protons make a difference?
--WDS: A better way to view this is: replace the word "stable" with "stable under pressure." See, I would claim that it is an illusion that there is no stable nucleus with atomic weight 1000. Actually, if you put it under enough pressure, then it would presumably become stable. The only problem is humans have no hope of sustaining pressures that large and the only known way to reach them is inside a neutron star. Anyhow, with suitable pressure ramp up, probably there is no "gap" at all, and practically the full range of atomic weights become reachable with stability.
Another thing is: the usual nuclei generally are in the ground state. Excited states that last long, are rare for nuclei. But for a neutron star, it presumably never reaches ground, there are too many excited states it gets trapped in for long periods.
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And that's why you would expect a mixture of protons and neutrons like iron on the surface, because that's the most stable ratio in nuclei Brent Meeker On 6/25/2014 2:49 PM, Allan Wechsler wrote:
One would expect an equilibrium between neutrons and protons plus electrons. The equilibrium position depends critically on temperature and pressure, which is why the equilibrium would favor neutrons inside a neutron star, but not elsewhere.
On Wed, Jun 25, 2014 at 4:49 PM, meekerdb <meekerdb@verizon.net> wrote:
I would suppose that a neutron star would continually have neutrons undergo beta decay, producing a proton and electron which are captured by gravity and a neutrino which isn't.
Brent Meeker
On 6/25/2014 10:29 AM, Warren D Smith wrote:
Whitfield Diffie I recall reading the intreaguing observation that stable neutron structures run up to around atomic wieght 300 and then their is a long gap before you get to the neutron stars with atomic weights around 10^50. Perhaps we should regard the neutron stars as isotopes of very heavy elements. The atomic numbers would be miniscule by comparison with the atomic weights but a mildely positively charged neutron star doesn't seem impossible: would adding a billion protons make a difference?
--WDS: A better way to view this is: replace the word "stable" with "stable under pressure." See, I would claim that it is an illusion that there is no stable nucleus with atomic weight 1000. Actually, if you put it under enough pressure, then it would presumably become stable. The only problem is humans have no hope of sustaining pressures that large and the only known way to reach them is inside a neutron star. Anyhow, with suitable pressure ramp up, probably there is no "gap" at all, and practically the full range of atomic weights become reachable with stability.
Another thing is: the usual nuclei generally are in the ground state. Excited states that last long, are rare for nuclei. But for a neutron star, it presumably never reaches ground, there are too many excited states it gets trapped in for long periods.
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On Wed, Jun 25, 2014 at 4:49 PM, meekerdb <meekerdb@verizon.net> wrote:
I would suppose that a neutron star would continually have neutrons undergo beta decay, producing a proton and electron which are captured by gravity and a neutrino which isn't.
Brent Meeker
The Physics of Neutron Stars, Lattimer and Prakash http://arxiv.org/pdf/astro-ph/0405262v1.pdf The Physics of Neutron Stars, Whitehead http://einstein.drexel.edu/~bob/Term_Reports/Whitehead_hw1.pdf The first paper describes a neutron star's inner and outer cores, crust, atmosphere and envelope, and their respective compositions. The second paper examines the p+ + e− ↔ n + ¯ν_e reaction and concludes neutrons predominate at the core's density, which is similar to that within an atomic nucleus. My understanding is that electrons there are under such pressure that they occupy every possible state, such that neutrons are unable to decay because the decay product has no place it can exist.
An isolated neutron decays into a proton, electron, and antineutrino, with Q = 782 keV energy shared among the three particles. However, a bound neutron can be stable, as in a nucleus or a neutron star. In a nucleus, there is a balance between neutrons and protons, and along a given isobar (equal mass number), there is a minimum energy nucleus. Nuclei with excess neutrons undergo beta decay by emitting electrons, those with excess protons capture an orbiting electron or emit a positron. Even mass isobars are a bit more complicated since even-even nuclei are more stable than odd-odd, and there can be local energy minima. Three minima occur for mass 124: tin, tellurium, and xenon. Even-even nuclei trapped in such a local minimum can only decay by double beta decay (or alpha decay, if allowed), with half-life > 10^19 years. The atomic electron cloud can affect nuclear stability. Fully ionized dysprosium-163 nuclei decay by electron emission to holmium-163 with a 48-day half life. But neutral Ho-163 atoms capture an electron forming Dy-163 with a 4570-year half-life. In a neutron star, neutrons, protons, and electrons are in equilibrium. The simplest model takes these particles as free and at zero temperature. Being fermions, they occupy the lowest allowed energy states from zero up to the Fermi energy. The Fermi energy εF is related to the number density n by εF = (1/2)(3π2)2/3 ℏ2 n2/3 / m (non-relativistic), εF = (3π2)1/3 ℏ c n1/3 (ultra-relativistic). The equilibrium is controlled by the neutron and electron Fermi energies. If we remove a neutron from its top occupied state, we remove energy mnc2 + εFn If we insert a proton and electron at their top occupied states, we must provide energy mpc2 + mec2 + εFp + εFe These must be equal at equilibrium. (mn - mp - me)c2 = Q = εFe + εFp - εFn Suppose the neutron density is nn = 1045 m-3. Then from the non-relativistic formula, the neutron Fermi energy is εFn = 3.2×10-11 J = 200 MeV. This is reasonably non-relativistic since the neutron mass is 930 MeV. This swamps out the proton Fermi energy, the electron mass, and Q, leaving εFe = εFn and from the ultra-relativistic formula, the electron density is ne = 0.04×1045 m-3 So the electron density is 4% of the neutron density, and by electrical neutrality the same holds for the proton density. Note that the electron density scales as the square of the neutron density, as long as the neutrons remain non-relativistic. So if we assume instead a neutron density of 1044 m-3, the electron density will be 0.4% of the neutron density. Also note that the Fermi energy of 200 MeV corresponds to a temperature of 2 trillion K, so the star's thermodynamic temperature of a billion K can be ignored. -- Gene
________________________________ From: meekerdb <meekerdb@verizon.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, June 25, 2014 1:49 PM Subject: Re: [math-fun] Neutron stars as atoms
I would suppose that a neutron star would continually have neutrons undergo beta decay, producing a proton and electron which are captured by gravity and a neutrino which isn't.
Brent Meeker
WD> Perhaps one should regard neutron stars as giant nuclei.
A better way to view this is: replace the word "stable" with "stable under pressure." See, I would claim that it is an illusion that there is no stable nucleus with atomic weight 1000. Actually, if you put it under enough pressure, then it would presumably become stable. The only problem is humans have no hope of sustaining pressures that large and the only known way to reach them is inside a neutron star.
This raises a question that seems by comparison real. Might there be enough pressure deep inside an ordinary star to produce elements that aren't stable in free space? If so, would that give rise to a nuclear chemistry that might have effects observable from outside the star? Whit
participants (7)
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Allan Wechsler -
Eugene Salamin -
Jeff Caldwell -
meekerdb -
Warren D Smith -
Whitfield Diffie -
Whitfield Diffie