X-Message-Number: 21872
Date: Wed, 4 Jun 2003 06:50:53 EDT
Subject: Pumping a nuclear X-rays laser.

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Nuclear x-ray laser:
This tool looks somewhat "Star War," it is an element of the quantum 

nondemolition x-ray scanner. A laser works by pumping a majority of atoms in an

excited state and then let them decay to the ground state by stimulated 

The classical scheme is to pump an electron from the ground state to some higher
state able to decay to a nearby metastable excited state. The laser emission 
is produced between the metastable and the ground state. The problem with high 
energy radiation such x-rays is that the state stability is inversely 

proportional to the fourth power of the energy. There is then no time to pump a

majority of atoms in a given excited state. Only gigantic pulsed lasers or 
explosions can do the job in the x-ray waveband.

Even worst, because of the fast decay mode, the emission takes in a broad 
band, this translates into a short wave packet, unsuitable for QND 

interferometer. There seems to be no solution with the linear electromagnetic 
structure of 
atoms. The way out is to use nuclear levels of protons in the nucleus. Because 
protons react to the strong nuclear force, their electromagnetic energy levels 
are strongly distorted and non linear. There are many long lived metastable 
levels suitable for an interferometer. Pumping them without nuclear reactions 

is not seen as an option by most physicists because the x-ray source would have
to be a very narrow band one.

My opinion is that this can be done with entangled states. My starting point 
is a 3 GHz generator coupled to a storage superconducing cavity the discharge 
is done with a mercury contactor, the pulse rising time is 3 ns with this 

device. The wave is produced in an elliptical polarization state. It is then 
between two flat mirrors so as to get entangled in the vertical polarization 
state. Taking as reference the sodium double line, each mirror is polished to 
one-tenth of wavelength so the slit between them is defined at one-fifth of 

wavelength or near 0.1 micrometer. This define the scale of first quantification
entanglement. It is one million smaller than the original radio wavelength, so 
we have entangled  on the order of one million radio photons.

Next, the wave goes throughout a second flat mirror pair producing a new 

entanglement in the horizontal polarization. The number of photons in the 
pulse is assumed to be infinite to simplify. So, each photon in a vertical 
entanglement will be entangled in the perpendicular plane with others coming 
from different entanglement bunches. So, at the exit one million of vertical 
entanglement bunches will be horizontally entangled. For a tilted linear 

polarization, there will be one trillion 3 GHz entangled photons with a 
energy near 10 MeV.

I recall that the target x-ray laser beam is in the 5 - 10 KeV range, so 
there is some margin. At the superconducing cavity exit there would be a delay 

line to keep the radio spectrum under some MHz wide. This spectrum would have a
width one-thousandth of  the main frequency. In the entangled bunch, this 

relative frequency dispersion is reduced by a factor equal to the square root of

the photon number. With one trillion photons, the relative narrowness get better
by a factor of one million. The wave packet is then 100,000 km long and fits 
well with nuclear energy levels.

The real concern at this level is not: Could this be done but: Would someone 
with garage level technology be able to do it?

The kW  class 3 GHz radio generator is on the market at affordable price. A 
niobium superconducing cavity, with high quality chemical polishing and liquid 
helium cryostat, could be bought at high price. I think an alternative would 
be to buy a sheet of beryllium and cool it down to LN2 temperature so its 

conductivity would be some hundred times better than room temperature cooper. It

would be sufficient for that application, so the superconductivity device could
be seen as an overkill.  High speed mercury contactor is in stock, no problem. 
The four mirrors could be cut from a single standard Pyrex slab, I can fit 3 
flat polishing posts on my large mirror polisher (two weeks work). The 

one-tenth of wavelength precision is not out of reach: many amateur telescope 
get down to 1/20th wave.

One problem is that the entangled wave gets out of the mirrors slit as light 
from an optical fiber: it spray in all directions. A lens concentrator must be 
added, it could be a graphite concave lens (x-rays have negative refraction 
index with many materials, so a concave lens concentrate them). The high lens 
curvature needs a special polishing machine to be implemented, something 
similar to what is used for Maksutov's telescope correcting lens making.

To conclude, I think a nuclear x-ray laser pumped by entangled radio waves is 
a workable option for advanced amateur experimentalist.

Yvan Bozzonetti.


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