X-ray emission by Zero Point Energy or simple QED?

PITTSBURGH - March 19, 2018 - PRLog -- .
Introduction
In 1913, Einstein and Stern developed the concept of zero point energy, or ZPE. However, the reality of ZPE as a source of energy is still questioned today. Recently, the ZPE at MeV levels has been proposed [1] to explain the bursts of X-rays observed [2] in LENR in glow discharge heating of a palladium Pd cathode even after the discharge ceases. LENR stands for low energy nuclear reactions.

The observation [2] of 1-6 keV X-rays in glow discharge of palladium Pd cathodes from 1 eV plasmas is not explained in the literature. Nuclear reactions as a source of diffuse X-ray emission that require MeV plasmas are not possible in 1 eV glow discharge while a collimated X-ray mechanism is not known to produce a 20 μs burst duration every 50 μs present up to 20 hours after switching off the glow discharge.

Problem
In 1900, Planck explained the radiation spectrum of a black body by treating the absorption of energy as discrete and not continuous. Apparently, Planck did not consider the energy between quantum levels as a temporary state depending on the amount of heat absorbed from the surroundings and instead treated the absorbed heat as the average energy E_av between (n -1) and n quantum levels,

E_av = ½ [ nhν + (n - 1)hν ] = ½ [ 2n - 1 ] hν.

In the ground state, n = 1, and therefore Planck defined the ZPE = ½ hν. However, this is a problem because the energy supplied to an atom may have any value, i.e., ZPE  < hν and most likely not ½ hν. Since ZPE < X-ray level, the ZPE at MeV levels cannot not exist. In this PR, the ZPE is treated as temporary and not a quantum state of the atom

Proposal
The X-ray bursts in glow discharge [2] are produced by the simple QED quantum state which is a consequence of QM that by Planck's law requires the heat capacity of the atom to vanish under high EM confinement. QM stands for quantum mechanics. Heat capacity vanishes because atoms have high surface-to-volume ratios that require heat Q to almost entirely be deposited in their surface. Precluded from thermal expansion, the surface heat places the atom under the high EM confinement necessary by the Planck law for heat capacity to vanish.

Absent heat capacity, the atom cannot conserve the heat Q by an increase in temperature. Instead, the simple QED transition from the ground to X-ray levels is made by converting the heat Q in the surface to non-thermal EM energy in the form of standing photons inside the atom having half-wavelength λ/2 = 2r, where r is the atomic radius. The Planck energy E of standing photons is, E = hν = hc/λ = hc/4r, where c is the speed of light. If the heat Q is sufficient to reach the X-ray level, the X-ray is emitted. But if not, the heat Q simply resides in a temporary state of the atom only to be promptly re-emitted as EM radiation at frequency ν to recombine with that from other atoms and allow the transition to X-ray levels. For applications of simple QED, see: http://www.nanoqed.org/, 2010 – 2018.

Application
The X-ray emission from glow discharge with a Pd cathode - Fig. 18 of [2] -  is reproduced in the thumbnail. For Pd atoms having radius r = 169 pm, simple QED gives E = 1.83 keV and wavelength λ = 0.676 nm. Experimentally, the X-ray peak occurs at 1.5 keV because sputtering produces clusters of Pd atoms having radii > 169 pm, not perfectly bare atoms. Taking the classical heat flow Q from the glow discharge plasma temperature T into the atom is, Q = πHr²T, where H =5.67 W/m²K is the natural convection heat transfer coefficient, and T the plasma temperature. Assuming T = 1 eV = 11,500 K, Q = 5.85 x 10^-15 J/s. The time  for an individual atom to reach the X-ray level is, τ = E/Q = 50 ms. But X-ray transitions require τ < 150 fs and the heat Q = 5.85 x 10^-15 J/s is not sufficient to induce the transition that requires Q > Q*, where Q* = E/τ = 1.95 x10^-3 J/s.

To emit X-rays at heat flow Q < Q*, a cooperative effect is required. In a collection of N_t atoms, a variant of the Dicke state is proposed to produce collimated superradiant X-ray emission in the direction of the heat flow Q. Unable make the X-ray transition, each atom spontaneously re-emits the heat flow Q as EM radiation at the same frequency ν that upon recombination with that from other atoms produces the heat Q* to make the X-ray transition in a smaller number N of atoms. In Fig. 4(b) of  [2], N is the number of collimated X-ray photons/burst ≈ 1.6 x 10⁸. Hence, a single X-ray photon requires 50 ms/150 fs ~ 3.33 x 10¹¹ atoms, i.e., only a small fraction of the N_t atoms emit X-ray photons. When the glow discharge is turned off, the N_t atoms are only heated by a decaying cathode temperature T_c. Although Q decreases with T_c, the number N of X-rays adjusts and may still be observed.

Conclusion
Simple QED and a variant of superradiance explain X-rays in LENR without ZPE or nuclear reactions.

References
[1] B. I. Ivlev, "Conversion of zero point energy into high-energy photons," Revista Mexicana de F´ısica, 62, 83-88, 2016.
[2] A. B. Karabut, et al., "Spectral and Temporal Characteristics of X-ray Emission from Metal Electrodes in High-current Glow Discharge, "J. Condensed Matter Nucl. Sci. 6, 217–240, 2012.