Atomic Nucleus Secret Revealed

We continue the exploration of RealNucleus as a RealQM model of an atomic nucleus consisting of 

• a kernel as an inner shell of non-overlapping $-1$ charge densities of total charge density $-Z$ 
• an outer shell of non-overlapping $+1$ charge densities of total charge $+2Z$
• interacting by Coulomb potentials.  

The key question is:

• Is such nucleus stable in the sense of having a negative total energy as the sum of kinetic and potential energy? 

Let us start with $Z=1$, thus with a -1 kernel surrounded by two +1 charges. The atom analog obtained by switching the sign of the charges is a proton surrounded by two electrons, which is an $H$ atom with an extra electrons.  This is the $H^-$ ion, which is known to be stable. RealNucleus confirms by computing the total energy 

Next, we consider $Z=2$, thus 4He with an inner shell of two -1 charges surrounded by an outer shell of four +1 charges. We use this code including potential energy from the kernel (but not yet kinetic energy) to get a total energy per nucleon of about -8 MeV, which gives clear sign of stability. 

It remains to include kinetic energy from the kernel. If the -1 charge densities are forced to vanish at the boundary between the inner shell and outer shell, then the kinetic energy will be large and destroy stability. On the other hand if charge densities can meet with continuity of intensity then the kinetic energy  can be smaller and stability maintained. 

We are thus lento the key circumstance of how the negative inner shell charges meet to outer shell positive charges. If they can meet just like two non-overlapping electron charge densities meet in the RealQM atom model, with continuity + zero normal derivative, the the observed stability of 4He can be explained by RealQNucleus with only Coulomb potential interaction and in so in particular without any strong force. 

RealNucleus

RealNucleus is a  model of an atomic nucleus which is an analog of RealQM for an atom, with shifted roles of electrons and protons. The RealNucleus model of a nucleus of charge $+Z$ thus consists of a shell system of $2Z$ non-overlapping charge densities of charge +1 held together by Coulomb attraction from a kernel of negative charge density $-Z$. RealNucleus is thus a model of  a nucleus which does not involve the ad hoc strong force of the Standard Model. 

RealNucleus has been added to the list of articles about RealQM. 

Update Fusion of 2H into 4He by RealQM

RealQM offers a new model of an atomic nucleus as a kernel of negative charge density surrounded by a shell structure positive charge density, as an analog of an atom with roles of protons (p) and electrons (e) switched. 

The model is parameter-free up to the change of scale from atoms to nuclei S and the radius of the kernel of the nucleus R, which can be used to fit the model to observations. Let us use this option to compute the binding energies E of the two basic nuclei of 2H (1e+2p) and 4He (2e+4p) by RealQM  using this code. We get the following results with a change of scale from atom to nucleus $S=2.5\times 10^{-6}$ with the size of an atom $10^{-10}$ m 

• 4He  E = 27 MeV,  R = 0 
• 2H    E = 2 MeV,  R = $2.5\times 10^{-17}$ m

We thus see that using the scale factor S we can fit E for 4He to observed 28.30 MeV and then using R to fit E with 2H. 

RealQM then offers a model of the fusion of two 2H into one 4He as the basic fusion process in the Sun with an energy release of 27-4 =23 MeV: 

Note that the atom analog of 2H nucleus is $H^-$ atomic ion, while the atom analog of 4He nucleus would be the ion $He^{-2}$, which is not stable. The 4He thus has 4 protons in a first shell, while the $He$ atom has no room for 4 electrons. 

The RealQM model for both atom and nucleus can be seen as the result of a shell packing problem, and thus comes with different shell structures. In an atom the first shell cannot contain more than two electrons, while in a nucleus the first shell appears to be able to hold up to 8 protons, thus with denser packing in a nucleus than in an atom. 

Modern Physics as Virtual Physics

Recents posts explore the possibility of extending the RealQM model of an atom, built by a positive nucleus attracting a negative electronic charge density around itself by the electromagnetic force, to a analogous model of a nucleus simply by switching the roles of proton and electron. 

In this model a nucleus is held together by the same electromagnetic force keeping an atom together, which is the electromagnetic force of classical physics as a force transmitted by an electric potential or field. This goes back to an idea naturally presenting itself as soon as an atom model was formed in the 1920s. But the idea was given up after the detection of the neutron by Chadwick in 1932 kicking out the electron from the nucleus preparing for the development of the Standard Model in the 1960s as the current model of a nucleus as part of StdQM. 

In the Standard Model a nucleus thus consists of protons and neutrons (not protons and electrons as in RealQM) each built as a triple of quarks held together by a strong force transmitted by force carrying particles named gluons (because they are supposed like a glue). From classical physics point of view this is a mind boggling model with both quarks and gluons beyond experimental detection thus as truly virtual and not real as detectable.

To make the Standard Model credible with its quarks and gluons, the ground-breaking idea of force carrying particles is extended to the old electromagnetic force, so well described as transmitted through electric potentials/fields, into a new explanation in terms of virtual photons as force carrier depicted by Feynman in this illuminating diagram explaining repulsion between two electrons through a $\gamma$-wiggle:

The argument is that if the well known electromagnetic force in fact is transmitted by photons (as depicted in Feynman diagrams), then it is not so strange to think of the strong force keeping a nucleus together by force carrying gluons. By expanding a fantasy story it can be made more credible, in the same way a big lie can be more credible than a small. 

A basic trouble with the Standard Model is that it contains more than 20 parameters, which have to be determined experimentally but that is impossible.

On the other hand, the only parameter in RealQM is change of scale between atom and atom nucleus (in the range $10^5$) which is possible to measure experimentally. 

We understand that modern physics with its virtual photons as force carriers of the electromagnetic force depicted in Feynman diagrams, can be be seen as a form of virtual physics fundamentally different from classical physics as real physics. 

Keep an eye on new post on RealQM as an alternative to the Standard Model for atomic nuclei.  

  

RealQM vs StdQM: Binding Energy of 4He

This is a clarification of recent posts on RealQM vs StdQM for small nuclei.

To determine the binding energy of the 4He nucleus built from 2 protons and 2 neutrons is an elementary exercise in high school physics: Compute the mass defect as the difference in mass of 2 free protons 2 + 2 free neutrons and the mass of 4He determined experimentally to be with c2 the speed of light squared:

• mass of a free proton $m_p= 938.272$ MeV/c2
• mass of a free neutron $m_n= 938.565 MeV/c2
• mass of nucleus 4He  $m_{4He}= 3727.38$ MeV/c2

and compute using Einstein's E=mc2 to find the binding energy BE as

• BE = $2m_p+2m_n-m_{4He} = 26.289$ MeV or 7.1 MeV per nucleon.

This value stands out as very large compared to 2.2 for 2H (Deuteron), 2.8 for 3H (Tritium) and 2.6 for  3He MeV per nucleon. It is explained as an expression of a doubly magic number present in the 2 protons and 2 neutrons of 4He. 

Is it possible that the BE for 4He determined from mass defect using E=mc2 as above, does not represent true physics? Is it possible that the rationalisation with reference to magic numbers is not real physics? 

Note that there is a gap in the above mass defect computation in the sense that the mass of the protons and neutrons inside the nucleus is not available to measurement and they enter into an energy budget required to break the nucleus apart. If the protons and neutrons in fact take on bigger mass inside the nucleus than outside then the binding energy will shrink maybe towards normality. The above high-school energy computation may reflect rather a convention than reality.

We compare with the BE about 1.7 MeV/nucleon for 4He computed by RealQM as a parameter free mathematical model without experimental input assuming a change of scale of $10^5$ between atom and atomic nucleus. Changing the scale a little then gives BE of about the same size as those above for 2H, 3H and 3He. 

Let us see what StdQM has to offer. We thus ask chatGPT if it is possible to determine BE without experimental input from the Standard Model (QCD) as the present mathematical model of atomic nuclei within StdQM.  Here is what chatGPT delivers as a conclusion of a lengthy report:

• A fully QCD-derived prediction of ⁴He’s binding energy without any experimental input is not yet realized, but current methods are closing in, and future simulations at physical quark masses are expected to reach this goal.

Summary: RealQM delivers BE for 4He in the range 2-3 MeV/nucleon with only experimental input the change of scale between nucleus and atom. StdQM struggles to deliver a result. The list value of 7.1 MeV/nucleon stands out as 2-3 times too large. 

What is Wrong with Newton's Law of Gravitation?

The corner stone of classical mechanics/physics is Newton's Law of Gravitation taking the form of the Newton/Poisson Equation NPE

• $\rho =\Delta\phi$         (*)

connecting mass density $\rho (x)$ to gravitational potential $\phi (x)$, where $x$ is the space coordinate of 3d Euclidean space. 

In modern physics this mathematical model is replaced by Einstein's Equation EE in "curved space-time" of his General Theory of Relativity GR preceded by the Special Theory of Relativity SR. EE reduces to PE in flat Euclidean space without time and so EE is viewed to be a generalisation of PE into curved space-time.   

To mark a shift between classical (obsolete) physics and modern physics a lot of effort has gone into showing that NPE contradicts observations and so must be replaced by EE. In particular NPE is viewed to contradict the following consequences of SR/GR:  

1. Finite speed of light.
2. Gravitational lensing. Bending of light 
3. Time dilation. Clock rates affected by motion and gravitation.
4. LIGO detection of gravitational waves with finite speed of propagation.
5. Precession of Mercury Perihelion.  

But NPE says nothing about propagation of light or the rates of clocks and so 1-3 cannot be viewed to contradict NPE. 

As concerns 4, it is well known that a delay in the action of the gravitational pull on Earth from the Sun will make the Earth orbit away from the Sun. Finite speed of propagation of gravitational force thus appears to contradict the stable orbit of the Earth. In EE this is explained as a form of compensation of the delay in some form of prediction effectively cancelling the delay to no delay. Strange.

So the evidence against NLG shrinks down to 5 with the claim that NPE gives an incorrect prediction of the observed orbit of Mercury, while that of SR/GR is correct. But making a prediction requires input of positions and velocities of all celestial objects in the Solar system at some specific time and in addition their masses and G. To claim that NPE gives the wrong prediction in the form of a very small deviation from observation requires a very accurate NPE computation taking all celestial objects including their internal motion correctly into account. Such a computation has not been made. 

Another argument against NPE is that it requires a notion of absolute time, something which is supposed to contradicts the relative time of SR. Is this a valid argument? 

In the sequence of posts on Neo-Newtonian Gravitation I have tested the idea that the gravitational potential $\phi (x)$ is primordial from which mass density is $\rho (x)$ is delivered by the local action of the Laplacian according to (*) as if time does not enter. 

Combining NPE with Newton's 2nd Law $F=am$ law brings in a notion of time since acceleration as change of velocity per unit of time refers to time, as well as velocity as change of position per unit of time. This gives a notion of local time for each body interacting with all other bodies through the time-less gravitational potential, which does not ask for coordination of local times into a global time. Maybe Newtonian mechanics in fact does not require a notion of global time? Only a notion of a global time-less gravitational potential. 

Binding Energy of a Nucleus from Mass Defect?

In the previous post when comparing binding energies by RealQM and StdQM for small nuclei, we were led to question the binding energies in StdQM computed from estimated mass defects with the masses of protons and neutrons as input. 

We find that the binding energy of nucleus according to StdQM is mainly potential energy created by the strong force, which does not depend on the mass of neutrons and protons. We thus learn that the binding energy of a nucleus does not depend on the mass of neutrons and protons. These masses only enters in a supplementary computation connecting energy to mass defect including $E=mc^2$. 

We can thus speak about two versions of binding energy:

1. Physical Binding Energy PBE determined by the strong force without input of the mass of neutron/proton.
2. Computed Binding Energy CBE from mass defect determined using $E=mc^2$ to make CBE=PBE.

It may then be tempting in a situation when PBE is impossible to assess either theoretically or experimentally, which is usually the case, to simply replace PBE by CBE and declare that CBE is physical binding energy and not just computed. 

Doing so StdQM delivers a very small drop of binding energy when changing one of the two neutrons of 3H into a proton thus forming 3He, which can be seen as a major change. RealQM gives here a large drop which maybe is more line with physics. 

Mystery of Nuclear Physics: StdQM vs RealQM

The Standard Model as part of Standard Quantum Mechanics StdQM delivers the following total binding energie E in MeV with p proton and n neutron 

• 2H     1p+1n   E = -1.71
• 3H     1p+2n   E = -7.97 
• 3He    2p+1n   E = -6.70
• 4He    2p+2n   E = -28.30

The large jump of more than 20 MeV by adding 1 neutron to 3He into 4He is viewed as very remarkable asking for an elaborate explanation in terms of the strong force within StdQM boiling down to 4He having a "doubly magic" number of protons and neutrons. 

RealQM delivers the following energies (with atom to nucleus size scaling set to $10^6$) and shell configuration indicated:  

• 2H      1p+1n  E= -0.5         1st shell: 2
• 3H      1p+2n   E = -2.7       1st shell: 1  2nd shell: 2 
• 3He    2p+1n   E = -0.5       1st shell: 2  2nd shell: 1
• 4He    2p+2n   E = -2.5       1st shell: 2  2nd shell: 2

We see in RealQM  the same large jumps from 2H to 3H and from 3He to 4He with roughly a factor 5 as in StdQM. This can in RealQM be understood from the fact that adding 1 neutron doubles the central negative charge density and so doubles the negative potential. 

RealQM thus captures a basic feature of StdQM in particular the "magic number" of 4He, which thus after all may not be so magic. 

But there is a notable difference in the change from 3H to 3He by replacing a neutron by a proton. StdQM gives a small decrease of energy, while RealQM gives a much bigger decrease. 

In RealQM this comes again from a decrease of central negative density. 

In StdQM the strong force is the same and the only difference is the proton-proton repulsion in 3He claimed to be small compared to the strong force. Recall that energy is not directly measured but is computed from mass defect using $E=mc^2$, where mass defect is not directly measure but computed  from measurements of proton and neutron mass. There is thus a lot computation involved which may not capture true physics. In any case it is strange that replacing a neutron by a proton has only marginal effect on energy.   

Summary:

• RealQM offers a model of a nucleus with only Coulomb forces.
• StdQM offers a model of a nucleus with an additional new strong force.
• Ockham's Razor would select RealQM, 

  

 

Binding Energy of 4He by Mass Defect?

RealQM gives using this code the following binding energy E per nucleon (in MeV) of atomic nuclei with charge Z=1,2,...,8, assuming a change of spatial scale from atom to nucleus with a factor $10^6$:

• Z=1  E = -0.5   2H
• Z=2  E =  -1.0  4He
• Z=3  E = -2.2   6Li
• Z=4  E = -3.2   8Be
• Z=5  E =  -5.0  10B
• Z=6  E = -5.5   12C
• Z=7  E = -6.5    14N
• Z=8  E = -6.6    16O

We see a nearly linear increase from Z=1 to Z=5 followed by much slower increase into constant value. 

We compare with the following list values (in MeV):

• Z=1  E = -0.86   2H
• Z=2  E =  -6.82  4He
• Z=3  E = -5.08
• Z=4  E = -6.81
• Z=5  E =  -6.22
• Z=6  E = -7.42
• Z=7  E = -7.22
• Z=8  E = -7.72

We see a very quick jump from 2H with Z=1 to 4He into nearly constant value, thus without the gradual increase suggested by RealQM. The explanation by StdQM for the surprisingly large jump is very complicated. A fusion process with two 2H being combined into one 4He would thus deliver about 25 MeV, to be compared with 2 MeV for RealQM. 

In this situation, it is natural to ask how the large binding energy for 4He is determined in StdQM. We recall that the fusion of two 2H into one 4He is the fusion process fueling the Sun. It is impossible to directly measure the energy release in a fusion process and so it is instead determined according to a certain standard, where mass is traded for energy according to Einstein's $E=mc^2$. But because of the factor $c^2$ is very large, the mass lost or mass defect in a fusion process is too small to be directly measured. The mass defect is instead computed according to a certain standard, from which the binding energy is computed using $E=mc^2$. 

We are thus led to ask if the large computed large binding energy of 4He is the real one? Is it possible that the smaller jump by RealQM is closer to reality? Which value is relevant for the Sun: 25 or 2? How can this question be answered?

 

We meet here a a situation where a certain standard procedure replaces direct measurement and the question is if the procedure captures reality. 

The Kinetic Energy of StdQM and RealQM

The Schrödinger Equation SE as the basic mathematical model of Standard Quantum Mechanics StdQM in terms of (here for simplicity) a one-electronic wave function $\Psi (x)$ depending on a 3d spatial coordinate $x$, gives rise to a contribution to total energy named kinetic energy of the form 

• $E_{kin}(\Psi )=\frac{h^2}{2m}\int\vert\nabla\Psi (x)\vert^2 dx$ with $\int\Psi^2(x)dx=1$, 

where $h$ is Planck's constant and $m$ the mass of the electron. If $\Psi (x)$ is globally defined with $\Psi (x)$ tending to zero for $\vert x\vert$ tending to infinity, the coefficient $\frac{h^2}{m}$ determines  the size of the electron to scale with the $\frac{h}{\sqrt{m}}$ with thus a larger size for smaller $m$. 

Viewed the other way around, $E_{kin}(\Psi )$ scales with the factor $D^{-2}$ with the size $D$ of the electron, which means that electron concentration comes with large kinetic energy. 

In RealQM as an alternative to StdQM an electronic wave function has local support over a domain in space and is not restricted to vanish on the boundary of the domain. This allows the kinetic energy to stay bounded with decreasing size of the electron. This is the secret of covalent bonding as shown here and allows RealQM to extend to a model of an atomic nucleus as shown here. 

The salient feature of RealQM is that electrons have wave functions with non-overlapping support representing non-overlapping unit charge densities which meet a free boundary with continuity. 

Covalent bonding is thus realised in RealQM by allowing electrons to meet between kernels without increase of kinetic energy. 

A RealQM model without need of a strong force of a nucleus can thus be built as an electron density of very small size surrounded by protons of larger size. Electrons thus appear in two sizes, large for an atom and small for a nucleus. 

Covalent bonding is not well explained within StdQM, and is still after 100 years subject to debate without conclusion. The Standard Model of a nucleus built by quarks and gluons/strong force is very complicated.