Stong Force Not Needed to Hold Nucleus Together

New popular science article on RealQM GitHub Gallery 

• Can electricity alone hold a nucleus together?

with affirmative answer. Read and comment! To get input check out RealQM Gallery.

To get perspective read: 

• The Defeat of Reason by Tim Maudlin Boston Review 2018
• What is Real by Adam Becker

RealQM is real. Who will make Boston Review aware of my article as follow up? I cannot suggest myself. Maudlin?

See also next post John Bell in Memoriam.

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. 

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.  

Russian Doll Fractal Atomic Physics

Big Doll = Atom with Nucleus = Small Doll .

RealQM presents a new Schrödinger equation for atomic physics as a positive nucleus of size $10^{-15}$ m surrounded by a collection of non-overlapping electrons densities without self-repulsion of size $10^{-10}$ m, which in ground/excited states organise into shells as solution to an energy minimisation packing problem under Coulomb attraction/repulsion.

RealQM is a classical continuum model in 3 spatial dimensions describing deterministic physics, fundamentally different from standardQM in multidimensional configuration space with unclear physics as statistics.  

Similarly RealQM presents a Schrödinger equation for an atomic nucleus of size $10^{-15}$ m as a negative kernel of size $10^{-20}$ m surrounded by a collection of non-overlapping proton densities without self-repulsion of size $10^{-15}$ m organizing into shells under Coulomb attraction/repulsion.

The change of spatial scale between atom and atomic nucleus of $10^5$ is translated to binding energies with the same factor.

The basic case is represented by two possible configurations of 1 proton and 1 electron: As a H atom with proton kernel surrounded by an electron density with binding energy 13.6. eV, and as a neutron N as an electron kernel surrounded by a proton density with binding energy 0.78 MeV with a factor of about $10^5$. 

What emerges is a form of Russian Doll with an H atom as a Big Doll with nucleus as a Small Doll composed in the same way with just a switch of sign of charge. It is possible to think of even bigger dolls built in a similar way such as planet systems around a star. 

In RealQM an atomic nucleus is held together by Coulomb attraction between electron kernel and surrounding proton density thus overpowering proton repulsion, in the same way an atomic ion is held together by Coulomb attraction between proton nucleus and surrounding electron density overpowering electron repulsion. There is here no need to ad hoc introduce a strong force as in the Standard Model. 

The configuration can in principle be repeated with an even smaller doll with positive kernel of even smaller size of $10^{-25}$ m. But that is beyond observation and so it seems reasonable to search for an explanation why there are so to speak only two atomic dolls: Atom = Big Doll and atomic  nucleus = Small Doll. 

That requires that the kernel of an atomic nucleus as a negative charge of strength more than 1 is free of self-repulsion, since it has no positive kernel overpowering repulsion as in Big and Small Doll. This remains to be understood. Can two electrons be compressed to a negative charge density -2 without self-repulsion? Is this possible by some form of quantum gravity? In any case this makes two electrons fundamentally different from two protons for which there is no need of compression to +2 without self-repulsion.

A Russian Doll system as a form of fractal system describing the Universe as a repeating pattern, would thus end with a Small Doll in the form of a nucleus as a negative charge density of size $10^{-20}$ m without self-repulsion surrounded by a collection of non-overlapping proton densities organised into shells as solution to an energy minimisation packing problem. Such a nucleus would be held together by Coulomb attraction overpowering repulsion without need of the strong force of the Standard Model.  

Recall that the early Bohr model of an atom was a planetary system of electrons/planets orbiting a nucleus/Sun. In RealQM this is replaced by a stationary system of non-overlapping electron densities surrounding a nucleus as solution to an energy minimisation packing problem. Compare with Fractal Cosmology. It seems that we can find fractals on largest scales governed by gravitational attraction and smallest scales governed by Coulomb electric attraction, but not on human scales showing more complexity.  

Note that it would be sensational if nuclei show to be held together by Coulomb attraction as classic physics, rather than by a residual of a strong force between quarks as postulated in the Standard Model. 

PS1 When I ask professional physicists if in the existing literature there is something like RealQM, they do not give any answer, but tell me that standard Quantum Mechanics, whatever that is, and the Standard Model are by far the best theories about physics ever created and that they agree with all experiments to an incredible precision and so there is no reason to look at anything else, in particular nothing from a mathematician. In the next moment they tell that in fact both models have severe shortcomings, which motivate more tax payer money to new fundamental theoretical physics to be discovered by a new much bigger Large Hadron Collider.

PS2 From A Search for Exotic Higgs Decays by Burzynski: In spite of the overwhelming successes of the SM, there are several glaring issues with the SM which remain unresolved. First and foremost, there are many fundamental phenomena observed in nature that are not predicted or explained by the SM. These include gravity, the nature of dark matter, neutrino masses, and the matter-antimatter asymmetry observed in the universe, among others. Second, there are theoretical problems with the SM which imply a lack of complete understanding of underlying phenomena. Examples include the hierarchy problem and the strong CP problem.

The Neutron as Key to a Periodic Table for Nuclei

In recent posts I have tested an idea to view a system comprised of 1 proton + 1 electron in two different ways held together by Coulomb attraction:

• Hydrogen atom H of size $10^{-10] m with point-like proton kernel surrounded by electron density.   (H)
• Neutron N of size $10^{-15}$ m (inside atomic nucleus) as point-like electron kernel surrounded by proton density with a change of spatial scale of $10^5$. (N) 

The observed spatial scale between H and N is thus $10^5$. A transition from H to N would correspond to "shrinking" by a factor $10^{10}$ of the electron density around a proton into forming a kernel of a proton density, thus a a very strong shrinking. 

The observed binding energy of 13.6 eV for H and 0.8 MeV for N correspond to a spatial scale $D=0.6\times 10^5\approx 10^5$, in accordance with the $\frac{1}{r}$ spatial scaling of a Coulomb potential. 

Both systems can be described by a RealQM Schrödinger equation in non-overlapping wave functions $\psi_e(x)$ and $\psi_p(x)$ for electron and proton densities, as minimisers of total energy $E$ given by: 

• $E(\psi_e,\psi_p, m_e, m_p)=\frac{1}{2m_e}\int\vert\nabla\psi_e(x)\vert^2dx+\frac{1}{2m_p}\int\vert\nabla\psi_p(x)\vert^2dx-\int\int\frac{\psi_e^2(x)\psi_p^2(y)}{\vert x-y\vert} dxdy$   (S)

as the sum of separate kinetic energies for electron and proton and common Coulomb potential energy, where $\frac{1}{m_e}$ and $\frac{1}{m_p}$ set spatial scales of electron and proton.    

The standard case H is represented by minimisation of E without proton kinetic energy (formally $m_p=\infty$) and central point-like proton into a binding energy of $13.6$ eV.    

The non-standard case N is represented by minimisation of E without electron kinetic energy (formally $m_e=\infty$) and central point-like electron, which agrees with observation with $\frac{m_p}{m_e}=D$. 

We understand that since the above Schrödinger model does not involve gravitation, only Coulomb attraction between charges of different sign, the physical meaning of the factors $m_e$ and $m_p$ in the kinetic energies, do not connect to mass but rather to (inverse) spatial scale. What determines the roles of protons and electrons is their spatial scale. 

The conception that the mass of proton is about 2000 times that of an electron is thus not in conflict with $D\approx 10^5$ in the above Schrödinger model.   

The basic idea is to view the formation of a neutron inside a nucleus as a form of "capturing" by a proton density of an electron into the center of the proton density in a process at high temperature/pressure driven by Coulomb attraction under release of 1 MeV. The idea of electron capturing by a nucleus was an important element of nuclear physics even before the advent of the Standard Model in the 1960s.

Further capturing of electrons can create nuclei as a negative kernel surrounded by non-overlapping positive proton densities organised into shells, as a direct analog to an atom with a positive kernel surrounded by non-overlapping negative electron densities organised into shells. 

Recall that in the Standard Model the strong force appears as an ad hoc invention of remarkable fanciness.  If you ask a professional physicist what keeps a nucleus together thus overpowering Coulombic repulsion between protons, you get the answer that it is a form of "glue" of unknown physical nature named "strong force" transmitted by "gluons" of 8 different "colors" serving as "force carriers" between 6 different "quarks", where a proton is turned into a neutron when one of its two "up-quarks" turns into a "down-quark". If you ask how this can be you get the help that since very much energy is released when H fuses to Helium in the Sun a very strong force must be involved and this is the ”strong force” thus proven to exist. But gravitation is missing in the Standard Model because no “graviton” as force carrier is believed to exist, which is a trauma of modern physics since 50 years without hope.

In RealQM a nucleus has a negative kernel surrounded by positive proton densities held together by Coulomb attraction, as an analog to an atom with a positive kernel surrounded by negative electron densities. The observed "periodic table for nuclei" starting with 2, 8, 20,...appears as an analog to the periodic table for atoms starting 2, 8, 18... 

In the Standard Model a nucleus consists of a collection of protons and neutrons, with each proton and neutron consisting of three quarks held together by gluons, without explanation of the observed periodic table for nuclei.  

The great triumph of modern physics was to model the atom in terms of Coulombic attraction/repulsion between + and - charges using a basic element of classical deterministic physics in a new setting of statistics. RealQM shows that the new setting is not needed. Both atom and atomic nucleus can be modeled within classical deterministic mathematical continuum physics. This should be met with relief by students of physics struggling with weird concepts of modern physics.

The next step is to understand the formation of the nucleus of Deuterium D consisting of 1 proton and 1 neutron, or in RealQM 2 proton densities surrounding 1 electron kernel. In the Standard Model D is held together by a residual strong force as a left-over of the strong force holding proton and neutron together, like a molecule held together by residuals of Coulomb forces holding atoms together.  RealQM makes this analog real for nuclei: Both atoms and nuclei are held together by Coulomb forces. 

RealQM for Atom and Nucleus

Real Quantum Mechanics RealQM offers a new model of atoms and atomic nuclei in the form of a classical 3d continuum system of partial differential equations describing a set of non-overlapping charge densities interacting through Coulomb potentials. This is a generalisation of Schrödinger's equation for the Hydrogen atom consisting of one proton and one electron, to configurations with many protons and electrons, which is different from the multi-dimensional Schrödinger equation in configuration space as the basic model of standard Quantum Mechanics stdQM. 

RealQM models an atom as a point-like nucleus/kernel of positive charge $+Z$ surrounded by $Z$ electron densities of charge -1 organised in shells with the innermost shell containing 2 electrons, the next shell a maximum of 8 electrons, the next 18 according to the pattern $2*n^2$ for $n=1,2,...$. The shell system is formed as resolution of an energy minimisation packing problem of non-overlapping electron densities of width scaling with (inverse of) the effective kernel potential reduced by shielding from electrons in inner shells, thus with increasing width for outer shells. 

RealQM models an atomic nucleus as a point-like kernel of negative charge $-Z$ surrounded in the basic case by $2*Z$ proton densities of charge +1. Only Coulomb potentials are involved. No need of strong/weak nuclear force as in the Standard Model of stdQM.

The basic difference between an atom and a nucleus both consisting of a system of protons and electrons, is then the geometric size of the system, with $10^{-10}$ m typical of an atom, and $10^{-15}$ m that of a nucleus, thus with a factor about $10^5$.

The binding energy of RealQM system scales with the geometric size of the system, and so we expect to pass from eV to MeV from atom to nucleus, which is what is observed and also computed by RealQM Nuclear Simulator. The basic reason is that a Coulomb potential scales with 1/distance.

RealQM thus offers an explanation of the $10^5$ factor between atomic and nuclear energies as a geometric scale effect. The basic element is here the concept of non-overlapping charge densities of different widths, which is not an element of stdQM. 

As an example consider the formation of the nucleus of Deuterium from 1 electron kernel surrounded by 2 proton densities (under high pressure and temperature) as a nucleus analog of a $H^-$ ion with 1 proton kernel surrounded by 2 electron densities, under the release of 1 MeV as an analog to the formation energy of about 10 eV of $H^-$. 

To form a $^4 He$ nucleus from 2 electrons surrounded by 4 proton densities, as an analog to $He^{2-}$, the two electrons have to be compressed (under high pressure and temperature) into a -2 kernel under additional release of energy to give the observed binding energy of about 7 MeV. This process remains to be explained.    

The binding energy in RealQM scales with $Z^3$ with only one shell, and with $Z^2$ with a typical sequence of shells as observed, and so with $Z$ per nucleon as roughly observed for $2\le Z\le 30$, which shows release of energy under fusion (up to $^{56}Fe$):

Recall that a nucleus in the Standard Model is viewed as an aggregate of protons and neutrons held together by a strong nuclear force as new physics, while in RealQM a nucleus is considered to be an aggregate of protons and electrons held together by classical Coulomb physics. Ockham would probably choose RealQM before the Standard Model. 

Real Quantum Mechanics for Atomic Nuclei

The Nobel Prize in Physics 1963 was awarded to  Maria Goeppert Mayer (1/4) and Hans Jensen (1/4) for a shell model of atomic nuclei with the protons and neutrons forming a nucleus arranged in shells in a attractive spherically symmetric potential. 

The model was inspired by the standard quantum mechanics (stdQM) model of an atom as a positive pointlike nucleus/kernel surrounded by electrons arranged in shells with shell $n$ containing $2*n^2$ when full, for $n=1,2,3...$. The shell model for atoms was motivated by the Pauli Exclusion Principle reflecting that electrons can have two forms of spin (up and down) and that two electrons with the same quantum identification including spin cannot occupy the same position. 

Real Quantum Mechanics RealQM offers a model of an atom as a system of non-overlapping electron densities interacting by Coulomb potentials, where an electron is identified by space occupancy only. RealQM gives a new explanation of the sequence $2*n^2$ as a natural solution of a packing problem where the size of an electron scales with the effective attraction from the kernel under shielding from electrons in inner shells. 

RealQM can be extended to a nucleus consisting of $Z$ protons and $N$ neutrons with in the basic case $N=Z$ appearing as a pointlike negative kernel of charge $-Z$ surrounded by $2*Z$ protons of total charge total $+2*Z$ again arranged in shells as a resolution of a packing problem (assuming a neutron contributes one proton and one electron). A nucleus is here held together by Coulomb potentials assuming that the negative kernel is not subject to internal repulsion, then without need of strong/weak nuclear force as a most remarkable feature. 

Deuterium consisting of one proton and one neutron would then switching signs correspond to an  $H^-$ ion consisting of one proton and two electrons. 

$4Helium$ consisting of two protons and two neutrons would then correspond to a $He2-$ ion. 

You are invited to test RealQM Nuclear Simulator to compute the energy of different ways of filling shells. You find some examples below if you hesitate to use the Simulator yourself. 

The shell model of the 1963 Nobel Prize is today complemented by the Standard Model where the protons and neutrons of a nucleus consist of triples of quarks.  Does that mean the shell model is obsolete or even worse incorrect? After all, it was considered to be (more or less) correct in 1963. Is there a shell model in the Standard Model?

Here are nuclear binding energie per nucleon computed by RealQM Nuclear Simulator:

• $Z=N=1$: 1 MeV (Deuterium)
• $Z=N=2$: 4 MeV  ($4Helium$)
• $Z=N=4$: 8 MeV

which roughly fits with observation.