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The paper discusses two cases showing crucial effects of error correction. It proves that contrary to the common belief, the electronic state of atoms having more than one electron has a multiconfiguration structure and that the central field approximation provides an inadequate description of the wave function. Fundamental isospin properties prove that baryonic quarks (like those of the

Error correction is regarded as a very important assignment of any human activity. Therefore, organizations dedicate efforts aiming to detect erroneous elements that may exist in the domain which is under its control. This is certainly a self-evident statement and specific aspects of this matter have acquired their own terminology. For example, QA (Quality Assurance) is used in industry; debugging is used in computer programming; devil’s advocate is used in theoretical debates. The present work describes two errors in theoretical physics which have not yet been corrected. Thus, it aims to make a contribution to this kind of activity among members of the physical community. Evidently, such an activity can only improve the understanding of different angles of the debated issue. The results which are derived below have a fundamental relevance to the present structure of theoretical physics. The basic nature of most of the arguments which are described in this paper means that all members of the physical community are expected to belong to its readership.

The paper discusses two topics: the form of atomic wave functions and interrelations between isospin states. These subjects are included in the physics curriculum as well as in relevant textbooks. The paper proves that corrections should be introduced to their presentation and that these corrections have far reaching consequences pertaining to the structure of theoretical physics.

The paper uses standard notation and units where

Atomic states have played a key role in the construction of quantum mechanics. The importance of this issue is explained in this section where atoms of more than one electron are considered. It means that, together with the atomic nucleus, we have a problem of more than two bodies. For the simplicity of the discussion let us examine the ground state of the helium atom whose spin-parity state is

A configuration of N electrons is an expression where each electron has a specific radial function n and an angular momentum l

where

The form (1) is used for the Schroedinger equation whereas the form (2) is used in a relativistic treatment where the Dirac equation holds. The form (2) is generally used below because of its broader validity. In physically interesting cases states of identical spin-1/2 particles are examined and an acceptable state abides by the Pauli exclusion principle.

It is well known that interactions conserves angular momentum. Furthermore, in the case of parity conserving interactions, like strong and electromagnetic interactions, each state has a well defined parity. Thus, our goal is to find the form of a quantum state where

It should be pointed out that in the general case a configuration does not describe a unique

This configuration can be used for a state where

Let us now turn to the primary problems of this section.

Problem #1: Can an atomic quantum state be correctly described by a single configuration?

The following lines explain why the answer is negative. Let us take the

and (3). Evidently, laws of angular momentum addition prove that each of these configurations can yield an antisymmetric

The relevant diagonal form of this matrix can be obtained from an application of a standard procedure of matrix algebra. The results prove that the lowest eigenvalue is smaller than a and c and that the associated eigenfunction of the He atom ground state is a linear combination of the functions described by the con- figurations (3) and (4). This is certainly not the final word because this analysis can be extended to the case of a larger number of configurations where each of which can yield a

Answer #1: Excluding hydrogen-like atoms, atomic eigenfunctions of the Hamiltonian have a multicon- figuration structure.

Now, another problem arises:

Problem #2: Is there a dominant configuration in the description of the Helium atom ground state?

The answer to this problem is found in results of numerical calculations. These calculations have already been carried out in the early days of the computer era [

Answer #2: There is no dominant configuration in the structure of the ground state wave function of the He atom.

This outcome certainly has a more conspicuous effect in cases of other atomic states that have more than 2 electrons and/or states where

Unfortunately, these answers are apparently ignored by the general community. For example, due to its own rules, Wikipedia describes the present consensus. Contrary to the results derived above, the Wikipedia item examines electronic state of atoms and (as of March 2016) it uses a single configuration for describing the electronic ground state of each atom. The same discrepancy can be found in quantum mechanical textbooks (see [

The results found above have very significant implications. In particular, everything which is said above on electrons apply also to quarks. Therefore, the state of the proton’s quarks must be described by many configurations, and in most of them quarks have a higher angular momentum. It follows that spatial angular momentum makes a dominant contribution to the total proton spin and the instantaneous direction of the spin of each quark may be either up or down. This statistical effect means that quark’s spin makes a small contribution to the total spin of the proton. The validity of this conclusion has already been confirmed experimentally [

Unfortunately, the general community assumes that the protons state is described by a single configuration of three quarks, where the two u quarks are described by the

It can be concluded that in the case of more than two particles the system takes a multiconfiguration structure, and that the Central Field Approximation does not yield a good description of the state.

Heisenberg suggested the isospin symmetry in the early days of nuclear physics (see [

The same formalism has later been found useful for describing hadronic states where the

As is well known, isospin raising and lowering operators have very useful applications. These operators, denoted respectively by

Here

・ All members of a given isospin multiplet have the same spin and parity and also a very similar mass and a very similar structure of their wave function.

Hereafter, these important features are called the main isospin properties. The mass and structural differences between members of the same isospin multiplet are ascribed to the electromagnetic interactions and to the proton-neutron (or

The following example demonstrates the significance of the main isospin properties. Consider the ^{14}O nucleus. This nucleus has a ^{14}N has a ^{14}O nucleus. More details of these nuclei are depicted in figure 7 of [

It turns out that in spite of the much smaller phase space, more than 99% of the ^{14}O ^{14}N. (The rest go to the ground state and to another

The main isospin properties explain this remarkable effect. The ground state of the ^{14}N nucleus is an isospin singlet. On the other hand, the following energy levels belong to an isospin triplet: the ground state of ^{14}C, the ^{14}N and the ground state of ^{14}O. Therefore, the main isospin properties show that the space-spin part of their wave function is (practically) the same. Hence, the nuclear matrix element of the ^{14}N nucleus is much larger than that of the transition to the ^{14}O

Let us examine another example which shows the usefulness of the isospin concept. This concept helps us understand the relationship between the multiplet of the two nucleons and that of the four

corresponding multiplet (in MeV). For the nucleons

The data depicted in ^{14}N nucleus of

As shown in

The main isospin properties and its foregoing outcome are ignored in quite a few textbooks. This matter has very far reaching consequences. For example, in order to prove the need for the QCD quark’s color degree of freedom, it is explained (see e.g. [

It is well known that QCD is the Standard Model sector of strong interactions. The discussion of this section shows that this theory has been constructed on the basis of an erroneous assumption which violates the outcome of the main isospin properties.

This work discusses two topics and proves that the relevant parts of presently accepted theories contain errors. The analysis relies on well documented physical properties which are shown in the reference.

The first issue is the quantum state of atoms that have more than one electron and the quark state of baryons. The second section arrives at the following conclusions.

・ It is proved that the wave function of atoms having more than one electron has a multiconfiguration structure.

・ An analogous structure is found for the proton’s quarks.

・ The multiconfiguration structure provides a straightforward explanation for the dilemma called the proton spin crisis.

・ The assumption called central field approximation does not provide a good description of the actual quantum state.

The second issue is isospin which is known since the early days of nuclear physics. The third section discusses isospin and arrives at the following conclusions.

・ Nuclear states and hadronic states can be organized in sets called isospin multiplets.

・ All members of a given isospin multiplet have the same spin and parity and also a very similar mass and a very similar structure of their wave function.

・ The data support the usefulness of isospin as a good description of quantum states.

・ In particular, the state of the

Error correction is an important task of every human community. This work points out two errors of presently accepted physical theories. In so doing it aims to launch a debate about the veracity of the results obtained above. Such a debate can certainly improve the understanding of several topics of theoretical physics.

Eliahu Comay, (2016) Elementary Errors in Contemporary Theoretical Physics. Open Access Library Journal,03,1-6. doi: 10.4236/oalib.1102585