Nuclear forces according to Evans
Citations of R.D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1969, Chater 10 and 11, are in quotation marks. Comments in italics.
1. General Characteristics of Specifically Nuclear Forces
a. Comparison of Atomic and Nuclear Forces
"no predominant central particle" : the nucleus has no nucleus like the atom
The forces have a very short range of action: the measurement of the range of action is undefined, unlike the radioactive decay period.
"In order to confine a nucleon to a region of this size, (…) its kinetic energy must be of the order of (…) 20 MeV. There is no experimental proof that the nucleons should have an orbital movement. Is there an orbital movement of the atoms in a molecule or a crystal? No. The usual shell model is an adaptation of the atomic model of Bohr and followers not necessarily applicable to the atomic nucleus.
b. Inadequacy of Classical Forces
"the total binding energy of nuclei is proportional to the number of nucleons A and not to A²". This is well known in chemistry and crystallography.
"The electrostatic potential energy between the same two nucleons is identically zero because the neutron is uncharged". The neutron is not uncharged, it contains electric charges with no net charge.
c. The Singlet and Triplet Forces between Nucleons
"Because the nucleons are fermions and obey the Pauli exclusion principle, there can be involved at most two neutrons (spin "up" and spin "down") and two protons in such a group". Nothing to say about it, except that there exists no physical explanation of the exclusion principle and its applicability to the nucleons.
"The possible forces therefore include three types of singlet forces (antiparallel spins) (…) The triplet forces (parallel spins) are restricted to one type for S states" Not very clear.
"The (pp) force represents the specifically nuclear attractive force between two protons and do not include their purely classical coulomb interaction". What is the experimental basis?
"That there exists also a strong attractive force (nn) between neutrons is shown by the fact that the neutron excess (N - Z) in nuclei varies approximately as A5/3 and appears to counterbalance the disruptive coulomb forces in heavy nuclei". Although this law (Evans p. 272) is somewhat better than the linear correlation, it is not a proof of the existence of the strong force.
d. Exchange Forces
"The clear experimental evidence that nuclear forces show saturation directs our attention toward the pureley quantum-mechanical concept of exchange forces". Saturation is not specific to the nucleus: it exists also in crystals like NaCl. In fact saturation is common in all materials where the chemical binding energy is proportional to the mass.
1. "Heisenberg forces in which there is an exchange of both the position and spin coordinates of the two interacting nucleons" Strange hypothesis.
"Heisenberg forces are ruled out by the clear experimental fact that the α particle is the saturation subunit". I would better say that the nucleons with Z and N larger than 2 contain α particles.
2."Majorana forces,in which there is exchange of the position coordinates but not of spin. Variant of Heisenberg forces.
3. "Bartlett forces, in which there is exchange of the spin coordinates but not of the position coordinates". Variant of Heisenberg forces.
e. Tensor Forces
"With central forces, the probability density of nucleons S states must be spherically symmetric". Of course.
"the strength of this noncentral force, or tensor force, depends not only on the separation between the interacting pair of particles but also on the angle between the spins of the particles and the line joining the particles, like the force between two magnets". This force may be really magnetic.
"some other small effects are explicable if there is admixed with the dominant central force a small amount of a noncentral force." This is a second order effect, the first order effect needs the knowledge of the universal constants characterizing the nuclear forces, still unknown.
f. Charge Independence of Singlet Forces between Nucleons
"It is found that the singlet forces between all pairs of nucleons are substantially equal, i.e. ¹(np) = ¹(nn) = ¹(pp)".
No information given about the experimental method used to obtain this result.
2. Ground Level of the Deuteron
a. Wave Function for the Rectangular-well Approximation
"For simplicity, we may choose at first the rectangular potential well, of depth D and radius b (…) where r is the distance between the proton and neutron. (…) The radial wave equation for the relative motion becomes
where M is the reduced mass of the proton and neutron (…). and W is their total energy (…). For the ground level of the deuteron, the total energy W is restricted to the single constant value W = - B where B =2.225 MeV is the observed binding energy of the deuteron". The calculation continues to obtain "the rationalized de Broglie wavelength λ of the relative motion of two particles having reduced mass M and sharing kinetic energy equal to the binding energy B of the deuteron".
This binding energy has never been calculated. Calculations improperly called ab initio never use universal constants because the universal constants of the nuclear forces are unknown.
Models of Nuclei
1. Summary of Experimental Evidence Which Should Be Represented by the Model
1. Nuclear angular momenta I of ground levels
For even-Z even-N nuclides, I=0.
For odd-Z odd-N nuclides, I = 1, 2, 3,…
For odd-A nuclides, I = ½, 3/2…
Mirror nuclei have equal I.
Extremes of triads have equal I.
No justification is given. Odd-A nuclides are of two different kinds : odd-Z even-N and even-Z odd-N. The independent parameters of a nucleus are N and Z, not A which is composite.
2. Magnetic dipole moments μ
They are summarized in Schmidt diagrams. Very low precision, due to theory or to measure?
3. Electric quadrupole moments Q
Systematic empirical variation with Z or N.
4. Existence of isomers
Statistical concentration in "islands of isomerism".
5. Relative parity of nuclear levels
As seen in β and γ decay.
6. Discontinuities of nuclear binding energy
and of neutron or proton separation energy, as seen for particular values of N and Z, especially 50, 82 and 126. These discontinuities at the so-called "magic numbers" are relatively small and diffuse.
7. Frequency of stable isotones and isotopes
Statistical concentration for particular values of N and Z (Chap. 8, Fig. 3.1?).
8. Pairing energy for identical nucleons
as seen in the occurrence of stable, nonadjacent, isobars (Chap. 8, Fig. 3.3). They correspond to a sequence of completed "four-shells" and suggest an α model for light nuclei (p. 298, Chap. 9, Fig. 3.1). They are very large for the light nuclei, particularly around ⁴He. They are very small but still detectable for the heaviest nuclides. There are peaks for even N independently of Z parity and also for even Z independently of N parity.
9. Constant density of nuclei
10. Neutron excess N-Z dependent on A5/3
etc…
The problem is to find what is the main thing.
For me it is the binding energies of the nuclides because they are best known with the best precision. Next, it is the magnetic moments, still unknown for the even-even nuclides. They are assumed to be zero but no experimental data can be found as can be seen in the Handbook of Chemistry and Physics.
eutron exces
