High angle neutron-proton scattering
1. Experimental Data
Only nucleons with high kinetic energy have enough resolutive power to be useful as probes in the study of the nucleonic potential. Therefore, the first neutron-proton scattering experiments were run with incident neutron energy of 90 MeV. When the deepness of the nucleonic potential is quite smaller than the incident neutron kinetic energy the maximum momentum that this potential can transfer to the neutron is quite smaller than its initial momentum and therefore a high change of the direction of the neutron momentum cannot occur. However neutron-proton scattering unexpectedly showed about 50% of low and high angle scattering (1- 7).
Fig.1: Mean total scattering cross-section s of neutrons by protons versus impinging neutron energy.
Fig.2: Differential cross-section s/ q of neutron-proton scattering. The observed n-p scattering is nearly symmetrical with respect to a scattering angle of 90o, evidencing thus an almost equal preference for high angle scattering than for small ones.
(a) (b)
Fig.3 (a and b): n-p scattering represented in the center of mass frame:
(a) When kinetic energies are high with respect to the deepness of the nucleonic potential the transfer of momentum is small and the scattering angles of the neutron and the proton are small too.
(b) Although the momentum transfer is equally necessarily small there is an apparent high angle scattering which proceeds from the transformation of the neutron into a proton and vice versa.
2. Phenomenological description
In Fig.2 the n-p scattering is viewed from a referential frame in which the center of mass is at rest: (a) if the kinetic energy of the impinging nucleons is high with respect to the nucleonic potential well, the momentum transfer is small (i.e. the collision is almost elastic) and the scattering angles are small too. (b) similar scattering conditions in which the momentum transfer keeps being small but in which the scattering angles are high due to the transmutation of the (impinging) proton into a (scattered) neutron and the (impinging) neutron into (scattered) proton.
Fig.5.a: Apparent high angle n-p scattering Fig.5.b: Effective high angle n-p scattering
The high angle n-p scattering is interpreted has a false high angle scattering which in fact is a low angle scattering in which n and p have transmutated during the collision through the strong interactions, leading to an apparent high angle scattering. The apparent high angle (n ® p and p ® n) and the low angle (n ® n and p ® p) scatterings occur in an equal probability of 50%. However, in fact 100% of the scattering is of low angle and the high angle scattering is an apparent process due to the n-p inversion in 50% of the cases. That is, in 50% of times the impinging p (in the center of mass frame, p is the target in the laboratory frame) remains as p after being scattered and so for the n, but in the other 50% of times the impinging p transforms into a scattered n and the impinging n transforms into a scattered p.
The physical interpretation of the high angle scattering is schematically shown in the animation (Fig.4). About half of the times during the scattering the neutron transforms into a neutron and the proton into a neutron (1) when getting in close contact, i.e. in the short range of strong interaction (about 2 Fm). The effect of such mutation process is to lead to an apparent high angle scattering. This process will be schematically interpreted in three different conceptual frames: (a) the standard model, (b) the Yukawa model and (c) the proposed orbital model.
3. Model Interpretations
3.a. Standard (Quark) Model
Within the Standard Model the corresponding process of transmutation implies: (a) the interchange of quarks between colliding proton and neutron, or (b) the transmutation of quarks.
(a) However the interchange of quarks cannot be retained since quarks are tightly confined and the bonding strength (from the gluonic field) increases with the separating distance. Their interchange would imply the formation of a quark plasma which would need much higher collision energies to be able to proceed. So, the possibility of quark exchange should be discarded. From another side in approximately half of the times high scattering angles occur implying thus about 50% proton-neutron transmutations, however the quark model does not implicitly lead to this 50% transmutation and it could as well differ from it.
The mutation of the impinging neutron into a scattered proton and vice versa seen from the perspective of the quark scheme from the Standard Model implies that the neutron (udd) quark d with charge -1/3 mutates into a quark u with charge +2/3 and inversely the proton (uud) quark u mutates into a quark d. The explanation of the synchronization of these mutations is not straightforward at all since it implies the mutation of charges into different fractional values and also the sign inversion of their electric charge. This would require appealing to hypothetical physical processes which are not evident at all and still less their necessary synchronization between the proton and neutron quarks.
3.b. Yukawa Model
This model implies that a negative pion p- is transferred from the neutron to the proton in order to change their electric charge. This process is much simpler than the equivalent quark one since it does not require the mutation of charges, appealing only to the exchange of a negative integer charge. It is correct in regard to the transfer of a carrier with integer electric charge but it is considered wrong in regard to the nature of the bonding entity and also to the cause of its short range. This process is much less twisted than the gluonic field, which appeals to height different field carriers, and thus with a much higher plausibility. However the Yukawa interpretation of strong interactions has been abandoned in favor of the highly unreliable gluon field of Quantum Chromo Dynamics (QCD).
3.c. Orbital Model
Let us now make the phenomenological description of the proton-neutron inversion from the orbital standpoint. It provides a straightforward answer (expressed in form of an animation of the scattering process) based on the neutron shell which is easily interchanged between protons. It presents some similitude with the Yukawa model but it differs in that instead of appealing to the exchange of a pion carrier it does to the exchange of the neutron shell with the impinging proton.
The orbital model leads straightforwardly to about 50% transmutation. When the proton and the neutron get into close contact the neutron shell gets then shared for a while (the time of interaction) and thus when getting apart again one of the two protons (the core proton of the neutron and the impinging proton) gets the shell, transforming hence into a neutron. Since the shell is equally shared by the two protons thus the probability to get bound to any one of them is thus roughly identical.
The neutron structure is considered embodied by two concentric orbitals with wave functions Y(+) and Y(-). The wave function Y(+) º Y(core) and its associated structural orbital is spun by a positive carrier in the quantum state corresponding to a proton: Y(core) º Y(proton) The wave function Y(-) º Y(shell) and its representative orbital wraps the core proton and is spun by a negative carrier. The orbitals are in different quantum states to which are associated different wave functions: the positive orbital has an energy of 938.27 MeV and corresponds to the one of the proton and the negative orbital is much lighter with an energy of only 1.29 MeV. This low energy orbital is considered to act as a shell and to be highly mutable making it fond of being shared with other protons, while the high energy one acts as a massive and hard core. Let us mention that at low energies of neutron-proton collision, i.e. at thermal neutron energies, n-p capture may occur with some significance (4).
An animation of the scattering process, from the point of view of the orbital model, has been effectuated in order to evidence the simplicity of the invoked process.
References
(1) R. Eisberg and R. Resnick, Quantum Physics, Section 17: Elementary Particles, John Wiley & Sons, Inc. (1974)
(2) Harald A. Endge, Introduction to Nuclear physics, Addison-Wesley Series in Physics (1966)
(3) D.J. Knecht, S. Meselt, E.D. Berners, L.C. Northeliffe, Physics Review 114, 550 (1959)
(4) C.I. Storrs and D.H. Frish, Physics Review 95, 1252 (1954)
(5) E. Melkonian, Physics Review 76, 1750 (1949)
(6) L.J. Rainwater, W.W. Havens, J.R. Dunning, C.S. Wu, Physics Review 73, 733 (1948)
(7) R. K. Adair, Review of Modern Physics 22, 249 (1950)