Physical Formulas - Nucleus Latice Energies

Resonance Node Taxonomy

Fundamental Entities

At the present stage of the Roton Quantum Theory (RQT), the fundamental building block of nuclear structures is taken to be the resonance node, denoted by:

$n$

Resonance Node (n)

A resonance node is not itself a particle. Rather, it represents the smallest nuclear-scale resonance entity considered within the current framework.

Resonance nodes occupy places in a lattice-like grid at interconnecting edge distances of the electron resonance distance span (e-span).

The previously introduced concepts Sonon, Roton and Reson serve different general purposes and are therefore not used as the fundamental nuclear building block in this context.

A resonance node may occupy different resonance modes depending on its local environment and resonance closure conditions.

Resonance Modes

Quon Mode (q)

$q$ or $n_q$

The quon mode represents a maximally resonant rotating node.

Characteristics:

• highest internal resonance activity
• characteristic resonance length l_q
• dominant contributor to internal confinement energy as q-span inertia
• energetically associated with the nucleon-scale resonance inventory

The term Quon is retained for this specific resonance mode and is not used as a synonym for the general resonance node.

Stationary Mode (s)

$s$ or $n_s$

The stationary mode represents a resonance node whose rotational degree of freedom is largely suppressed.

Characteristics:

• stationary resonance center
• carries an externally open e-span resonance channel
• associated with observable electric charge
• contributes primarily e-span inertia

Within the current interpretation, stationary nodes act as persistent charge-carrying centers.

Compensation Mode (c)

$c$ or $n_c$

The compensation mode represents a reduced-energy precessional state.

Characteristics:

• lower-energy resonance mode
• not axially stable in isolation
• requires pairing with an opposite compensation mode
• forms a self-compensating resonance channel (c-span)

Compensation nodes therefore naturally occur in pairs:

$c^2$

and may provide stabilization for otherwise unstable resonance configurations.

Nucleon Structures

Proton ($P$)

Isolated proton:

$P = q^3 s$

The proton consists of three quon-mode nodes and one stationary node.

The stationary node provides the persistent open e-span resonance channel associated with positive charge.

Compound proton:

Not considered fundamentally different.

Neutron ($N$)

Isolated neutron:

$N = q^3 c^2$

The neutron consists of three quon-mode nodes and a compensating pair of compensation nodes.

The compensation pair provides a self-stabilizing resonance closure without requiring a stationary charge-carrying node.

Compound Neutron ($N$)

Inside a stable nuclear structure, a neutron is assumed to exist in a different resonance configuration:

$N_{\mathrm{compound}} = q^3$

The surrounding nuclear resonance network provides the stabilization otherwise supplied by the compensation pair.

The compensation nodes therefore emerge only when a neutron becomes isolated.

Composite Nuclear Structures

Deuteron ($D$)

$D = q^6 s$

The deuteron consists of six quon-mode nodes and one stationary node.

The stationary node provides the residual open resonance channel associated with the compound.

Alpha Structure ($\alpha$)

$\alpha = q^{12} s^2$

The alpha structure consists of twelve quon-mode nodes and two stationary nodes.

The alpha configuration represents the simplest fully symmetric and strongly closed nuclear resonance structure presently considered.

Neutron Structures ($\alpha$)

$\nu= n*q^{2}$

Combined Neutron structures might appear in places where a $P$, $D$, $T$ (Tritium) or $\alpha$ cluster would normally sit. They can occupy compound places where a structures with otherwise stationary node(s) $n_s$ would feel too much frustration or symmetrical instability.

Frustrated Lattice positions within the nucleus might for instance be occupied by a $6 x q^2$ (or $q12$) neutron like cluster instead of a charged $\alpha$ type cluster.

Compound structures

All further compound structures are considered as being built from the basic described building blocks: P, N, D, T, A, N2, N4.

Energy Assignment

The present taxonomy distinguishes three energy contributions:

1. Internal Node Inertia

The internal resonance inventory associated with:

$q,\quad s,\quad c$

Each resonance mode contributes a characteristic amount of confined resonance energy.

These contributions are intended to be related to experimentally observed inertia scales (MeV).

2. Compound Resonance Energy

Additional energy emerges from the interaction and confinement of multiple resonance nodes within a common structure.

Examples:

$P,\quad N,\quad D,\quad \alpha$

The compound inertia is therefore not necessarily equal to the simple sum of individual node contributions.

Other binding examples:

• deuteron binding
• external alpha-cluster coupling

3. Residual Separation Energy

A separate energy contribution is assigned to resonance coupling between nuclear compounds.

This quantity corresponds to the residual quon/nucleon separation energy.

Examples include:

• nucleon–nucleon coupling
• maybe deuteron binding
• possible N_2 and N_4 resonance structures
• linear nucleon resonance chains

This residual energy appears only between already-formed nuclear compounds and is conceptually distinct from the internal confinement energy of the resonance nodes themselves.

The long-term objective is to assign experimentally grounded inertia values (MeV) to the resonance modes q, s, and c, and to determine whether the observed proton, neutron, deuteron, alpha-particle, and nuclear binding energies can be reproduced from a consistent resonance-energy bookkeeping scheme.

Prove of concept

This consists of deriving a residual nucleon resonance binding e_r and mapping it to the geometric number of icosahendral links in alpha cluster constellations.

This shows a $e_r$ of around 2.40-2.45 MeV for C-12, O-16 and Si-28 and also when adding excess Neutrons Ne-22: 2.42

Other