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Role of tensor forces in nuclei

Yu. P. Lyakhno

TL;DR

Tensor forces in realistic nucleon-nucleon interactions are shown to profoundly influence clustering and reaction pathways in nuclei with $A>4$. Using NN potentials such as CD-Bonn and AV18 with partial waves up to $J≤4$, and modeling the interaction in a four-dimensional space (distance, L, S, T), the work demonstrates that tensor forces modify internal configurations while preserving external quantum numbers. Zero-L subsystems predominantly form $^1S_0$ clusters, whereas nonzero-L subsystems prefer lower-energy configurations like $^5D_0$, enabling explanations for the long lifetime of $^8$Be and the Hoyle state in $^{12}$C, as well as shifted thresholds for sequential $ abla$-emission processes; estimates include $E_ ext{threshold}$ around 7.65 MeV for $^{12}$C breakup and about 15.01 MeV for $^{16}$O into 4α, with corrections tied to $ riangle M(D)$. The analysis argues against a universal 'power center' in the nucleus and emphasizes the natural role of the Pauli exclusion principle, suggesting broad implications for clustering and reaction mechanisms in medium-to-heavy nuclei.

Abstract

Recently, calculations of the ground states of the lightest nuclei have been performed using highly accurate data on realistic internucleon forces. In this paper, these results were used to describe the properties of nuclei with nucleon numbers $A>4$. Taking into account tensor forces leads to the conclusion that the four subsystems in the nucleus with zero nucleon orbital momenta are combined predominantly into the $^1S_0$ cluster. Subsystems with nonzero orbital momenta also combine into clusters with lower potential energy. This approach allows us to consistently explain the lifetime of the $^8$Be nucleus, the Hoyle state, the sequential mechanism of the reaction with the emission of $α$ particles, the shift of the reaction threshold, and more. The assumption of the existence of a one-dimensional effective interaction of nucleons in the nucleus leads to the conclusion that the nucleus contains a "power center" and, accordingly, nucleons have orbital angular momenta relative to this "power center." Our approach does not predict the presence of such a "power center" in the nucleus.

Role of tensor forces in nuclei

TL;DR

Tensor forces in realistic nucleon-nucleon interactions are shown to profoundly influence clustering and reaction pathways in nuclei with . Using NN potentials such as CD-Bonn and AV18 with partial waves up to , and modeling the interaction in a four-dimensional space (distance, L, S, T), the work demonstrates that tensor forces modify internal configurations while preserving external quantum numbers. Zero-L subsystems predominantly form clusters, whereas nonzero-L subsystems prefer lower-energy configurations like , enabling explanations for the long lifetime of Be and the Hoyle state in C, as well as shifted thresholds for sequential -emission processes; estimates include around 7.65 MeV for C breakup and about 15.01 MeV for O into 4α, with corrections tied to . The analysis argues against a universal 'power center' in the nucleus and emphasizes the natural role of the Pauli exclusion principle, suggesting broad implications for clustering and reaction mechanisms in medium-to-heavy nuclei.

Abstract

Recently, calculations of the ground states of the lightest nuclei have been performed using highly accurate data on realistic internucleon forces. In this paper, these results were used to describe the properties of nuclei with nucleon numbers . Taking into account tensor forces leads to the conclusion that the four subsystems in the nucleus with zero nucleon orbital momenta are combined predominantly into the cluster. Subsystems with nonzero orbital momenta also combine into clusters with lower potential energy. This approach allows us to consistently explain the lifetime of the Be nucleus, the Hoyle state, the sequential mechanism of the reaction with the emission of particles, the shift of the reaction threshold, and more. The assumption of the existence of a one-dimensional effective interaction of nucleons in the nucleus leads to the conclusion that the nucleus contains a "power center" and, accordingly, nucleons have orbital angular momenta relative to this "power center." Our approach does not predict the presence of such a "power center" in the nucleus.

Paper Structure

This paper contains 3 sections, 2 figures.

Table of Contents

  1. Introduction
  2. Discussion of the structure of nuclei with the number of nucleons $A>4$ based on realistic NN interaction.
  3. Conclusions

Figures (2)

  • Figure 1: Phases $\delta$ and mixing coefficients $\varepsilon$ for np scattering with a) T=0 and b) T=1 for NN potential CD-Bonn up to the total angular momentum of the two-nucleon system J$\leq$4.
  • Figure 2: Possible configurations of nucleons in a) S and b) D clusters in nuclei. Arrows indicate the direction of nucleon spins.