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Generalised Bohr Hamiltonian for Gogny interactions

C. Azam, D. Davesne, Y. Lallouet, L. Próchniak, M. Frosini, A. Pastore

TL;DR

The paper addresses describing quadrupole collective excitations in even-even Gd isotopes using a generalised Bohr Hamiltonian (BH) with microscopic mass parameters derived from constrained HFB calculations based on Gogny interactions. The mass parameters are obtained via perturbative cranking and the collective potential $V_{pot}$ is computed for each isotope, with spectra and $B(E2;2^+ o 0^+)$ transitions obtained by diagonalizing the BH in a $eta$-$ abla$ basis. Across Gogny parametrisations ($D1S$, $D1N$, $D1M$, $D3G3M$), the low-lying energies and $B(E2)$ values are largely insensitive to the chosen interaction and agree well with experimental data; for example, $^{154}$Gd shows a prolate minimum at $eta \,\approx \,0.3$. The study demonstrates robustness and computational efficiency of using a microscopic input BH framework for systematic nuclear spectroscopy along an isotopic chain, while noting limitations from the cranking approximation that tends to underpredict high-energy level densities.

Abstract

Using a generalised Bohr Hamiltonian formalism together with the Gogny interaction to provide a microscopic input of the required mass parameters, we present the potential energy surface and the evolution of the first excited 2$^+$ state for the gadolinium isotopic chain. We observe that the energies and electromagnetic transitions of low-lying states are fairly similar for the various parametrisations and are in good agreement with experimental data.

Generalised Bohr Hamiltonian for Gogny interactions

TL;DR

The paper addresses describing quadrupole collective excitations in even-even Gd isotopes using a generalised Bohr Hamiltonian (BH) with microscopic mass parameters derived from constrained HFB calculations based on Gogny interactions. The mass parameters are obtained via perturbative cranking and the collective potential is computed for each isotope, with spectra and transitions obtained by diagonalizing the BH in a - basis. Across Gogny parametrisations (, , , ), the low-lying energies and values are largely insensitive to the chosen interaction and agree well with experimental data; for example, Gd shows a prolate minimum at . The study demonstrates robustness and computational efficiency of using a microscopic input BH framework for systematic nuclear spectroscopy along an isotopic chain, while noting limitations from the cranking approximation that tends to underpredict high-energy level densities.

Abstract

Using a generalised Bohr Hamiltonian formalism together with the Gogny interaction to provide a microscopic input of the required mass parameters, we present the potential energy surface and the evolution of the first excited 2 state for the gadolinium isotopic chain. We observe that the energies and electromagnetic transitions of low-lying states are fairly similar for the various parametrisations and are in good agreement with experimental data.

Paper Structure

This paper contains 4 sections, 4 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Formalism
  3. Results
  4. Conclusions

Figures (3)

  • Figure 1: Potential energy surface $V_{pot}$, expressed in MeV, of the $^{154}$Gd obtained with HFB constrained calculations with the Gogny effective interaction D3G3M re-scaled to its energy minimum. The contour lines connect points of equal energy.
  • Figure 2: Experimental (EXP) data, taken from ENSDF database ENSDF, and calculated (BH) level schemes (expressed in keV) with D3G3M and the corresponding electromagnetic transition strengths (in Weisskopf units) for $^{154}$Gd.
  • Figure 3: Evolution of the first excited $2^+$ level and the B$(E2;2^+ \to 0^+)$ transition strength for $^{152-160}$Gd. Dashed lines correspond to BH calculations with various Gogny interactions, while the solid line denotes the experimental data.