First observation of multi-phonon $γ$-vibrations in an odd-odd nuclear system

The identification of the first multi-phonon $γ$-vibrational bands in an odd-odd neutron-rich nucleus of the nuclear chart is presented. These high spin structures of hard to access $^{104}{41}$Nb${63}$, produced in fission, were studied by combining a spectrometer with isotopic resolution coupled to a $γ$-ray tracking array and independently high-fold $γ$ coincidence measurements. Triaxial Projected Shell Model calculations for the high-spin states are in good agreement with the measured observables for the yrast, one-phonon and two-phonon $γ$ bands. The possibility of an oblate shape of an isomeric state and coexistence of triaxial and oblate configurations are investigated from the decay of the 141 keV isomer. The present work illustrates the robustness of vibration excitations in the presence of odd valence proton and neutron as well as the possibly coexisting shapes beyond the $N=60$ transitional region.

💡 Research Summary

The paper reports the first observation of multi‑phonon γ‑vibrational bands in an odd‑odd, neutron‑rich nucleus, ⁴¹Nb₆₃ (ⁱ⁴⁰⁴Nb). High‑spin structures of this hard‑to‑access isotope were investigated using two complementary experimental approaches. The first employed a ²⁵²Cf spontaneous fission source with a high‑purity germanium detector array (Gammasphere) to acquire three‑ and four‑fold γ‑coincidence data. The second used a ²³⁸U beam on a ⁹Be target at GANIL, where fission fragments were identified event‑by‑event with the VAMOS++ spectrometer (providing A and Z via Bρ and velocity measurements) while prompt γ rays were recorded with the AGATA tracking array and delayed γ rays with EXOGAM. This combination allowed unambiguous assignment of γ rays to ¹⁰⁴Nb, the separation of prompt high‑spin yrast cascades from the low‑spin 141 keV isomeric decay (T₁/₂≈5 s), and the construction of a comprehensive level scheme comprising seven rotational bands and additional levels.

The key result is the identification of a one‑phonon (K = 7) and a two‑phonon (K = 9) γ‑vibrational band built on the yrast (K = 5) band. Their band‑head energies (≈656 keV for the 1γ band and ≈1.19 MeV for the 2γ band) lie well below the proton (2Δₚ≈1.7 MeV) and neutron (2Δₙ≈2.1 MeV) pairing gaps, ruling out a simple four‑quasiparticle interpretation. The high K values cannot be generated by coupling a single proton and a single neutron (each with K≤5/2), indicating that the excitations are collective γ‑phonons. Angular‑correlation measurements of the 656 → 532 keV cascade give A₂ = 0.09(3) and A₄ = 0.02(5), consistent with pure E2 character. Extracted B(M1)/B(E2) ratios and (g_K–g_R)/Q₀ values are ~0.07–0.08 for all three bands, demonstrating that the multi‑phonon γ‑bands share the same electromagnetic properties as the ground‑state band, as expected for K‑conserving rotational structures.

The experimental observables were reproduced with the Triaxial Projected Shell Model (TPSM). Using deformation parameters ε = 0.32, ε′ = 0.19 and pairing strengths G₁ = 20.12 MeV, G₂ = 13.13 MeV, the model space includes one neutron coupled to one proton, three protons coupled to one proton, and three protons coupled to three neutrons. TPSM calculations generate three low‑lying bands with K = 5, 7, 9 that correspond precisely to the observed yrast, 1γ, and 2γ bands. The calculated energies, moments of inertia J(1), and B(M1)/B(E2) ratios match the data, confirming that the observed bands are indeed multi‑phonon γ‑vibrations rather than multi‑quasiparticle excitations. Notably, the moments of inertia of the 0γ, 1γ, and 2γ bands are essentially identical, a hallmark of vibrational, not rotational, behavior.

The delayed γ‑ray spectrum reveals a 141 keV transition feeding a low‑spin band (band 6) associated with a known isomeric state (T₁/₂≈4.9 s). Analysis of its decay pattern and g‑factor suggests an oblate shape for the isomer, in contrast to the triaxial shape inferred for the high‑spin bands. This points to a possible shape coexistence scenario in ¹⁰⁴Nb, where triaxial γ‑vibrational structures coexist with an oblate configuration at low spin.

In summary, the work (i) provides the first experimental evidence of one‑ and two‑phonon γ‑vibrational bands in an odd‑odd nucleus, (ii) demonstrates the feasibility of combining high‑resolution γ‑tracking with event‑by‑event fragment identification to study weakly populated high‑spin states in neutron‑rich fission fragments, (iii) validates the TPSM as a reliable tool for describing multi‑phonon excitations in odd‑odd systems, and (iv) uncovers possible shape coexistence beyond the N = 60 transitional region. These findings broaden our understanding of collective excitations in complex many‑body quantum systems and highlight the robustness of vibrational modes even in the presence of unpaired valence nucleons.