Probing the shape evolution and shell structures in neutron-rich N=50 nuclei

TL;DR

The paper develops a VS-IMSRG($3f_2$)–based shell-model Hamiltonian in the $p$-$\nu(sdg)$ space and employs the advanced Monte Carlo Shell Model to study shape evolution and shell structures around $N=50$. By minimally correcting single-particle energies and analyzing intrinsic deformation through T-plots and ESPEs, it reproduces the observed shell-closure behavior in $^{78}$Ni while revealing a deformed excited band and shape coexistence. The work highlights central-force–driven intruder configurations as the main mechanism for deformation in $^{78}$Ni, rather than tensor-monopole effects, and shows consistent results with other ab initio and shell-model predictions across nearby isotones. This approach provides a scalable, first-principles–informed path to understand shell evolution and collective phenomena in neutron-rich nuclei near doubly magic regions.

Abstract

The structure of low-lying states of $N=50$ nuclei is investigated by the advanced Monte Carlo shell model (MCSM) in the $π{(fp)}$-$ν{(sdg)}$ model space. We have employed the shell-model Hamiltonian based on the valence-space in-medium similarity renormalization group, with minimal phenomenological adjustments to the single-particle energies. The MCSM results with the modified Hamiltonian nicely predict the shape coexistence of $^{78}$Ni, consistent with recent experimental data. The evolution of intrinsic shapes from the spherical shape to prolate shapes in the ground state of $N=50$ nuclei is discussed using the "T-plot" and effective single-particle energies, which visualize the intrinsic quadrupole deformation of the MCSM wave function. The present result shows that the monopole part of the tensor force does not enhance the shape coexistence of $^{78}$Ni, unlike the case of $^{68}$Ni.

Figures (5)

• Figure 1: First $2^+$ excitation energies of the Cr, Fe, Ni, and Zn isotope chains with $N= 44-54$ compared with the available experimental data nndc2024.
• Figure 2: Energy levels of $^{78}$Ni obtained from the present MCSM calculations (labeled with MCSM) in comparison to the available experimental data Tanuuchi2019nature and several theoretical predictions such as the MCSM calculations with the extended version of A3DA Hamiltonian (labeled with A3DAext) Tanuuchi2019nature, large-scale shell model calculation with PFSDG-U interaction (labeled with PFSDG-U) Nowacki2016PRL, and two more recent ab initio calculations, namely the coupled-cluster (CC) calculations HU2024PLB and the valence-space density matrix renormalization group (VS-DMRG) TICHAI2024PLB. The $B(E2; 2^+\to 0_2^+)$ values are depicted by arrow in ${\rm e}^2{\rm fm}^4$ units.
• Figure 3: The MCSM excitation energy spectra of the $^{76}$Fe, $^{74}$Cr, and $^{72}$Ti with the modified VS-IMSRG($3{\rm f}_2$) in comparison to large-scale shell models predicted with PFSDG-U interaction Nowacki2016PRL, coupled-cluster (CC) calculations HU2024PLB, and valence-space density matrix renormalization group (VS-DMRG) TICHAI2024PLB. The $B(E2;2^+_1\to 0_1^+)$ values are depicted by the arrow in ${\rm e}^2{\rm fm^4}$ units.
• Figure 4: Potential energy surfaces (PESs) of $N=50$ nuclei with $Z=22-30$, which is coordinated by the intrinsic quadrupole $Q_0$ and $Q_2$. The circles on PESs demonstrate the shapes of the MCSM basis vectors (see the text).
• Figure 5: Calculated effective single-particle energies (ESPEs) for (a) the protons as a function of neutron number, (b) the $0_1^+$ ground state and the $0^+_2$ state, (c) the neutrons as a function of neutron number and (d) the ground state $0_1^+$ and first excited state $0^+_2$ using the occupation number of the resultant MCSM wave function.