Excited states of $^4$He are studied in four-body calculations with explicitly correlated Gaussian bases. All the levels below $E_{\rm x}$=26 MeV are reproduced reasonably well using realistic potentials. An analysis is made to show how the $0^+_2$ state becomes a resonance but those having almost the same structure as this state in different spin-isospin channels are not observed as resonances. The role of tensor force is stressed with a particular attention to the level spacing between the two $0^-$ states. The calculation of spectroscopic amplitudes, nucleon decay widths, and spin-dipole transition strengths demonstrates that the $0^+_2$ state and the three lowest-lying negative-parity states with $0^-$ and $2^-$ have $^3$H+$p$ and $^3$He+$n$ cluster configurations, leading to the interpretation that these negative-parity states are the inversion doublet partners of the $0^+_2$ state.
We studied the ground and excited states properties for Zr isotopes starting^M from proton to neutron drip-lines using the relativistic and non-relativistic mean field formalisms with BCS and Bogolyubov pairing. The celebrity NL3 and SLy4 parameter sets are used in the calculations. We find spherical ground and low-lying^M superdeformed excited states in most of the isotopes. Several couples of^M $Ω^π=1/2^{\pm}$ parity doublets configurations are found,^M while analyzing the single-particle energy levels of the superdeformed ^M configurations.
A new way to study the spin-isospin dependence of the $ΞN$ interaction is explored through the energy levels of $ΞNα$ and $ΞNαα$ systems with $α$ being a spectator to attract the $ ΞN$ pair without changing its spin-isospin structure. By using the Gaussian expansion method (GEM) with the state-of-the-art $ΞN$ potential obtained from lattice QCD calculations, it is found that $ΞNαα$ has spin-doublet bound states with $J^π={1^-}$ and $2^-$ in both isospin triplet and singlet channels. The inversion of the $1^-$-$2^-$ spin-doublet between the iso-triplet and the iso-singlet is found to be strongl…
[Background] Various cluster states of astrophysical interest are expected to exist in the excited states of $^{28}{\rm Si}$. However, they have not been identified firmly, because of the experimental and theoretical difficulties. [Purpose] To establish the $^{24}$Mg+$α$, $^{16}$O+$^{12}$C and $^{20}$Ne+2$α$ cluster bands, we theoretically search for the negative-parity cluster bands that are paired with the positive-parity bands to constitute the inversion doublets. We also offer the isoscalar monopole and dipole transitions as a promising probe for the clustering. We numerically show that th…
The hyperfine splitting of the ground and low-energy $3/2^+(7.8 \pm 0.5$ eV) levels in the $^{229}$Th nucleus in muonic atom ($μ^-_{1S_{1/2}}{}^{229}$Th$)^*$ has been calculated considering the distribution of the nuclear magnetization in the framework of collective nuclear model with the wave functions of the Nilsson model for the unpaired neutron. It is shown that (a) the hyperfine splitting of the $3/2^+$ isomeric state is anomalously weak, and the reduction of hyperfine structure in comparison with the model of a point nuclear magnetic dipole is close to 100\%, (b) partial inversion of lev…
Isospin is an approximate symmetry in atomic nuclei, arising from the rather similar properties of protons and neutrons. Perhaps the clearest manifestation of isospin within nuclei is in the near-identical structure of excited states in mirror nuclei: nuclei with inverted numbers of protons and neutrons. Isospin symmetry, and therefore mirror-symmetry, is broken by electromagnetic interactions and the difference in the masses of the up and down quarks. A recent study by Hoff and collaborators presented evidence that the ground-state spin of $^{73}$Sr is different from that of its mirror, $^{73…
Properties of excited states in $^{147}$Nd have been studied with multispectra and $γγ$ coincidence measurements. Twenty-four new $γ$-lines and three new levels have been introduced into the level scheme of $^{147}$Nd. Lifetimes of eight excited levels in $^{147}$Nd, populated in the $β$ decay of $^{147}$Pr, have been measured using the advanced time-delayed $βγγ$(t) method. Reduced transition probabilities have been determined for 30 $γ$-transitions in $^{147}$Nd. Potential energy surfaces on the ($β_{2}$,$β_{3}$) plane calculated for $^{147}$Nd using the Strutinsky method predict two single …
We study masses and decay widths of positive and negative parity nucleons using a three-flavor parity doublet model, in which we introduce three representations, $\left[({\bf 3} , \bar{\bf 3})\oplus (\bar{\bf 3} , {\bf 3})\right]$, $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$, and $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ of the chiral U$(3)_{\rm L}\times$U$(3)_{\rm R}$ symmetry. We find an extended version of the Goldberger-Treiman relation among the mass differences and the coupling constants for pionic transitions. This relation leads to an upper bound fo…
A continuum approach to the three valence-quark bound-state problem in quantum field theory is used to perform a comparative study of the four lightest $(I=1/2,J^P = 1/2^\pm)$ baryon isospin-doublets in order to elucidate their structural similarities and differences. Such analyses predict the presence of nonpointlike, electromagnetically-active quark-quark (diquark) correlations within all baryons; and in these doublets, isoscalar-scalar, isovector-pseudovector, isoscalar-pseudoscalar, and vector diquarks can all play a role. In the two lightest $(1/2,1/2^+)$ doublets, however, scalar and pse…
We investigate the application of the distillation smearing approach, and the use of the variational method with an extended basis of operators facilitated by this approach, on the calculation of the nucleon isovector charges $g_S^{u-d}$, $g_A^{u-d}$, and $g_T^{u-d}$. We find that the better sampling of the lattice enabled through the use of distillation yields a substantial reduction in the statistical uncertainty in comparison with the use of alternative smearing methods, and furthermore, appears to offer better control over the contribution of excited-states compared to use of a single, loc…
