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Register a new userPossible chiral symmetry in $^{138}$Nd
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The pheomenological Generalized Coherent State Model Hamiltonian is amended with a many body term describing a set of nucleons moving in a shell model mean-field and interacting among themselves with paring, as well as with a particle-core interaction involving a quadrupole-quadrupole and a hexadecapole-hexdecapole force and a spin-spin interaction. The model Hamiltonian is treated in a restricted space consisting of the core projected states associated to the bands ground, $beta, gamma,widetilde{gamma}, 1^+$ and $widetilde{1^+}$ and two proton aligned quasiparticles coupled to the states of the ground band. The chirally transformed particle-core states are also included. The Hamiltonian contains two terms which are not invariant to the chiral transformations relating the right handed trihedral $({bf J_F}, {bf J_p}, {bf J_n})$ and the left handed ones $(-{bf J_F}, {bf J_p}, {bf J_n})$, $({bf J_F}, -{bf J_p}, {bf J_n})$, $({bf J_F}, {bf J_p}, -{bf J_n})$ where ${bf J_F}, {bf J_p}, {bf J_n}$ are the angular momenta carried by fermions, proton and neutron bosons, respectively. The energies defined with the particle-core states form four chiral bands, two of them being degenerate. Electromagnetic properties of the chiral bands are investigated. Results are compared with the experimental data on $^{138}$Nd.
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A triaxial projected shell model including configurations with more than four quasiparticles in the configuration space is developed, and applied to investigate the recently reported five chiral doublets candidates in a single even-even nucleus $^{136}$Nd. The energy spectra and transition probability ratios $B(M1)/B(E2)$ are reproduced satisfactorily. The configuration mixing along the rotational bands is studied by analyzing the intrinsic composition of the eigenfunctions. The chiral geometry of these nearly degenerate bands is examined by the textit{K plot} and the textit{azimuthal plot}, and the evolution from the chiral vibration to the static chirality with spin is clearly demonstrated for four pairs of partner bands. From the features in the textit{azimuthal plot}, it is difficult to interpret the other candidate as chiral partners.
Soft-pion theorems are used to show how chiral symmetry constrains the contributions of low-momentum pions to the quark condensate, the pion decay constant and hadron masses, all of which have been proposed as signals of partial restoration of chiral symmetry in matter. These have contributions of order T^2 for a pion gas or of order m_pi for cold nuclear matter, which have different coefficients in all three cases, showing that there are no simple relations between the changes to these quantities in matter. In particular, such contributions are absent from the masses of vector mesons and nucleons and so these masses cannot scale as any simple function of the quark condensate. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.
Two new bands have been identified in $^{137}$Nd from a high-statistics JUROGAM II gamma-ray spectroscopy experiment. Constrained density functional theory and particle rotor model calculations are used to assign configurations and investigate the band properties, which are well described and understood. It is demonstrated that these two new bands can be interpreted as chiral partners of previously known three-quasiparticle positive- and negative-parity bands. The newly observed chiral doublet bands in $^{137}$Nd represent an important support to the existence of multiple chiral bands in nuclei. The present results constitute the missing stone in the series of Nd nuclei showing multiple chiral bands, which becomes the most extended sequence of nuclei presenting multiple chiral bands in the Segre chart.
We review the main achievements of the research programme for the study of nuclear forces in the framework of chiral symmetry and discuss some problems which are still open.
We study the nuclear modification of the scalar QCD susceptibility, calculated as the derivative of the quark condensate with respect to the quark mass. We show that it has two origins. One is the low lying nuclear excitations. At normal nuclear density this part is constrained by the nuclear incompressibility. The other part arises from the individual nucleon response and it is dominated by the pion cloud contribution. Numerically the first contribution dominates. The resulting increase in magnitude of the scalar susceptibility at normal density is such that it becomes close to the pseudoscalar susceptibility, while it is quite different in the vacuum. We interpret it as a consequence of chiral symmetry restoration in nuclei.
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