The particle-number conserving method based on the cranked shell model is adopted to investigate the possible antimagnetic rotation bands in $^{100}$Pd. The experimental kinematic and dynamic moments of inertia, together with the $B(E2)$ values are r
eproduced quite well. The occupation probability of each neutron and proton orbital in the observed antimagnetic rotation band is analyzed and its configuration is confirmed. The contribution of each major shell to the total angular momentum alignment with rotational frequency in the lowest-lying positive and negative parity bands is analyzed. The level crossing mechanism of these bands is understood clearly. The possible antimagnetic rotation in the negative parity $alpha=0$ branch is predicted, which sensitively depends on the alignment of the neutron ($1g_{7/2}$, $2d_{5/2}$) pseudo-spin partners. The two-shears-like mechanism for this antimagnetic rotation is investigated by examining the closing of the proton hole angular momentum vector towards the neutron angular momentum vector.
The recently observed two and four-quasiparticle high-spin rotational bands in the odd-odd nuclei $^{166, 168, 170, 172}$Re are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method. The e
xperimental moments of inertia and alignments can be reproduced well by the present calculation if appropriate bandhead spins and configurations are assigned for these bands, which in turn confirms their spin and configuration assignments. It is found that the bandhead spins of those two rotational bands observed in $^{166}$Re~[Li {it et al.}, Phys. Rev. C 92 014310 (2015)] should be both increased by $2hbar$ to get in consistent with the systematics of the experimental and calculated moments of inertia for the same configurations in $^{168, 170, 172}$Re. The variations of the backbendings/upbendings with increasing neutron number in these nuclei are investigated. The level crossing mechanism is well understood by analysing the variations of the occupation probabilities of the single-particle states close to the Fermi surface and their contributions to the angular momentum alignment with rotational frequency. In addition, the influence of the deformation driving effects of the proton $1/2^-[541]$ ($h_{9/2}$) orbtial on the level crossing in $^{172}$Re is also discussed.
Despite the large baryon-anti-baryon asymmetry in the observable Universe, the closely related phenomenon -- the violation of the combined charge and parity symmetry ($C!P$V) -- has not been observed in the baryon sector in laboratories. In this pape
r, a new strategy for searching for $C!P$V in heavy hadron multi-body decays is proposed, in which a set of novel observables measuring $C!P$V in such decays -- the partial wave $C!P$ asymmetries (PW$C!P$As) -- are introduced. This strategy is model-independent and applicable to multi-body decays of heavy hadrons with arbitrary spin configurations in both initial and final states, and with any number of particles in the final state. It is especially applicable for $C!P$V investigations in multi-body decays of heavy baryons. As applications of this strategy, we suggest to measure the PW$C!P$As in some decay channels of bottom baryons such as $Lambda_b^0to p pi^-pi^+pi^-$, $Lambda_bto p K^- pi^+pi^-$, $Lambda^0_bto ppi^-K^+K^-$, $Lambda_b^0toLambda K^+pi^-$, and $Lambda_b^0to p pi^- K_s$.}
A novel observable measuring the $C!P$ asymmetry in multi-body decays of heavy mesons, which is called the forward-backward asymmetry induced $C!P$ asymmetry (FBI-$C!P$A), $A_{CP}^{FB}$, is introduced. This observable has the dual advantages that 1)
it can isolate the $C!P$ asymmetry associated with the interference of the $S$- and $P$-wave amplitude from that associated with the $S$- or $P$-wave amplitude alone; 2) it can effectively almost double the statistics comparing to the conventionally defined regional $C!P$ asymmetry. We also suggest to perform the measurements of FBI-$C!P$A in some three-body decay channels of charm and beauty mesons.
The $X(3872)$, whose mass coincides with the $D^0bar D^{*0}$ threshold, is the most extended hadron object. Since its discovery in 2003, debates have never stopped regarding its internal structure. We propose a new object, the $X$ atom, which is the
$D^pm D^{*mp}$ composite system with positive charge parity and a mass of $(3879.89pm0.07)$ MeV, formed mainly due to the Coulomb force. We show that a null signal of the $X$ atom can be used to put a lower limit on the binding energy of the $X(3872)$. From the current knowledge of the $X(3872)$ properties, the production rate for the $X$ atom relative to the $X(3872)$ in $B$ decays and at hadron colliders should be at least $1times10^{-3}$. New insights into the $X(3872)$ will be obtained through studying the $X$ atom.
We study the $CP$ asymmetry of $B^pmto omega K^pm$ with the inclusion of the $rho-omega$ mixing mechanism. It is shown that the $CP$ asymmetry of $B^pmtoomega K^pm$ experimentally measured ($A_{CP}^{text{exp}}$) and conventionally defined ($A_{CP}^{t
ext{con}}$) are in fact different, which relation can be illustrated as $A_{CP}^{text{exp}}=A_{CP}^{text{con}}+Delta A_{CP}^{rhoomega}$, with $Delta A_{CP}^{rhoomega}$ the $rho-omega$ mixing contribution to $A_{CP}^{text{exp}}$. $A_{CP}^{text{exp}}$ is in fact the regional $CP$ asymmetry of $B^pmtopi^+pi^-pi^0 K^pm$ when the invariant mass of the three pions lies in the vicinity of the $omega$ resonance. The numerical value of $Delta A_{CP}^{rhoomega}$ is extracted from the experimental data of $B^pmtopi^+pi^-K^pm$ and is found to be comparable with $A_{CP}^{text{exp}}$, hence, nonnegligible. The conventionally defined $CP$ asymmetry, $A_{CP}^{text{con}}$, is obtained from the values of $A_{CP}^{text{exp}}$ and $Delta A_{CP}^{rhoomega}$, and is compared with the theoretical calculations in the literature.
High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number
projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.
The rotational bands in the neutron-rich nuclei $^{153-157}$Pm are investigated by a particle-number conserving method. The kinematic moments of inertia for the 1-quasiparticle bands in odd-$A$ Pm isotopes $^{153, 155, 157}$Pm are reproduced quite we
ll by the present calculation. By comparison between the experimental and calculated moments of inertia for the three 2-quasiparticle bands in the odd-odd nuclei $^{154, 156}$Pm, their configurations and bandhead spins have been assigned properly. For the 2-quasiparticle band in $^{154}$Pm, the configuration is assigned as $pi5/2^-[532]otimes u3/2^-[521]$ ($K^pi=4^+$) with the bandhead spin $I_0=4hbar$. In $^{156}$Pm, the same configuration and bandhead spin assignments have been made for the 2-quasiparticle band with lower excitation energy. The configuration $pi5/2^+[413]otimes u5/2^+[642]$ ($K^pi=5^+$) with the bandhead spin $I_0=5hbar$ is assigned for that with higher excitation energy.
The particle-number-conserving method based on the cranked shell model is used to investigate the antimagnetic rotation band in $^{104}$Pd. The experimental moments of inertia and reduced $B(E2)$ transition probabilities are reproduced well. The $J^{
(2)}/B(E2)$ ratios are also discussed. The occupation probability of each orbital close to the Fermi surface and the contribution of each major shell to the total angular momentum alignment with rotational frequency are analyzed. The backbending mechanism of the ground state band in $^{104}$Pd is understood clearly and the configuration of the antimagnetic rotation after backbending is clarified. In addition, the crossing of a four quasiparticle states with this antimagnetic rotation band is also predicted. By examining the the closing of the four proton hole angular momenta towards the neutron angular momenta, the two-shears-like mechanism for this antimagnetic rotation is investigated and two stages of antimagnetic rotation in $^{104}$Pd are seen clearly.
The multi-particle states and rotational properties of two-particle bands in $^{254}$No are investigated by the cranked shell model (CSM) with pairing correlations treated by a particle-number conserving (PNC) method. For the first time, the rotation
al bands on top of two-particle $K^{pi}=3^+,8^-$ and $10^+$ states and the pairing reduction are studied theoretically in $^{254}$No. The experimental excitation energies and moments of inertia for the multi-particle state are reproduced well by the calculation. Better agreement with the data are achieved by including the high-order deformation $varepsilon_{6}$ which leads to enlarged $Z=100$ and $N=152$ deformed shell gaps. The rise of the $J^{(1)}$ in these two-particle bands compared with the ground-state band is attributed to the pairing reduction due to the Pauli blocking effects.
