Lifetime of resonant state in a spherical quantum dot

This paper calculates the lifetime of resonant state and transmission probability of a single electron tunnelling in a spherical quantum dot （SQD） structure by using the transfer matrix technique. In the SQD, the electron is confined both transversally and longitudinally, the motion in the transverse and longitudinal directions is separated by using the adiabatic approximation theory. Meanwhile, the energy levels of the former are considered as the effective confining potential. The numerical calculations are carried out for the SQD consisting of GaAs/InAs material. The obtained results show that the bigger radius of the quantum dot not only leads significantly to the shifts of resonant peaks toward the low-energy region, but also causes the lengthening of the lifetime of resonant state. The lifetime of resonant state can be calculated from the uncertainty principle between the energy half width and lifetime.

New measurement of 4^(H)e and proton decays from resonant states in^(19)Ne

A^(6)Li(^(16)O,^(19)Ne^(∗))^(3)H multi-nucleon transfer-reaction experiment was performed to populate the highly excited states in^(19)Ne.The subsequent decay particles,^(4)He or protons from the^(19)Ne resonant states,were detected in coincidence with the recoil 3 H.The excitation-energy spectra of^(19)Ne were reconstructed using the detected proton or^(4)He and the deduced^(18)F or^(15)O data,respectively.A broad resonance at about 7.85 MeV(1/2^(+))was observed,with partial decay widths different from the previously reported values,which may have a significant impact on the destruction of 18 F in astrophysical processes.Several resonances up to very high excitation energies have been identified with a largeα-clustering strength,which confirm the formation of the cluster structure with a one-hole configuration in light nuclei and encourage further systematic studies of the cluster structure in^(19)Ne.

Explanation of Y(4630) as a hadronic resonant state

Theorists have given various explanations for the discovery of Y(4630).We find that if Y(4630)is inter-preted as the D-wave resonant state of the ∧_(c)∧_(c)。system,the particle mass,decay width,and all quantum numbers are consistent with experimental observations.We use the Bonn approximation to obtain the interaction potential of the one boson exchange model.Then,we extend the complex scaling method to calculate the bound and resonant states.The results indicate that the ∧_(c)∧_(c) system can form not only the bound state of the S wave but also the reson-ant state of the high angular momentum,and the ^(3)D_(1) wave resonant state can explain the structure of Y(4630)very Well.

Influence of different fields of mesons on the pseudospin symmetry in single-neutron resonant states

In the framework of the relativistic mean field theory combined with the complex momentum representation method,we elucidate the pseudospin symmetry in the single-neutron resonant states and its dependence on the σ,ω,and ρ meson fields.Compared with the effect of theρfield,the τandωfields provide the main contributions to the pseudospin energy and width splitting of the resonant pseudospin doublets.Especially,we compare quantitatively the pseudospin wave functions's plittings in resonant doublets,and investigate their dependencies on different fields of mesons,which is consistent with that of energy and width splittings.Current research is helpful to understand the mechanism and properties of pseudospin symmetry for resonant states.

Single-particle resonant states with Green’s function method

This study employs the relativistic mean field theory with the Green's function method to study the single-particle resonant states.In contrast to our previous work[Phys.Rev.C,90:054321(2014)],the resonant states are identified by searching for the poles of Green's function or the extremes of the density of states.This new approach is highly effective for all kinds of resonant states,no matter whether they are broad or narrow.The dependence on the space size for the resonant energies,widths,and the density distributions in the coordinate space has been checked and was found to be very stable.Taking ^120Sn as an example,four new broad resonant states 2g7/2,2g9/2,2h11/2,and 1j13/2 were observed,and the accuracy for the width of the very narrow resonant state 1h9/2 was highly improved to 1×10^−8 MeV.Further,our results are very close to those obtained using the complex momentum representation method and the complex scaling method.

Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

The breaking of spin symmetry in the single-particle resonances in deformed nuclei

The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.

Fukui Functions for the Temporary Anion Resonance States of Be^-, Mg^-, and Ca^-

In this work,the Fukui functions of the two ~2P resonance states of Be,a ~2P resonance state of Mg~–,and a ~2D resonance state of Ca~– have been determined.The trajectories of these resonance states,in conjunction with the complex rotation of the Hamiltonian,were used to determine their wave functions.The electron densities,Fukui functions,and values of the hyper-radius<r^2>were computed from these wave functions.The Fukui functions have negative regions in the valence shell in addition to the inner shell regions,indicating screening effects of the outer temporary electron.Selected configuration interactions with up to quadruple excitations were used along the trajectories and for computing the final wave function.Based on this data,the densities,Fukui functions,and<r^2>were calculated.

Scattering Resonance States and Partial Potential Energy Surface of Reaction I+HI(v=0)→IH(v′=0) +I

The partial potential energy surface of the I ＋ HI →IH ＋ I reaction involving the translational and vibrational motions has been constructed at the QCISD（ T ）//MP4SDQ level with the pseudo potential method that is helpful to interpreting the scattering resonance states. The lifetimes of the scattering resonance states in the title reaction obtained from the partial potential energy surface are about 90-120 fs, which agrees with the result of high-resolved threshold photodetachment spectroscopy of anion IHI^- measured by Neumark.

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

Theoretical Studies on Formation Mechanism of Resonance States for Na+I_2→Na^++I_2^-System

An extended linear combination of arrangement channels-scattering wave-function(LCAC-SW) quantum scattering dynamic method combined with ab initio quantum chemical calculation was used to study the formation mechanism of the resonance states for the collinear Na+I 2→Na ++I - 2 ion-pair formation process on Aten-Lanting-Los potential energy surface. The resonance energy and the resonance width or the lifetime for the first resonance peak were calculated. The resonance can be identified as the Feshbach type and the physical interpretation is given. The geometric structure of the resonance state for the title system has been optimized.

Theoretical Study of the Scattering Resonance State, Reaction Mechanism and Partial Potential Energy Surface of the F+CH4→HF+CH3 Reaction

The partial potential energy surface was constructed by ab initio method [QCISD（T）/6- 311＋＋G（2df,2pd）]for F＋CH4→HF＋CH3 reaction system. It not only explained the reaction mechanism brought forward by Diego Troya by means of quasiclassical trajectory （QCT） but also successfully validated Kopin Liu＇s experimental phenomena about the existence of the reactive resonance. The lifetime of the scattering resonance state was about 0.07 ps. All these were in agreement with the experiments.

Generating Squeezed States of Nanomechanical Resonator via a Flux Qubit in a Hybrid System

We propose a scheme for generating squeezed states based on a superconducting hybrid system. Our system consists of a nanomeehanical resonator, a superconducting flux qubit, and a superconducting transmission line resonator. Using our proposal, one can easily generate the squeezed states of the nanomechanical resonator. In our scheme, the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as ＇nonlinear media＇ with a tunable Josephson energy. The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state, which can greatly decrease the effect of the decoherenee of the flux qubit on the squeezed ef^ciency.

Research on the influence of quadrupole deformation and continuum effects on the exotic properties of 15,17,19B with the complex momentum representation method

The properties of exotic nuclei are the focus of the present research.Two-neutron halo structures of neutron-rich17,19B were experimentally confirmed.We studied the formation mechanism of halo phenomena in17,19B using the complex momentum representation method applied to deformation and continuum coupling.By examining the evolution of the weakly bound and resonant levels near the Fermi surface,s–d orbital reversals and certain prolate deformations were observed.In addition,by analyzing the evolution of the occupation probabilities and density distributions occupied by valence neutrons,we found that the ground state of15B did not exhibit a halo and the ground states of17B and19B exhibited halos at 0.6≤β2≤0.7 and0.3≤β2≤0.7,respectively.The low-l components in the valence levels that are weakly bound or embedded in the continuous spectrum lead to halo formation.

Fano Resonances Can Provide Two Criteria to Distinguish Majorana Bound States from Other Candidates in Experiments

There are still debates on whether the observed zero energy peak in the experiment by Stevan et al. [Science 346 （2014） 602] reveals the existence of the long pursued Ala.jorana bound states （MBSs）. We propose that, by mounting two scanning tunneling microscopic tips on top of the topological superconducting chain and measuring the transmission spectrum between these two metallic tips, there are two kinds of characteristics on the spectrum that are caused by A.IBSs uniquely： One is symmetric peaks with respect to zero energy and the other is 4~r period caused by a nearby dosephson junction. The former refers to the fact that MBSs are eomposited by Alajorana fermions which distributed in the particle and hole subspaees equally. The latter is based on the well known 4w period of Josephson effect in topological superconductor. We think that such two characteristics can be used as criteria to distinguish MBSs from other candidates, such as impurities, Kondo effect and traditional Andreev bound states.

Exploration of the ground state properties of neutron-rich sodium isotopes using the deformed relativistic mean field theory in complex momentumrepresentations with BCS pairings

This study explores the ground-state characteristics of neutron-rich sodium isotopes,encompassing two-neutron separation energies,root-mean-square radii,quadrupole moments of proton and neutron distributions,single-particle levels of bound and resonant states,and neutron density distributions and shapes.Simultaneously,special attention is paid to the distinctive physical phenomena associated with these isotopes.The deformed relativistic mean field theory in complex momentum representations with BCS pairings(DRMF-CMR-BCS)employed in our research provides resonant states with real physics,offering insights into deformed halo nuclei.Four effective interactions(NL3,NL3^(*),PK1,and NLSH)were considered to assess the influence of continuum and deformation effects on halo structures.Calculations for odd-even nuclei ^(35–43)Na revealed the dependence on the chosen effective interaction and number of considered resonant states.Neutron occupation patterns near the Fermi surface,particularly in orbitals 1/2^(−)_(3) and 3/2^(−)_(2),were determined to be crucial in halo formation.The study provided detailed insights into the density distributions,shape evolution,and structure of neutron-rich sodium isotopes,contributing valuably to the field of nuclear physics.

Spectroscopic factors of resonance states with the Gamow shell model

We provide an investigation of the spectroscopic factor of resonance states in A=5-8 nuclei,utilizing the Gamow shell model(GSM).Within the GSM,the configuration mixing is taken into account exactly with the shell model framework,and the continuum coupling is addressed via the complex-energy Berggren ensemble,which treats bound,resonance,and non-resonant continuum single-particle states on an equal footing.As a result,both the configuration mixing and continuum coupling are meticulously considered in the GSM.We first calculate the low-lying states of helium isotopes and isotones with the GSM,and the results are compared with that of ab initio no-core shell model(NCSM)calculations.The results indicate that GSM can reproduce the low-lying resonance states more accurately than the NCSM.Following this,we delve into the spectroscopic factors of the resonance states as computed through both GSM and NCSM,concurrently conducting systematic calculations of overlap functions pertinent to these resonance states.Finally,the calculated overlap function and spectroscopic factor of6He(01+)■νp3/2→^(7)He(3/2_(1)-)with GSM are compared with the results from ab initio NCSM,variational Monte Carlo,and Green’s function Monte Carlo calculations,as well as available experimental data.The results assert that wave function asymptotes can only be reproduced in GSM,where resonance and continuum coupling are precisely addressed.

Properties of Titanium isotopes in complex momentum representation within relativistic mean-field theory

The self-consistent quadruple potential is deduced within the relativistic mean-field(RMF)framework and substituted into the Hamiltonian,which is calculated using the complex momentum representation(CMR).Considering even-even titanium isotopes as an example,this study investigated various properties,including the resonant states of neutron-rich nuclei in the RMF-CMR model,and used them to describe the binding energy.The abrupt decrease in the two-neutron separation energy(S_(2n))corresponds to the traditional magic number.The resonant and bound states are simultaneously exposed in the complex moment plane,where the continuum is along the integration contour.The four oblate neutron-rich nuclei^(72-78)Ti are weakly bound or resonant because their Fermi energies are approximately 0 MeV.The root-meansquare(RMS)radii of these nuclei increase suddenly compared with those of others(neutron number N<48).Moreover,^(78)Ti and^(76)Ti are determined as drip-line nucleons by the value of S_(2n) and the energy levels,respectively.Finally,the weak-bounded character can be represented by diffuse density probability distributions.

Complex coordinate rotation method based on gradient optimization

In atomic,molecular,and nuclear physics,the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states.Here,we propose a novel implementation of this method based on the gradient optimization(CCR-GO).The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function;instead,a mathematically well-defined optimization path can be followed.Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems,and can significantly improve the accuracy of the results.As a special case,the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy,which is traditionally achieved through the usual extreme conditions of energy itself.

Efficacy of acupuncture at ghost points combined with fluoxetine in treating depression:A randomized study

BACKGROUND Depression affects more than 350 million people worldwide.In China,4.2%(54 million people)of the total population suffers from depression.Psychotherapy has been shown to change cognition,improve personality,and enhance the ability to cope with difficulties and setbacks.While pharmacotherapy can reduce symptoms,it is also associated with adverse reactions and relapse after drug withdrawal.Therefore,there has been an increasing emphasis placed on the use of non-pharmacological therapies for depression.The hypothesis of this study was that acupuncture at ghost points combined with fluoxetine would be more effective than fluoxetine alone for the treatment of depression.AIM To investigate the efficacy of acupuncture at ghost points combined with fluoxetine for the treatment of patients with depression.METHODS This randomized controlled trial included patients with mild to moderate depression(n=160).Patients received either acupuncture at ghost points combined with fluoxetine(n=80)or fluoxetine alone(control group,n=80).Needles were retained in place for 30 min,5 times a week;three treatment cycles were administered.The Mann–Whitney U test was used to compare functional magnet resonance imaging parameters,Hamilton depression rating scale(HAMD)scores,and self-rating depression scale(SDS)scores between the acupuncture group and control group.RESULTS There were no significant differences in HAMD or SDS scores between the acupuncture group and control group,before or after 4 wk of treatment.The acupuncture group exhibited significantly lower HAMD and SDS scores than the control group after 8 wk of treatment(P<0.05).The acupuncture group had significantly lower fractional Amplitude of Low Frequency Fluctuations values for the left anterior wedge leaf,left posterior cingulate gyrus,left middle occipital gyrus,and left inferior occipital gyrus after 8 wk.The acupuncture group also had significantly higher values for the right inferior frontal gyrus,right insula,and right hippocampus(P<0.05).After 8 wk of treatment,the effective rates of the acupuncture and control groups were 51.25%and 36.25%,respectively(P<0.05).CONCLUSION The study results suggest that acupuncture at ghost points combined with fluoxetine is more effective than fluoxetine alone for the treatment of patients with mild to moderate depression.