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.

The complex momentum representation approach and its application to low‑lying resonances in 17 O and^(29,31)F

Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear theory.Accordingly,we explored the viability of the complex momentum representation(CMR)approach coupled with new potentials.We focus on predicting the energy of the low-lying 2p_(3∕2)resonance in 17 O,which is critical for s-process nucleosynthesis and missing in previous theoretical research.Using a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy,we successfully predicted the resonant energy of this level for the first time.Our predictions of the bound levels and 1d_(3∕2)resonance agree well with the measurement results.Additionally,we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in^(29,31)F.We found that the CMR-based predictions of the bound-level energies and unbound 1f7∕2 level agree well with the results obtained using the scattering phase shift method.Subsequently,we successfully found a solution for the 2p_(3∕2)resonance with energy just above the threshold,which is decisive for halo formation.

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.

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.

Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

Normalized Excited Squeezed Vacuum State and Its Applications

By using the intermediate coordinate-momentum representation in quantum optics and generating function for the normalization of the excited squeezed vacuum state （ESVS）, the normalized ESVS is obtained. We find that its normalization constants obtained via two new methods are uniform and a new form which is different from the result obtained by Zhang and Fan [Phys. Lett. A 165 （1992） 14]. By virtue of the normalization constant of the ESVS and the intermediate coordinate-momentum representation, the tomogram of the normalized ESVS and some useful formulae are derived.

Exploring the halo phenomena of medium-mass nuclei having approximately Z=40 with point-coupled parameters in complex momentum representations

To explore the properties of neutron-rich nuclei with approximately 40 protons,the density-dependent point coupling(DD-PC1)effective interaction parameter is adopted in the relativistic mean-field theory with the complex momentum representation(RMF-CMR).The calculated two-neutron separation energy(S_(2n))and root-mean-square(rms)radii support the halo structure that appear in Mo and Ru isotopic chains.Besides,the neutron skin structures appear in Kr and Sr isotopes.The conclusions drawn are also supported by the single-particle energy levels and their occupancy probability and density distribution.Particularly,the energy levels,which reduce to bound states or are approximately 0 MeV with a small orbital angular momentum,are suggested to provide the primary contribution to increasing the neutron radius.Moreover,the single-particle energy levels significantly reflect the shell structure.In addition,the neutron drip line nuclei for Kr,Sr,Mo,and Ru elements are proposed via the changes in S_(2n).

Morse Potential in the Momentum Representation

The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that [q2（p）l is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[（p）], It is interesting to see that the [~ （p）[ is symmetric with respect to the axis p = 0 and the number of wave crest of [ （p）[ is equal to n ＋ 1. We also study the variation of ]k（p）l with respect to . The arnplitude of ｜ψ（p）] first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments.

Exploration of resonances by using complex momentum representation

Resonance research is a hot topic in nuclear physics,and many methods have been developed for resonances.In this paper,we explore resonances by solving the Schrodinger equation in complex momentum representation,in which the bound states and resonant states are separated completely from the continuum and exposed clearly in the complex momentum plane.We have checked the convergence of the calculations on the grid numbers of the Gauss-Hermite quadrature and the Gauss-Legendre quadrature,and the dependence on the contour of momentum integration.Satisfactory results are obtained.^17O is chosen as an example,and we have calculated the bound and resonant states to be in excellent agreement with those calculated in the coordinate representation.

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

The computational approach for solving the Faddeev-Merkuriev equations in total orbitalmomentum representation is presented.These equations describe a systemof three quantumcharged particles and arewidely used in bound state and scattering calculations.The approach is based on the spline collocation method and exploits intensively the tensor product formof discretized operators and preconditioner,which leads to a drastic economy in both computer resources and time.