Negative-parity Excited States Research Articles

Electroexcitation Form Factors and Deformation of 20,22Ne Isotopes Based on the Shell Model and Hartree-Fock plus BCS Calculations

Nuclear structure of 20,22Ne isotopes has been studied via the shell model with Skyrme-Hartree-Fock calculations. In particular, the transitions to the low-lying positive and negative parity excited states have been investigated within three shell model spaces; sd for positive parity states, spsdpf large-basis (no-core), and zbme model spaces for negative parity states. Excitation energies, reduced transition probabilities, and elastic and inelastic form factors were estimated and compared to the available experimental data. Skyrme interaction was used to generate a one-body potential in the Hartree-Fock calculations for each selected excited states, which is then used to calculate the single-particle matrix elements. Skyrme interaction was used to calculate the radial wave functions of the single-particle matrix elements, from which a one-body potential in Hartree-Fock theory with SLy4 parametrization can be generated. Furthermore, we have explored the interplays among neutron and proton density profiles in two dimensions, along with the deformations of 20,22Ne using Hartree-Fock plus BCS calculations.

Complete set of bound negative-parity states in the neutron-rich nucleus N18

High-resolution gamma-ray spectroscopy of 18N is performed with the Advanced GAmma Tracking Array AGATA, following deep-inelastic processes induced by an 18O beam on a 181Ta target. Six states are newly identified, which together with the three known excitations exhaust all negative-parity excited states expected in 18N below the neutron threshold. Spin and parities are proposed for all located states on the basis of decay branchings and comparison with large-scale shell-model calculations performed in the p-sd space, with the YSOX interaction. Of particular interest is the location of the 0^-_1 and 1^-_2 excitations, which provide strong constrains for cross-shell p-sd matrix elements based on realistic interactions, and help to simultaneously reproduce the ground and first-excited states in 16N and 18N, for the first time. Understanding the 18N structure may also have significant impact on neutron-capture cross-section calculations in r-process modeling including light neutron-rich nuclei.

Heavy baryon spectrum with chiral multiplets of scalar and vector diquarks

Chiral effective theory of scalar and vector diquarks is formulated according to the linear sigma model. The main application is to describe the ground and excited states of singly heavy baryons with a charm or bottom quark. Applying the potential quark model between the diquark and the heavy quark ($Q=c, b$), we construct a heavy-quark--diquark model. The spectra of the positive- and negative-parity states of $\Lambda_Q$, $\Sigma_Q$, $\Xi^{(')}_Q$ and $\Omega_Q$ are obtained. The masses and interaction parameters of the effective theory are fixed partly from the lattice QCD data and also from fitting low-lying heavy baryon masses. We find that the negative parity excited states of $\Xi_Q$ (flavor $\bar{\bf 3}$) are different from those of $\Lambda_Q$, because of the inverse hierarchy of the pseudoscalar diquark. On the other hand, $\Sigma_Q, \Xi'_Q$ and $\Omega_Q$ (flavor ${\bf 6}$) baryons have similar spectra. We compare our results of the heavy-quark--diquark model with experimental data as well as the quark model.

Alternating Parity Band in Octupole-Soft 140Xe with Axial Vibrational-Rotational Model and Triaxial Rigid Rotor Model**Supported by the National Natural Science Foundation of China under Grant Nos 11675094 and 11622540, and the Young Scholars Program of Shandong University under Grant No 2015WHWLJH01.

Energies of the yrast positive- and negative-parity excited states in 140Xe are reproduced by two different models considering quadrupole-octupole deformations, namely the axial vibrational-rotational model and the triaxial rigid rotor model, and compared with the stable octupole-deformed 222Th. The origin of the energy difference between the opposite parity sequences is considered from two different mechanisms, the vibration in axial deformed energy minima and the rotation considering the effective triaxial deformation. The success of reproducing the data in both the models implies that these two mechanisms are equivalent on some level for the octupole-soft nuclei. By investigating the probability distributions for projection of total angular momentum in the triaxial rigid rotor model, it is found that such an energy difference is associated with the difference of orientation of the rotational axis.

An efficient method for obtaining the ground and excited states mass spectrum of doubly heavy $ \Omega$ Ω baryons

In this paper, we obtained the ground state masses and the positive and negative parity excited state masses of doubly heavy $ \Omega$ baryons. For this goal we have analytically solved the radial Schrodinger equation for three identical particles with the hypercentral potential by using the ansatz method. In this study the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential which has a two-body character and turns out to be exactly hypercentral. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term and tensor term) to the hypercentral potential. Our calculations have been performed for the radial excited states as well as orbital excited states for $ \Omega_{cc}$ , $ \Omega_{bb}$ and $ \Omega_{bc}$ systems. The masses obtained are compared with other theoretical reports, which could be a benefit tool for the interpretation of experimentally unknown doubly heavy baryons spectrum. The doubly heavy baryons masses are experimentally unknown so that the Regge trajectories are plotted using calculated masses to assign the quantum numbers of baryons unknown states.

A New Model for Calculating the Ground and Excited States Masses Spectra of Doubly Heavy Ξ Baryons

Since the doubly heavy baryons masses are experimentally unknown (except Ξcc+ and Ξcc++), we present the ground state masses and the positive and negative parity excited state masses of doubly heavy Ξ baryons. For this purpose, we have solved the six-dimensional hyperradial Schrödinger equation analytically for three particles under the hypercentral potential by using the ansatz approach. In this paper, the hypercentral potential is regarded as a combination of the color Coulomb plus linear confining term and the six-dimensional harmonic oscillator potential. We also added the first-order correction and the spin-dependent part contains three types of interaction terms (the spin-spin term, spin-orbit term, and tensor term) to the hypercentral potential. Our obtained masses for the radial excited states and orbital excited states of Ξccd, Ξccu, Ξbbd, Ξbbu, Ξbcd, and Ξbcu systems are compared with other theoretical reports, which could be a beneficial tool for the interpretation of experimentally unknown doubly heavy baryons spectrum.

Negative-parity nucleon excited state in nuclear matter

Spectral functions of the nucleon and its negative parity excited state in nuclear matter are studied using QCD sum rules and the maximum entropy method (MEM). It is found that in-medium modifications of the spectral functions are attributed mainly to density dependencies of the $\langle \bar{q}q \rangle $ and $\langle q^{\dagger}q \rangle $ condensates. The MEM reproduces the lowest-energy peaks of both the positive and negative parity nucleon states at finite density up to $\rho \sim \rho_N$ (normal nuclear matter density). As the density grows, the residue of the nucleon ground state decreases gradually while the residue of the lowest negative parity excited state increases slightly. On the other hand, the positions of the peaks, which correspond to the total energies of these states, are almost density independent for both parity states. The density dependencies of the effective masses and vector self-energies are also extracted by assuming the mean-field green functions for the peak states. We find that, as the density increases, the nucleon effective mass decreases while the vector self-energy increases. The density dependence of these quantities for the negative parity state on the other hand turns out to be relatively weak.

Excited state mass spectra of doubly heavy baryons $${\Omega _{cc}}$$ Ω c c , $${\Omega _{bb}}$$ Ω b b , and $${\Omega _{bc}}$$ Ω b c

We discuss the mass spectrum of $$\Omega $$ baryon with two heavy quarks and one light quark (ccs, bbs, and bcs). The main goal of the paper is to calculate the ground state masses and after that, the positive and negative parity excited states masses are also obtained within a hypercentral constituent quark model, using Coulomb plus linear potential framework. We also added a first order correction to the potential. The mass spectra up to 5S for radial excited states and 1P–5P, 1D–4D, and 1F–2F states for orbital excited states are computed for $$\Omega _{cc}$$ , $$\Omega _{bb}$$ , and $$\Omega _{bc}$$ baryons. Our obtained results are compared with other theoretical predictions, which could be a useful complementary tool for the interpretation of experimentally unknown heavy baryon spectra. The Regge trajectory is constructed in both the ( $$n_r$$ , $$M^{2}$$ ) and the (J, $$M^{2}$$ ) planes for $$\Omega _{cc}$$ , $$\Omega _{bb}$$ , and $$\Omega _{bc}$$ baryons and their slopes and intercepts are also determined. Magnetic moments of doubly heavy $$\Omega '$$ s are also calculated.

Constituent-quark model description of triply heavy baryon nonperturbative lattice QCD data

This paper provides results for the spectra of triply charmed and bottom baryons based on a constituent-quark model approach. We take advantage of the assumption that potential models are expected to describe triply heavy baryons to a similar degree of accuracy as the successful results obtained in the charmonium and bottomonium sectors. The high precision calculation of the ground state and positive and negative parity excited states recently reported by nonperturbative lattice QCD provides us with a unique opportunity to confront model predictions with the data. This comparison may also help to build a bridge between two difficult to reconcile lattice QCD results, namely, the lattice SU(3) QCD static three-quark potential and the recent results of nonperturbative lattice QCD for the triply heavy baryon spectra.

Deformation and cluster structures in12C studied with configuration mixing using Skyrme interactions

We report an investigation of the structure of $^{12}$C nucleus employing a newly developed configuration-mixing method. In the three-dimensional coordinate-space representation, we generate a number of Slater determinants with various correlated structures using the imaginary-time algorithm. We then diagonalize a many-body Hamiltonian with the Skyrme interaction in the space spanned by the Slater determinants with parity and angular momentum projections. Our calculation reasonably describes the ground and excited states of $^{12}$C nucleus, both for shell-model-like and cluster-like states. The excitation energies and transition strengths of the ground-state rotational band are well reproduced. Negative parity excited states, $1_1^-$, $2_1^-$, and $3_1^-$, are also reasonably described. The second and third $0^+$ states, $0_2^+$ and $0_3^+$, appear at around 8.8 MeV and 15 MeV, respectively. The $0_2^+$ state shows a structure consistent with former results of the \alpha-cluster models, however, the calculated radius of the $0_2^+$ state is smaller than those calculations. The three-{\alpha} linear-chain configuration dominates in the $0_3^+$ state.

Parity projection of QCD sum rules for the nucleon

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. First, we rederive the parity projected sum rules for baryons using ``old-fashioned'' correlation functions. Doing this, the method is generalized so that higher order operator product expansion terms can be calculated unambiguously. We then apply this approach to the nucleon channel taking into account all known first order ${\ensuremath{\alpha}}_{s}$ corrections to the Wilson coefficients of the operator product expansion. As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. Simultaneously, this phase rotation strongly suppresses the continuum contribution and improves the convergence of the operator product expansion. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive- and negative-parity states.

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order αs cor- rections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly sup- presses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.

THE 6He+6He AND α+8He CLUSTER STATES IN 12Be VIA α-INELASTIC SCATTERING

Cluster structures in the neutron-rich nucleus 12 Be were experimentally investigated via α-inelastic scattering. Excited states in the 12 Be nucleus were populated by a 12 Be (αα') reaction at 60 A MeV in the inverse kinematics, and identified by measuring a 6 He +6 He and α+8 He breakup channels in coincidence. The differential cross section and the angular correlations between the decay particles were obtained for each excitation energy at 10–20 MeV for 6 He +6 He and at 9–19 MeV for α+8 He , respectively, reconstructed by the measured momentum vectors of the two helium isotopes. A multipole decomposition analysis based on the distorted-wave Born approximation was applied for the angular distribution of the inelastic scattering together with the angular correlation between the decay particles with respect to the directions of the incident beam and to the momentum transfer simultaneously. From the decomposed excitation energy spectra for J=0-4, several new excited states were identified. The 0+ excited states were candidates of the band-head of a largely deformed rotational band. The 11.3-MeV 0+ state was found to decay only into the 6 He +6 He channel. This result support the recent theoretical result by the generalized two-center cluster model. Several negative-parity excited states were observed in the α+8 He channel. These excited states possibly forming a negative-parity rotational band, which is very closed to the positive-parity band, can be connected to the existence of the extremely developed cluster structure in 12 Be .

Excited state nucleon spectrum with two flavors of dynamical fermions

Highly excited states for isospin $\frac{1}{2}$ baryons are calculated for the first time using lattice QCD with two flavors of dynamical quarks. Anisotropic lattices are used with two pion masses, ${m}_{\ensuremath{\pi}}=416(36)\text{ }\text{ }\mathrm{MeV}$ and 578(29) MeV. The lowest four energies are reported in each of the six irreducible representations of the octahedral group at each pion mass. The lattices used have dimensions ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$, spatial lattice spacing ${a}_{s}\ensuremath{\approx}0.11\text{ }\text{ }\mathrm{fm}$, and temporal lattice spacing ${a}_{t}=\frac{1}{3}{a}_{s}$. Clear evidence is found for a $\frac{{5}^{\ensuremath{-}}}{2}$ state in the pattern of negative-parity excited states. This agrees with the pattern of physical states and spin $\frac{5}{2}$ has been realized for the first time on the lattice.

Evolution of the N = 20 shell gap

Stucture of N = 17,18 nuclei has been investigated via proton inelastic scattering and neutron removal reactions up to the neutron dripline in inverse kinematics by use of radioctive ion beams provided by the RIKEN isotope separator, RIPS. Low energy excited states have been found in all the 26,27F and 27Ne nuclei, which are out of the neutron sd shell configuration space and are considered as intruder states arisng from cross shell excitations. Monte-Carlo shell model calculations with the sdpf-m interaction predict low energy negative parity excited states from neutron cross shell excitation at N = 17,18, which is in agreement with our experimental results. Observation of intruder states even at N = 17, especially the p3/2 state in 27Ne at 765 keV is a clear indication of a vanishing N = 20 shell gap at Z = 8 as predicted by the sdpf-m shell model calculations.

Spectral analysis of excited nucleons in lattice QCD with maximum entropy method

We study the mass spectra of excited baryons with the use of the lattice QCD simulations. We focus our attention on the problem of the level ordering between the positive-parity excited state N′(1440) (the Roper resonance) and the negative-parity excited state N∗(1535). Nearly perfect parity projection is accomplished by combining the quark propagators with periodic and anti-periodic boundary conditions in the temporal direction. Then we extract the spectral functions from the lattice data by utilizing the maximum entropy method. We observe that the masses of the N′ and N∗ states are close for wide range of the quark masses (Mπ=0.61–1.22 GeV) and for the physical point after the extrapolation in terms of the quark mass. The latter aspect is in contrast to the phenomenological prediction of the phenomenological quark models. The role of the Wilson doublers in the baryonic spectral functions is also studied.

Roper resonance and [formula omitted] from lattice QCD

Using the constrained-curve fitting method and overlap fermions with the lowest pion mass at 180 MeV, we observe that the masses of the first positive and negative parity excited states of the nucleon tend to cross over as the quark masses are taken to the chiral limit. Both results at the physical pion mass agree with the experimental values of the Roper resonance (N1/2+(1440)) and S11 (N1/2−(1535)). This is seen for the first time in a lattice QCD calculation. These results are obtained on a quenched Iwasaki 163×28 lattice with a=0.2 fm. We also extract the ghost η′N states (a quenched artifact) which are shown to decouple from the nucleon interpolation field above mπ∼300 MeV. From the quark mass dependence of these states in the chiral region, we conclude that spontaneously broken chiral symmetry dictates the dynamics of light quarks in the nucleon.

Lattice study of the nucleon excited states with domain wall fermions

We present results of our numerical calculation of the mass spectrum for isospin one-half and spin one-half nonstrange baryons, i.e., the ground and excited states of the nucleon, in quenched lattice QCD. We use a new lattice discretization scheme for fermions, domain wall fermions, which possess almost exact chiral symmetry at nonzero lattice spacing. We make a systematic investigation of the negative-parity ${N}^{*}$ spectrum by using two distinct interpolating operators at $\ensuremath{\beta}{=6/g}^{2}=6.0$ on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32\ifmmode\times\else\texttimes\fi{}16$ lattice. The mass estimates extracted from the two operators are consistent with each other. The observed large mass splitting between this state, ${N}^{*}(1535),$ and the positive-parity ground state, the nucleon $N(939),$ is well reproduced by our calculations. We have also calculated the mass of the first positive-parity excited state and find that it is heavier than the negative-parity excited state for the quark masses studied.

Exactly solvable models of baryon spectroscopy

We present an exactly solvable model of baryon spectroscopy which has O(7) dynamic symmetry and is based on a hyperCoulomb three-body quark potential. The corresponding form factors, which are calculated analytically, show a power-law behavior as a function of momentum transfer Q 2. Because of the O(7) symmetry there is a degeneracy between the Roper resonance and the negative parity excited states, in qualitative agreement with the observed spectrum. A linear confinement term is also added. The SU(6) symmetry is broken by a spin-spin interaction and by a small tensor term.

The charm and bottom hyperons in a chiral quark model

The spectrum of the C=1 hyperons is well described by the constituent quark model, if the fine structure interaction between the light and strange quarks is mediated by the $SU(3)_F$ octet of light pseudoscalar mesons, which are the Goldstone bosons of the hidden approximate chiral symmetry of QCD. With the addition of a phenomenological flavor exchange interaction of the same form between the light and the charm quarks to describe the $\Sigma_c-\Sigma_c^*$ and $\Xi_c^s-\Xi_c^*$ splittings, the splittings between the C=1 states fall within 10-30 MeV of the empirical values. Predictions are presented for the lowest negative parity excited states and the magnetic moments as well. Corresponding predictions for the B=-1 hyperon states are also given.