Competition of isoscalar and isovector proton-neutron pairing in nuclei

We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus ⁴⁶V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in ⁴⁶V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.     

Shell model Monte Carlo studies of N = Zpf-shell nuclei with pairing-plus-quadrupole Hamiltonian

We perform shell model Monte Carlo calculations of selected N = Z pf-shell nuclei with a schematic Hamiltonian containing isovector pairing and quadrupole-quadrupole interactions. Compared to realistic interactions, this Hamiltonian does not give rise to the SMMC “sign problem”, while at the same time resembles essential features of the realistic interactions. We study pairing correlations in the ground states of N = Z nuclei and investigate the thermal dependence of selected observables for the odd-odd nucleus ⁵⁴Co and the even-even nuclei ⁶⁰Zn and ⁶⁰Ni. Comparison of the present results to those with the realistic KB3 interaction indicates a transition with increasing temperature from a phase of isovector pairing dominance to one where isoscalar pairing correlations dominate. In addition, our results confirm the qualitative reliability of the procedure used to cure the sign problem in the SMMC calculations with realistic forces.     

Soft Giant Dipole Modes in Ca Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ca isotopes is investigated in the framework of the fully consistent relativistic random phase approximation.The calculations are performed in an effective Lagrangian with a parameter set NL3,which was proposed for satisfactorily describing nuclear ground state properties.It is found that a soft isovector dipole mode for Ca isotopes near drip lines exists at energy around 6-7MeV.The soft dipole states are mainly due to the excitation of the weakly bound and pure neutron (proton)states near Fermi surface as well as the correlation of isoscalar and isovector operators.For nuclei with the extreme value of N/Z,the contributions of isoscalar mesons in the isovector mode play a non-negligible role.     

Nuclear scissors with pairing and continuity equation

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low-lying modes (including scissors) is studied with the help of the Wigner-function-moment method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the time-dependent Hartree-Fock-Bogoliubov equations in the harmonic-oscillator model with quadrupole—quadrupole residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation. The text was submitted by the authors in English.     

Pairing and the structure of the -shell nuclei

The influence of the isoscalar and isovector pairing components of the effective nucleon-nucleon interaction is evaluated for several isobaric chains, in the framework of full shell model calculations. We show that the combined effect of both isospin channels of the pairing force is responsible for the appearance of ground states in odd-odd nuclei. However, no evidence is found relating them to the Wigner energy. We study the dependence of their contributions to the total energy on the rotational frequency in the deformed nucleus Cr. Both decrease with increasing angular momentum and go to zero at the band termination. Below the backbending their net effect is a reduction of the moment of inertia, more than half of which comes from the proton-neutron channel.     

Microscopic structure of fundamental excitations in N = Z nuclei

An extended mean-field model is presented that describes states of different isospin in odd-odd and even-even nuclei. Excitation energies of the T = 1 states in even-even as well as T = 0 and T = 1 states in odd-odd N = Z nuclei are calculated. It is shown that the structure of these states can be determined in a consistent manner when both isoscalar and isovector pairing collectivity as well as isospin projection (treated here within the isocranking approximation) are taken into account. In particular, in odd-odd N = Z nuclei, the interplay between quasiparticle excitations (relevant for the case of T = 0 states) and isorotations (relevant for the case of T = 1 states) explains the near degeneracy of these states.     

A quark shell model calculation of nuclear magnetic moments

The “Schmidt lines” for nuclear magnetic moments are calculated in a quark shell model. In the pairing scheme proposed by Petry et al., the single-nucleon magnetic moment is simply related to the single quark value. The isoscalar part is essentially the same as that of the conventional Schmidt moment while the isovector part increases too rapidly as the angular momentum increases. Possibilities of improving the model are briefly discussed.     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.     

Pairing of Neutrons and Protons in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> Nuclei

Values of neutron–proton pairing based on mass relations are estimated. It is shown that substantially different formulas for calculating the np-pairing energy in self-conjugate nuclei yield similar results. Comparison of the obtained values and the structure of ground state multiplet spectra shows that mass relations can be used to describe the isovector (T = 1) component of np-pairing to sufficient accuracy, but provides little or no information on isoscalar component T = 0.     

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei

competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0~+ and 1~+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.     

Magnetic dipole moment of the Δ(1232) in chiral perturbation theory

The magnetic dipole moment of the Δ(1232) is calculated in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the Δ(1232), at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.     

Skyrme张量相互作用对可能的等待点原子核β衰变半衰期的影响(英文)

使用基于Skyrme相互作用的HFB+QRPA模型研究N~82和126的同中子异位素链的β-衰变的半衰期。在计算中所使用的张量相互作用和同位旋标量（IS）对相互作用都是很好地被约束了的。比较了张量相互作用和IS对相互作用对半衰期的影响。IS对相互作用的强度与相应的同位旋矢量（IV）对相互作用的强度相当时,对N~82和126的同中子异位素链中有大的中子过剩的原子核的半衰期影响很微弱。而张量相互作用采用最近约束的强度时对半衰期的影响非常显著。The β-decay half-lives of N ~ 80 and 126 isotonic chains are calculated with HFB+QRPA models based on Skyrme force. In the calculations, the well constrained Skyrme tensor interaction and isoscalar spin-triplet (IS) pairing interaction are included so that to study their effects on the half-lives. The effects of tensor interaction and IS pairing interaction on the half-lives are compared. The IS pairing interaction with strength similar to that of isovector (IV) one produces only a trivial effect in N ~82 nuclei, and N ~126 nuclei with big neutron excess. While the tensor interaction with presently constrained strengths produces an obvious effect.     

Exact solution of the spin-isospin proton-neutron pairing Hamiltonian

The exact solution of the proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with nondegenerate single-particle orbits and equal pairing strengths is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled nonlinear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for a system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.     

Spin-dependent isoscalar response functions and interpretation of polarization-transfer measurements

The correlations of tensor character are found to affect the integrated isoscalar spin-isospin response functions as much as the isovector ones, but with opposite signs. These effects can modify the interpretation of the recent polarization-transfer measurements in (p, p′) reactions.     

Microscopic description of the E0, E2 and E1 giant resonances in 40Ca, 48Ca and 56Ni

The isovector E1 as well as the isoscalar, isovector and full electromagnetic E2 and E0 strength distributions for ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been calculated in a large energy range up to 50 MeV of excitation. The microscopic model used includes the continuum RPA, 1p1h⊗phonon configurations and ground state correlations induced by these configurations. It is shown that the latter effect gives an increase of the energy weighted sum rules of 4–7%. In all these nuclei the isoscalar E0 and E2 resonances are spread out over the broad energy region. We obtained a reasonable good agreement with the available experimental data including the recent ones for the isoscalar E0 resonance in ⁴⁰Ca. The theoretical transition densities show a rather strong dependence on the excitation energy.     

对关联对核基态和集体激发态性质的影响

基于相对论平均场和BCS理论,研究了共振连续对奇特核对关联性质的影响. 利用S矩阵方法，通过设定合理的散射态边界条件来得到单粒子共振态的能量和宽度. 通过引入连续态能级密度的方法来处理共振态宽度对核对关联的贡献. 计算结果显示合理地处理共振态对对关联性质的贡献在研究滴线附近核性质时很重要. 它可以影响中子的对隙、费米能级、对关联能以及总结合能. 其次,基于RMF+BCS基态,采用线性响应理论给出了描述开壳核集体激发态性质的准粒子相对论无规位相近似理论. 并且将该方法应用于开壳核120Sn的各种同位旋标量集体激发态性质的研究中. 研究表明：对关联对核的集体激发性质的影响主要表现在低能集体激发态上,考虑对关联后的相对论无规位相近似理论能够很好地再现低能集体激发的实验结果.     

Energy-weighted sum rules for spin operators and ground-state correlations

Energy-weighted sum rules are obtained for the spin part, both isoscalar and isovector, of the magnetic dipole operator. The same interaction is used to evaluate the relevant double commutator as is used to induce ground-state correlations. First a spin-dependent delta interaction is used; then a tensor interaction is considered. The main point of this work is that there is a lot of energy-weighted strength at high energies.     

Nonlinear dynamics of giant resonances in atomic nuclei

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicates regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.     

Phase space moments with pair correlations on the example of nuclear scissors

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for relevant collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations. Especial care is taken of the continuity equation. The inclusion of pair correlations leads also to the appearance of the isoscalar low lying mode.     

Linear responses in time-dependent Hartree-Fock-Bogoliubov method with Gogny interaction

A numerical method to integrate the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center of mass in the small amplitude vibrations of ²⁰O . The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes, ^{18, 20, 22, 24}O , titanium isotopes, ^{44, 50, 52, 54}Ti , neon isotope, ²⁶Ne , and magnesium isotopes, ^{24, 34}Mg . The isoscalar quadrupole and isovector dipole strength functions are calculated from the expectation values of the isoscalar quadrupole and isovector dipole moments.