We build and train the artificial neural network model (ANN) based on the experimental $α$-decay energy ($Q_α$) data. Besides decays between the ground states of parent and daughter nuclei, decays from the ground state of parent nuclei to the excited state of daughter nuclei are also included. By this way, the number of samples are increased dramatically. The results calculated by ANN model reproduce the experimental data with a good accuracy. The root-mean-square (rms) relative to the experiment data is 0.105 MeV. The influence of different input is investigated. It is found that either the shell effect or the pairing effect results in an obvious improvement of the predictive power of ANN model, and the shell effect plays a more important role. The optimal result can be obtained as both the shell and pairing effects are considered simultaneously. Application of ANN model in prediction of the $α$-decay energy shows the neutron magic number at $N=184$, and a possible sub-shell gap around $N=174$ or 176 in the superheavy nuclei region.
We analyze the observed shell gaps in N=Z nuclei determined from the binding energy differences. It is found that the shell gaps can be described by the combined contributions from the single-particle level spacing, the like-nucleon pairing, and the proton-neutron pairing interaction. This conclusion is consistent with that of Chasman in Phys. Rev. Lett. 99 (2007) 082501. For the double-closed shell N=Z nuclei, the single-particle level spacings calculated with Woods-Saxon potential are very close to those obtained by subtracting the nn pairing interaction from the observed shell gap. For the …
From the experimental data on odd-even staggering of masses, we have shown that variation of pairing as a function of neutron number plays an important role in many distinctive features like occurrence of new shell closures, shell erosion, anomalous reduction of the energy of the first 2+ state and slower increase in the B(E2, 2_{+}^{1} \rightarrow 0_{+}^{1}) in the neutron-rich even-even nuclei in different mass regions. New predictions have been made in a model independent way. Results of theoretical calculations support the phenomenological findings.
Background: Pairing correlations play a critical role in determining numerous properties of open-shell nuclei. Traditionally, they are included in a mean-field description of atomic nuclei through the approximate Bardeen-Cooper-Schrieffer or Hartree-Fock-Bogoliubov formalism. Purpose: We propose a new hybrid ''relativistic-mean-field-plus-pairing'' approach in which pairing is treated exactly so the number of particles is conserved. To verify the reliability of the formalism, we apply it to the study of both ground-state properties and isoscalar monopole excitations of the Tin isotopes. Method…
In this talk I shall introduce our recent works on general pairing interactions and pair truncation approximations for fermions in a single-j shell, including the spin zero dominance, features of eigenvalues of fermion systems in a single-j shell interacting by a $J-$pairing interaction.
A shell-model study of proton-neutron pairing in f - p shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{46}$Ti and $^{48}$Cr.
Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered. Based on the experimental mass values of the Ca, Sn, and Pb isotopes, the dependence of the energy gap on the neutrons number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown. In nuclei with closed proton shells, effects directly related to neutron pairing and effects of nucleon shells are discussed.
Interplay between Nuclear Shell Structure and Pairing around Doubly Magic $^{132}$Sn
TRIUMF；University of British Columbia（不列颠哥伦比亚大学）；University of Manitoba（曼尼托巴大学）；University of Victoria（维多利亚大学）；Justus-Liebig-Universität（吉森大学）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森FAIR赫尔姆霍茨研究学院）；University of Western Ontario（韦仕敦大学）
A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{45}$Ti, $^{46}$Ti, $^{46}$V and $^{48}$Cr to assess how proton-neutron pair correlations emerge under different scenarios. We also study how the presence of a one-body …
This paper starts with a brief historical overview of pairing in nuclei, which fulfills the purpose of properly framing the main subject. This concerns the pairing properties of a realistic shell-model effective interaction which has proved very successful in describing nuclei around doubly magic 132Sn. We focus attention on the two nuclei 134Te and 134Sn with two valence protons and neutrons, respectively. Our study brings out the key role of one particle-one hole excitations in producing a significant difference between proton and neutron pairing in this region.
The shell-model-like approach (SLAP) based on cranking covariant density functional theory (CDFT) with a separable pairing force is developed. The developed cranking CDFT-SLAP with separable pairing force is applied to investigate the rotational spectra in $^{60}$Fe, including the positive-parity yrast band and two negative-parity signature partner bands, in comparison with the cranking CDFT-SLAP with monopole pairing force calculations. Excellent agreement with the available data is achieved.
Rotational motion of heated 72-Ge is studied within the microscopic Shell Model Monte Carlo approach. We investigate the the angular momentum alignment and nuclear pairing correlations associated with J-pi Cooper pairs as a function of the rotational frequency and temperature. The reentrance of pairing correlations with temperature is predicted at high rotational frequencies. It manifests itself through the anomalous behavior of specific heat and level density.
The three main contributions to the nuclear Hamiltonian - monopole, quadrupole and pairing - are analyzed in a shell model context. The first has to be treated phenomenologically, while the other two can be reliably extracted from the realistic interactions. Due to simple scaling properties, the realistic quadrupole and pairing interactions eliminate the tendency to collapse of their conventional counterparts, while retaining their basic simplicity.
We perform a systematic study of Gamow-Teller (GT) transitions in the 2p1f shell, using the nuclear shell model with two schematic Hamiltonians. The use of the shell model provides flexibility to analyze the role of different proton-neutron pairing modes in the presence of nuclear deformation. The schematic Hamiltonians that are used contain a quadrupole-quadrupole interaction as well as isoscalar (T=0) and isovector (T=1) pairing interactions, but differ in the single particle energies. The objective of the work is to observe the behavior of GT transitions in different isoscalar and isovector…
We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) into a shell model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell model interaction. A similar procedure is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Using the grou…
The recently-proposed effective shell-model interaction, the pairing-plus-multipole Hamiltonian with the monopole interaction obtained by empirical fits starting from the monopole-based universal force (PMMU), is systematically applied to nuclei of the pf5/2g9/2 shell region. It is demonstrated that the calculation describes reasonably well a wide range of experimental data, including not only the low-lying and high-excitation spectra, E2 transitions, quadrupole moments, and magnetic moments, but also the binding energies, for Ni, Cu, Zn, Ga, Ge, As, and Se isotopes with A=64-80. In particular…
Survival of Pairing Correlations and Shell Effects at Scission in Finite-Temperature Nuclear Fission: Implications for Odd-Even Staggering
National Centre for Nuclear Research（国家核研究中心）；China Institute of Atomic Energy, Nuclear Data Center（中国原子能科学研究院核数据中心）；Department of Theoretical Physics, Maria Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学理论物理系）；Department of Physics, Tsinghua University（清华大学物理系）
A systematic study of the pairing correlations as a function of temperature and angular momentum has been performed in the sd-shell region using the spherical shell model approach. The pairing correlations have been derived for even-even, even-odd and odd-odd systems near N=Z and also for the asymmetric case of N=Z+4. The results indicate that the pairing content and the behavior of pair correlations is similar in even-even and odd-mass nuclei. For odd-odd N=Z system, angular momentum I=0 state is an isospin, t=1 neutron-proton paired configuration. Further, these t=1 correlations are shown to…
The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions. The isoscalar spin-triplet pairing correlation provides a substantial quenching effect on the spin magnetic dipole transitions, especially the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction influences the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The effect of the $Δ$ ($Δ_{33}$ resonance)-hole coupl…
The ground-state bands (GSBs) in the even-even hafnium isotopes $^{170-184}$Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency $\hbarω\approx0.5$ MeV observed (predicted) in $^{172}$Hf ($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $\pi1i_{13/2}$ $(1/2^{+}[660])$, $\pi1h_{9/2}$ $(1/2^{-}[541])$ and orbital $\pi1h_{11…
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 Co54 and the even-even nuclei Zn60 and Ni60. Comparison of the present results to tho…
The pairing correlation energy for two-nucleon configurations with the spin-parity and isospin of $J^π=0^+$, $T$=1 and $J^π=1^+$, $T$=0 are calculated with $T$=1 and $T$=0 pairing interactions, respectively. To this end, we consider the $(1f2p)$ shell model space, including single-particle angular momenta of $l=3$ and $l=1$. It is pointed out that a two-body matrix element of the spin-triplet $T$=0 pairing is weakened substantially for the $1f$ orbits, even though the pairing strength is much larger than that for the spin-singlet $T$=1 pairing interaction. In contrast, the spin-triplet pairing…
The role of L=0 pairing interactions (both T=0 and T=1) in three selected bands with the total isospin T=0 in 22Na, 48Cr and 90Rh nuclei is discussed in the spherical shell model. These bands were selected requiring termination in a most unfavourable way. The investigated effects coming from pairing interactions include the change of nuclear wavefunction, quadrupole properties and state energy. To follow the gradual change of nuclear properties, the investigation is performed in a perturbative approach by defining the Hamiltonian with a variable content of the pairing interaction. It is shown …
The long standing problem of neutron-proton pairing correlations is revisited by employing the Hartree-Fock-Bogoliubov formalism with neutron-proton mixing in both the particle-hole and particle-hole channels. We compare numerical calculations performed within this method with an exact pairing model based on the $SO(8)$ algebra. The neutron-proton mixing is included in our calculations by performing rotations in the isospin space using the isocranking technique.
Pairing rotations are the low-energy excitations of finite superfluid systems, connecting systems that differ in their number of Cooper pairs. This paper presents a model-independent derivation of pairing rotations within an effective theory that exploits the emergent breaking of U(1) phase symmetries. The symmetries are realized nonlinearly and the Nambu-Goldstone modes depend only on time because the system is finite. Semi-magic nuclei exhibit pairing rotational bands while the pairing spectrum becomes an elliptical paraboloid for open-shell nuclei. Model-independent relations between double…
A simple approximation to shell model is proposed in which the low energy excitation spectra corresponds to the identical nucleons occupying the same single particle states where they preferred to form pairs for the ground states. We call this approximation as nonzero angular momentum pairing shell model. It not only reduces the dimensionality of the shell model but also matches the number of low energy levels in experimental spectra for few cases where exact shell model predicts many more states. The special focus has been done to consider the realistic interaction derived from free nucleon-n…
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relat…
We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector $T=1$ pairing interaction and an average proton-neutron isoscalar $T=0$ interaction, where the $T=0$ term describes the average interaction between non-paired protons and neutrons. This Hamil…
Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies a…
The shell structures for weakly interacting fermions in harmonic oscillator traps at zero temperature undergo several transitions depending on the number of particles in the trap and their interaction strength. Calculations of the one and two particle spectra give the pairing gaps, and the many particle state is constructed by the seniority scheme. For sufficiently few particles, $N\la 10^4$, the pairing field exceeds the mean-field splitting of single particle levels at the Fermi surface and the greater number of almost degenerate states due to the SU(3) symmetry in the harmonic oscillator sh…
The influence of the isoscalar and isovector L=0 pairing components of the effective nucleon-nucleon interaction is evaluated for several isobaric chains, in the framework of full pf shell model calculations. We show that the combined effect of both isospin channels of the pairing force is responsible for the appearance of T=1 ground states in N=Z 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 frecuency in the deformed nucleus 48Cr. Both decrease with increasing angular momen…
The empirical pairing gaps derived from four different odd-even mass staggering formulas are compared. By performing single-$j$ shell and multi-shell seniority model calculations as well as by using the standard HFB approach with Skyrme force we show that the simplest three-point formula $Δ_C^ {(3)}(N)=\frac{1}{2}\left[B(N,Z)+B(N-2,Z)-2B(N-1,Z)\right]$ can provide a good measure of the neutron pairing gap in even-$N$ nuclei. It removes to a large extent the contribution from the nuclear mean field as well as contributions from shell structure details. It is also less contaminated by the Wigner…
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 rotational bands on top of two-particle $K^π=3^+,8^-$ 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 $\vare…
A simple model based on the group SO(5) suggests that both the like-particle and neutron-proton components of isovector pairing correlations in odd-A nuclei are Pauli blocked. The same effect emerges from Monte Carlo Shell-model calculations of proton-rich nuclei in the full fp shell. There are small differences between the two models in their representation of the effects of an odd nucleon on the competition between like-particle and neutron-proton pairing, but they can be understood and reduced by using a two-level version of the SO(5) model. On the other hand, in odd-odd nuclei with N not e…
The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairi…
The antisymmetrized quasi-cluster model (AQCM) was proposed to describe α-cluster and $jj$-coupling shell models on the same footing. In this model, the cluster-shell transition is characterized by two parameters; $R$ representing the distance between α clusters and α describing the breaking of α clusters, and the contribution of the spin-orbit interaction, very important in the $jj$-coupling shell model, can be taken into account starting with the α cluster model wave function. Not only the closure configurations of the major shells, but also the subclosure configurations of the $jj$-coupling…
The pairing gap plays a fundamental role in the nuclear many-body problem and many large scale and accurate mass formula fits suggest the smooth nuclear mass dependence $Δ\sim 6(1)~ A^{-1/3}~{\rm MeV}$ in the liquid drop model which lacks a theoretical motivation. Within the BCS theory we analyze the impact of phase equivalent interactions on the pairing gap for a translational invariant many-fermion system such as nuclear and neutron matter. To that end we use explicitly the Similarity Renormalization Group (SRG) transformations. We show that in the on-shell and continuum limits the pairing g…
A model combining self-consistent mean-field and shell-model techniques is used to study the competition between particle like and proton-neutron pairing correlations in fp-shell even-even self-conjugate nuclei. Results obtained using constant two-body pairing interactions as well as more sophisticated interactions are presented and discussed. The standard BCS calculations are systematically compared with more refined approaches including correlation effects beyond the independent quasi-particle approach. The competition between proton-neutron correlations in the isoscalar and isovector channe…
The pairing gap for $^{53}$Ca obtained from new experimental data on the masses of $^{52-54}$Ca has the smallest value yet observed. This is explained in the framework of the nuclear shell model with schematic and realistic Hamiltonians as being due to shell gaps around the low-$ j $ orbital $ 1p_{1/2} $. Minima in the pairing gaps for all nuclei are shown and discussed
In 1928 G. Gamow as well as Condon and Gurney gave the first explanation of alpha decay as a quantum tunnelling of a preformed particle at the nuclear surface. Soon after experimental discovery in 1984 by Rose and Jones of cluster radioactivity, confirming earlier (1980) predictions by Sandulescu, Poenaru and W. Greiner, a microscopic theory also explained the phenomenon in a similar way. Here we show for the first time that in a spontaneous cold fission process the shell plus pairing corrections calculated with Strutinsky's procedure may give a strong argument for preformation of a light fiss…
The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions taking into accout enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. It was shown that the IS pairing and the effective spin operators gives a large quenching effect on the IV spin transitions to be consistent with observed data by $(p,p')$ experiments. On the other hand, the observed IS spin strength show much smaller quenching effect than expected by the calculated results. The IS pai…
The linear response approach to nuclear transport has been extended to pair correlations. The latter are treated within a mean field approximation to a pairing interaction with constant matrix elements $G$. The constraint of particle number conservation has been accounted for on a time dependent average, which leads to modified response functions, both in the pairing degree of freedom as well as in the shape variable. The former is expressed by the gap parameter $Δ$ and the latter by a $Q$ which specifies the elongation of a fissioning nucleus. The tensors for friction and inertia correspondin…
We study a trapped system of fermions with an attractive zero-range two-body interaction using the Shell-Model Monte Carlo method. The method provides {\em ab initio} results in the low $N$ limit where mean-field theory is not applicable. The energy and pairing properties are presented as functions of interaction strength, particle number, and temperature. In the interesting region where typical matrix elements of the two-body interaction are comparable to the level spacing of the trap we find large odd-even effects and signatures of shell structure. As a function of temperature, we observe th…
The heat capacity of iron isotopes is calculated within the interacting shell model using the complete $(pf+0g_{9/2})$-shell. We identify a signature of the pairing transition in the heat capacity that is correlated with the suppression of the number of spin-zero neutron pairs as the temperature increases. Our results are obtained by a novel method that significantly reduces the statistical errors in the heat capacity calculated by the shell model Monte Carlo approach. The Monte Carlo results are compared with finite-temperature Fermi gas and BCS calculations.
We analyse how the spatial localisation properties of pairing correlations are changing in a major neutron shell of heavy nuclei. It is shown that the radial distribution of the pairing density depends strongly on whether the chemical potential is close to a low or a high angular momentum level and has very little sensitivity to whether the pairing force acts in the surface or in the bulk. The averaged pairing density over one major shell is however rather flat, practically independent of the pairing force. Hartree-Fock-Bogoliubov calculations for the isotopic chain $^{100-132}$Sn are presente…
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell, there are degeneracies between the states corresponding to less and more than half full shell. We also provide a technique to solve the equations of Bethe ansatz.
Absolute values of two-particle transfer cross sections along the Sn-isotopic chain from closed shell to closed shell (100Sn,132Sn) are calculated taking properly into account nuclear correlations, as well as the successive, simultaneous and non-orthogonality contributions to the differential cross sections. The results are compared with systematic, homogeneous bombarding conditions (p, t) data. The observed agreement, almost within statistical errors and without free parameters, testify to the fact that theory is able to be quantitative in its predictions.
The Monte Carlo shell model is a powerful technique for computational nuclear structure. Only a certain class of nuclear interactions, however, such as pairing and quadrupole, are free of the numerical noise known as the sign problem.This paper presents sum rules that relate the sign problem to the J=0 pairing matrix elements, thus illuminating the extrapolation procedure routinely used for realistic shell-model interactions.
We perform Shell Model Monte Carlo calculations to study pair correlations in the ground states of $N=Z$ nuclei with masses A=48-60. We find that $T=1$, $J^π=0^+$ proton-neutron correlations play an important, and even dominant role, in the ground states of odd-odd $N=Z$ nuclei, in agreement with experiment. By studying pairing in the ground states of $^{52-58}$Fe, we observe that the isovector proton-neutron correlations decrease rapidly with increasing neutron excess. In contrast, both the proton, and trivially the neutron correlations increase as neutrons are added. We also study the therma…
We present an analysis of two-proton shell gaps in Sn isotopes. As the theoretical tool we use self-consistent mean-field models, namely the relativistic mean-field model and the Skyrme-Hartree-Fock approach, both with two different pairing forces, a delta interaction (DI) model and a density-dependent delta interaction (DDDI). We investigate the influence of nuclear deformation as well as collective correlations and find that both effects contribute significantly. Moreover, we find a further significant dependence on the pairing force used. The inclusion of deformation plus correlation effect…
A new theoretical approach is presented that combines the Hartree-Fock variational scheme with the exact solution of the pairing problem in the finite orbital space. Using this formulation in the sd-space as an example, we show that the exact pairing significantly improves the results for the ground state energy
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the $T=1$ pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-…
Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for $0\hbarΩ$ no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body int…
We investigate the extent to which theories of collective motion can capture the physics that determines the nuclear matrix elements governing neutrinoless double-beta decay. To that end we calculate the matrix elements for a series of isotopes in the full $pf$ shell, omitting no spin-orbit partners. With the inclusion of isoscalar pairing, a separable collective Hamiltonian that is derived from the shell model effective interaction reproduces the full shell-model matrix elements with good accuracy. A version of the generator coordinate method that includes the isoscalar pairing amplitude as a…
In this paper, eit is shown for a single-$j$ shell that the intrinsic excitations induced by the quadrupole-quadrupole interaction can be viewed as that due to the inverted surface-delta interaction whose multipole-pairing component with the largest spin is the dominant term and is attractive. This allow us to trace the origin of the recently introduced optimum pair description of rotation and leads naturally to analytical expressions for the rotational energies for the various bands in a single $j$-shell with the quadrupole-quadrupole interaction.
We develop a model of off-mass-shell pairing correlations in nuclear systems, which is based on the meson-exchange picture of nuclear interactions. The temporal retardations in the model are generated by the Fock-exchange diagrams. The kernel of the complex gap equation for baryons is related to the in-medium spectral function of mesons, which is evaluated nonperturbatively in the random phase approximation. The model is applied to the low-density neutron matter in neutron star crusts by separating the interaction into a long-range one-pion-exchange component and a short-range component parame…
