The physical conditions for the emergence of the extremely low-lying nuclear isomer ${}^{229m}\mathrm{Th}$ at approximately 8 eV are investigated in the framework of our recently proposed nuclear structure model. Our theoretical approach explains the ${}^{229m}\mathrm{Th}$-isomer phenomenon as the result of a very fine interplay between collective quadrupole-octupole and single-particle dynamics in the nucleus. We find that the isomeric state can only appear in a rather limited model space of quadrupole-octupole deformations in the single-particle potential, with the octupole deformation being of a crucial importance for its formation. Within this deformation space the model-described quantities exhibit a rather smooth behavior close to the line of isomer–ground-state quasidegeneracy determined by the crossing of the corresponding single-particle orbitals. Our comprehensive analysis confirms the previous model predictions for reduced transition probabilities and the isomer magnetic moment, while showing a possibility for limited variation in the ground-state magnetic moment theoretical value. These findings prove the reliability of the model and suggest that the same dynamical mechanism could manifest in other actinide nuclei giving a general prescription for the search and exploration of similar isomer phenomena.

The region of neutron-rich Cr isotopes has garnered much attention in recent years due to a rapid onset of collectivity near neutron number $N=40$. We report here on the first $\gamma$-ray spectroscopy beyond the $\left(4_1^{+}\right)$ state in ${}^{62,64}\mathrm{Cr}$, using nucleon removal reactions from several projectiles within a rare-isotope beam cocktail. A candidate for the $6^{+}$ state in ${}^{64}\mathrm{Cr}$ is presented as well as one for, possibly, the second excited $0^{+}$ state in ${}^{62}\mathrm{Cr}$. The results are discussed in comparison to the LNPS shell-model predictions that allow for neutron excitations across the $N=40$ harmonic oscillator gap into the $g_{9/2}$ and $d_{5/2}$ orbitals. The calculated level schemes for ${}^{62,64}\mathrm{Cr}$ reveal intriguing collective structures. From the predicted neutron particle-hole character of the low-lying states in these Cr isotopes, ${}^{62}\mathrm{Cr}$ emerges as a transitional system on the path to the center of the $N=40$ island of inversion.

The increase in strangeness production with charged particle multiplicity, as seen by the ALICE collaboration at CERN in $p\text{−}p$, $p$-Pb, and Pb-Pb collisions, is investigated in the hadron resonance gas model taking into account interactions among hadrons using $S$-matrix corrections based on known phase shift analyses. Strangeness conservation is taken into account in the framework of the canonical strangeness ensemble. A very good description is obtained for the variation of the strangeness content in the final state as a function of the number of charged hadrons in the midrapidity region using the same fixed temperature value as obtained in the most central Pb-Pb collisions and with a fixed strangeness suppression factor ${\gamma }_s=1$. It is shown that the number of charged hadrons is linearly proportional to the volume of the system. For small multiplicities the canonical ensemble with local strangeness conservation restricted to midrapidity leads to a stronger suppression of (multi)strange baryons than seen in the data. This is compensated by introducing a global conservation of strangeness in the whole phase-space which is parametrized by the canonical correlation volume larger than the fireball volume at the midrapidity. The results on comparing the hadron resonance gas model with and without S-matrix corrections, are presented in detail. It is shown that the interactions introduced by the phase shift analysis via the $S$-matrix formalism are essential for a better description of the yields data.

The $J=1/2$ iso-doublet double-$\mathrm{\Lambda }$-hypernuclei, namely, ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^5\mathrm{H}$ and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}{}^5\mathrm{He}$, are examined as the three-body cluster states, $\mathrm{\Lambda }\mathrm{\Lambda }t$ ($t\equiv {}^3$H or triton) and $\mathrm{\Lambda }\mathrm{\Lambda }h$ ($h\equiv {}^3$He or helion), respectively, in a model-independent framework utilizing pionless halo effective theory. Both singlet and triplet states of the constituent $\mathrm{\Lambda }T$ ($T\equiv t,h$) subsystem are used in the elastic channel for the study of ${}_{\mathrm{\Lambda }}^4$H-$\mathrm{\Lambda }$ and ${}_{\mathrm{\Lambda }}^4$He-$\mathrm{\Lambda }$ scattering processes. A prototypical leading-order investigation using a sharp momentum cutoff regulator ${\mathrm{\Lambda }}_c$ in the coupled integral equations for each type of the $\mathrm{\Lambda }T$ subsystem spin states yields identical renormalization group limit cycle behavior when the respective three-body contact interactions are taken close to the unitary limit. Furthermore, irrespective of the type of the elastic channel chosen, almost identical cutoff dependence of the three-body binding energy or the double-$\mathrm{\Lambda }$-separation energy ($B_{\mathrm{\Lambda }\mathrm{\Lambda }}$) is obtained for the mirror partners, evidently suggesting good isospin symmetry in these three-body systems. Subsequently, upon normalization of our solutions to the integral equation with respect to a single pair of input data from an ab initio potential model analysis for each mirror hypernuclei, yields $B_{\mathrm{\Lambda }\mathrm{\Lambda }}$ which agrees fairly well with various erstwhile regulator independent potential models for our choice of the cutoff, ${\mathrm{\Lambda }}_c\sim 200$ MeV. This is either consistent with pionless effective theory or with its slightly augmented version with a hard scale of ${\mathrm{\Lambda }}_H\gtrsim 2m_{\pi }$, where low-energy $\mathrm{\Lambda }-\mathrm{\Lambda }$ interactions dominated by $\pi \pi$ or $\sigma$-meson exchange. Finally, to demonstrate the predictability of our effective theory, we present preliminary estimates of the $S$-wave $\mathrm{\Lambda }\mathrm{\Lambda }T$ three-body scattering lengths and the $\mathrm{\Lambda }$-separation energies by using a range of currently accepted values of the double-$\mathrm{\Lambda }$ scattering length from a variety of existing phenomenological predictions that is constrained by the recent experimental data from relativistic heavy-ion collisions.

The deuteron-deuteron elastic and three- and four-body breakup scattering cross section have been calculated using the Faddeev-Yakubovskii (FY) chain-of-partition momentum-space equations. In this calculation the initial two-cluster potential is split into separable and nonseparable components, and the effective potential is reduced to elastic two-body and three- and four-body breakup open channels and a closed-channel many-body contribution. The closed-channel contribution is determined by minimizing a variational bound. The Coulomb interaction was included by expanding the initial and final Coulomb states in a Coulomb-Sturmian basis. The three sets of chain-of-partition integral equations were solved for the elastic and three- and four-body breakup scattering amplitudes. The calculations were performed for the $S=2\mathrm{spin}/L=0$ angular-momentum state. The elastic and double-breakup calculations were performed for energies up to $E=5.48\mathrm{MeV}$, while the single-breakup calculations were performed for energies up to $E=4.17\mathrm{MeV}$. In the case of elastic scattering, the calculated scattering length of ${}^5{a}_{dd}=7.8\pm 0.3$ fm is in good agreement with a FY cluster reduction calculation. The calculated phase shift is smaller than that predicted by the resonating group model and this difference is believed to be due to the differences in the potential and calculation methods. The breakup cross sections were calculated as a function of initial deuteron momentum and fragmented-deuteron momentum. The $d+d\to d+n+p$ cross sections were compared with neutron yield measurements and, while the measurements also included the $L>0$ components, the general features were consistent. Estimates of the calculational uncertainties/bias are provided.

We report on the first application of the stochastic Laplacian Heaviside method for computing multiparticle interactions with lattice QCD to the two-nucleon system. Like the Laplacian Heaviside method, this method allows for the construction of interpolating operators which can be used to construct a set of positive-definite two-nucleon correlation functions, unlike nearly all other applications of lattice QCD to two nucleons in the literature. It also allows for a variational analysis in which optimal linear combinations of the interpolating operators are formed that couple predominantly to the eigenstates of the system. Utilizing such methods has become of paramount importance to help resolve the discrepancy in the literature on whether two nucleons in either isospin channel form a bound state at pion masses heavier than physical, with the discrepancy persisting even in the SU(3)-flavor-symmetric point with all quark masses near the physical strange quark mass. This is the first in a series of papers aimed at resolving this discrepancy. In the present work, we employ the stochastic Laplacian Heaviside method without a hexaquark operator in the basis at a lattice spacing of $a\approx 0.086$ fm, lattice volume of $L=48a\approx 4.1$ fm and pion mass $m_{\pi }\approx 714$ MeV. With this setup, the observed spectrum of two-nucleon energy levels strongly disfavors the presence of a bound state in either the deuteron or dineutron channel.

The electromagnetic structure of ${}^{66}\mathrm{Zn}$ at low excitation energy was investigated via low-energy Coulomb excitation at INFN Legnaro National Laboratories, using the Gamma Array of Legnaro Infn Laboratories for nuclEar spectrOscopy (GALILEO) $\gamma$-ray spectrometer coupled to the SPIDER (Silicon PIe DEtectoR). A set of reduced $E2, E3$, and $M1$ matrix elements was extracted from the collected data using the gosia code, yielding 12 reduced transition probabilities between the low-spin states and the spectroscopic quadrupole moment of the ${2_1}^{+}$ state. The $B\left(E2\right)$ values for transitions depopulating the ${0_2}^{+}$ state have been determined for the first time, allowing for the lifetime of this state to be deduced and, consequently, the ${\rho }^2(E0;{0_2}^{+}\to {0_1}^{+})$ monopole transition strength to be extracted. In addition, the $B(E3;{3_1}^{-}\to {0_1}^{+})$ value has been determined for the first time in a Coulomb excitation experiment. The obtained results resolve the existing discrepancies between literature lifetimes and demonstrate that ${}^{66}\mathrm{Zn}$ cannot be described by using simple collective models. Therefore, new state-of-the-art beyond-mean-field and large-scale shell-model calculations were performed in order to interpret the structure of this nucleus. Both the experimental and theoretical results suggest that the triaxial degree of freedom has an important impact on electromagnetic properties of ${}^{66}\mathrm{Zn}$, while the unique features of the ${0_2}^{+}$ state indicate its distinct and rather isolated structure.

We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasiparticle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of ${}^{132}\mathrm{Ba}$ in the $50\le Z,N\le 82$ model space. We also discuss the feasibility of this scheme in the case of the ${}^{150}\mathrm{Nd}$ in the $50\le Z\le 82$ and $82\le Z\le 126$ model space and demonstrate that its neutrinoless double-$\beta$-decay matrix element is obtained showing good convergence.

Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify.

Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations.

Methods: We employ the fission simulation model freya, which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in freya and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of ${}^{235}\mathrm{U}$ relative to the ground state.

Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins, which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, ${}^{235\mathrm{m}}\mathrm{U}$($n_{\mathrm{th}}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energies.

Conclusions: While the initial angular momentum of the fissioning nucleus tends to have little effect on the observables, those of the produced fragments influence the emitted neutrons and photons in a significant and correlated manner which may be exploited experimentally to elucidate the fission process.

We calculate the electric dipole moment of the nucleon induced by the quantum chromodynamics $\theta$ term. We use the gradient flow to define the topological charge and use $N_f=2+1$ flavors of dynamical quarks corresponding to pion masses of 700, 570, and $410\mathrm{MeV}$, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at three different lattice spacings in the range of $0.07\mathrm{fm}<a<0.11\mathrm{fm}$ at a single value of the pion mass, to enable control on discretization effects. We also investigate finite-size effects using two different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuumlike behavior of the nucleon electric dipole moment toward the chiral limit. Under this assumption our results read $d_n=-0.00152\left(71\right)\overline{\theta }e\text{fm}$ and $d_p=0.0011\left(10\right)\overline{\theta }e\text{fm}$. Assuming the $\theta$ term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\overline{\theta }\right|<1.98\times {10}^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_p=0.50\left(59\right)\times {10}^{-4}\overline{\theta }e{\text{fm}}^3$ and $S_n=-0.10\left(43\right)\times {10}^{-4}\overline{\theta }e{\text{fm}}^3$.

Background: The competing ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reactions control the production of neutrons for the weak $s$ process in massive and asymptotic giant branch (AGB) stars. In both systems, the ratio between the corresponding reaction rates strongly impacts the total neutron budget and strongly influences the final nucleosynthesis. A number of experimental studies have been performed over recent years which necessitate the reevaluation of the ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reaction rates. Evaluations of the reaction rates following the collection of new nuclear data presently show differences of up to a factor of 500, resulting in considerable uncertainty in the resulting nucleosynthesis.

Purpose: To reevaluate the ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reaction rates using updated nuclear data from a number of sources including updating spin and parity assignments.

Methods: With updated spin and parity assignments, the levels which can contribute to the reaction rates are identified. The reaction rates are computed using a Monte Carlo method which has been used for previous evaluations of the reaction rates in order to focus solely on the changes due to modified nuclear data.

Results: The evaluated ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ reaction rate remains substantially similar to that of Longland et al. but, including recent results from Texas A&M, the ${}^{22}\mathrm{Ne}(\alpha ,n){}^{25}\mathrm{Mg}$ reaction rate is lower at a range of astrophysically important temperatures. Stellar models computed with newton and mesa predict decreased production of the weak branch $s$ process due to the decreased efficiency of ${}^{22}\mathrm{Ne}$ as a neutron source. Using the new reaction rates in the mesa model results in ${}^{96}\mathrm{Zr}/{}^{94}\mathrm{Zr}$ and ${}^{135}\mathrm{Ba}/{}^{136}\mathrm{Ba}$ ratios in much better agreement with the measured ratios from presolar SiC grains.

Conclusion: The ${}^{22}\mathrm{Ne}+\alpha$ reaction rates ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha .n){}^{25}\mathrm{Mg}$ have been recalculated based on more recent nuclear data. The ${}^{22}\mathrm{Ne}(\alpha ,\gamma ){}^{26}\mathrm{Mg}$ reaction rate remains substantially unchanged since the previous evaluation but the ${}^{22}\mathrm{Ne}(\alpha .n){}^{25}\mathrm{Mg}$ reaction rate is substantially decreased due to updated nuclear data. This results in significant changes to the nucleosynthesis in the weak branch of the $s$ process.

Low-energy level scheme of doubly odd transfermium nucleus ${}_{101}^{252}{\mathrm{Md}}_{151}$ is constructed using our well-tested two-quasiparticle rotor model with explicit inclusion of residual n-p interaction contribution. Energy levels thus deduced are examined critically to assign spin-parity $J^{\pi }K$ and two-quasiparticle (2qp) configurations to the ${}^{252}\mathrm{Md}$ ground state and other energy levels with $E_x<400$ keV. Our low-energy level structures are then examined to predict a high-spin $(J^{\pi }=8^{+})$ long-lived isomer with $E_x\approx 125$ keV and possibly also a lower-lying short-lived isomeric state. Comparison with ${}^{256}\mathrm{Lr}$ $\left(\alpha \right)$ populated ${}^{252}\mathrm{Md}$ excited states leads to $J^{\pi }K$ and 2qp assignment to each of these experimentally postulated levels. Further, the five $\gamma$'s ascribed to ${}^{252}\mathrm{Md}$ from $\alpha \text{−}\gamma$ coincidence experiments are placed in our evaluated levels corresponding to $\mathrm{\Delta }I=2$ transition in each case. Additionally, exploration of the upward extended radioactive connection of ${}^{232}\mathrm{Th}$ heading the $A=4n$ naturally occurring radioactive series to the heaviest known superheavy element with $A=4n$, namely ${}_{111}^{272}{\mathrm{Rg}}_{161}$, has led us to establish landmark position of ${}^{252}\mathrm{Md}$ in this ${}^{272}\mathrm{Rg}\text{−}{}^{232}\mathrm{Th}$ extended decay chain.

Event-by-event long-range correlations of azimuthal anisotropy Fourier coefficients $\left(v_n\right)$ in 8.16 TeV $p\mathrm{Pb}$ data, collected by the CMS experiment at the CERN Large Hadron Collider, are extracted using a subevent four-particle cumulant technique applied to very low multiplicity events. Each combination of four charged particles is selected from either two, three, or four distinct subevent regions of a pseudorapidity range from $-2.4$ to 2.4 of the CMS tracker, and with transverse momentum between 0.3 and 3.0 GeV. Using the subevent cumulant technique, correlations between $v_n$ of different orders are measured as functions of particle multiplicity and compared to the standard cumulant method without subevents over a wide event multiplicity range. At high multiplicities, the $v_2$ and $v_3$ coefficients exhibit an anticorrelation; this behavior is observed consistently using various methods. The $v_2$ and $v_4$ correlation strength is found to depend on the number of subevents used in the calculation. As the event multiplicity decreases, the results from different subevent methods diverge because of different contributions of noncollective or few-particle correlations. Correlations extracted with the four-subevent method exhibit a tendency to diminish monotonically toward the lowest multiplicity region (about 20 charged tracks) investigated. These findings extend previous studies to a significantly lower event multiplicity range and establish the evidence for the onset of long-range collective multiparticle correlations in small system collisions.

In this paper, we present a systematic study of Xe-Xe collisions at 5.44-TeV center-of-mass energy. We employ the Monte Carlo (hydrodynamics plus jets) $\mathrm{HYDJET}++$ model to calculate the pseudorapidity distribution, transverse momentum $\left(p_T\right)$ spectra and the elliptic flow $\left(v_2\right)$ of charged hadrons with different parameters in two geometrical configurations: body-body and tip-tip type of Xe-Xe collisions. The kinematic ranges $0<p_T<50\mathrm{GeV}/c$ and $\left|\eta \right|<0.8$ are considered for our paper. Results are obtained for seven classes of centrality. For comparison, we have shown results from the AMPT model with the string-melting version. The results obtained for Xe-Xe collision systems for minimum bias at midrapidity match well with the experimental data of the ALICE/CMS Collaborations. We observe that the pseudorapidity density depends on the size and geometry of the colliding system. The centrality dependence of average transverse momentum ($\langle p_T\rangle$) and average elliptic flow ($\langle v_2\rangle$) is also observed. The charged hadron properties also show clear dependence on the geometrical configuration of the collisions. Our model results have been compared to results obtained in the AMPT model. The $\mathrm{HYDJET}++$ model justifies data more closely than the AMPT model, the latter mostly overpredicts the experimental data.

The nuclear level densities (NLDs) and the $\gamma$-ray strength functions ($\gamma \mathrm{SFs}$) of ${}^{153,155}\mathrm{Sm}$ have been extracted from ($d,p\gamma$) coincidences using the Oslo method. The experimental NLD of ${}^{153}\mathrm{Sm}$ is higher than the NLD of ${}^{155}\mathrm{Sm}$, in accordance with microscopic calculations. The $\gamma \mathrm{SFs}$ of ${}^{153,155}\mathrm{Sm}$ are in fair agreement with QRPA calculations based on the D1M Gogny interaction. An enhancement is observed in the $\gamma \mathrm{SF}$ for both ${}^{153,155}\mathrm{Sm}$ nuclei around 3 MeV in excitation energy and is attributed to the $M1$ scissors resonance (SR). Their integrated strengths were found to be in the range 1.3–2.1 and 4.4–6.4 ${\mu }_N^2$ for ${}^{153}\mathrm{Sm}$ and ${}^{155}\mathrm{Sm}$, respectively. The strength of the SR for ${}^{155}\mathrm{Sm}$ is comparable to those for deformed even-even Sm isotopes from nuclear resonance fluorescence measurements, while that of ${}^{153}\mathrm{Sm}$ is lower than expected.

The persistently mysterious deviations from unity of the ratio of nuclear target structure functions to those of deuterium as measured in deep inelastic scattering (often termed the “EMC effect”) have become the canonical observable for studies of nuclear medium modifications to free nucleon structure in the valence regime. The structure function of the free proton is well known from numerous experiments spanning decades. The free neutron structure function, however, has remained difficult to access. Recently it has been extracted in a systematic study of the global data within a parton distribution function extraction framework and is available from the CTEQ–Jefferson Lab (CJ) Collaboration. Here, we leverage the latter to introduce a new method to study the EMC effect in nuclei by reexamining existing data in light of the the magnitude of the medium modifications to the free neutron and proton structure functions independently. From the extraction of the free neutron from world data, it is possible to examine the nuclear effects in deuterium and their contribution to our interpretation of the EMC effect. In this study, we observe that the ratio of the deuteron to the sum of the free neutron and proton structure functions has some $x_B$ and $Q^2$ dependencies that impact the magnitude of the EMC effect as typically observed. Specifically, different EMC slopes are obtained when data from different $x_B$ and $Q^2$ values are utilized. While a linear correlation persists between the EMC and short range correlation effects, the slope is modified when deuteron nuclear effects are removed.

The shear viscosity ($\eta$) of nuclear matter is investigated in different nuclei (nuclear mass $A\approx 59–194$) using experimental giant dipole resonance (GDR) width ($\mathrm{\Gamma }$) at high angular momenta ($J=12–54$ $\hslash$) and temperatures ($T=1.2–2.1$ MeV) collected from the existing literature. $\eta$, calculated from $\mathrm{\Gamma }$, is found to increase with $T$ and $J$. We show that critical temperature included fluctuation model (CTFM) successfully describes $J$-induced $\eta$ even beyond critical angular momentum $J_c$ at different values of $T$. However, the Fermi liquid drop model (FLDM) could not explain the data at higher angular momenta. We propose the addition of a $J$-dependent term with the FLDM $\eta$ to improve the prediction at such high-$J$ region. The $\eta /s$ ratio, highly important for measuring fluidity, is calculated using $\eta$ and the entropy density $s$. The latter is estimated using the Fermi gas formula. Interestingly, the experimental value of the ratio is independent of $J$ and $A$ and comes within 2.6–6.0 $\hslash /4\pi k_{\mathrm{B}}$, which is very close to those of a partonic system like quark gluon plasma at high temperature.

The diagonalization technique for two-body propagator in nuclear matter is generalized by inclusion of the two-hole continuum. In the approach, the total effective two-body Hamiltonian is introduced which allows us to find the complete propagator as well as the reaction $T$ matrix at many energies and relative momenta simultaneously from a single diagonalization procedure for the Hamiltonian matrix. Explicit treatment of bound and continuum states allows us to determine forward- and backward-propagating parts of the $T$ matrix in a closed form which simplifies strongly the evaluation of single-particle and single-hole self-energies. Special attention is paid to the bound-state contribution to the reaction matrix in case of pairing instability when complex conjugated eigenvalues of the effective Hamiltonian appear. A generalization of the approach to calculation of pairing gaps in case of nonzero center-of-mass momentum of the pair is also presented.