Search

Our study employs the nuclear shell model to systematically compute the half-lives of $\beta$ -decay for nuclei in the mass range of $A = 18-39$, encompassing the majority of $sd$ shell nuclei. This analysis utilizes the USDB and SDNN Hamiltonians. The theoretical outcomes contain calculations of various parameters such as $Q$ -values, half-lives, excitation energy, log$ft$ values, and branching ratios. We explore these results with axial-vector coupling constant for weak interactions, denoted as $g_A$$(= 1.27)$, and $\kappa$ value $(= 6289)$. We perform calculations of Gamow Teller matrix elements for 116 decay processes to calculate the quenching factor; we found a quenching factor of $q = 0.794\pm0.05 $ for the USDB interaction and $q = 0.815\pm0.04 $ for the SDNN interaction. We have also calculated superallowed transitions $0^+ \rightarrow 0^+$ for seven nuclei. Further, we have also included the electron capture phase space factor for the required nuclei to calculate the half-lives. This inclusion leads to small contribution in results, particularly for nuclei where electron capture (EC) plays a significant role. The overall results are in agreement with the experimental data., Comment: 16 pages, 4 figures

In this study, we developed and tested various isospin symmetry-breaking (ISB) versions of the microscopic DJ16A interaction. Starting with the isospin symmetric DJ16A interaction, we introduced two different Coulomb interactions-Coulomb-CD and Coulomb-w/SRC-along with phenomenological charge symmetry breaking (CSB) and charge independence breaking (CIB) effects. We also considered CSB and CIB parts of the Argonne v18 (AV18) interaction. We examined two sets of interactions for each Coulomb interaction and employed these interactions to calculate $b$- and $c$-parameters of the isobaric multiplet mass equation for $|T_z| = 1/2$ and $|T_z| = 1$ nuclei across the $sd$-shell. Our results indicate that the DJ16A$^\dagger$+CD interaction provides the most accurate $b$-parameter predictions up to $A = 33$ mirror pairs. Additionally, we explored mirror energy differences (MEDs) in low-energy spectra around $A = 20$ and demonstrated that large MEDs are primarily associated with high occupancies of the $1s_{1/2}$ orbital. Furthermore, $E2$ transition strengths were calculated using all four DJ16A-based ISB interactions agreed with the experimental data, with minimal ISB effects observed on these transitions. Overall, the DJ16A$^\dagger$+CD interaction serves as a complementary set to the newly developed USD-family interactions, USDC, and USDCm and can be further tested for other mirror nuclei across the $sd$-shell to study nuclear structure properties and ISB effects in nuclear $\beta$-decay., Comment: 18 pages, 14 figures

In the present work, we have predicted the half-lives for the $\beta^{-}$ decay for higher forbidden unique transitions in the mass range of nuclei from A = 40-138. For these transitions, the experimental data for half-lives are not available except for a few cases. The calculations for half-lives are performed within the framework of the nuclear shell model (SM). We have used the effective interactions sdpf-mu, gxpf1a, gwbxg, G-matrix, snet, sn100pn, and jj56pnb to perform the SM calculations in different mass regions. A comprehensive discussion has been made between the SM-predicted half-lives and the scaled half-lives from proton-neutron quasiparticle random-phase approximation (pnQRPA). The results of the present study will be useful to plan new experiments to measure half-lives for these higher forbidden unique $\beta^{-}$ transitions., Comment: 8 pages, 2 figures

Recently, a linear relationship between product of bound energy, a thermodynamic quantity, of a ground state with system size and square of half-chain entanglement entropy has been established for free fermionic chain with nearest neighbor hopping and conjectured to be true for all 1D conformal field theories [Phys. Rev. B, 107,075116(20230]. We probe this relationship in domain where conformal symmetry is broken using 1D Kitaev model with pairing term which decays with distance as a power-law with exponent $\alpha$. We analytically show that for $\alpha=1$, this relationship persists with same slope as found in $\alpha \to \infty$ case where conformal symmetry is unbroken. We recall that conformal symmetry is broken for $\alpha<3/2$ [Phys. Rev. Lett., 113,156402(2014)]. We numerically show that linearity persists for intermediate values of $\alpha$. The presence of long range pairing helps in extracting more energy for the work i.e. ergotropy. We show analytically that ergotropy increases logarithmically with system size for $\alpha=1$ and becomes proportional to system size for $\alpha=0$ (numerically).

We study the energy transfer process in the recently proposed sunburst quantum Ising model, which consists of two interacting integrable systems: a transverse Ising chain with a very small transverse field and a finite number of external isolated qubits. We show that in this model of the quantum battery, coupling between the battery and charger can be used to optimize the ergotropy, which is the maximum amount of energy that can be extracted from the battery. At the same time, maximum charging power increases with the coupling strength, allowing for the simultaneous optimization of both ergotropy and charging power in the strong coupling limit. Furthermore, we show that both ergotropy and charging power are independent of the initial state of the charger.

The isoscalar and isovector components and their contributions to $M1$ transitions are discussed in the odd-$A$, $T=1/2$ mirror nuclei with mass ranging from $A=23$ to 37. The orbital contributions in various $M1$ transitions and ground state magnetic moments are calculated by comparing analogous $M1$ and Gamow-Teller transitions between mirror pairs. The orbital contributions in different $M1$ transitions are explained on the basis of configurations of the initial and final states involved. In magnetic moments, the orbital contributions are found to be dependent on the deformation and single-particle nature of the states. All the $T=1/2$ mirror pairs are studied using isospin non-conserving interaction. The results are also compared with predictions from \textit{ab initio} effective interaction derived from realistic nuclear forces., Comment: 13 pages, 7 figures

High-spin states in the transitional $^{217}$Ac nucleus are established up to 3.8 MeV excitation energy and $I^{\pi} =$ 41/2$^+$ with the addition of around 20 new transitions. The structure of the yrast and near-yrast states below the 29/2$^+$ isomer is revisited. The inconsistencies in the level schemes reported earlier are resolved. The level structure above the 29/2$^+$ isomer is established for the first time. Large-basis shell-model calculations with the KHPE interaction are performed to compare the experimentally observed level energies with the theoretical predictions. A comparison with the systematics of the N = 128 isotones suggests that the yrast structures result from a weak coupling of the odd proton to the even-even 216Ra core, which is consistent with the shell-model configurations. Furthermore, alpha decay of the 29/2$^+$ isomer is revisited and the decay scheme established from this work is discussed in the framework of the shell model., Comment: 11 pages, 9 figures

The importance of the isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon-nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the $N=Z$ system in the density functional approach., Comment: 44 pages, 19 figures

In this work, we have studied the $2\nu\beta\beta$ decay of $^{76}$Ge and $^{96}$Zr isotopes utilizing large-scale shell-model calculations. The GWBXG effective interaction has been employed in the calculation of $2\nu\beta\beta$-decay nuclear matrix elements (NMEs). We have tested the effective interaction by comparing the predicted spectroscopic properties, such as energy spectra and transition probabilities, with the available experimental data. The variation of cumulative NMEs with respect to the $1^+$ state energies of the intermediate nucleus is also studied, corresponding to $0^+_{\rm g.s}\rightarrow0^+_{\rm g.s}$, $0^+_{\rm g.s}\rightarrow0^+_{2}$, and $0^+_{\rm g.s}\rightarrow2^+_{1}$ transitions between the parent and granddaughter nuclei. The extracted half-lives using the shell-model predicted NMEs show good agreement with the recent experimental data. The comparison of the shell-model predicted NMEs with previous NMEs available in the literature is discussed. Also, the computed branching ratios for the $2\nu\beta\beta$ decay of $^{76}$Ge and both the $2\nu\beta\beta$ and single-$\beta$ decay of $^{96}$Zr are reported., Comment: 10 pages, 5 figures, 4 tables

In this work, we have performed systematic shell-model calculations for Bi isotopes with $A=$ 204-213 using KHH7B and KHM3Y effective interactions. We have reported yrast and non-yrast shell-model states corresponding to the available experimental data. From the comparison with the experimental data, we could assign spin and parity of several unconfirmed states. We have also calculated electromagnetic properties and compared them with the available experimental data and predicted where experimental data are not available. This study also includes a detailed discussion of multiple isomeric states based on computed shell-model configurations and their respective half-lives., Comment: Journal of Physics G: Nuclear and Particle Physics (2024)

The masses of $^{84}$Br, $^{105}$Mo, $^{115,119,121}$Pd, $^{122}$Ag, $^{127,129}$In, $^{132}$Sb and their respective isomeric states have been measured with the JYFLTRAP Penning trap mass spectrometer using the phase-imaging ion-cyclotron-resonance technique. The excitation energies of the isomeric states in $^{132}$Sb and $^{119}$Pd were experimentally determined for the first time, while for $^{84}$Br, $^{115}$Pd and $^{127,129}$In, the precision of the mass values was substantially improved. In $^{105}$Mo and $^{121}$Pd there were no signs of a long-lived isomeric state. The ground-state measurements of $^{119}$Pd and $^{122}$Ag indicated that both are significantly more bound than the literature values. For $^{122}$Ag, there was no indication of a proposed third long-lived state. The results for the $N=49$ nucleus $^{84}$Br and isomers close to doubly magic $^{132}$Sn have been compared to the shell-model and the microscopic quasiparticle-phonon model calculations., Comment: 14 pages, 10 figures

In the present work, beta-decay properties such as $\log ft$ values and half-lives have been systematically studied corresponding to Ba isotopes using large-scale shell-model calculations. An extensive comparison of beta decay results corresponding to $^{141}$Ba$\rightarrow$ $^{141}$La using shell-model calculations is made with the recently available experimental data. In addition, we have also calculated the nuclear and beta decay properties corresponding to $^{139}$Ba$\rightarrow$ $^{139}$La and $^{140}$Ba$\rightarrow$ $^{140}$La transitions. The model-space considered here is $Z=50-82$ and $N=82-126$ with $^{132}$Sn core, and the interaction employed here is jj56pnb interaction. The beta decay results using shell-model calculations for all the mentioned isotopes are compared with the available experimental data. This is the first theoretical interpretation corresponding to recent experimental data., Comment: 26 pages, 7 figures

Systematic shell-model calculations are presented for odd-mass Cd isotopes with $N=51-81$ utilizing a combination of a $G$-matrix interaction and a semiempirical one. The excited energy spectra and electromagnetic transition probabilities are compared with the recently available experimental data. We have found that the observed quadrupole moments in the $11/2^-_1$ states that linearly change with the neutron number are well accounted for by the dominance of prolate shapes throughout the Cd isotope chain. We have also described the properties of several isomeric states in neutron-rich $^{127-131}$In isotopes that were recently observed in Jyv\"askyl\"a., Comment: 16 pages, 13 figures

The properties of a nanosecond isomer in $^{32}$Si, disputed in previous studies, depend on the evolution of proton and neutron shell gaps near the `island of inversion'. We have placed the isomer at 5505.2(2) keV with $J^{\pi} = 5^-$, decaying primarily via an $E3$ transition to the $2^+_1$ state. The $E3$ strength of 0.0841(10) W.u. is unusually small and suggests that this isomer is dominated by the $(\nu d_{3/2})^{-1} \otimes (\nu f_{7/2})^{1}$ configuration, which is sensitive to the $N=20$ shell gap. A newly observed $4^+_1$ state is placed at 5881.4(13) keV; its energy is enhanced by the $Z=14$ subshell closure. This indicates that the isomer is located in a `yrast trap', a feature rarely seen at low mass numbers., Comment: Accepted, Physical Review C

In the present work, the $^{204-210}$Tl isotopes have been investigated by performing large-scale shell-model calculations, including configurations allowing both neutron and proton core excitations across the $Z$ = 82 and $N$ = 126 shell gaps. Inspired by the recent high-spin experimental data, the structure of Tl isotopes has been studied for a considerably large model space. The KHHE interaction has been used for $^{204-206}$Tl isotopes, KHH7B interaction for $^{204-210}$Tl isotopes, and additionally KHM3Y interaction has been used for $^{208}$Tl isotope. The core excitation has been performed using the KHH7B and KHM3Y interactions. The level spectra of $^{204-210}$Tl isotopes are comprehensively described and explained by multi-nucleon couplings of single-particle-hole orbitals within the valence space and by core excitations across $^{208}$Pb core. The well-known isomeric states are analyzed in terms of the shell model configurations., Comment: 17 pages, 8 figures

Large-scale shell-model calculations have been performed for the study of two neutrino double-beta ($2\nu\beta\beta$) decay in $^{82}$Se, $^{94}$Zr, $^{108}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{136}$Xe, and $^{150}$Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for $2\nu\beta\beta$ decay in $^{82}$Se. In the case of $^{94}$Zr, the glekpn effective interaction is used. For $^{108}$Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of $^{124}$Sn, $^{128,130}$Te and $^{136}$Xe, the sn100pn effective interaction is employed. For $^{150}$Nd, we have used KHHE effective interaction based on holes in a $^{208}$Pb core. We have extracted the half-lives of these nuclei for the $2\nu\beta\beta$ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative $2\nu\beta\beta$ NME with respect to the excitation energy of the intermediate $1^+$ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate $1^+$ states as much as possible in comparison to results available in the literature., Comment: 17 pages, 2 figures, 2 tables

We have done a systematic no-core shell-model study of $^{20-23}$Na isotopes. The low-energy spectra of these sodium isotopes consisting of natural and un-natural parity states were reported, considering three realistic interactions: inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K), and the chiral next-to-next-to-next-to-leading order (N$^3$LO). We also present the mirror energy differences in the low-energy spectra of $|T_z|$ = 1/2 mirror pair ($^{21}$Na - $^{21}$Ne). Apart from the energy spectra, we have also reported the electromagnetic transition strengths and moments. Finally, considering all three realistic interactions, we report the point-proton radii and neutron skin thicknesses., Comment: 18 pages, 17 figures

In the present work, we have reported $\beta^+$/EC-decay half-lives for $Z = 21 -30$ nuclei using large-scale shell-model. %and N $\leq$ A recent study shows that some proton-rich nuclei in this region belong to the island of inversion. We have performed calculations for these nuclei using KB3G effective interaction, while for Ni, Cu, and Zn nuclei we have used JUN45 effective interaction in the $f_{5/2}pg_{9/2}$ model space. The calculated quenching factors for $fp$ and $f_{5/2}pg_{9/2}$ space using KB3G and JUN45 effective interactions are also reported. Shell-model results of $\beta$-decay half-lives, excitation energies, log$ft$ values, and branching fractions are discussed and compared with the available experimental data. We have obtained a reasonable agreement with the available data., Comment: 12 pages, 4 figures, 4 Tables, The European Physical Journal A : Hadrons and Nuclei (2023)

The large-scale shell-model calculations have been performed for the neutron-rich nuclei in the south region of $^{208}$Pb in the nuclear chart. The $\beta$-decay properties, such as the $\log ft$, average shape factor values, half-lives, and partial decay rates are calculated for these neutron-rich nuclei using recent effective interaction for the $^{208}$Pb region. These calculations have been performed without truncation in a particular model space for nuclei $N\leq 126$; additionally, particle-hole excitations are included in the case of core-breaking nuclei ($Z\leq 82, N>126$). An extensive comparison with the experimental data has been made, and spin parities of several states have been proposed., Comment: 16 pages, 6 figures

Neutron-rich $^{120-124}$In isotopes have been studied utilizing the double Penning trap mass spectrometer JYFLTRAP at the IGISOL facility. Using the phase-imaging ion-cyclotron-resonance technique, the isomeric states were resolved from ground states and their excitation energies measured with high precision in $^{121,123,124}$In. In $^{120,122}$In, the $1^+$ states were separated and their masses were measured while the energy difference between the unresolved $5^+$ and $8^-$ states, whose presence was confirmed by post-trap decay spectroscopy was determined to be $\leq15$ keV. In addition, the half-life of $^{122}$Cd, $T_{1/2} = 5.98(10)$ s, was extracted. Experimental results were compared with energy density functionals, density functional theory and shell-model calculations., Comment: 11 pages, 7 figures

In the noisy intermediate-scale quantum era, variational algorithms have become a standard approach to solving quantum many-body problems. Here, we present variational quantum eigensolver (VQE) results of selected oxygen isotopes within the shell model description. The aim of the present work is to locate the neutron drip line of the oxygen chain using unitary coupled cluster (UCC) type ansatze with different microscopic interactions (DJ16, JISP16, and N3LO), in addition to a phenomenological USDB interaction. While initially infeasible to execute on contemporary quantum hardware, the size of the problem is reduced significantly using qubit tapering techniques in conjunction with custom circuit design and optimization. The optimal values of ansatz parameters from classical simulation are taken for the DJ16 interaction, and the tapered circuits are run on IonQ's Aria, a trapped-ion quantum computer. After applying gate error mitigation for three isotopes, we reproduced exact ground state energies within a few percent error. The post-processed results from hardware also clearly show $^{24}$O as the drip line nucleus of the oxygen chain. Future improvements in quantum hardware could make it possible to locate drip lines of heavier nuclei., Comment: 13 pages, 10 figures, 8 tables

In the present work, we report a systematic theoretical study of the $\log ft$ values for the forbidden $\beta^-$ decay transitions in the $^{208}$Pb region. For this, we have considered $^{206}$Hg $\rightarrow$ $^{206}$Tl, $^{208}$Hg $\rightarrow$ $^{208}$Tl, $^{206}$Tl $\rightarrow$ $^{206}$Pb and $^{208}$Tl $\rightarrow$ $^{208}$Pb transitions. We have performed shell model calculations using KHH7B interaction in valence shell 58-114 for protons and 100-164 for neutrons by considering ${\it 1p-1h}$ excitations for both protons and neutrons simultaneously for daughter nuclei. This study presents the first shell model results of $\beta^-$-decay corresponding to the recent experimental data., Comment: 4 pages, 1 figure, 1 table, Journal of Physics: Conference Series [28th International Nuclear Physics Conference (INPC 2022) held at Cape Town, South Africa]

We report systematic large-scale shell-model calculation for Po isotopes with $A=$ 200 to 210. We have performed calculations using KHH7B interaction in the model space $Z$ = 58-114 and $N$ = 100-164 around doubly-magic $^{208}$Pb. We allow valence neutrons to occupy in the $1f_{5/2}$, $2p_{3/2}$, $2p_{1/2}$, and $0i_{13/2}$ orbitals, while two valence protons beyond $Z=82$ are occupied in $0h_{9/2}$, $1f_{7/2}$ and $0i_{13/2}$ orbitals. The calculated energies and electromagnetic properties are compared with the available experimental data and predicted where experimental data are not available. We have also reported shell-model results for different isomeric states of these nuclei., Comment: 35 pages, 12 figures

In the present work, newly developed microscopic effective $sd$-valence shell interactions such as chiral next-to-next-to-next-to-leading order (N3LO), $J$-matrix inverse scattering potential (JISP16), Daejeon16 (DJ16), and monopole-modified DJ16 (DJ16A) are employed to study the nuclear structural properties of sulphur, chlorine, and argon isotopes with $N \geq Z$. These interactions are derived using the \textit{ab initio} no-core shell-model and the OLS unitary transformation method. We calculate energy spectra and electromagnetic properties to test the predictive strength of the effective interactions for these heavier $sd$-shell nuclei. For a complete systematic study, we compare the microscopic results with the phenomenological USDB results and experimental data. By looking at the excitation energies of these nuclei, the DJ16A interaction is found to be {the} most suitable for these $sd$-shell nuclei among all microscopic interactions. The electric quadrupole transition strength and excitation energy of the first $2^+$ state data of even-even sulphur isotopes indicate the presence of the $N=20$ shell closure. Quadrupole moment predictions are also made using these interactions where experimental data are unknown. Magnetic moments are in excellent agreement with the experimental values. The root-mean-square deviations are also calculated to provide an idea of how accurate the interactions are., Comment: 14 pages, 7 figures, The European Physical Journal A-Hadrons and Nuclei (accepted)

We present systematic shell-model studies of even-even $^{98-130}$Cd isotopes using a realistic effective shell-model interaction derived from the G-matrix approach with an inert core $^{88}$Sr. Our calculated low-lying excited energy spectra and electromagnetic properties are compared with the experimental data. On the basis of recently available experimental data, we predict spins and parities corresponding to unconfirmed states. We also discuss the properties of $8^+$ isomeric states in $^{98-104,130}$Cd isotopes., Comment: 20 pages, 13 figures

In this work, the large-scale shell-model calculations for $\beta$-decay properties have been done. The $\beta$-delayed $\gamma$-ray spectroscopy has been performed recently at ILL, Grenoble [M. Si \textit{et al.}, Phys. Rev. C {\bf 106}, 014302 (2022)] to study $\beta$-decay properties corresponding to $^{137}$Te (($7/2^-))$ $\rightarrow$ $^{137}$I ($J_f$) transitions. We have done a systematic shell-model study for nuclear structure properties and compared the obtained results with the experimental data. Finally, the $\beta$-decay properties such as the $\log ft$ values and average shape factors have been reported. This is the first theoretical calculation for the $\log ft$ values corresponding to these new experimental data. In addition, we have also reported calculated $\log ft$ results for $^{135}$Te (($7/2^-))$ $\rightarrow$ $^{135}$I ($J_f$) transitions., Comment: 16 pages, 1 figure, 4 tables, Accepted in Nuclear Physics A (2023)

We study the non-equilibrium dynamics of an isolated bipartite quantum system, the sunburst quantum Ising model, under interaction quench. The pre-quench limit of this model is two non-interacting integrable systems, namely a transverse ising chain and finite number of isolated qubits. As a function of interaction strength, the spectral fluctuation property goes from Poisson to Wigner-Dyson statistics. We chose entanglement entropy as a probe to study the approach to thermalization or lack of it in post-quench dynamics. In the near-integrable limit, as expected, the linear entropy displays oscillatory behavior while in the chaotic limit, it saturates. Along with the chaotic nature of the time evolution generator, we show the importance of the role played by the coherence of the initial state in deciding the nature of thermalization. We further show that these findings are general by replacing the Ising ring with a disordered $XXZ$ model with disorder strength putting it in the many-body localized phase.

We investigate the level spacing distribution for three ensembles of real symmetric matrices having additional structural constraint to reduce the number of independent entries to only $ (n+1)/2 $ in contrast to the $ n(n+1)/2 $ for a real symmetric matrix of size $ n \times n $. We derive all the results analytically exactly for the $ 3\times 3 $ matrices and show that spacing distribution display a range of behaviour based on the structural constraint. The spacing distribution of the ensemble of reverse circulant matrices with additional zeros is found to fall slower than exponential for larger spacing while that of symmetric circulant matrices has poisson spacings. The palindromic symmetric toeplitz matrices on the other hand show level repulsion but the distribution is significantly different from Wigner. The behaviour of spacings for all the three ensembles clearly show the departure from universal result of Wigner distribution for real symmetric matrices. The deviation from universality continues in large $ n $ cases as well, which we study numerically.

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, contrary to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon., Comment: 11 pages, 1 figure

In this work, Na isotopes with mass varying from $A=$ 20 to 31 have been studied using DJ16A, JISP16 and N3LO microscopic effective interactions in the $sd$-shell. These effective interactions are derived for $sd$-shell using no-core shell model wavefunctions and a unitary transformation method. We have also performed calculation with IMSRG effective interactions targeted for a particular nucleus. The studies include a detailed analysis of ground state binding energy, low-lying spectra, and electromagnetic properties such as reduced electric quadrupole transition strengths, quadrupole and magnetic dipole moments of the Na chain. The results obtained from these microscopic effective interactions were compared with the experimental data as well as with the results of phenomenological interaction USDB. The charge radii of Na isotopes are evaluated using shell model harmonic oscillator wave functions. In addition to charge radii, matter radii and neutron skin thickness in the Na chain are discussed with a focus on neutron-deficient Na isotopes., Comment: 26 pages, 6 figures

Yrast and near-yrast states above the known 25/2$^{+}$ isomer in $^{207}$At are established for the first time. The level scheme is extended up to 47/2$\hbar$ and 6.5 MeV with the addition of about 60 new $\gamma$-ray transitions. The half-life of the 25/2$^{+}$ isomer is revisited and a value of $T_{1/2}$ = 107.5(9) ns is deduced. Evidence of a hitherto unobserved 29/2$^{+}$ isomer in $^{207}$At is presented. A systematic study of $B(E3)$ values for the transitions de-exciting the 29/2$^{+}$ isomer in the neighboring odd-$A$ At isotopes suggests a half-life in the 2$-$4.5 $\mu$s range for this state in $^{207}$At. The experimental results are compared with large-scale shell-model calculations performed using the KHM3Y effective interaction in the $Z$ = 50$-$126, $N$ = 82$-$184 model space and an overall good agreement is noted between the theory and the experiment. A qualitative comparison of the excited states and the isomers with analogous states in neighboring nuclei provides further insight into the structure of $^{207}$At., Comment: 16 pages, 14 figures

We present a systematic study of the $^{10-14}\text{C}$ isotopes within the \textit{ab initio} no-core shell model theory. We apply four different realistic nucleon-nucleon (NN) interactions: (i) the charge-dependent Bonn 2000 (CDB2K) potential (ii) the inside non-local outside Yukawa (INOY) potential (iii) the next-to-next-to-next-to-leading order (N$^3$LO) potential, and (iv) the optimized next-to-next-to-leading order (N$^2$LO$_{opt}$) potential. We report the low-lying energy spectra of both positive and negative parity states for the $^{10-14}\text{C}$ isotopes and investigate the level structures. We also calculate electromagnetic properties such as transition strengths, quadrupole and magnetic moments. The dependence of point-proton radii on the harmonic oscillator frequency and basis space is shown. We present calculations of the translation invariant one-body density matrix in the no-core shell model and discuss isotopic trends in the density distribution. The maximum basis space reached is $10 \hbar \Omega$ for $^{10}\text{C}$ and $8 \hbar \Omega$ for $^{11-14}\text{C}$, with a maximum M-scheme dimension of $1.3 \times 10^{9}$ for $^{10}\text{C}$. We found that while the INOY interaction gives the best description of the ground state energies, the N$^3$LO interaction best reproduces the point-proton radii., Comment: 21 pages, 12 figures

We implement the ab initio no-core shell model approach to study neutron-rich $^{18}$C, $^{19}$C and $^{20}$C isotopes. For this purpose, we employ charge-dependent Bonn 2000 (CDB2K), inside non-local outside Yukawa (INOY) and chiral next-to-next-to-next-to-leading order (N$^{3}$LO) nucleon-nucleon interactions. Low-lying energy spectra, electromagnetic properties and point-proton radii for these nuclei up to basis space $N_{\rm max}$ = 4 are calculated. Binding energies obtained with INOY interaction are in better agreement with the experimental values as compared to other \textit{ab initio} interactions. We also show the behavior of ground state energy and point-proton radii with the NCSM parameters, $\hbar$$\Omega$ and $N_{\rm max}$. We report a strong sensitivity of the B(E2) values from the first excited $2^+$ to the ground state of $^{18}$C and $^{20}$C to the nuclear interaction. Shell model calculations with YSOX interaction are also performed, and corresponding results are compared with ab initio one., Comment: Nuclear Physics A 1029, 122565 (2023)

Comment on "Backflow in relativistic wave equations" by I. Bialynicki-Birula, Z. Bialynicka-Birula, and S. Augustynowicz [Journal of Physics A: Mathematical and Theoretical, volume 55, page 255702 (2022)]., Comment: 2 pages, no figures