The symmetry-conserving density functional theory (DFT)-based no-core configuration-interaction (DFT-NCCI) framework is applied for the first time to investigate the impact of configuration interaction (CI) on the Coulomb (isospin) impurity, α_ C, in the ground and excited states of ^10C, ^10B, and ^14N, as well as on the isospin-symmetry-breaking (ISB) correction to the superallowed 0^+ → 0^+ β decay of ^10C. We demonstrate, among other findings, that within the DFT-NCCI framework CI has a negligible effect on the ground-state isospin impurities, which are dominated by a single doorway state. In contrast, CI significantly modifies the impurities in excited states, including the isobaric analogue I=0^+, T=1 state in ^10B. Hence, it also has a non-negligible impact on the ISB correction to the superallowed β decay of ^10C. Our calculations yield _ C=0.45(4)% when the Coulomb interaction is taken as the sole source of ISB, and _ ISB=0.46(6)% when short-range charge-symmetry-breaking (CSB) terms are included in addition. Hence, no statistically significant dependence of the ISB correction on the short-range CSB interaction is observed for this decay. Comparison with our previous results reveals a strong sensitivity to the nuclear symmetry energy, which governs the strength of the isospin-restoring force and whose value in finite nuclei remains difficult to constrain because of its intricate dependence on the momentum-dependent terms of the effective interaction.

We present a theoretical study of the two-neutrino 0^+ → 0^+ double beta decay of ^76Ge within the No-Core Configuration-Interaction framework based on the Skyrme SV density functional. We analyze three allowed decay scenarios distinguished by the [n,m] ≡ [(νg_9/2)^n, (πg_9/2)^m] occupancy of the 0g_9/2 intruder orbital, which remains conserved to high precision, as well as by the triaxiality of the daughter nucleus. The resulting 2νββ nuclear matrix element is found to depend strongly on the scenario. For the energetically favored [4,2] occupancy, we obtain |ℳ^2ν| = 0.069(7) MeV^-1. For the [6,0] occupancy, the matrix element further depends on the triaxiality parameter γ of the two coexisting, closely lying minima in ^76Se, yielding |ℳ^2ν| = 0.040(4) MeV^-1 at γ= 17.7^∘ and |ℳ^2ν| = 0.22(2) MeV^-1 at γ= 41.9^∘. The latter result is consistent with the empirical value reported by A. S. Barabash, |ℳ^2ν| = 0.204(14) MeV^-1, while the two former results are comparable to existing calculations based on energy-density-functional frameworks. Our calculations reveal challenges in the precise determination of the |ℳ^2ν| for the ^76Ge decay. The structural complexity, triaxiality, and shape coexistence identified in the analyzed nuclei imply a strong sensitivity to fine details of the interaction and configuration mixing. This, in turn, explains the difficulties in theoretical modeling of the |ℳ^2ν| matrix elements for the ^76Ge decay, which vary by almost an order of magnitude in the available literature.

We present a seminal calculation of the nuclear matrix element for the two-neutrino double beta ($2\nu\beta\beta$) decay of ${}^{48}\text{Ca} \rightarrow {}^{48}\text{Ti}$ using a post-Hartree-Fock (HF) Density Functional Theory-based No-Core Configuration-Interaction (DFT-NCCI) framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent mean-field configurations obtained by solving the HF equations with the density-independent local Skyrme interaction. Our calculations yield $|\mathcal{M}_{2\nu\beta\beta}| = 0.056(6)$ MeV$^{-1}$ for the nuclear matrix element describing this process. This result is in very good agreement with shell-model studies - for example, with the calculations by Horoi {\it et al.\/} [Phys. Rev. C 75, 034303 (2007)], which yielded 0.054 (0.064) MeV$^{-1}$ for the GXPF1A (GXPF1) interactions, respectively. It is also in a reasonable agreement with the most recent experimental estimate from the review by Barabash, which is 0.068(6) MeV$^{-1}$, assuming quenching $qg_\text{A} \approx 1$. The consistency of our prediction with the shell-model results increases our confidence in the nuclear modeling of this second-order, very rare process which is of paramount importance for further modeling of the neutrinoless double beta ($0\nu\beta\beta$) decay process.

We present a calculation of the nuclear matrix element for the two-neutrino double-beta (2 nu beta beta) decay of 48Ca -> 48Ti using a post-Hartree-Fock (HF) density functional theory-based no-core configuration-interaction framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent meanfield configurations obtained by solving the HF equations with the density-independent local Skyrme interaction. Our calculations yield |M2 nu beta beta | = 0.056(6) MeV-1 for the nuclear matrix element describing this process. This result is in very good agreement with shell-model studies-for example, with the calculations by Horoi et al. [Phys. Rev. C 75, 034303 (2007)], which yielded 0.054 (0.064) MeV-1 for the GXPF1A (GXPF1) interactions, respectively. It is also in a reasonable agreement with the most recent experimental estimate from the review by Barabash, which is 0.068(6) MeV-1, assuming quenching qgA approximate to 1. The consistency of our prediction with the shell-model results increases our confidence in the nuclear modeling of this second-order, very rare process which is of paramount importance for further modeling of the neutrinoless double-beta (0 nu beta beta) decay process.

We present a seminal calculation of the nuclear matrix element for the two-neutrino double beta (2νββ) decay of ^48Ca→^48Ti using a post-Hartree-Fock (HF) Density Functional Theory-based No-Core Configuration-Interaction (DFT-NCCI) framework developed by our group [Phys. Rev. C 94, 024306 (2016)]. In the present calculation, we utilize a variant of the approach that restores rotational symmetry and mixes states projected from self-consistent mean-field configurations obtained by solving the HF equations with the density-independent local Skyrme interaction. Our calculations yield |ℳ_2νββ| = 0.056(6) MeV^-1 for the nuclear matrix element describing this process. This result is in very good agreement with shell-model studies - for example, with the calculations by Horoi et al. [Phys. Rev. C 75, 034303 (2007)], which yielded 0.054 (0.064) MeV^-1 for the GXPF1A (GXPF1) interactions, respectively. It is also in a reasonable agreement with the most recent experimental estimate from the review by Barabash, which is 0.068(6) MeV^-1, assuming quenching qg_A≈ 1. The consistency of our prediction with the shell-model results increases our confidence in the nuclear modeling of this second-order, very rare process which is of paramount importance for further modeling of the neutrinoless double beta (0νββ) decay process.

At a fundamental level, the interactions between protons and protons, protons and neutrons, and neutrons and neutrons are not identical. Such isospin nonconserving interactions emerge when comparing the excitation energy of analog states in T = 1 triplet nuclei. Here, we extend such an analysis to the A = 78, T = 1 triplet system-the heaviest system for which such complete data exists-and find strong disagreement with contemporary theory. This was achieved by pioneering the technique of recoil-/3-/3 tagging to identify excited states in 78Zr. We also established a 78Zr half-life of 25+17 -8 ms and extended the T = 1 band in 78Y to Jn = (10+).

The ground states of the nuclei Mg40 and Na39 are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective n-n and Mg38+n interactions is built for Mg40 based on the available data. We also give predictions for the low-lying spectrum of Na38=37Na+n and two-neutron separation energy of the Na39 nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in Mg40 for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for Na39. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the 2p3/2 and 1f7/2 orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

The binding energy of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus. Since magic nuclei are significantly lighter, or more bound, compared to their neighbors, the presence of nucleonic shell structure makes an imprint on nuclear masses. In this work, using a carefully designed binding-energy indicator, we catalog the appearance of spherical and deformed shell and subshell closures throughout the nuclear landscape. After presenting experimental evidence for shell and subshell closures as seen through the lens of nuclear masses, we study the ability of global nuclear mass models to predict local binding-energy variations related to shell effects.

The electromagnetic structure of Sc-45 at low excitation energy was investigated via low-energy Coulomb excitation at the Heavy Ion Laboratory (HIL) of the University of Warsaw and at the Inter-University Accelerator Centre (IUAC) in New Delhi. A set of reduced E2, E3, and M1 matrix elements was extracted from the collected data using the GOSIA code. The reduced transition probability B(E2; 11/2(-) -> 7/2(-)) has been determined, allowing us to deduce the lifetime of the 11/2(-) state at 1237 keV. In addition, the upper limit on the reduced transition probability B(E3; 7/2(-) -> 5/2(+)) has been determined for the first time. New large-scale shell-model and beyond-mean-field calculations were performed to interpret the structure of this nucleus.

Symmetry-conserving density-functional theory (DFT) based no-core-configuration-interaction framework (DFT-NCCI) is an excellent tool for precision calculation of diverse (pseudo-)observables related to isospin symmetry breaking from elusive isospin impurities through isospin corrections to superallowed beta decays to mirror- and triplet-displacement energies and mirror energy differences (MED) along rotational bands. In our recent work [Phys. Rev. C 106, 024327 (2022)] we performed axial DFT-NCCI calculations and failed to reproduce a sign of MED in positive-parity ($\ensuremath{\pi}=+$) bands of $^{45}\mathrm{Sc}/^{45}\mathrm{Cr}, T=3/2$ mirror pair what casts a shadow on credibility of the model. In this work we aim to perform a thorough analysis of this case with the focus on sensitivity of our predictions with respect to ($i$) low-energy constants (LECs) of our effective contact charge symmetry breaking force and ($\mathit{ii}$) nuclear shape. We demonstrate, among other things, that inclusion of triaxial $\ensuremath{\pi}=+$ ground state---which is actually the global $\ensuremath{\pi}=+$ minimum in our unconstrained mean-field calculation---in the DFT-NCCI calculations instead of the axial one used before leads to MED which are consistent with experimental data concerning both their sign as well as magnitude without any need for fine-tuning of the model's LECs.

Symmetry conserving density functional theory (DFT) based no-core-configuration-interaction framework (DFT-NCCI) is an excellent tool for precision calculation of diverse (pseudo-)observables related to isospin symmetry breaking from elusive isospin impurities trough isospin corrections to superallowed beta decays to mirror- and triplet-displacement energies and mirror energy differences (MED) along rotational bands. In our recent work [Phys. Rev. C {\bf 106}, 024327 (2022)] we performed axial DFT-NCCI calculations and failed to reproduce a sign of MED in positive-parity bands of 45Sc/45Cr T=3/2 mirror pair what casts a shadow on credibility of the model. In this work we aim to perform a thorough analysis of this case with the focus on sensitivity of our predictions with respect to: (i) low-energy constants (LECs) of our effective contact charge symmetry breaking (CSB) force and (ii) nuclear shape. We demonstrate, among the other, that inclusion of triaxial positive-parity ground-state - which is actually the global positive-parity minimum in our unconstrained mean-field calculation - in the DFT-NCCI calculations instead of the axial one used before leads to MED which are consistent with experimental data concerning both their sign as well as magnitude without any need for fine-tuning of the model's LECs.

Level schemes of the proton-rich nuclei, Mn-47 (Z = 25, N = 22) and Cr-45 (Z = 24, N = 21), have been established for the first time. The technique of mirrored one- and two-nucleon knockout reactions was applied to the secondary beams of V-48/Mn-48 and V-47/Cr-47 to populate states in Ti-47/Mn-47 and Sc-45/Cr-45, respectively. Mirror energy differences (MED) have been studied between the mirrored T = 3/2 states for both mirror pairs and interpreted using both a shell-model approach and a density-functional-theory approach using the no-core configuration-interaction method. MED in this mass region provide a stringent test of the model prescriptions since both integral p- and sd-shell orbitals are active and, in Cr-45, spherical and well-deformed structures coexist near the ground state. The inclusive and exclusive one-nucleon removal cross sections have been determined for the populated states in Ti-47/Mn-47 and compared with results from reaction-model calculations.

We present systematic study of isospin impurities ($\alpha_{\rm ISB}$) to the wave functions of $T=1/2$, $11\leq A \leq 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections ($\delta_{\rm ISB}^{\rm V}$) to their ground state vector $\beta$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of $\alpha_{\rm ISB}$ and $\delta_{\rm ISB}^{\rm V}$ as compared to the results obtained within MR-DFT that uses Coulomb interaction as the only source of ISB. This, in turn, increases a central value of the $V_{\rm ud}$ element of the CKM matrix extracted from the $T=1/2$ mirrors bringing it closer to the value obtained form the purely vector superallowed $0^+ \to 0^+$ transitions. In order to compute the value of $V_{\rm ud}$, we performed precision calculation of the Fermi matrix elements in $A=19, 21, 35$, and 37 mirror nuclei using DFT-rooted configuration-interaction model that includes all relevant axially-deformed particle-hole configurations built upon Nilsson orbitals originating from the spherical $sd$ shell. Our calculations yield $|V_{\rm ud}|=0.9736(16)$.

Level schemes of the proton-rich nuclei, 47 Mn (Z = 25, N = 22) and 45 Cr (Z = 24, N = 21), have been established for the first time.The technique of mirrored one-and two-nucleon knockout reactions was applied to the secondary beams of 48 V/ 48 Mn and 47 V/ 47 Cr to populate states in 47 Ti/ 47 Mn and 45 Sc/ 45 Cr, respectively.Mirror energy differences (MED) have been studied between the mirrored T = 3 2 states for both mirror pairs and interpreted using both a shell-model approach and a density-functional-theory approach using the no-core configuration-interaction method.MED in this mass region provide a stringent test of the model prescriptions since both fp-and sd-shell orbitals are active and, in 45 Cr, spherical and well-deformed structures coexist near the ground state.The inclusive and exclusive one-nucleon removal cross sections have been determined for the populated states in 47 Ti/ 47 Mn and compared with results from reaction-model calculations.

The ?? decay of 22,23Si by emission of delayed charged particles was investigated in an experiment at the Cyclotron Institute of Texas A&M University by means of an optical-readout time-projection chamber. The previously-known decay of the two isotopes by ??-delayed one- and two-proton emission was confirmed. For the first time, a new, rare, decay mode for 23Si, ??-delayed three-proton emission, was observed and ??-delayed proton-?? emission tentatively identified. Moreover, the ??-decay pattern for the ground state of 23Si was studied by means of multireference density-functional-rooted calculations.

We describe the new version (v3.06h) of the code HFODD that solves the universal nonrelativistic nuclear DFT Hartree-Fock or Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we implemented the following new features: (i) zero-range three- and four-body central terms, (ii) zero-range three-body gradient terms, (iii) zero-range tensor terms, (iv) zero-range isospin-breaking terms, (v) finite-range higher-order regularized terms, (vi) finite-range separable terms, (vii) zero-range two-body pairing terms, (viii) multi-quasiparticle blocking, (ix) Pfaffian overlaps, (x) particle-number and parity symmetry restoration, (xi) axialization, (xii) Wigner functions, (xiii) choice of the harmonic-oscillator basis, (xiv) fixed omega partitions, (xv) consistency formula between energy and fields, and we corrected several errors in the previous versions.

Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks, leads to isospin symmetry breaking. The isospin nonconservation affects a broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent density functional theory (DFT) that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of mirror and triplet displacement energies in a very broad range of masses. The aim of this work is to further test the chargedependent functional by studying mirror energy differences (MEDs) in the function of angular momentum I. Methods: To compute MEDs we use a DFT-rooted no core configuration interaction model. This post-mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants. Results: We applied the model to f(7/2)-shell mirror pairs of A = 43, 45, 47, and 49 focusing on MEDs in the low-spin part (below band crossing), which allowed us to limit the model space to seniority one and three (one broken pair) configurations. Conclusions: We demonstrate that, for spins I <= 15/2 being the subject of the present study, our model reproduces well experimental MEDs, which vary strongly in the function of I and A. The quality of the model's predictions forMEDs is comparable to the nuclear shell-model results by Bentley et al.

Energy differences between isobaric analogue states have been extracted for the A=79, 79Zr/79Y mirror pair following their population via nucleon-knockout reactions from intermediate-energy rare-isotope beams. These are the heaviest nuclei where such measurements have been made to date. The deduced mirror energy differences (MED) are compared with predictions from a new density-functional based approach, incorporating isospin-breaking effects of both Coulomb and nuclear charge-symmetry breaking and configuration mixing.

The Charge-Symmetry-Breaking (CSB) character of the nucleon-nucleon interaction is well established. This work presents two different ways of introducing such effects into a nuclear Energy Density Functional (EDF). CSB terms are either coming from the effective theory expansion or are derived from electromagnetic mixing of $\rho^0$ and $\omega$ mesons. These terms are then introduced to Skyrme and Quark-Meson-Coupling EDFs, respectively.