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We report on the masses and hyperfine structure of ground and isomeric states in $^{114,116,118,120}$Ag isotopes, measured with the phase-imaging ion-cyclotron-resonance technique (PI-ICR) with the JYFLTRAP mass spectrometer and the collinear laser spectroscopy beamline at the Ion Guide Isotope Separator On-Line (IGISOL) facility, Jyv\"askyl\"a, Finland. We measured the masses and excitation energies, electromagnetic moments, and charge radii, and firmly established the nuclear spins of the long-lived states. A new isomer was discovered in $^{118}$Ag and the half-lives of $^{118}$Ag long-lived states were reevaluated. We unambiguously pinned down the level ordering of all long-lived states, placing the inversion of the $I = 0^-$ and $I = 4^+$ states at $A = 118$ $(N = 71)$. Lastly, we compared the electromagnetic moments of each state to empirical single-particle moments to identify the dominant configuration where possible., Comment: 11 pages paper (excl. references) + 3 pages of supplementary material

A Novikov conformal algebra is a conformal algebra such that its coefficient algebra is right-symmetric and left commutative (i.e., it is an ``ordinary'' Novikov algebra). We prove that every Novikov conformal algebra with a uniformly bounded locality function on a set of generators can be embedded into a commutative conformal algebra with a derivation. In particular, every finitely generated Novikov conformal algebra has a commutative conformal differential envelope. For infinitely generated algebras this statement is not true in general., Comment: 13 pages

In both real and complex cases, we establish the connection of the problem about $2$-dimensional linear subspaces the most deviating from the coordinate ones with one simply formulated optimization problem for isoperimetric polygons in Euclidean spaces. This study thereby provides a new geometrical point of view on the $2$-dimensional case of the problem formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997}, and at the same time presents a new application of the results by Hausmann and Knutson \cite{HK1997}.

The masses of the ground and isomeric states in $^{124,125}$Ag have been measured using the phase-imaging ion-cyclotron-resonance technique at the JYFLTRAP double Penning trap mass spectrometer. The ground states of $^{124}$Ag and $^{125}$Ag were found to be 30(250) keV and 250(430) keV less bound but 36 and 110 times more precise than in the Atomic Mass Evaluation 2020, respectively. The excitation energy of $^{124}$Ag$^{m}$, ${E_x = 188.2(25)}$ keV, was determined for the first time. The new precise mass values have been utilised to study the evolution of nuclear structure via two-neutron separation energies. The impact on the astrophysical rapid neutron capture process has been investigated via neutron-capture reaction rate calculations. The precision measurements indicate a more linear trend in two-neutron separation energies and reduce the mass-related uncertainties for the neutron-capture rate of $^{124}$Ag$(n,\gamma)^{125}$Ag by a factor of around 100. The new mass values also improve the mass of $^{123}$Pd, previously measured using $^{124}$Ag as a reference., Comment: 9 pages, 4 figures

A direct measurement of the ground-state-to-ground-state electron-capture decay $Q$ value of $^{95}$Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The $Q$ value was determined to be 1695.92(13) keV by taking advantage of the high resolving power of the phase-imaging ion-cyclotron-resonance technique to resolve the low-lying isomeric state of $^{95}$Tc (excitation energy of 38.910(40) keV) from the ground state. The mass excess of $^{95}$Tc was measured to be $-$86015.95(18) keV/c$^2$, exhibiting a precision of about 28 times higher and in agreement with the value from the newest Atomic Mass Evaluation (AME2020). Combined with the nuclear energy-level data for the decay-daughter $^{95}$Mo, two potential ultra-low $Q$-value transitions are identified for future long-term neutrino-mass determination experiments. The atomic self-consistent many-electron Dirac--Hartree--Fock--Slater method and the nuclear shell model have been used to predict the partial half-lives and energy-release distributions for the two transitions. The dominant correction terms related to those processes are considered, including the exchange and overlap corrections, and the shake-up and shake-off effects. The normalized distribution of the released energy in the electron-capture decay of $^{95}$Tc to excited states of $^{95}$Mo is compared to that of $^{163}$Ho currently being used for electron-neutrino-mass determination., Comment: 13 pages, 5 figures

We state the Problem of Knot Identification as a way to achieve consensus in dynamic networks. The network adversary is asynchronous and not oblivious. The network may be disconnected throughout the computation. We determine the necessary and sufficient conditions for the existence of a solution to the Knot Identification Problem: the knots must be observable by all processes and the first observed knot must be the same for all processes. We present an algorithm KIA that solves it. We conduct KIA performance evaluation.

We present TRAIL: an algorithm that uses a novel consensus procedure to tolerate failed or malicious shards within a blockchain-based cryptocurrency. Our algorithm takes a new approach of selecting validator shards for each transaction from those that previously held the assets being transferred. This approach ensures the algorithm's robustness and efficiency. TRAIL is presented using PBFT for internal shard transaction processing and a modified version of PBFT for external cross-shard validation. We describe TRAIL, prove it correct, analyze its message complexity, and evaluate its performance. We propose various TRAIL optimizations: we describe how it can be adapted to other Byzantine-tolerant consensus algorithms, how a complete system may be built on the basis of it, and how TRAIL can be applied to existing and future sharded blockchains.

The absolute mass of $^{84}$Sr was determined using the phase-imaging ion-cyclotron-resonance technique with the JYFLTRAP double Penning trap mass spectrometer. A more precise value for the mass of $^{84}$Sr is essential for providing potential indications of physics beyond the Standard Model through high-precision isotope shift measurements of Sr atomic transition frequencies. The mass excess of $^{84}$Sr was refined to be -80649.229(37) keV/c$^2$ from high-precision cyclotron-frequency-ratio measurements with a relative precision of 4.8$\times$10$^{-10}$. The obtained mass-excess value is in agreement with the adopted value in the Atomic Mass Evaluation 2020, but is 30 times more precise. With this new value, we confirm the previously observed nonlinearity in the study of the isotope shift of strontium. Moreover, the double-beta ($2\beta^{+}$) decay $Q$ value of $^{84}$Sr was directly determined to be 1790.115(37) keV, and the precision was improved by a factor of 30., Comment: 7 pages, 4 figures

We present BeRGeR: the first asynchronous geometric routing algorithm that guarantees delivery of a message despite a Byzantine fault without relying on cryptographic primitives or randomization. The communication graph is a planar embedding that remains three-connected if all edges intersecting the source-target line segment are removed. We prove the algorithm correct and estimate its message complexity.

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

Precision mass measurements of $^{104}$Y, $^{106}$Zr, $^{104,104m,109}$Nb, and $^{111,112}$Mo have been performed with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility. The order of the long-lived states in $^{104}$Nb was unambiguously established. The trend in two-neutron separation energies around the $N=66$ neutron midshell appeared to be steeper with respect to the Atomic Mass Evaluation 2020 extrapolations for the $_{39}$Y and $_{40}$Zr isotopic chains and less steep for the $_{41}$Nb chain, indicating a possible gap opening around $Z=40$. The experimental results were compared to the BSkG2 model calculations performed with and without vibrational and rotational corrections. All of them predict two low-lying minima for $^{106}$Zr. While the unaltered BSkG2 model fails to predict the trend in two-neutron separation energies, selecting the more deformed minima in calculations and removing the vibrational correction, the calculations are more in line with experimental data. The same is also true for the $2^+_1$ excitation energies and differences in charge radii in the Zr isotopes. The results stress the importance of improved treatment of collective corrections in large-scale models and further development of beyond-mean-field techniques., Comment: 10 pages, 4 figures

The first direct determination of the ground-state-to-ground-state ${\beta^{-}}$-decay $Q$-value of $^{77}$As to $^{77}$Se was performed by measuring their atomic mass difference utilizing the double Penning trap mass spectrometer, JYFLTRAP. The resulting $Q$-value is 684.463(70) keV, representing a remarkable 24-fold improvement in precision compared to the value reported in the most recent Atomic Mass Evaluation (AME2020). With the significant reduction of the uncertainty of the ground-state-to-ground-state $Q$-value and knowledge of the excitation energies in $^{77}$Se from $\gamma$-ray spectroscopy, the ground-state-to-excited-state $Q$-value of the transition $^{77}$As (3/2$^{-}$, ground state) $\rightarrow$ $^{77}$Se$^{*}$ (5/2$^{+}$, 680.1035(17) keV) was refined to be 4.360(70) keV. We confirm that this potential low $Q$-value ${\beta^{-}}$-decay transition for neutrino mass determination is energetically allowed at a confidence level of about 60$\sigma$. Nuclear shell-model calculations with two well-established effective Hamiltonians were used to estimate the partial half-life for the low $Q$-value transition. The half-life was found to be of the order of 10$^{9}$ years for this first-forbidden non-unique transition, which rules out this candidate a potential source for rare-event experiments searching for the electron antineutrino mass., Comment: 8 pages, 4 figures

Isomers close to the doubly magic nucleus $^{78}$Ni ($Z=28$, $N=50$) provide essential information on the shell evolution and shape coexistence far from stability. The existence of a long-lived isomeric state in $^{76}$Cu has been debated for a long time. We have performed high-precision mass measurements of $^{76}$Cu with the JYFLTRAP double Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line facility and confirm the existence of such a isomeric state with an excitation energy $E_x=64.8(25)$ keV. Based on the ratio of detected ground- and isomeric-state ions as a function of time, we show that the isomer is the shorter-living state previously considered as the ground state of $^{76}$Cu. The result can potentially change the conclusions made in previous works related to the spin-parity and charge radius of the $^{76}$Cu ground state. Additionally, the new $^{76}$Cu$(n,\gamma)$ reaction $Q$-value has an impact on the astrophysical rapid neutron-capture process., Comment: 8 pages, 4 figures

We report on new precision mass measurements of neutron-rich $^{137}$Sb and $^{136-142}$I isotopes from the JYFLTRAP double Penning trap mass spectrometer. We confirm the value from the previous Penning-trap measurement of $^{137}$Sb at the Canadian Penning Trap and therefore rule out the conflicting result from the Experimental Storage Ring. The ground state and isomer in $^{136}$I were resolved and measured directly for the first time. The isomer excitation energy, $E_x = 215.1(43)$ keV, agrees with the literature but is three times more precise. The measurements have improved the precision of the mass values and confirmed previous results in the majority of cases. However, for $^{138,140}$I the results differ by 17(6) keV and 23(12) keV, respectively. This could be explained by an unresolved contamination or different ratio of unresolved isomeric states in the case of $^{140}$I., Comment: 8 pages, 6 figures

High-precision mass measurements of exotic $^{95-97}$Ag isotopes close to the $N = Z$ line have been conducted with the JYFLTRAP double Penning trap mass spectrometer, with the silver ions produced using the recently commissioned inductively-heated hot cavity catcher laser ion source at the Ion Guide Isotope Separator On-Line facility. The atomic mass of $^{95}$Ag was directly determined for the first time. In addition, the atomic masses of $\beta$-decaying 2$^+$ and 8$^+$ states in $^{96}$Ag have been identified and measured for the first time, and the precision of the $^{97}$Ag mass has been improved. The newly measured masses, with a precision of $\approx$ 1 keV/c$^2$, have been used to investigate the $N =$ 50 neutron shell closure confirming it to be robust. Empirical shell-gap and pairing energies determined with the new ground-state mass data are compared with the state-of-the-art \textit{ab initio} calculations with various chiral effective field theory Hamiltonians. The precise determination of the excitation energy of the $^{96m}$Ag isomer in particular serves as a benchmark for \textit{ab initio} predictions of nuclear properties beyond the ground state, specifically for odd-odd nuclei situated in proximity to the proton dripline below $^{100}$Sn. In addition, density functional theory (DFT) calculations and configuration-interaction shell-model (CISM) calculations are compared with the experimental results. All theoretical approaches face challenges to reproduce the trend of nuclear ground-state properties in the silver isotopic chain across the $N =$50 neutron shell and toward the proton drip-line., Comment: 9 pages, 3 figures

The multinucleon transfer (MNT) reaction approach was successfully employed for the first time to measure the isomeric ratios (IRs) of $^{211}$Po (25/2$^+$) isomer and its (9/2$^+$) ground state at the IGISOL facility using a 945 MeV $^{136}$Xe beam impinged on $^{209}$Bi and $^{\rm nat}$Pb targets. The dominant production of isomers compared to the corresponding ground states was consistently revealed in the $\alpha$-decay spectra. Deduced IR of $^{211}$Po populated through the $^{136}$Xe+$^{\rm nat}$Pb reaction was found to enhance $\approx$1.8-times than observed for $^{136}$Xe+$^{209}$Bi. State-of-the-art Langevin-type model calculations have been utilized to estimate the spin distribution of an MNT residue. The computations qualitatively corroborate with the considerable increase in IRs of $^{211}$Po produced from $^{136}$Xe+$^{\rm nat}$Pb compared to $^{136}$Xe+$^{209}$Bi. Theoretical investigations indicate a weak influence of target spin on IRs. The enhancement of the $^{211}$Po isomer in the $^{136}$Xe+$^{\rm nat}$Pb over $^{136}$Xe+$^{209}$Bi can be attributed to the different proton ($p$)-transfer production routes. Estimations demonstrate an increment in the angular momentum transfer, favorable for isomer production, with increasing projectile energy. Comparative analysis indicates the two entrance channel parameters, projectile mass and $p$-transfer channels, strongly influencing the population of the high-spin isomer of $^{211}$Po (25/2$^+$). This is the first experimental and theoretical investigation on the IRs of nuclei produced via different channels of MNT reactions, with the latter quantitatively underestimating the former by a factor of two., Comment: 5 figures

Isomers close to doubly-magic $^{78}_{28}$Ni$_{50}$ provide essential information on the shell evolution and shape coexistence near the ${Z=28}$ and ${N=50}$ double shell closure. We report the excitation energy measurement of the $1/2^{+}$ isomer in $^{79}_{30}$Zn$_{49}$ through independent high-precision mass measurements with the JYFLTRAP double Penning trap and with the ISOLTRAP Multi-Reflection Time-of-Flight Mass Spectrometer. We unambiguously place the $1/2^{+}$ isomer at 942(10) keV, slightly below the $5/2^+$ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with Discrete Non Orthogonal shell-model calculations which are used here the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other ${N=49}$ isotones. The $1/2^{+}$ isomer is interpreted as the band-head of a low-lying deformed structure akin to a predicted low-lying deformed band in $^{80}$Zn, and points to shape coexistence in $^{79,80}$Zn similar to the one observed in $^{78}$Ni. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart., Comment: 10 pages, three figures, two tables. Accepted to Phys. Rev. Lett

Collinear laser spectroscopy was performed on the isomer of the aluminium isotope $^{26m}$Al. The measured isotope shift to $^{27}$Al in the $3s^{2}3p\;^{2}\!P^\circ_{3/2} \rightarrow 3s^{2}4s\;^{2}\!S_{1/2}$ atomic transition enabled the first experimental determination of the nuclear charge radius of $^{26m}$Al, resulting in $R_c$=\qty{3.130\pm.015}{\femto\meter}. This differs by 4.5 standard deviations from the extrapolated value used to calculate the isospin-symmetry breaking corrections in the superallowed $\beta$ decay of $^{26m}$Al. Its corrected $\mathcal{F}t$ value, important for the estimation of $V_{ud}$ in the CKM matrix, is thus shifted by one standard deviation to \qty{3071.4\pm1.0}{\second}., Comment: 5 pages, 2 figures, submitted to Phys. Rev. Lett

A simple and clear method is proposed to calculate the averaged motion of the apsis line in the Moon orbit. The obtained result is $3^{\circ}1'12''$ for the starry period of the Moon revolution around the Earth or $40^{\circ}22'48''$ per year. The modern observed value of the latter quantity is $40^{\circ}41'$ per year. In "Principia" Newton derived $1^{\circ}31'28''$ for the Moon month and $20^{\circ}12''$ per year. That is approximately two times less than the observable values. Unlike the Newton approach we use a simple and obvious averaging of the Sun disturbing force for the starry period of the Moon revolution around the Earth. The applicability of the obtained formulae to satellites of other planets and to the planets themselves is grounded. Comparing Newton's calculation with our method we reveal the reason, rather convincing, that brings Newton to inadequate result., Comment: 13 pages, 1 figure

Dipole toroidal modes appear in many fields of physics. In nuclei, such a mode was predicted more than 50 years ago, but clear experimental evidence was lacking so far. Using a combination of high-resolution inelastic scattering experiments with photons, electrons and protons, we identify for the first time candidates for toroidal dipole excitations in the nucleus $^{58}$Ni and demonstrate that transverse electron scattering form factors represent a relevant experimental observable to prove their nature., Comment: 13 pages, 8 figures

Using the 4th and the 3rd degree spherical harmonics as the representations for volumetric frames, we describe a simple algebraic technique for combining multiple frame orientation constraints into a single quadratic penalty function. This technique allows to solve volumetric frame fields design problems using a coarse-to-fine strategy on hierarchical grids with immersed boundaries. These results were presented for the first time at the FRAMES 2023 European workshop on meshing.

The dipole electric ($E1$) and magnetic ($M1$) strengths in strongly deformed $^{156}$Gd are investigated within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) with Skyrme forces SVbas, SLy6 and SG2. We inspect, on the same theoretical footing, low-lying dipole states and the isovector giant dipole resonance in $E1$ channel and the orbital scissors resonance as well as the spin-flip giant resonance (SFGR) in $M1$ channel. Besides, $E1$ toroidal mode and low-energy spin-flip $M1$ excitations are considered. The deformation splitting and dipole-octupole coupling of electric excitations are analyzed. The origin of SFGR gross structure, impact of the residual interaction and interference of orbital and spin contributions to SFGR are discussed. The effect of the central exchange $\textbf{J}^2$-term from the Skyrme functional is demonstrated. The calculations show a satisfactory agreement with available experimental data, except for the recent NRF measurements of M. Tamkas et al for $M1$ strength at 4-6 MeV, where, in contradiction with our calculations and previous $(p,p')$ data, almost no $M1$ strength was observed., Comment: 13 pages, 6 figures, 8 tables

We report on the first direct mass measurements of the $^{118,119}$Cd and $^{117-119}$In isotopes performed at the Ion Guide Isotope Separator On-Line facility using the JYFLTRAP double Penning trap mass spectrometer. The masses of $^{117}$In and $^{118}$Cd isotopes are in agreement with the literature, while $^{118,119}$In and $^{119}$Cd differ from literature by 49, 13 and 85 keV (6.1, 1.9 and 2.1 standard deviations), respectively. The excitation energy of the $^{118}$In first isomeric state, $E_x = 40.3(25)$ keV, was determined for the first time. The updated mass values removed the fluctuations observed in the two-neutron separation energies and lead to a smoother linear decrease of both isotopic chains. The $\log(ft)$ value for the $^{118}$Cd decay is also found to increase from 3.93(6) to 4.089(8). The reported results indicate an absence of significant structural changes around $N=70$., Comment: 8 pages, 3 figures

The equivalent representations for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment $a^{\text{HVP}}_{\mu}$ in the presence of the quark flavour thresholds are studied. Specifically, the explicit relations between the contributions given by the integration over a finite kinematic interval to $a^{\text{HVP}}_{\mu}$ expressed in terms of the hadronic vacuum polarization function, Adler function, and the $R$-ratio of electron-positron annihilation into hadrons are derived. It is shown that the quark flavour thresholds of the hadronic vacuum polarization function generate additional contributions to $a^{\text{HVP}}_{\mu}$ expressed in terms of the Adler function and the $R$-ratio and the explicit expressions for such contributions are obtained. The commonly employed dispersion relations, which bind together hadronic vacuum polarization function, Adler function, and $R$-ratio, are extended to account for the effects due to the quark flavour thresholds. The examined additional contributions due to the heavy quark thresholds to $a^{\text{HVP}}_{\mu}$ expressed in terms of the $R$-ratio appear to be quite sizable, that can be of a particular relevance for the data-driven method of assessment of the hadronic part of the muon anomalous magnetic moment., Comment: 22 pages, 5 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

The $\beta^-$ decay $Q$-value of $^{136}$Cs ($J^\pi = 5^+$, $t_{1/2} \approx 13$~days) was measured with the JYFLTRAP Penning trap setup at the Ion Guide Isotope Separator On-Line (IGISOL) facility of the University of Jyv\"askyl\"a, Finland. The mono-isotopic samples required in the measurements were prepared with a new scheme utilised for the cleaning, based on the coupling of dipolar excitation with Ramsey's method of time-separated oscillatory fields and the phase-imaging ion-cyclotron-resonance (PI-ICR) technique. The $Q$ value is determined to be 2536.83(45) keV, which is $\sim$4 times more precise and 11.4(20) keV ($\sim$ 6$\sigma$) smaller than the adopted value in the most recent Atomic Mass Evaluation AME2020. The daughter, $^{136}$Ba, has a 4$^+$ state at 2544.481(24) keV and a $3^-$ state at 2532.653(23) keV, both of which can potentially be ultralow $Q$-value end-states for the $^{136}$Cs decay. With our new ground-to-ground state $Q$ value, the decay energies to these two states become -7.65(45) keV and 4.18(45) keV, respectively. The former is confirmed to be negative at the level of $\sim$ 17$\sigma$, which verifies that this transition is not a suitable candidate for neutrino mass determination. On the other hand, the slightly negative $Q$ value makes this transition an interesting candidate for the study of virtual $\beta$-$\gamma$ transitions. The decay to the 3$^{-}$ state is validated to have a positive low $Q$ value which makes it a viable candidate for neutrino mass determination. For this transition, we obtained a shell-model-based half-life estimate of $2.1_{-0.8}^{+1.6}\times10^{12}$ yr., Comment: 9 pages, 8 figures

We report on precision mass measurements of $^{113,115,117}$Ru performed with the JYFLTRAP double Penning trap mass spectrometer at the Accelerator Laboratory of University of Jyv\"askyl\"a. The phase-imaging ion-cyclotron-resonance technique was used to resolve the ground and isomeric states in $^{113,115}$Ru and enabled for the first time a measurement of the isomer excitation energies, $E_x(^{113}$Ru$^{m})=100.5(8)$ keV and $E_x(^{115}$Ru$^{m})=129(5)$ keV. The ground state of $^{117}$Ru was measured using the time-of-flight ion-cyclotron-resonance technique. The new mass-excess value for $^{117}$Ru is around 36 keV lower and 7 times more precise than the previous literature value. With the more precise ground-state mass values, the evolution of the two-neutron separation energies is further constrained and a similar trend as predicted by the BSkG1 model is obtained up to the neutron number $N=71$., Comment: 12 pages, 9 figures, submitted to Physical Review C