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We present a study of the spectroscopic factors for the (d,p) stripping reactions to the ${11/2}^-$ states in the chain of odd-mass Sn (A = 115 - 131) isotopes by using a multi-j generalized seniority approach. The results are in line with realistic shell model calculations and explain the experimental trend quite well. The multi-j configuration used in these calculations is consistent with earlier calculations for moments etc., and therefore, lends credence to the generalized seniority interpretation. To the best of our knowledge, this work presents the first calculation of spectroscopic factors from such an approach.

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for actinides and superheavy elements, namely beta and gamma deformation variables, and compare these with predictions by relativistic and non-relativistic mean-field theories. Furthermore, we make predictions for B(E2) transition rates of deformed nuclei and compare these with existing data and predictions of other theoretical approaches., Comment: 6 pages, 3 figures, to appear in the proceedings of the 26th Annual Symposium of the Hellenic Nuclear Physics Society (HNPS2017), Anavyssos, Greece, 9-10 June 2017, ed. Ch. Tsabaris, R. Vlastou, M. Kokkoris, and D. Patiris. arXiv admin note: text overlap with arXiv:1711.09201, arXiv:1711.08596

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. However, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. We introduce a new fermionic approximation, called the proxy-SU(3), and we discuss how some of its novel predictions come out as a consequence of the short range of the nucleon-nucleon interaction and the Pauli principle., Comment: 6 pages, 2 tables, to appear in the proceedings of the 26th Annual Symposium of the Hellenic Nuclear Physics Society (HNPS2017), Anavyssos, Greece, 9-10 June 2017, ed. Ch. Tsabaris, R. Vlastou, M. Kokkoris, and D. Patiris

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for deformed nuclei, namely beta and gamma deformation variables, and compare them with empirical data and with predictions by relativistic and non-relativistic mean-field theories. Furthermore, analytic expressions are derived for B(E2) ratios within the proxy-SU(3) model, free of any free parameters, and/or scaling factors. The predicted B(E2) ratios are in good agreement with the experimental data for deformed rare earth nuclides., Comment: 12 pages, 5 figures, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minkov

We show that within the proxy-SU(3) scheme the wave functions of the normal parity orbitals in a given nuclear shell are affected very little as a result of the replacement of the abnormal parity orbitals by their 0[110] proxy-SU(3) counterparts., Comment: 9 pages, 5 tables, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minkov

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. On the other hand, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. A new fermionic approximation, called the proxy-SU(3), has been recently introduced and applied to the even rare earths. We show that the applicability of proxy-SU(3) can be extended to even nuclei in the 28-50 proton shell, to even superheavy elements, as well as to odd-odd and odd rare earths. Parameter free predictions for the beta and gamma deformation parameters are presented and compared to alternative theoretical predictions and to existing data., Comment: 13 pages, 9 figures, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minkov

Using a new approximate analytic parameter-free proxy-SU(3) scheme, simple predictions for the global feature of prolate dominance and for the locus of the prolate-oblate shape transition have been made and compared with empirical data. Emphasis is placed on the mechanism leading to the breaking of the particle-hole symmetry, which is instrumental in shaping up these predictions. It turns out that this mechanism is based on the SU(3) symmetry and the Pauli principle alone, without reference to any specific Hamiltonian., Comment: 10 pages, 4 tables, to appear in the proceedings of the Workshop on Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects (SDANCA17, Sofia 2017), ed. N. Minkov

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make predictions of shape observables for deformed nuclei, namely beta and gamma deformation variables, and compare these with empirical data and with predictions by relativistic and non-relativistic mean-field theories., Comment: 6 pages, 11 figures, Proceedings of the 4th Workshop of the Hellenic Institute of Nuclear Physics on New Aspects and Perspectives in Nuclear Physics (HINPw4),Ioannina, Greece, 5-6 May 2017, ed. A. Pakou

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make simple predictions for the global feature of prolate dominance in deformed nuclei and the locus of the prolate-oblate shape transition and compare these with empirical data., Comment: 5 pages, 1 figure, 3 tables, Proceedings of the 4th Workshop of the Hellenic Institute of Nuclear Physics on New Aspects and Perspectives in Nuclear Physics (HINPw4), Ioannina, Greece, 5-6 May 2017, ed. A. Pakou

An approximate SU(3) symmetry appears in heavy deformed even-even nuclei, by omitting the intruder Nilsson orbital of highest total angular momentum and replacing the rest of the intruder orbitals by the orbitals which have escaped to the next lower major shell. The approximation is based on the fact that there is a one-to-one correspondence between the orbitals of the two sets, based on pairs of orbitals having identical quantum numbers of orbital angular momentum, spin, and total angular momentum. The accuracy of the approximation is tested through calculations in the framework of the Nilsson model in the asymptotic limit of large deformations, focusing attention on the changes in selection rules and in avoided crossings caused by the opposite parity of the proxies with respect to the substituted orbitals., Comment: 7 pages, 1 figure, 3 tables, Proceedings of the 4th Workshop of the Hellenic Institute of Nuclear Physics on New Aspects and Perspectives in Nuclear Physics (HINPw4),Ioannina, Greece, 5-6 May 2017, ed. A. Pakou

The SU(3) symmetry realized by J. P. Elliott in the sd nuclear shell is destroyed in heavier shells by the strong spin-orbit interaction. However, the SU(3) symmetry has been used for the description of heavy nuclei in terms of bosons in the framework of the Interacting Boson Approximation, as well as in terms of fermions using the pseudo-SU(3) approximation. We introduce a new fermionic approximation, called the proxy-SU(3), and we comment on its similarities and differences with the other approaches., Comment: 4 pages, 1 figure, Proceedings of the 4th Workshop of the Hellenic Institute of Nuclear Physics on New Aspects and Perspectives in Nuclear Physics (HINPw4),Ioannina, Greece, 5-6 May 2017, ed. A. Pakou

Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make simple predictions of shape observables for deformed nuclei, namely gamma and beta deformation variables, the global feature of prolate dominance and the locus of the prolate-oblate shape transition. The predictions are compared with empirical results., Comment: 14 pages, 6 figures, 4 tables

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper., Comment: 24 pages, 6 figures, 15 tables

Statistical measures of chaos have long been used in the study of chaotic dynamics in the framework of the interacting boson model. The use of large number of bosons renders additional studies of chaos possible, that can provide a direct comparison with similar classical studies of chaos. We intend to provide complete quantum chaotic dynamics at zero angular momentum in the vicinity of the arc of regularity and link the results of the study of chaos using statistical measures with those of the study of chaos using classical measures. Statistical measures of chaos are applied on the spectrum and the transition intensities of 0+ states in the framework of the interacting boson model. The energy dependence of chaos is provided for the first time using statistical measures of chaos. The position of the arc of regularity was also found to be stable in the limit of large boson numbers. The results of the study of chaos using statistical measures are consistent with previous studies using classical measures of chaos, as well as with studies using statistical measures of chaos, but for small number of bosons and states with angular momentum greater than 2., Comment: 13 pages, 8 figures

Enhanced proton-neutron interactions occur in heavy nuclei along a trajectory of approximately equal numbers of valence protons and neutrons. This is also closely aligned with the trajectory of the saturation of quadrupole deformation. The origin of these enhanced p-n interactions is discussed in terms of spatial overlaps of proton and neutron wave functions that are orbit-dependent. It is suggested for the first time that nuclear collectivity is driven by synchronized filling of protons and neutrons with orbitals having parallel spins, identical orbital and total angular momenta projections, belonging to adjacent major shells and differing by one quantum of excitation along the z-axis. These results may lead to a new approach to symmetry-based theoretical calculations for heavy nuclei., Comment: 6 pages, 4 figures

Storage-ring mass spectrometry was applied to neutron-rich $^{197}$Au projectile fragments. Masses of $^{181,183}$Lu, $^{185,186}$Hf, $^{187,188}$Ta, $^{191}$W, and $^{192,193}$Re nuclei were measured for the first time. The uncertainty of previously known masses of $^{189,190}$W and $^{195}$Os nuclei was improved. Observed irregularities on the smooth two-neutron separation energies for Hf and W isotopes are linked to the collectivity phenomena in the corresponding nuclei., Comment: 10 pages, 9 figures, 2 tables

Using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the Interacting Boson Approximation (IBA) model, a line is found inside the symmetry triangle of the IBA, along which the SU(3) symmetry is preserved. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases, and lies within the Alhassid--Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions. In addition to providing an explanation for the existence of the arc of regularity, the present line represents the first example of an analytically determined approximate symmetry in the interior of the symmetry triangle of the IBA. The method is applicable to algebraic models possessing subalgebras amenable to contraction. This condition is equivalent to algebras in which the equilibrium ground state (and its rotational band) become energetically isolated from intrinsic excitations, as typified by deformed solutions to the IBA for large numbers of valence nucleons., Comment: 22 pages, 2 figures

The first example of an empirically manifested quasi dynamical symmetry trajectory in the interior of the symmetry triangle of the Interacting Boson Approximation model is identified for large boson numbers. Along this curve, extending from SU(3) to near the critical line of the first order phase transition, spectra exhibit nearly the same degeneracies that characterize the low energy levels of SU(3). This trajectory also lies close to the Alhassid-Whelan arc of regularity, the unique interior region of regular behavior connecting the SU(3) and U(5) vertices, thus offering a possible symmetry-based interpretation of that narrow zone of regularity amidst regions of more chaotic spectra., Comment: 4 pages, LaTeX, 5 eps figures

The energies of subsets of excited 0+ states in geometric collective models are investigated and found to exhibit intriguing regularities. In models with an infinite square well potential, it is found that a single formula, dependent on only the number of dimensions, describes a subset of 0+ states. The same behavior of a subset of 0+ states is seen in the large boson number limit of the Interacting Boson Approximation (IBA) model near the critical point of a first order phase transition, in contrast to the fact that these 0+ state energies exhibit a harmonic behavior in all three limiting symmetries of the IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of the underlying group theoretical framework of the different models., Comment: 9 pages, 3 figures, added reference [38]

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become sharper in the large boson number limit, revealing in parallel regularities previously unnoticed, although they survive to a large extent for finite boson numbers as well. Several of these regularities will be discussed. It will be shown that in all of the three limiting symmetries of the IBA [U(5), SU(3), and O(6)], energies of 0+ states grow linearly with their ordinal number. Furthermore, it will be proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0_2^+)=E(6_1^+), E(0_3^+) =E(10_1^+), E(0_4^+)=E(14_1^+), the energy ratio E(6_1^+) /E(0_2^+) turning out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0+ states near the point of the first order shape/phase transition between U(5) and SU(3) will be shown to grow as n(n+3), where n is their ordinal number, in agreement with the rule dictated by the relevant critical point symmetries studied in the framework of special solutions of the Bohr Hamiltonian. The underlying dynamical and quasi-dynamical symmetries are also discussed., Comment: 8 pages, 5 postscript figures, LaTeX. To appear in the Proceedings of the 17th Symposium of the Hellenic Nuclear Physics Society (Ioannina, Greece, May 30-31, 2008)

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained., Comment: 35 pages, 11 postscript figures, LaTeX

A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored., Comment: 4 pages, 3 postscript figures, uses revTeX

A simple, empirical signature of a first order phase transition in atomic nuclei is presented, the ratio of the energy of the 6+ level of the ground state band to the energy of the first excited 0+ state. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Data in the Nd-Dy region show these characteristics. In addition, a repeating degeneracy between alternate yrast states and successive excited 0+ states is found to correspond closely to the line of a first order phase transition in the framework of the Interacting Boson Approximation (IBA) model in the large N limit, pointing to a possible underlying symmetry in the critical region., Comment: 4 pages, 4 postscript figures, uses revTeX

Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0_n^+ states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0_2^+)=E(6_1^+), E(0_3^+)=E(10_1^+), E(0_4^+)=E(14_1^+), while the energy ratio E(6_1^+) /E(0_2^+) turns out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0_n^+ states near the point of the first order shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in agreement with the rule dictated by the relevant critical point symmetries resulting in the framework of special solutions of the Bohr Hamiltonian. The underlying partial dynamical symmetries and quasi-dynamical symmetries are also discussed., Comment: 6 pages, 4 postscript figures, LaTeX. To appear in the Proceedings of the International Conference on Nuclear Physics and Astrophysics: From Stable Beams to Exotic Nuclei (Cappadocia, 2008)

Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.

A study of the energies of the first excited $0^+$ states in all even-even $Z$ $\geq$ 8 nuclei reveals an anomalous behavior in some nuclei with $N$ = $Z$, $Z$ $\pm$ 2. We analyze these irregularities in the framework of the shell model. It is shown that proton-neutron correlations play an important role in this phenomenon., Comment: 4 pages, 5 figures

It is shown that strong 0+2 -> 0+1 E0 transitions provide a clear signature of phase transitional behavior in finite nuclei. Calculations using the IBA show that these transition strengths exhibit a dramatic and robust increase in spherical-deformed shape transition regions, that this rise matches well the existing data, that the predictions of these E0 transitions remain large in deformed nuclei, and that these properties are intrinsic to the way that collectivity and deformation develop through the phase transitional region in the model, arising from the specific d-boson coherence in the wave functions, and that they do not necessarily require the explicit mixing of normal and intruder configurations from different IBA spaces., Comment: 6 pages, 3 figures

The $N_pN_n$ scheme, which has been extensively applied to even-even nuclei, is found to be a very good benchmark for odd-even, even-odd, and doubly-odd nuclei as well. There are no apparent shifts in the correlations for these four classes of nuclei. The compact correlations highlight the deviant behavior of the Z=78 nuclei, are used to deduce effective valence proton numbers near Z=64, and to study the evolution of the Z=64 subshell gap., Comment: 10 pages, 4 figures

We present the first extensive test of the critical point symmetry X(5) for the gamma degree of freedom, based in part on recent measurements for the gamma-band in 152 Sm. The agreement is good for some observables including the energies and most intra- and interband transitions, but there is also a serious discrepancy for one transition., Comment: 8 pages, 6 tables and 3 figures, erratum new figure 3, conclusions unchanged

The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the turning points of the discussed quantities, establishing the singular character of these points in nuclear phase transition regions between vibrational and rotational nuclei, with a finite number of particles., Comment: 12 pages, 7 figures, elsart, revised version, considerable changes and additions

The predictions of the IBM two-body random ensemble are compared to empirical results on nuclei from Z=8 to 100. Heretofore unrecognized but robust empirical trends are identified and related both to the distribution of valence nucleon numbers and to the need for and applicability of specific, non-random interactions. Applications to expected trends in exotic nuclei are discussed., Comment: 7 pages, 5 figures, revtex with eps figures

In terms of the Interacting Boson Model, shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and, for the first time, over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and gamma-soft rotor structures, and one that is related to shape coexistence, are identified., Comment: 10 pages, ReVTeX, epsf, 2 Postscript figures included

The study of spherical-deformed ground--state phase transitions in finite nuclei as a function of N and Z is hindered by the discrete values of the nucleon number. A resolution of the integer nucleon number problem, and evidence relating to phase transitions in finite nuclei, are discussed from the experimental point of view and interpreted within the framework of the interacting boson model., Comment: 8 pages Latex + 8 figs (postscript). In Phys Rev Lett, June 1999

The wavefunctions of the lowest odd spin positive parity yrast states in the IBA are shown to be nearly pure multiple quadrupole-phonon excitations even outside the three dynamical symmetries. The empirical data for collective nuclei with 30 < Z < 80 confirm these predictions. The quadrupole-phonon purity of the 2^+_1 state can be measured from E2-branching ratios of the 3^+_1 state. These data show a high correlation to the 2^+_1 Q-phonon purity deduced from the E2-decay of 2^+ states., Comment: 9 pages, 4 figures