The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon-nucleon interaction, non-vanishing values of the collective variable gamma almost everywhere across the nuclear chart. Substantial triaxiality with gamma between 15 and 45 degrees is proved to be expected along horizontal and vertical stripes on the nuclear chart, covering the nucleon numbers 22-26, 34-48, 74-80, 116-124, 172-182. Empirical support for these stripes is found by collecting all even-even nuclei for which the first two excited 2+ states are known, along with the B(E2)s connecting them, as well as the second 2+ state to the ground state. The stripes are related to regions in which oblate SU(3) irreducible representations appear, bearing similarity to the appearance of triaxiality within the SU(3)* dynamical symmetry of the interacting boson model-2. Detailed comparisons of the proxy-SU(3) predictions to the data and to predictions by state-of-the-art Monte Carlo shell model calculations for deformed N=94, 96, 98 isotones in the rare earth region show good overall agreement, with the exception of Z=70 and N=94, which correspond to fully symmetric proxy-SU(3) irreps, suggesting that the latter are an artifact of the method which can be amended by considering the influence of the neighboring irreps.

We investigate the isotopes of Se, Zr, Mo and Nd in the regions with N = 40, 60 and 90, where a first-order shape / phase transition, from spherical to deformed, can be observed. The signs of phase transitional behavior become evident by examining structure indicators, such as certain energy ratios and B(E2) transition rates and, in particular, how they evolve with neutron number. Microscopic mean-field calculations using the Skyrme-Hartree-Fock + Bardeen-Cooper-Schrieffer framework also reveal structural changes when considering the evolution of the resulting potential energy curves as functions of deformation. Finally, macroscopic calculations, using the Algebraic Collective Model, specifically for 74Se, 102Mo and 150Nd, after fitting its parameters to experimental spectra, result in potentials that resemble some of the potentials proposed in the framework of the Bohr Hamiltonian to describe shape transitions in nuclei. A more detailed account can be found in [1].

The proxy-SU(3) symmetry predicts, in a parameter-free way, the collective deformation variables β and γ in even–even atomic nuclei away from closed shells based on the highest weight irreducible representations (irreps) of SU(3) in the relevant proton and neutron shells, which are the most symmetric irreps allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interactions. The special cases in which the use of the next-highest-weight irrep of SU(3) becomes necessary are pointed out, and numerical results are given for several regions of the nuclear chart, which can be used as input for irrep-mixing calculations.

. - We study photoproduction of kaons on protons within the framework of isobar model. Our models were constructed using consistent formalism for exchanges of high-spin resonances and with energy-dependent widths of nucleon resonances. For adjusting free parameters of the model to experimental data we employ regularization techniques, which prevent us from overfitting the data and help us select the appropriate model. We analysed the abundant data on the K+Lambda channel as well as the recent data on K+Sigma- channel and show comparisons of the results with data.

We investigate the photoproduction off a proton target in the channel with K+ and Sigma(0) in the final state. The model of our choice for description of this process is based on effective Lagrangians at the tree level; it is the so-called isobar model. This formalism was developed previously for description of K(+)A photoproduction, and the aim of this study is to provide an extension of this description towards Sigma photoproduction channels. Our fitting strategy has two stages. In the first stage we employ standard chi(2) minimization using a set of resonances, based on previous works. In the second stage, we apply a model selection procedure to the same set of resonances using L-1 regularization in combination with criteria from information theory, and we obtain a sparser model. This gives us two fits which we compare with data and comment on their behavior. Some of the available data (CLAS differential cross sections at energies W > 2.4 GeV, SAPHIR differential cross sections, and C-x and C-z' polarizations) are not included in the fits, but are used to test the predictive power of the two models. The sparser model shows better agreement with the unfitted data compared to the full model.

In this paper we focus on three mass regions where first-order phase transitions occur, namely, for N = 40, 60, and 90. We investigate four isotopic chains (Se, Zr, Mo, and Nd) in the framework of microscopic Skyrme-Hartree-Fock+Bardeen-Cooper-Schrieffer calculations for 15 different parametrizations. The microscopic calculations show the typical behavior expected for first-order phase transitions. To find the best candidate for the critical point phase transition we propose different microscopic position and occupation indices calculated for positive-parity and negative-parity proton and neutron single-quasiparticle states around the Fermi level. The microscopic calculations are completed by macroscopic calculations within the algebraic collective model (ACM), and compared with the experimental data for 74Se, 102Mo, and 150Nd, considered to be the best candidates for the critical-point nuclei.

A formulation of the equations of motion phonon method (EMPM) suited for hypernuclei is outlined and illustrated through an application to B ∧ 12 . A self-consistent calculation using realistic modern potentials is performed using a multiphonon basis which enables us to couple the Λ-particle-proton-hole (pΛ - h) Tamm-Dancoff (TDΛ) states to the excitations of the nuclear core. The impact of such a coupling on the energy levels and on the electroproduction cross section of B ∧ 12 suggests that complex configurations accounting for the excitation of the nuclear core are needed for approaching the experimental data.

The electroproduction of selected $p$- and $sd$-shell hypernuclei was studied within a many-body approach using realistic interactions between the constituent baryons. The cross sections were computed in distorted-wave impulse approximation using two elementary amplitudes for the electroproduction of the $\Lambda$ hyperon. The structure of the hypernuclei was investigated within the framework of the self-consistent $\Lambda$-nucleon Tamm-Dancoff approach and its extension known as the $\Lambda$-nucleon equation of motion phonon method. Use was made of the NNLOsat chiral potential plus the effective Nijmegen-F YN interaction. The method was first implemented on light nuclei for studying the available experimental data and establishing a relation to other approaches. After this proof test, it was adopted for predicting the electroproduction cross section of the hypernuclei $^{40}_{~\Lambda}$K and $^{48}_{~\Lambda}$K in view of the E12-15-008 experiment in preparation at JLab. On the ground of these predictions, appreciable effects on the spectra are expected to be induced by the YN interaction.

We employed the isobar model for investigating the $K^+Λ$ photoproduction process. We paid special attention to the recent CLAS polarization data and enhanced the $χ^2$ minimization by adding a penalty term. Without changing the set of included resonances used by the model, this technique known as Ridge regression leads to reduced couplings that in previous studies acquired unreasonably large values. As a result, we have arrived at a much more robust model with hyperon couplings which are reduced to more physical values. This model serves us to extract valuable information on the background to the $K^+Λ$ photoproduction and particularly on the role of various hyperon resonances. The set of the nucleon resonances is the same with respect to previous fits but their role may have changed due to different couplings which they acquire in the present fit.

We present two methods, the Nucleon-Lambda Tamm Dancoff Approximation (NΛ TDA) and the Equation of Motion Phonon Method (EMPM) suitable for calculating hypernuclear energy spectra and structure. These methods are applicable for hypernuclei of wide range of masses with one Λ particle replacing one nucleon in an even-even nuclear cores. Using an effective Lambda-nucleon (ΛN) potential both methods were applied to calculate the energy spectrum of 12ΛB and also one body density matrix elements (OBDME). The OBDME were applied to calculate the electroproduction cross section of 12ΛB. We obtained better agreement with the experimental data by using EMPM than NΛ TDA. We plan to provide theoretical prediction (by applying the same methods and ΛN potentials) of the cross section in electroproduction of 40ΛK and 48ΛK.

We utilise an isobar model to investigate the $K^+ \Sigma^-$ photoproduction off a neutron in the resonance region. Except for the Born terms, we include high-spin (spin-3/2 and spin-5/2) nucleon resonances in the consistent formalism together with a few $\Delta$ and kaon resonances to achieve an acceptable agreement with data. Interestingly, we reveal that no hyperon resonances are needed to achieve a reasonable description of data. On the other hand the $N(1720)3/2^+$ resonance was found to be very important for correct description of data. The free parameters of the model were fitted to experimental data from the LEPS and CLAS Collaborations on either differential cross sections or photon beam asymmetry. The novel feature of the fitting procedure is the use of a regularization method, the Least Absolute Shrinkage Selection Operator, and information criteria in order to choose the best fit.

Using in the Bohr Hamiltonian the approximations leading to the Bohr and Mot- telson description of wobbling motion in even nuclei, a W(5) model for wobbling bands, coexisting with a X(5) ground state band, is obtained. Separation of vari­ ables is achieved by assuming that the relevant potential has a sharp minimum at 70, which is the only parameter entering in the spectra and B(E2) transition rates (up to overall scale factors). B(E2) transition rates exhibit the features expected in the wobbling case.

A γ-rigid solution of the Bohr Hamiltonian for 7 = 30° is derived, its ground state band being related to the second order Casimir operator of the Euclidean algebra E(4). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are in close agreement to the E (5) critical point symmetry, as well as to experimental data in the Xe region around A = 130.

The N=90 isotones 150Nd, 152Sm, 154Gd, and 156Dy, which are known to provide the best examples of the X(5) critical point symmetry between quadrupole vibrations [U(5)] and axial quadrupole deformation [SU(3)], are proved to lie on the border between the regions of stable axial octupole deformation and octupole vibrations, described in terms of an Analytic Quadrupole Octupole Axially symmetric (AQOA) model including tunneling effects.

The N=90 isotones 1 5 Nd, Sm, 1 5 Gd, and Dy, which are known to provide the best examples of the X(5) critical point symmetry between quadrupole vibrations [U(5)] and axial quadrupole deformation [SU(3)], are proved to lie on the border between the regions of stable axial octupole deformation and octupole vibrations, described in terms of an Analytic Quadrupole Octupole Axially symmetric (AQOA) model including tunneling effects.

Embedding the five-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a six-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is proportional to the quadrupole-quadrupole interaction in the SU(3) (rotational) symmetry limit, and to the difference of the pairing interactions among s, d bosons and d bosons alone in the O(6) (gamma-soft) limit. The presence of these interactions leads to a curved 5D space in the classical limit of IBM, in contrast to the flat 5D space of the original Bohr Hamiltonian, which is made curved by the introduction of the DDM.

Approximate analytical solutions in closed form are obtained for the 5-dimensional Bohr Hamiltonian with the Woods-Saxon potential, taking advantage of the Pekeris approximation and the exactly soluble one-dimensional extended Woods-Saxon potential with a dip near its surface. Comparison to the data for several gamma-unstable and prolate deformed nuclei indicates that the potential can describe well the ground state and gamma-1 bands of many prolate deformed nuclei corresponding to large enough "well size" and diffuseness, while it fails in describing the beta-1 bands, due to its lack of a hard core, as well as in describing gamma-unstable nuclei, because of the small "well size" and diffuseness they exhibit.

Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the Kratzer potentials, by employing techniques from supersymmetric quantum mechanics. Apart from the new set of analytic solutions, the newly introduced Deformation-Dependent Mass (DDM) model offered a remedy to the problematic behaviour of the moment of inertia in the Bohr Hamiltonian, where it appears to increase proportionally to the square of beta. In the DDM model the moments of inertia increase at a much lower rate, in agreement with experimental data. The current work presents an application of the DDM-model suitable for the description of nuclei at the point of shape/phase transitions between vibrational and gamma-unstable or prolate deformed nuclei and is based on a method that was successfully applied before in the context of critical point symmetries.

The analytic quadrupole octupole axially symmetric model, which had successfully predicted 226Ra and 226Th as lying at the border between the regions of octupole deformation and octupole vibrations in the light actinides using an infinite well potential (AQOA-IW), is made applicable to a wider region of nuclei exhibiting octupole deformation, through the use of a Davidson potential (AQOA-D). Analytic expressions for energy spectra and B(E1), B(E2), B(E3) transition rates are derived. The spectra of 222-226Ra and 224,226Th are described in terms of the two parameters phi_0 (expressing the relative amount of octupole vs. quadrupole deformation) and beta_0 (the position of the minimum of the Davidson potential), while the recently determined B(EL) transition rates of 224Ra, presenting stable octupole deformation, are successfully reproduced. A procedure for gradually determining the parameters appearing in the B(EL) transitions from a minimum set of data, thus increasing the predictive power of the model, is outlined.

Quantum shape-phase transitions in odd-even nuclei are investigated in the framework of the interacting boson-fermion model. Classical and quantum analysis show that the presence of the odd fermion strongly influences the location and nature of the phase transition, especially near the critical point. Experimental evidence for the occurrence of spherical to axially-deformed transitions in odd-proton nuclei Pm, Eu and Tb (Z=61, 63, 65) is presented.