The paper considers quantal many-boson systems that are described by a rotationally invariant and boson-number conserving Hamiltonian. The properties of a generic model are studied, which treats N bosons of p different kinds with non-zero angular momenta & ell;1,& ell;2,& mldr;,& ell;p, possibly augmented with a (number of) scalar s boson(s). The order k of the interaction between the bosons is arbitrary, and closed formulas are given for matrix elements between N-boson states for any k if p=1 and p=2. A recursive procedure is defined for arbitrary k and p. With the expressions derived in the paper, it is possible to express symbolically a Hamiltonian matrix element between N-boson states as a linear combination of k-body interaction matrix elements. More generally, the formulas allow the evaluation of matrix elements of tensor operators that are not necessarily scalar nor boson-number conserving. The numerical implementation of the formalism is discussed and illustrated with a few examples.

Lifetimes of low-lying excited states in 102Mo populated in the two-neutron transfer reaction 100Mo(18O, 16O) 102Mo were measured using the recoil distance Doppler shift method at the IFIN-HH Tandem accelerator. Lifetimes of the 2+1, 0+2 , 4+1, 22+, 23+, 3+1, 6+1, (0+3 ), 4+2 , (3-1 ), and (5-1 ) states were obtained. The deduced electromagnetic transition strengths have been compared to calculations performed in the interacting boson model framework including models representing the U(5) and X(5) symmetries. It is found that 102Mo lies between the U(5) limit and the X(5) critical point symmetry.

The low-energy octupole 3- state of 208Pb is investigated within the framework of the nuclear shell model with realistic nucleon-nucleon interactions. It is shown that the large correlation energy of this state is essentially due to the scattering of fully-aligned nucleon pairs, with the dominant role played by the scattering of high angular momentum fully-aligned neutron-proton pairs. A large fragmentation of the one-particle one-hole wave function, together with the coherence of the wave function, leads to the collective character of the octupole state. This coherence is shown to be a generic property of yrast natural-parity eigenstates of the nuclear many-body Hamiltonian. It induces a constructive accumulation of interaction strength, which may lead to a significant fragmentation of the wave function and a large correlation energy. Electric transitions from the octupole state to the ground state also benefit from this coherence property, resulting in a large enhancement of the transition probability.

How is the B (E2; 2 + 1 → 0 + 1 ) value in an even-even nucleus related to corresponding B (E2; J i → J f ) values in a neighbouring odd-mass nucleus? If either neutrons or protons are confined to a single- j orbital and if the nucleon-nucleon interaction conserves seniority, a simple relation between the two properties is obtained, which may differ from what is found in the weak-coupling limit of the core-particle model. This single- j relation is substantially perturbed if several non-degenerate orbitals are considered. An application to recently measured B (E2) values in neutron-deficient tin isotopes is presented.

Assuming a seniority-conserving interaction, single- j calculations for (j) n configurations with n = 1,..,2j+1 can be performed using a semi-empirical approach, provided that the energies and absolute electromagnetic transition rates are known for the two-particle (hole) nucleus. Using those and the coefficients of fractional parentage, all needed matrix elements for the (j) n configurations can be predicted. At the Cologne Tandem Accelerator of the Institute for Nuclear Physics these relations were tested by measuring lifetimes of excited states in (π9/2) n isotones with N = 50 and N = 126 over the last years. The studies started in the two-proton nucleus 210 Po where the abnormal B(E2:2 1 + → 0 1 + ) value was remeasured, providing important input for the other N = 126 configurations. Then lifetimes of excited states in 211 At were measured using the electronic γ-γ fast timing technique, the Recoil Distance Doppler Shift (RDDS) method, and the Doppler Shift Attenuation (DSA) method. Very good agreement with the analytical single -j calculation is obtained. For N = 50 isotones, we recently started by measuring the previously unknown B(E2:4 1 + → 2 1 + ) value in 92 Mo needed for the prediction of other N = 50 isotones. We also report on experiments on 93 Tc and 94 Ru.

The 247-keV state in ^{54}Sc, populated in the β decay of ^{54}Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the 1^{+} member of the πf_{7/2}⊗νf_{5/2} spin-coupled multiplet, which decays to the 3^{+},πf_{7/2}⊗νp_{1/2} ground state. The new half-life corresponds to a pure E2 transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous B(E2) value in the neutron-rich fp region to date for a nucleus with valence protons above Z=20. Notably, it is roughly 4 times larger than the B(E2;1/2^{-}→5/2^{-}) value in ^{55}Ca. The results, as compared to semiempirical and ab initio shell-model calculations, indicate (1) a weak N=34 subshell gap relative to N=32, (2) a large E2 enhancement in Sc as compared to Ca due to 1p-1h proton excitations across Z=28, and (3) empirical effective proton and neutron charges e_{π}=1.30(8)e and e_{ν}=0.452(7)e, respectively, that are in contrast to reports of e_{π}≈1.1-1.15e and e_{ν}≈0.6-0.8e for fp-shell nuclei near N=Z. We demonstrate that these reports are erroneous and that, in fact, a universal set of effective charges can be used across the sd and fp shells.

We present a shell-model analysis of N = 51 isotones, 93Mo, 95Ru, 97Pd, and 99Cd to quantify the role of neutron-proton interactions in shaping the location and half-life of isomeric states. The study is motivated by the anomalous behavior of the 21/2+ isomeric state in 93Mo, a prominent candidate for nuclear excitation by electron capture (NEEC), which misses an E2 decay branch due to a higher-lying 17/2+ state and instead proceeds via a long-lived E4 isomeric transition. Employing a consistent configuration space and empirically derived effective interaction, we extract and compare the proton-proton and neutron-proton matrix elements for the four N = 51 isotones. Our results show a distinct dominance of the neutron-proton interaction in 93Mo, in contrast to its neighbors (95Ru, 97Pd, and 99Cd) where no analogous isomeric behavior emerges due to structural evolution. These findings reveal that the favorable structure for NEEC in 93Mo stems from subtle interaction systematics that do not persist across the chain. We find that the E2 strength of the key NEEC transition is reduced by 40% compared to the previously estimated value. The analysis provides microscopic insights into the origin of long-lived isomerism in medium-mass nuclei and outlines a framework for identifying future candidates in other mass regions for exploiting the potential energy storage capacities of isomeric states.

The work addresses the isotopic shift of nuclear radii for the even-even 36-52Ca isotopes using the interacting boson model (IBM) that includes the mixing from normal and intruder configurations. We obtain a good agreement between the calculated and experimental data, particularly for the dip at 48Ca. A direct correlation between nuclear size and electric monopole transitions is established to compute the electric monopole transition strengths, rho 2(E0). We further study the isotopic shift for the even-even 32-46Ar and 44-50Ti isotopes.

We show that a vibrational interpretation and good U(5) symmetry are maintained for the majority of low-lying normal states in( 11o,112,114,116)Cd isotopes, consistent with the empirical data. The observed deviations from this paradigm are properly treated by an interacting boson model Hamiltonian which breaks the U(5) symmetry in selected non-yrast states, while securing a weak mixing with coexisting SO(6)-like intruder states. The results demonstrate the relevance of the U(5) partial dynamical symmetry notion to this series of isotopes.

Low-lying excited states in Tc-93 and Ru-94 were populated using the two fusion-evaporation reactions Zr-90(Li-6, 3n) Tc-93 and Mo-92(alpha, 2n) Ru-94 at the Cologne FN Tandem accelerator and their lifetimes were measured using a hybrid setup of high-purity germanium and fast cerium doped lanthanum bromide detectors for gamma-gamma fast-timing. The measured lifetimes fill gaps in the experimental data for electromagnetic transition probabilities B(sigma lambda) along the N = 50 isotonic chain and provide more insight for ambiguous cases, such as the lifetime of the 4(1)(+) state in Ru-94. The experimental data are compared with theoretical B(E2) values from a single-j approximation, with state-dependent effective charges derived from Mo-92 and with the results from shell-model calculations performed using the SR88MHJM interaction in the pi(1p(1/2), 0g(9/2)) model space.

The known I^{π}=8_{1}^{+}, E_{x}=2129-keV isomer in the semimagic nucleus ^{130}Cd_{82} was populated in the projectile fission of a ^{238}U beam at the Radioactive Isotope Beam Factory at RIKEN. The high counting statistics of the accumulated data allowed us to determine the excitation energy, E_{x}=2001.2(7)  keV, and half-life, T_{1/2}=57(3)  ns, of the I^{π}=6_{1}^{+} state based on γγ coincidence information. Furthermore, the half-life of the 8_{1}^{+} state, T_{1/2}=224(4)  ns, was remeasured with high precision. The new experimental information, combined with available data for ^{134}Sn and large-scale shell model calculations, allowed us to extract proton and neutron effective charges for ^{132}Sn, a doubly magic nucleus far-off stability. A comparison to analogous information for ^{100}Sn provides first reliable information regarding the isospin dependence of the isoscalar and isovector effective charges in heavy nuclei.

Seniority is the number of nucleons not in pairs coupled to zero angular momentum. Conditions for the conservation of seniority are well known and are shown here to be related to particle–hole conjugation. The symmetry of seniority gives rise to selection rules in the γ decay of nuclei, which may lead to the formation of isomers. Examples of seniority isomers are discussed in the nickel and lead isotopes, and in the N=50 , 82 and 126 isotones. It is shown that a strong attractive quadrupole matrix element of the nucleon–nucleon interaction disfavours the existence of seniority isomers.

Excited states in the yrast and negative parity bands in 92Mo were populated in two different experiments using the 90Zr(alpha, 2n) 92Mo and 93Nb(p, 2n) 92Mo fusion-evaporation reactions at the Cologne FN Tandem accelerator and measured using a hybrid setup of high purity germanium and lanthanum bromide detectors. Lifetimes of the excited 2+ 1 , 4+ 1 , 6+ 1 , 8+ 1 , 5- 1 , 7- 1 , and 9- 1 states were measured using the gamma -gamma fast-timing technique. The newly measured lifetime of the 4+ 1 state differs from the recently published value measured using the recoil distance Doppler shift method. Experimental B(E2) strengths of excited states in 92Mo are used to predict theoretical B(E2) values in the N = 50 isotones from 93Tc up to 95Rh using semiempirical calculations in the single-j orbital 0g9/2 for the protons.

We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state through so-called Fermi transitions and to Jπ=1+ states by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.

The empirical spectra and $E2$ decay rates in $^{110,112,114,116}$Cd are shown to be consistent with a vibrational interpretation for low-lying normal states, coexisting with a single deformed $γ$-soft band of intruder states. The observed deviations from this paradigm show up in particular non-yrast states, which are properly described by a Hamiltonian with U(5) partial dynamical symmetry. The latter is characterized by a good (broken) symmetry in most (in selected) normal states, weakly coupled to intruder states.

Lifetimes of low-energy states in the semimagic nucleus 211At were measured employing the recoil-distance Doppler shift and the Doppler-shift attenuation methods. The deduced transition probabilities are compared to two shell-model calculations, one using the modified Kuo-Herling interaction in a multi-j model space and the other using a semiempirical interaction for protons confined to the single-j 0h9/2 orbital. The Kuo-Herling calculations overestimates some of the ground-state transition probabilities, possibly due to contributions not included in the calculated ground-state wave function of 211At. A strong underestimation of the E2 strengths involving the 7/2-1 state is also observed. Therefore, a modification of a single two-body matrix element of the Kuo-Herling interaction is introduced which improves the agreement with the experimental data significantly. The calculations in the single-j approximation agree very well with the measured transition probabilities, indicating that seniority can be regarded as a good quantum number in 211At.

The β-decay of the even-even nucleus 70Kr with Z=N+2, has been investigated at the Radioactive Ion Beam Factory (RIBF) of the RIKEN Nishina Center using the BigRIPS fragment separator, the ZeroDegree Spectrometer, the WAS3ABI implantation station and the EURICA HPGe cluster array. Fifteen γ-rays associated with the β-decay of 70Kr into 70Br have been identified for the first time, defining ten populated states below Eexc=3300 keV. The half-life of 70Kr was derived with increased precision and found to be t1/2=45.19±0.14 ms. The β-delayed proton emission probability has also been determined as εp=0.545(23)%. An increase in the β-strength to the yrast 1+ state in comparison with the heaviest Z=N+2 system studied so far (62Ge decay) is observed that may indicate increased np correlations in the T=0 channel. The β-decay strength deduced from the results is interpreted in terms of the proton-neutron quasiparticle random-phase approximation (pnQRPA) and also with a schematic model that includes isoscalar and isovector pairing in addition to quadrupole deformation. The application of this last model indicates an approximate realization of pseudo-SU(4) symmetry in this system.