In this paper we study the microscopic mechanism for the retarded decay of K-isomers to lower K bands. We do angular momentum projection from suitable intrinsic states. The retardation arises from poor overlap between the low K and high K bands in the integral over Euler angles. Deformed HF and angular momentum projection calculations are done for the decay of the $K=10^+$ isomer band to the ground band of $^{182}W$. K-mixing is unimportant and the K quantum numbers of the bands are quite good. There is significant difference in the reduced matrix elements of transition operators in our formalism and that in the rotational model. Angular momentum projection gives J-selection rule but there is no K selection rule for reduced matrix elements of electromagnetic multipole operators. Thus, E2 and M1 transitions from the K isomer to the ground band of $^{182}W$ are finite but retarded in angular momentum projection theory, as in experiments. This provides a theoretical basis for the study of K-isomers and their decay modes. Quantitative results are presented. The microscopic model gives J-selection rule and angular momentum conservation for combined matter and radiation systems.

High-K isomers are well known in the rare-earth region and provide unique access to the high spin structures of the nuclei. With the current interest in the study of neutron-rich rare-earth nuclei at Radioactive Ion Beam (RIB) facilities, we present here theoretical results of the band structures of neutron-rich Gd and Dy nuclei, including the high-K isomers. Apart from the already known K-isomers, we predict some more K-isomers and these are suggested for future studies at RIB facilities. Self-consistent Deformed Hartree-Fock and Angular Momentum Projection theories are used to get the intrinsic structures, band-spectra and electromagnetic transitions probabilities of the ground band as well as bands based on isomers.

Very neutron-rich $Z\ensuremath{\sim}60$ isotopes produced by in-flight fission of a 345 MeV/nucleon $^{238}\mathrm{U}$ beam at the RI Beam Factory, RIKEN Nishina Center, have been studied by delayed $\ensuremath{\gamma}$-ray spectroscopy. New isomers were discovered in the neutron-rich $N=100$ isotones $^{162}\mathrm{Sm}, ^{163}\mathrm{Eu}$, and $^{164}\mathrm{Gd}$. Half-lives, $\ensuremath{\gamma}$-ray energies, and relative intensities of these isomers were obtained. Level schemes were proposed for these nuclei and the first ${2}^{+}$ and ${4}^{+}$ states were assigned for the even-even nuclei. The first ${2}^{+}$ and ${4}^{+}$ state energies decrease as the proton numbers get smaller. The energies and the half-lives of the new isomers are very similar to those of ${4}^{\ensuremath{-}}$ isomers known in less neutron-rich $N=100$ isotones $^{168}\mathrm{Er}$ and $^{170}\mathrm{Yb}$. A deformed Hartree-Fock with angular momentum projection model suggests ${K}^{\ensuremath{\pi}}={4}^{\ensuremath{-}}$ two-quasiparticle states with $\ensuremath{\nu}7/2[633]\ensuremath{\bigotimes}\ensuremath{\nu}1/2[521]$ configurations with similar excitation energy. The results suggest that neutron-rich $N=100$ nuclei are well deformed and the deformation gets larger as $Z$ decreases to 62. The onset of $K$ isomers with the same configuration at almost the same energy in $N=100$ isotones indicates that the neutron single-particle structures of neutron-rich isotones down to $Z=62$ do not change significantly from those of the $Z=70$ stable nuclei. Systematics of the excitation energies of new isomers can be explained without the predicted $N=100$ shell gap.

The study of neutron rich nuclei at the drip-line and around closed shells gained momentum with recent advancements of experimental techniques using radioactive ion beams and fission fragment. Fission from fast particles has become an important tool and it has been the richest source of neutron-rich intermediate-mass nuclei. Fission of Uranium and neighbouring nuclei produce two neutronrich fragments of unequal A ∼ 90 and 140, (besides a few neutrons). As the two fragments proceed to the point of separation they become quite deformed. It is thus essential to study the shapes and microscopic structures of these neutron-rich fragments [1]. Deformed rotational bands have been observed experimently in Ge by Hwang et al. [2]. Recently, we have studied theoretically this kind of bands in Ge and Se by considering deformed configuration obtained by constrained Hartree-Fock calculation [3].

Very neutron-rich Z similar to 60 isotopes produced by in-flight fission of a 345 MeV/nucleon U-238 beam at the RI Beam Factory, RIKEN Nishina Center, have been studied by delayed gamma-ray spectroscopy. New isomers were discovered in the neutron-rich N = 100 isotones Sm-162, Eu-163, and Gd-164. Half-lives, gamma-ray energies, and relative intensities of these isomers were obtained. Level schemes were proposed for these nuclei and the first 2(+) and 4(+) states were assigned for the even-even nuclei. The first 2(+) and 4(+) state energies decrease as the proton numbers get smaller. The energies and the half-lives of the new isomers are very similar to those of 4(-) isomers known in less neutron-rich N = 100 isotones Er-168 and Yb-170. A deformed Hartree-Fock with angular momentum projection model suggests K-pi = 4(-) two-quasiparticle states with nu 7/2[633] circle times nu 1/2[521] configurations with similar excitation energy. The results suggest that neutron-rich N = 100 nuclei are well deformed and the deformation gets larger as Z decreases to 62. The onset of K isomers with the same configuration at almost the same energy in N = 100 isotones indicates that the neutron single-particle structures of neutron-rich isotones down to Z = 62 do not change significantly from those of the Z = 70 stable nuclei. Systematics of the excitation energies of new isomers can be explained without the predicted N = 100 shell gap.

Rotational structures of neutron-rich Gd and Dy nuclei in the REE peak region are studied with deformed Hartee-Fock (HF) and angular momentum (J) projection model. Spectra of ground band and a few more excited, positive and negative parity bands have been studied up to high spin values. Some 4-quasiparticle K-isomeric bands and their electromagnetic properties are predicted.

Band structure and electromagnetic properties of bands of 160,162,164Gd are studied theoretically upto high spin values using self-consisstent mean field theory. Predictions for the band structures are made. A K = 6− isomer at fairly low energy is predicted. Four quasi-particle bands involving i13/2 neutron and h11/2 protons are also studied.

Summary High spin states in70Ge nucleus have been studied in two different experiments using heavy ion fusion evaporation reaction. The Gamma Detector Array comprising of eight Compton-suppressed High Purity Ge detectors, was used in conjunction with a Recoil Mass Spectrometer — the HIRA — in order to identify and measure the transitions of this weakly populated nucleus. The level scheme is extended up to an excitation energy of13MeV for spin-parity 21- with several newly observed transitions placed in it. A rotational like band is also observed in this nucleus for the first time.

The structures of Ne, Na, Mg, Al, Si, P and S nuclei near the neutron drip-line region are investigated in the frame-work of relativistic mean field theory and non-relativistic Skyrme Hartree-Fock formalism. The recently discovered nuclei 40Mg and 42Al, which are beyond the drip-line predicted by various mass formulae are located within these models. We find many largely deformed neutron-rich nuclei, whose structures are analyzed. From the structure anatomy, we find that at large deformation low orbits of opposite parities (e.g. \(\frac{1}{2}^ +\) and \(\frac{1}{2}^ -\)) occur close to each other in energy.

. The deformed configurations and rotational band structures in N = 50 Ge and Se nuclei are studied by deformed Hartree–Fock with quadrupole constraint and angular momentum projection. Apart from the ‘almost’ spherical HF solution, a well-deformed configuration occurs at low excitation. A deformed well-mixed Ω = 1/2 + neutron orbit comes down in energy (from the shell above N = 50) to break the N = 50 spherical shell closure. A K = 7 − isomer is predicted in 84 Se at fairly low excitation energy. At higher excitation energies (8 MeV), a deformed band with Ω = 7/2 + – 1/2 − (based on h 11/2 ) neutron 1p–1h excitation, for 82 Ge and 84 Se, is shown in our calculation. Our study gives insight into possible deformed structures at spherical shell closure.

In the present work excited states in 98,99Rh nuclei were populated in the fusion-evaporation reaction 75As(28Si,xpyn) at Elab = 120MeV. The de-excitations have been investigated through in-beam γ-ray spectroscopic techniques. The present level scheme of 98Rh and 99Rh has been established up to J ∼ 23ℏ and 29ℏ respectively. In the doubly-odd 98Rh nucleus new band structure and isomeric states have been identified at lower spins. New states below the previously assigned 2+ ground state (T1/2 = 8.5m) are identified. The low lying band structures in 99Rh are based on πp1/2 and πg9/2 quasiparticles which further evolve into high spin structures following (νh11/2)2 alignment. Multifragmentations at the positive and negative parity bands at spins around 20ℏ is observed, which are likely to be maximally spin aligned states similar to the ones observed in 101Rh.

The study of high spin phenomena of highly unstable nucleus is always interesting. To study the interesting structural phenomena, one has to populate the excited states in nuclei at high spin. The collective model emphasizes the coherent behaviour of all of the nucleons. For odd mass nuclei the coupling of single particle and collective rotational degree of freedom gives a variety of bands structure. In many cases rotational states are known upto very high spins. Among the odd mass nuclei, a number of one and multi-quasiparticle bands have been experimentally observed [1, 2]. With proper energetic ion beams and large detector arrays nuclei can be populated to considerably high spins as well as excitation energies. It is thus necessary to have microscopic theoretical results for such nuclei, which will encourage experimental studies of highly unstable nuclei. In the present work, we have theoretically investigated the rotational bands of highly neutron deficient odd A Rhenium nuclei with deformed Hartree-Fock and Angular Momentum Projection (DHF) model [3]. Nuclei under study are 161,163 Re. Experimentally 29 gammas have been observed which have been placed with four different bands for 161 Re [4]. Out of four bands, two in one quasiparticle and two is three quasiparticle bands. Similarly in the case of 163 Re, 10 gammas have been observed which have been place in one band [5]. We have tried to explain the experimentally observed one and three quasiparticle bands and assigned configuration to all the bands whose configuration have not been assigned yet. At the same time we have predicted a few more bands for future experimental verification. Theoretical Framework

The idea of Surface Delta Interaction (SDI) is that because of Pauli principle, the interaction between nucleons is peaked near the surface of the nucleus. The delta potential is short ranged like free NN interaction. It has some interesting properties which makes it a quite “realistic” interaction [1], to use. SDI gives matrix elements which are quite close to empirical matrix elements found from shell model studies [2]. Also this interaction reproduces deformation properties quite well in complex nuclei [3–5]. We compare SDI matrix elements with two modern interactions, namely, JUN45 and Gf5pg9 interaction of Ref. [6] and report some applications to finite nuclei.

The high spin states of Ba-131 have been populated in the fusion evaporation reaction Sn-122 (C-13,(4)n)Ba-131 at E-beam = 65 MeV. The gamma transitions belonging to various band structures were detected using an array of fifteen Clover Germanium detectors. Some of new transitions have been placed in high spin states. Spin and parity for a band has been calculated for first time in Ba-131. The said band is interpreted in term of multi-quasiparticle configurations, based on Total Rothian Surfaces (TRS) calculations.

The deformed rotational bands in N = 50 Ge nucleus are studied using angular momentum projected Hartree-Fock (PHF) model. These bands are formed by well-deformed HF solutions obtained using a quadrupole constraint, other than the 'almost' spherical solutions which give ground band systematics. A deformed well-mixed Omega = 1/2(+) neutron orbit comes down in energy to break the N = 50 spherical shell closure.

The structure of neutron rich even-even Sm150-164 nuclei is investigated in the framework of deformed Hartree-Fock, Skyrme Hartree-Fock + BCS, and relativistic mean-field formalisms. We analyze the bulk as well as the microscopic properties of these nuclei to investigate the proposed "island of stability" near the neutron drip line for N = 100, Z approximate to 62.