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We review the phenomenological versus microscopic description of α -clustering in nuclei above A = 100 . The even–odd staggering in pair binding energies along α -lines is explained in terms of the so-called isospin pairing. We compare the pocket-like potential on the nuclear surface, where α -clusters are formed with significant probability, to the local equivalent potential provided by the microscopic cluster mean field approach. The systematics of the α -decay width shows significantly larger cluster probabilities above magic numbers. The relation of α -clustering to electromagnetic and weak processes is analyzed. [ABSTRACT FROM AUTHOR]

We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the angular Wentzel–Krames–Brillouin (WKB) and linearized WKB with its approximation, known as Fröman WKB method. We define the semiclassical fundamental matrix of solutions, describing the effect of the deformed field. Its inverse, proportional to the so-called propagator matrix, connects the solution in two points. A comparison between the coupled channels fundamental matrix of solutions to various semiclassical counterparts evidences close results in the barrier region. We express the scattering amplitudes in terms of the propagator matrix multiplied by the ratio between internal wave function components and irregular Coulomb waves. The relative influence of nuclear and Coulomb action terms together with nuclear and Coulomb centrifugal barriers upon the penetration process reveals the dominance of the Coulombian parts. An analysis of alpha-emission processes between ground states and to excited states of even–even nuclei in terms of the propagator matrix evidenced the important role played by deformation of the Coulomb field and the shape of the nuclear interaction. [ABSTRACT FROM AUTHOR]

We compare the quantum mechanical procedures to estimate the total α-decay width from deformed nuclei in the laboratory and intrinsic systems of coordinates. Our analysis shows that the total half-life estimated in the intrinsic frame by neglecting the rotational motion of the core (adiabatic approach) is one order of magnitude smaller at β2 = 0.3 than the corresponding value in the spherical case. A similar calculation in the laboratory system of coordinates by considering the core motion (giving the correct theoretical estimate) predicts a reduction by only a factor of 2. The widely used "angular WKB" (Wentzel-Kramers-Brillouin) semiclassical procedure provides decay widths which are comparable to the adiabatic approach. We propose a new and very simple semiclassical "angular momentum WKB" procedure to evaluate the decay width in deformed nuclei. It provides decay widths very close to the ones obtained by the exact laboratory coupling channels procedure. [ABSTRACT FROM AUTHOR]

We systematize the available experimental material concerning α-decay transitions to low-lying excited states in even-even and odd-mass emitters. We generalize our previous theoretical prediction concerning the linear dependence between hindrance factors and the excitation energy for transitions in even-even α emitters. Thus, we show that α intensities for transitions to excited states depend linearly upon the excitation energy for all known even-even and odd-mass α emitters. It turns out that the well-known Viola-Seaborg law for α-decay transitions between ground states can be generalized for transitions to excited states. This rule can be used to predict any α-decay half-life to a low-lying excited state. [ABSTRACT FROM AUTHOR]

In this paper we present a timely application of the proton-neutron deformed quasiparticle random-phase approximation (p/i-dQRPA), designed to describe in a consistent way the I+ Gamow-Teller states in oddodd deformed nuclei. For this purpose we apply a projection before variation procedure by using a singleparticle basis with projected angular momentum, provided by the diagonalization of a spherical mean field plus quadrupole-quadrupole interaction. The residual Hamiltonian contains pairing plus proton-neutron dipole terms in particle-hole and particle-particle channels, with constant strengths. As an example we describe the two-neutrino double-beta (Ivββ) decay of 150Nd to the ground state of b0Sm. The experimental (p,n) type of strength in 150Nd and the (n.p) type of strength in 150Sm are reasonably reproduced and the 2vββ decay matrix element depicts a strong dependence upon the particle-particle strength grp. The experimental half-life is reproduced for gpp = 0.05. It turns out that the measured half-lives for 2vββ transitions between other deformed superfluid partners with mass numbers A = 82,96,100,128,130,238 are reproduced with fairly good accuracy by using this value of gpp. [ABSTRACT FROM AUTHOR]

We systematically analyze the coherence length in even-even nuclei. The pairing coherence length in the spin-singlet channel for the effective density-dependent delta (DDD) and Gaussian interaction is estimated. We consider in our calculations bound states as well as narrow resonances. It turns out that the pairing gaps given by the DDD interaction are similar to those of the Gaussian potential if one renormalizes the radial width to the nuclear radius. The correlations induced by the pairing interaction have, in all considered cases, a long-range character inside the nucleus and a decrease towards the surface. The mean coherence length is larger than the geometrical radius for light nuclei and approaches this value for heavy nuclei. The effect of the temperature and states in the continuum is investigated. Strong shell effects are put in evidence, especially for protons. We generalize this concept to quartets by considering similar relations, but between proton and neutron pairs. The quartet coherence length has a similar shape, but with larger values on the nuclear surface. We provide evidence of the important role of proton-neutron correlations by estimating the so-called alpha coherence length, which takes into account the overlap with the proton-neutron part of the α-particle wave function. It turns out that it does not depend on the nuclear size and has a value comparable to the free α-particle radius. We have shown that pairing correlations are mainly concentrated inside the nucleus, while quarteting correlations are connected to the nuclear surface. [ABSTRACT FROM AUTHOR]

We analyze the α-decay fine structure to excited 02+ states in Hg and Rn isotopes. These states are described as minima in the potential energy surface (PES) provided by the standard deformed Woods-Saxon plus pairing approach. We also investigate a decay from the excited state P(02+) in the parent nucleus by evaluating the corresponding hindrance factor (HF). By analyzing the experimental HF's we find the remarkable property that the ground and excited states D(01+) and D(02+) in the daughter nuclei are occupied with almost equal probabilities if there is no excited P(0+) states in the parent nucleus. Moreover, if there exists an excited state P(02+) then the occupation probability of this state is 25%. [ABSTRACT FROM AUTHOR]

Self-consistent random-phase approximation is rederived in a consistent way with the help of the coupled cluster ground state wave function truncated at the two-body level. An exact killing operator for this wave function is introduced allowing for a detailed discussion of the approximation scheme. Several exactly solvable models are reanalyzed under this new perspective giving rise to a quantitative evaluation of the performances of this many-body method. [ABSTRACT FROM AUTHOR]

We describe electromagnetic and α-decay transitions to low-lying excited states in even-even nuclei within the coherent state model (CSM). We reproduced the energies and B(E2) values for ground state bands in 40 daughter nuclei with known a-branching ratios to 2+ states. To this purpose we used two parameters, namely the deformation parameter and the strength of the harmonic CSM Hamiltonian. The Hamiltonian describing the α-emission process is given by two terms. The first term describes the dynamics of the daughter nucleus. The second α-daughter component contains the monopole potential, estimated within the double folding procedure with M3 Y interaction plus a repulsive core simulating Pauli principle and a quadrupole-quadrupole (QQ) interaction. The decaying states are identified with the lowest narrow outgoing resonances in this potential. The α-branching ratios to 2+ states were reproduced by using the QQ strength depending linearly on the deformation parameter, as predicted by CSM. The theoretical intensities to 4+ and 6+ states are in a reasonable agreement with available experimental data. We found out that the QQ coupling strength is by one order of magnitude larger in the region above 208Pb, where the α clustering is known to be stronger, in comparison to other nuclei. This formalism is able to simultaneously describe electromagnetic and a decays to excited states in spherical, transitional, and well deformed nuclei. [ABSTRACT FROM AUTHOR]

It is shown that the standard shell-model representation is inadequate to explain cluster decay processes due to a deficient asymptotic behavior of the corresponding single-particle wave functions. A new representation is proposed which is derived from a mean field consisting of the standard Woods-Saxon plus spin-orbit potential of the shell model, with an additional attractive pocket potential of a Gaussian form localized on the nuclear surface. The eigenvectors of this new mean field provide a representation which retains all the benefits of the standard shell model while at the same time reproducing well the experimental absolute α-decay widths from heavy nuclei. [ABSTRACT FROM AUTHOR]

A two-center shell model provides the possibility to characterize precisely scission configurations. Therefore, low-energy disintegration processes could be described within such models. A Woods-Saxon two-center shell model, recently elaborated, was used to investigate the cluster decay, the low-energy fission and the synthesis of superheavy elements. In the following, the model is applied to the alpha-decay of superheavy elements as superasymmetric fission. [ABSTRACT FROM AUTHOR]

The two-proton decay process is studied by using a simple approach within the framework of scattering theory. We assume that the decaying nucleus is in a pairing state and, therefore, the two-particle wave function on the nuclear surface corresponds to the two protons moving in time-reversed states. This allows us to sustain a simplified version of the decay where the protons are simultaneously emitted with the same energies. We thus obtain a coupled system of radial equations with outgoing boundary conditions. We use similar proton-proton interactions to solve BCS equations and to describe external two-proton dynamics. A strong dependence of the pairing gap and decay width upon the proton-proton interaction strength is revealed. The experimental half-lives of 45Fe and 48Ni are reproduced by using a realistic proton-proton interaction. [ABSTRACT FROM AUTHOR]

The 7Li+130Te reaction was used to populate excited states in 132Te and 134Xe. The experiment at the Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania, used an array of high-purity germanium (HPGe) and cerium-doped lanthanum bromide (LaBr3(Ce)) detectors to measure sub-nanosecond half-lives using fast-timing techniques. The half-lives of the yrast 4+ and 6+ levels were measured in the N = 80 nuclei 132Te and 134Xe, respectively. An upper limit of T½ ≤ 40 ps was assigned to the 4+ level in 132Te and T½ = 1075(155) ps was assigned to the 6+ level in 134Xe. The systematics of the B(E2) strengths around the N = 82 shell closure are discussed. [ABSTRACT FROM AUTHOR]

We describe low-lying collective states in deformed even-even nuclei within a deformed quasiparticle random-phase approximation (dQRPA) by using a single-particle basis with good angular momentum. The statistical factors, accounting for the level occupancy, appear in the dQRPA in a natural way as rotation coefficients that take the intrinsic system to the laboratory system. We have used our model by performing a systematic analysis of E2 transitions from the first 2+ state to the ground state for all superfluid nuclei in the range 50 < Z≤ 100 by using a common charge polarization parameter χ = 0.2. In spite of its similarity to the QRPA, this method is able to describe in an unified way gross features of electromagnetic transitions from vibrational to rotational nuclei. [ABSTRACT FROM AUTHOR]

The intraband electromagnetic transitions in 210Po and 210Pb are well described within the shell model approach. In contrast, similar transitions in 212Po are one order of magnitude smaller than the experimental values, suggesting the existence of an &agr;-cluster component in the structure of this nucleus. To probe this assumption we introduced Gaussian-like components in the single-particle orbitals. We thus obtained an enhancement of intraband transitions, as well as a proper description of the absolute &agr;-decay width in 212Po. We analyzed the recently measured unnatural parity states I- in 212Po in terms of the collective octupole excitation in 208Pb coupled to positive parity states in 210Pb. They are connected by relatively large dipole transitions to yrast positive natural parity states. We described E1 transitions by using the same &agr;-cluster component and an effective neutron dipole charge eμ = -- eZ/A. B(E2) values and absolute &agr;-decay width in 212Po are simultaneously described within the shell model plus a cluster component depending upon one free strength parameter. [ABSTRACT FROM AUTHOR]

Excited states in Po have been populated by $ \alpha$ transfer using the Pb(O,C) reaction at 85MeV beam energy and studied with the EUROBALL IV $ \gamma$ multi-detector array. The level scheme has been extended up to ∼ 3.2 MeV excitation energy from the triple- $ \gamma$ coincidence data. Spin and parity values of most of the observed states have been assigned from the $ \gamma$ angular distributions and $ \gamma$ - $ \gamma$ angular correlations. Several $ \gamma$ -lines with E < 1 MeV have been found to be shifted by the Doppler effect, allowing for the measurements of the associated lifetimes by the DSAM method. The values, found in the range [0.1-0.6]ps, lead to very enhanced E1 transitions. All the emitting states, which have non-natural parity values, are discussed in terms of $ \alpha$ - Pb structure. They are in the same excitation-energy range as the states issued from shell-model configurations. [ABSTRACT FROM AUTHOR]

PURPOSE:: The purpose of this study was to compare muscle activity and patterns during deep water running (DWR) and treadmill running (TMR) at equivalent levels of RPE. METHODS:: Subjects (n = 7, 26.3 +/- 4.3 yr, 158.2 +/- 9.9 cm, 61.0 +/- 6.6 kg) performed DWR and TMR at RPE values of 11 (fairly light), 13 (somewhat hard), and 15 (hard). Surface EMG was used to evaluate muscle activity of the rectus femoris (RF), biceps femoris (BF), tibialis anterior (TA), and gastrocnemius (GA) with average EMG calculated across a 30-s window. Five cycles of data were extracted from smoothed EMG profiles on the basis of the selection of distinct RF peaks. These cycles were reduced to create ensemble muscle activity patterns per condition. Average EMG for each muscle was analyzed using a repeated-measures ANOVA with Bonferroni's post hoc tests. RESULTS:: TA and GA muscle activity magnitudes during DWR were significantly lower than during TMR (mean decrease of 72%-86%, P < 0.05) for any RPE level. BF and RF muscle activity magnitudes were either not different or tended to be lower during DWR than TMR for matched RPE (P = 0.051 and P = 0.121, respectively). CONCLUSIONS:: Whereas TA and GA muscle activity magnitudes were each clearly lower during DWR than TMR regardless of RPE, higher levels of intensity (RPE 15) during DWR can be used to elicit similar muscle activity levels as lower intensity (RPE 11) TMR. [ABSTRACT FROM AUTHOR]

The strength and shape of α-clusters in medium and heavy nuclei are analyzed by using α-decay experimental data. It turns out that the emitters above magic nuclei contain an important α-cluster component, not described within the standard mean field plus pairing approach. [ABSTRACT FROM AUTHOR]

We introduce the idea of estimating the interaction between substructures in many-body systems by considering them to be independent except for the fact that they live in model spaces whose dimensionality is effectively reduced due to each other's Pauli blocking. We apply this idea to the study of isovector pairing correlations within the the quartet condensation model, based on the improved analytical relations method. We study both N=Z and N>Z nuclei, where a natural decomposition may be performed in terms of quartet and pair degrees of freedom. [ABSTRACT FROM AUTHOR]

We use the available experimental Gamow-Teller β- and β+/EC (electron-capture) decay rates between 0+ and 1+ ground states in neighboring even-even and odd-odd nuclei, combined with 2νββ half-lives, to analyze the influence of the nuclear environment on the weak axial-vector strength gA. For this purpose, the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA), with schematic dipole residual interaction is employed. The Hamiltonian contains particle-hole (ph) and particle-particle (pp) channels with mass-dependent strengths. In deriving the equations of motion we use a self-consistent procedure in terms of a single-particle basis with projected angular momentum provided by the diagonalization of a spherical mean field plus the quadrupole-quadrupole interaction. Our analysis evidenced a quenched average effective value 〈gA〉≈0.7 with a root-mean-square deviation of σ≈0.3 for transitions from even-even emitters and σ≈0.6 for transitions from odd-odd emitters. [ABSTRACT FROM AUTHOR]

We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the quartet condensation model (QCM) from a particle-hole perspective, and we introduce the representation of the QCM quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. We also present a new bosonic approximation for both PBCS and QCM. In each case, the starting point is the reformulation of the pair and quartet condensate states in terms of particle-hole excitations with respect to the Hartree-Fock state. The main simplification of our approach is the assumption that the pair operators corresponding to both particle and hole states obey bosonic commutation relations. This simplifies tremendously the computations and allows for an analytic derivation of the averaged Hamiltonian on the condensate state as a function of the mixing amplitudes. We study both the pure bosonic approach and the renormalized version and compare the particle-hole bosonic version to the naive prescription of applying the boson approximation directly to the original condensate state. We compare the fermionic and the renormalized particle-hole bosonic approaches in the case of a picket-fence model of doubly degenerate states and in a realistic shell-model space with an effective interaction for the N=Z nuclei above 100Sn. [ABSTRACT FROM AUTHOR]

Background: Within the quartet condensation model (QCM), the isovector pairing correlations for N = Z nuclei are described with a very high accuracy by a "condensate" of a -like quartets. The usual approach involves cumbersome recurrence relations in order to compute numerically the relevant quantities of the model: the norm of the quartet states and the mean value of the isovector pairing Hamiltonian as functions of the pair mixing amplitudes. Purpose: We present the final analytical expressions for the above-mentioned quantities, for all cases up to four quartets in the valence shell. Method: The analytical QCM expressions were obtained by a straightforward implementation of the SO(5) algebra in the symbolic computer algebra system CADABRA2. Results: The norm of the quartet states and the mean value of the Hamiltonian are polynomial functions of the mixing amplitudes. The numerical implementation of the QCM model is thus made trivial as a matter of copying and pasting the presented formulas. Conclusions: We introduce in this work a method of computer-aided analytical calculus for a many-body setting. In particular, we provide precise and easy-to-use tools for the description of isovector pairing correlations. [ABSTRACT FROM AUTHOR]

Quasimolecular α-like ground rotational bands were evidenced a long time ago in light nuclei, but they cannot be detected in heavy nuclei due to large Coulomb barriers. In order to search for rotational bands built on excited states in these nuclei, we investigate the shape of an α-nucleus quasimolecular potential matched to a realistic external α-daughter interaction by using as input data α-decay widths. It turns out that its Gaussian length parameter lies in a narrow interval, b0∈[0.6,0.8] fm, and the equilibrium radius is slightly larger than the predicted Mott transition point from nucleonic to the α-cluster phase in finite nuclei, confirming that α clusters are born on the nuclear surface at low densities. We point out that the α emitters above magic nuclei have the largest spectroscopic factors Sα∼10%. In addition, we predict that for nuclei with b0>0.75 fm, the first excited vibrational resonant state in the quasimolecular potential is close to the Coulomb barrier and therefore the rotational band built on it can be evidenced by the structure of the α-scattering cross section versus energy. Moreover, its detection by a highly sensitive γ-ray beam produced by laser facilities would provide an additional proof for the existence of α molecules in heavy nuclei. [ABSTRACT FROM AUTHOR]

We investigate the influence of a strong laser electromagnetic field on the α-decay rate by using the Hennenberger frame of reference. We introduce an adimensional parameter D=S0/R0, where R0 is the geometrical nuclear radius and S0~√I/ω² is a length parameter depending on the laser intensity I and frequency ω. We show that the barrier penetrability has a strong increase for intensities corresponding to D>Dcrit=1, due to the fact that the resulting Coulomb potential becomes strongly anisotropic even for spherical nuclei. As a consequence, the contribution of the monopole term increases the barrier penetrability by 2 orders of magnitude, while the total contribution has an effect of 6 orders of magnitude at D~3Dcrit. In the case of deformed nuclei, the electromagnetic field increases the penetrability by an additional order of magnitude for a quadrupole deformation β2~0.3. The influence of the electromagnetic field can be expressed in terms of a shifted Geiger-Nuttal law by a term depending on S0 and deformation. [ABSTRACT FROM AUTHOR]

We apply the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA) to describe the low-lying (E≤6 MeV) 1+ Gamow-Teller (GT) strength functions in odd-odd deformed nuclei which participate as intermediate nuclei in two-neutrino double-β-decay (2νββ) transitions within the mass range A=70-176. In deriving equations of motion we use a single-particle basis with projected angular momentum, provided by the diagonalization of a spherical mean field furnished with a quadrupole-quadrupole interaction. The schematic residual Hamiltonian contains pairing and proton-neutron interaction terms in particle-hole (ph) and particle-particle (pp) channels, with constant strengths. By adopting constant particle-hole and particle-particle strengths we are able to describe the positions of the giant GT resonance and the measured half-lives of the 2νββ decays over the whole mass range A=70-176. At the same time we obtain a good agreement with the measured low-lying GT β-strength functions. By using the adopted ph and pp strengths, we predict the half-lives of a number of deformed 2νββ emitters and the low-lying GT strength functions of the corresponding odd-odd intermediate nuclei for their possible experimental tests in the future. [ABSTRACT FROM AUTHOR]

It is known that the α particle reduced width has the largest values in the region above 100Sn, and this behavior is usually attributed to the proton-neutron correlations. To reproduce the reduced α-decay width we use an additional pocket-like surface potential in the single-particle mean field that simulates four-body correlations. We show that the strength of this interaction has a universal linear dependence on the experimental reduced width above the double magic nuclei 100Sn and 208Pb. Moreover, we demonstrate that proton-neutron pairing correlations have a small influence on this dependence and therefore cannot explain the larger reduced decay widths above 100Sn. We give an indication of the possibility of detecting Sn+nα structures as dipole Pigmy-like resonances. [ABSTRACT FROM AUTHOR]

We evidence a staggering effect of the experimental spectroscopic factors corresponding to even-even and odd-mass (odd-mass and odd-odd) α emitters. The comparison to the theoretical estimate within the standard Bardeen-Cooper-Schrieffer (BCS) approach reveals a similar staggering, but with a different behavior. It turns out that the ratio between corresponding experimental and theoretical spectroscopic factors is proportional to the experimental reduced decay width. A similar dependence was found in a previous work between the strength of the quadrupole-quadrupole α-core interaction, describing the α-decay fine structure and the reduced width. Thus, the even-odd staggering effect in the spectroscopic factor is a new evidence of the α-clustering phenomenon in medium and heavy nuclei. [ABSTRACT FROM AUTHOR]

We describe electromagnetic and favored a transitions to rotational bands in odd-mass nuclei built upon a single particle state with angular momentum projection Ω≠1/2 in the region 88≤Z≤98. We use the particle coupled to an even-even core approach described by the coherent state model and the coupled channels method to estimate partial α-decay widths. We reproduce the energy levels of the rotational band where favored α transitions occur for 26 nuclei and predict B(E2) values for electromagnetic transitions to the band head using a deformation parameter and a Hamiltonian strength parameter for each nucleus, together with an effective collective charge depending linearly on the deformation parameter. Where experimental data are available, the contribution of the single particle effective charge to the total B(E2) value is calculated. The Hamiltonian describing the α-nucleus interaction contains two terms, a spherically symmetric potential given by the double-folding of the M3Y nucleon-nucleon interaction plus a repulsive core simulating the Pauli principle and a quadrupole-quadrupole (QQ) interaction. The α-decaying state is identified as a narrow outgoing resonance in this potential. The intensity of the transition to the first excited state is reproduced by the QQ coupling strength. It depends linearly both on the nuclear deformation and the square of the reduced width for the decay to the band head, respectively. Predicted intensities for transitions to higher excited states are in a reasonable agreement with experimental data. This formalism offers a unified description of energy levels, electromagnetic and favored α transitions for known heavy odd-mass α emitters. [ABSTRACT FROM AUTHOR]

The half-life of the yrast IΠ = 2+ state in the neutron-rich nucleus 188W has been measured using fast-timing techniques with the HPGe and LaBniCe array at the National Institute of Physics and Nuclear Engineering, Bucharest. The resulting value of t1/2 = 0.87(12) ns is equivalent to a reduced transition probability of B(E2;21 →01 +) = 85(12) W.u. for this transition. The B(E2;21 →01 +) is compared to neighboring tungsten isotopes and nuclei in the Hf, Os, and Pt isotopic chains. Woods-Saxon potential energy surface (PES ) calculations have been performed for nuclei in the tungsten isotopic chain and predict prolate deformed minima with rapidly increasing y softness for l84-192W and an oblate minimum for l94W. [ABSTRACT FROM AUTHOR]