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A salient feature of quantum mechanics is the inherent property of collective quantum motion, when apparent independent quasiparticles move in highly correlated trajectories, resulting in strongly enhanced transition probabilities. To assess the extend of a collective quantity requires an appropriate definition of the uncorrelated average motion, often expressed by single particle units. A well known example in nuclear physics is the Weisskopf unit for electromagnetic transitions which reveals different aspects of collective motion. In this paper we define the corresponding single particle unit for alpha decay as induced by four uncorrelated/non-interacting protons and neutrons. Our definition facilitates an unified description of all alpha decay processes along the nuclear chart, revealing a simple mass dependence. The comparison of the uncorrelated decay rates with the experimentally observed ones, shows a significant enhancement of the decay rates pointing towards collective alpha like correlations in the nuclear ground state. As a limiting case, the formalism presented here is applied to proton decay revealing its single particle nature.

Excited states in the extremely neutron-deficient nucleus $$^{172}{\mathrm {Pt}}$$172Pt were populated via $$^{96}\mathrm {Ru}(^{78}\mathrm {Kr},2p)$$96Ru(78Kr,2p) and $$^{92}\mathrm {Mo}(^{83}\mathrm {Kr},3n)$$92Mo(83Kr,3n) reactions. The level scheme has been extended up to an excitation energy of $$\approx 5~\hbox {MeV}$$≈5MeV and tentative spin-parity assignments up to $$I^\pi = 18^+$$Iπ=18+. Linear polarization and angular distribution measurements were used to determine the electromagnetic E1 character of the dipole transitions connecting the positive-parity ground-state band with an excited side-band, firmly establishing it as a negative-parity band. The lowest member of this negative-parity structure was firmly assigned spin-parity $$3^-$$3-. In addition, we observed an E3 transition from this $$3^-$$3- state to the ground state, providing direct evidence for octupole collectivity in $$^{172}{\mathrm {Pt}}$$172Pt. Large-scale shell model (LSSM) and total Routhian surface (TRS) calculations have been performed, supporting the interpretation of the $$3^-$$3- state as a collective octupole-vibrational state.

The process leading to cluster emission from superheavy nuclei in the range 100 122 has been systematically investigated. This topic is of importance because it opens up the possibility of identify ...

Lifetimes of the first excited 2(+) and 4(+) states in the extremely neutron -deficient nuclide Pt-172 have been measured for the first time using the recoil-distance Doppler shift and recoil-decay tagging techniques. An unusually low value of the ratio B(E2: 4(1)(+) -> 2(1)(+)/B(E2: 2(1)(+) -> 0(gs)(+)) = 0.55(19) was found, similar to a handful of other such anomalous cases observed in the entire Segre chart. The observation adds to a cluster of a few extremely neutron -deficient nuclides of the heavy transition metals with neutron numbers N approximate to 90-94 featuring the effect. No theoretical model calculations reported to date have been able to explain the anomalously low B(E2: 4(1)(+) -> 2(1)(+)/B(E2: 2(1)(+) -> 0(gs)(+)) ratios observed in these cases. Such low values cannot, e.g., be explained within the framework of the geometrical collective model or by algebraic approaches within the interacting boson model framework. It is proposed that the group of B(E2: 4(1)(+) -> 2(1)(+)/B(E2: 2(1)(+) -> 0(gs)(+)) ratios in the extremely neutron-deficient even-even W, Os, and Pt nuclei around neutron numbers N approximate to 90-94 reveal a quantum phase transition from a seniority-conserving structure to a collective regime as a function of neutron number. Although a system governed by seniority symmetry is the only theoretical framework for which such an effect may naturally occur, the phenomenon is highly unexpected for these nuclei that are not situated near closed shells.

The advent and intensive use of new detector technologies as well as radioactive ion beam facilities have opened up possibilities to investigate alpha, proton and cluster decays of highly unstable nuclei. This article provides a review of the current status of our understanding of clustering and the corresponding radioactive particle decay process in atomic nuclei. We put alpha decay in the context of charged-particle emissions which also include one- and two-proton emissions as well as heavy cluster decay. The experimental as well as the theoretical advances achieved recently in these fields are presented. Emphasis is given to the recent discoveries of charged-particle decays from proton-rich nuclei around the proton drip line. Those decay measurements have shown to provide an important probe for studying the structure of the nuclei involved. Developments on the theoretical side in nuclear many-body theories and supercomputing facilities have also made substantial progress, enabling one to study the nuclear clusterization and decays within a microscopic and consistent framework. We report on properties induced by the nuclear interaction acting in the nuclear medium, like the pairing interaction, which have been uncovered by studying the microscopic structure of clusters. The competition between cluster formations as compared to the corresponding alpha-particle formation are included. In the review we also describe the search for super-heavy nuclei connected by chains of alpha and other radioactive particle decays., Comment: 58 pages, submitted to Prog. Part. Nucl. Phys

The emissions of $\ensuremath{\alpha}$ particles and protons are the dominant decay channels in the neutron-deficient nuclei corresponding to the $sdg$ major shell. The possibility of cluster emission is explored here. It is shown that the cluster decay mode has a small yet sizable branching ratio.

It was recently found that the formation probabilities of $\ensuremath{\alpha}$ particles in Te isotopes are larger than the corresponding probabilities in Po isotopes. We have done a full microscopic calculation within the framework of the multistep shell model to analyze in detail the formation probabilities and subsequent decays of $\ensuremath{\alpha}$ particles from $^{212}\mathrm{Po}$ and $^{104}\mathrm{Te}$. We have also calculated the spectra of these two decaying nuclei and found that the tentatively assigned spin $({18}^{+})$ at 2.922 MeV in $^{212}\mathrm{Po}$ (National Nuclear Data Center, www.nndc.bnl.gov) is predicted to be a state ${16}^{+}$. We also present for the first time the full energy spectrum of $^{104}\mathrm{Te}$. The evaluated formation amplitudes in both nuclei show that in $^{104}\mathrm{Te}$ there is indeed a superallowed $\ensuremath{\alpha}$-decay transition.

A partial conservation of the seniority quantum number in j = 9 / 2 shells has been found recently in a numerical application. In this paper an analytic proof for this problem is derived as an extension of the work [L. Zamick, P. Van Isacker, Phys. Rev. C 78 (2008) 044327]. We analyze the properties of the non-diagonal interaction matrix elements with the help of the one-particle and two-particle coefficients of fractional parentage (cfpʼs). It is found that all non-diagonal (and the relevant diagonal) matrix elements can be re-expressed in simple ways and are proportional to certain one-particle cfpʼs. This remarkable occurrence of partial dynamic symmetry is the consequence of the peculiar property of the j = 9 / 2 shell, where all v = 3 and 5 states are uniquely defined.

A lifetime measurement has been made for the first excited 11/2(+) state in the proton-unbound nucleus (109)(53)I56 using the recoil-distance Doppler-shift method in conjunction with recoil-proton ...

Using a cluster model based on the Woods-Saxon potential, alpha-particle decays from excited states in 24Mg have been systematically investigated. Calculations can in general reproduce experimental data, noticing the fact that the preformation factor P of alpha particle in alpha-decaying nuclei is of order from 100 to 10−2. This can be the evidence for the α+20Ne structure in 24Mg. Meanwhile, the results also show the existence of other configurations, such as 16O+2α. Since the calculated decay widths are very sensitive to the angular momentum carried by the outgoing cluster (α particle), our results could serve as a guide to experimental spin assignments.

One- and two-quasi particle states are studied in the complex energy plane. It is found that the pairing interaction does not change the character of the complex state. If a normal state is a physi ...

We compare the quantum mechanical procedures to estimate the total $\ensuremath{\alpha}$-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 ${\ensuremath{\beta}}_{2}=0.3$ 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.

Systematic investigation of the known even-even transactinide cluster emitters has been carried out by considering the cluster as a point particle and using the exact quantum mechanical treatment of the decay process. It is shown that the cluster decay phenomenon can be described reasonably well using a simple Woods-Saxon mean field. Sensitivity of the half-lives on various aspects of the mean field has been investigated in detail.

We analyze the alpha-decay fine structure to excited 0(2)(+) 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 alpha decay from the excited state P(0(2)(+)) 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(0(1)(+)) and D(0(2)(+)) 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(0(2)(+)) then the occupation probability of this state is 25%.

Processes occurring in the continuum part of the spectrum are described by using a basis consisting of bound and antibound states plus Gamow resonances and the continuum background. The calculations, performed in the complex energy plane, are applied to the study of weakly bound nuclei. The influence of antibound states upon physical quantities in halo nuclei is assessed.

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two-particle states are calculated by using a single-particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long-lived resonances are mostly determined by either bound states or by narrow Gamow resonances. However, they are significantly affected by wide resonances and the continuum background itself.

By extending the notion of states to functionals acting on the space of observables we obtain a well-defined complex spectral decomposition for the time evolution of quantum-decaying systems, where Gamov states play a fundamental role. It is shown that Gamov vectors are well-defined state functionals and, therefore, they stand on the same footing as plane waves.

The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with the energy of the escaping $\alpha$ particle and contains for every isotopic chain two experimentally determined coefficients. The expression is supported by several phenomenological approaches, however its coefficients lack a fully microscopic basis. In this paper we will show that: 1) the empirical coefficients that appear in the GN law have a deep physical meaning and 2) the GN law is successful within the restricted experimental data sets available so far, but is not valid in general. We will show that, when the dependence of logarithm values of the $\alpha$ formation probability on the neutron number is not linear or constant, the GN law is broken. For the $\alpha$ decay of neutron-deficient nucleus $^{186}$Po, the difference between the experimental half-life and that predicted by the GN Law is as large as one order of magnitude., Comment: 4 pages, 5 figures, to appear in Phys. Lett. B

The neutron-deficient semimagic (neutron number N = 50) Rh-95 nucleus has been produced at high spins using the projectile-target system Ca-40 + Ni-58 at 125 MeV beam energy. The gamma-decays of le ...

The magnetic moments of the first excited 2(+) state in even-even nuclei Sn102-130 and the low-lying yrast states in odd-mass nuclei Sn-101-109,Sn-123-131 are calculated within the framework of the nucleon-pair approximation (NPA) of the shell model, by using the standard multipole-multipole interaction. Our calculations agree reasonably well with available experimental data. The g(2(1)(+)) values, as well as the contributions from their spin and orbital angular momentum components, are evaluated in terms of the small NPA subspace spanned by S and D nucleon pairs. The magnetic moment is suggested to be a sensitive probe of the nuclear wave function in this region.

Linear polarization and angular correlations of gamma-rays depopulating excited states in the neutron-deficient nucleus Ru-94(44)50 have been measured, enabling firm spin-parity assignments for several excited states in this nucleus. The deduced multipolarities of strong transitions in the yrast structure were found to be mostly of stretched M1, E1, and E2 types and, in most cases, in agreement with previous tentative assignments. The deduced multipolarity of the 1869 keV and the connecting 257 and 1641 keV transitions indicates that the state at 6358 keV excitation energy has spin parity 12(1)(-) rather than 12(3)(+) as proposed in previous works. The presence of a 12(1)(-) state is interpreted within the framework of large-scale shell-model calculations as a pure proton-hole state dominated by the pi(p(1/2)(-1)circle times g(9/2)(-5)) and pi(p(3/2)(-1) g(9/2)(-5)) configurations. A new positive-parity state is observed at 6103 keV and is tentatively assigned as 12(2)(+). The 14(1)(-) state proposed earlier is reassigned as 13(4)(-) and is interpreted as being dominated by neutron particle-hole core excitations. The strengths of several E1 transitions have been measured and are found to provide a signature of core-excited configurations.

A single particle basis consisting of two different harmonic oscillator representations is introduced with the aim of studying microscopically alpha and cluster decay processes. A correct description of the wave functions at large distances is obtained within a minimal single particle basis. Experimental data corresponding to a large number of alpha decay transitions from even-even nuclei are well reproduced. Applications to 14 C decay from Ra isotopes are presented.

Measurements of γ-ray, γγ-coincidence and internal conversion electron spectra from the 106 Cd( α , nγ ) 109 Sn reaction were carried out at 15–20 MeV α-particle bombarding energies with Ge(HP) γ-ray and superconducting magnetic lens plus Si(Li) electron spectrometers. The energies, relative intensities, internal conversion coefficients and coincidence relations of the 109 Sn transitions were determined, and a more complete, consistent level scheme has been deduced. Spin and parity values have been determined from the internal conversion coefficients, the bombarding-energy dependence of the side-feeding intensities of the states and the available γ-ray angular distribution data. The level scheme was interpreted in the framework of the quasi-particle shell model.

The half-lives ${T}_{1/2}$ for proton decay from the nuclei ${}_{53}^{109}\mathrm{I},$ ${}_{63}^{131}\mathrm{Eu},$ and ${}_{67}^{141}\mathrm{Ho}$ are evaluated exactly, assuming that the emitted proton moves in a deformed single particle Nilsson level. The calculated values of ${T}_{1/2},$ consistent with experiments, suggest a deformation of $\ensuremath{\beta}\ensuremath{\approx}0.14$ for ${}_{53}^{109}\mathrm{I}$ and $\ensuremath{\beta}\ensuremath{\approx}0.3--0.4$ for ${}_{63}^{131}\mathrm{Eu}$ and ${}_{67}^{141}\mathrm{Ho}.$ The corresponding most likely candidate states as ground states are ${K=1/2}^{+},$ ${K=5/2}^{+},$ and ${K=7/2}^{\ensuremath{-}}$ for the above three nuclei, respectively. The recently found isomeric state in ${}_{67}^{141}\mathrm{Ho}$ is interpreted as a ${K=1/2}^{+}$ state.

The absolute decay width of a single-particle level in a deformed potential is evaluated exactly. Experimental data are analyzed by using the formalism developed here. It is found that proton decay is a powerful tool to determine the deformation of nuclei as well as to probe small components of the wave functions of the decaying states. This will allow one to study the behavior of single-particle resonances in nuclei close to the drip line, and may guide future experiments.

Isovector $E1$ giant resonances in nonmagic nuclei are calculated by using a method which takes into account the single-particle continuum in the framework of a continuum quasiparticle random-phase approximation. A special procedure is formulated which gives the spurious dipole state at zero energy. The calculations are performed in a stable nonmagic tin isotope as well as unstable magic and nonmagic tin isotopes. The role of the single-particle continuum and the spurious dipole state is discussed. It turned out that the first ingredient has a noticeable influence on the resonance form.

Giant resonances manifest themselves as broad bumps in the nuclear spectra above the neutron emission threshold. It has been established that the structure of these states consists of a large number of relevant particle-hole configurations, all of them contributing in phase to the excitation process. Be- cause of this, giant resonances are the most collective vibra- tional states in nuclei. Alternatively, given the strong collectivity of the giant resonances and the many degrees of freedom that influence their properties, one may consider that a statistical modeling of the formation and decaying processes including concepts like mean values and variances is an appropriate path to at- tact this difficult problem. In this paper, we adopt such a point of view. We consider a collective coordinate q and its vibrational modes determined by a harmonic oscillator po- tential. That is, we consider that the giant resonance corre- sponds to the first excitation of the harmonic oscillator, with energy \v 0, and the GR2 to the second excitation, with two quantum oscillations and energy 2\v 0 . Besides these exci- tations, we distinguish an ''environment'' of all the other excitations. In Sec. II we derive Lindblad's quantum master equation using physical concepts, since the original derivation @15# is rather abstract. We also derive a form of this equation which includes friction and diffusion @16,17#. It has been shown that this equation gives very accurate descriptions of pro- cesses in optics @18# as well as in nuclear physics @19,20# .I n Sec. III we obtain the energy mean value and width of the giant resonance and of the GR2. The corresponding equa- tions turn out to be analytically integrable. The decay spec- trum of the giant resonances is presented in Sec. IV and a summary and conclusions are in Sec. V.

A microscopic description of heavy-cluster decay using a single particle basis suited to describe the continuum part of the spectrum is presented. The role of pairing correlations and quadrupole deformations is analyzed. The stability of the results as a function of the number of major shells included in the calculation is attested. {copyright} {ital 1997} {ital The American Physical Society}

Temperature dependent shell corrections are calculated taking into account the continuum spectrum of a finite depth mean field potential. The effect of the continuum is split up into a discret term which includes Gamow resonances and an integral along a contour in the complex energy plane. The resonances appear in the formalism in the same manner as bound states and at low temperatures they give the main part of the contribution due to the continuum. The method is applied to the particular case of {sup 208}Pb. The temperature for which the shell corrections are washed out completly is estimated at T{approx}2.5 MeV. {copyright} {ital 1997} {ital The American Physical Society}

The BCS equations are extended to incorporate the contribution of the resonant part of the continuum single-particle spectrum. The effect of the resonant continuum appears in the new set of equations through the generalized level density. A numerical application is presented for the nucleus 170 Sn.

To understand the low-energy structure of the neutron deficient iodine isotopes, lifetimes for the low-lying $9/{2}^{+}$ and $11/{2}^{+}$ positive-parity states in ${}^{113}$I have been measured as $\ensuremath{\tau}=28(4)$ ps and $\ensuremath{\tau}=3.7(7)$ ps, respectively. The lifetime for the $11/{2}^{\ensuremath{-}}$ state, which feeds the $9/{2}^{+}$ and $11/{2}^{+}$ states, was remeasured with improved accuracy as $\ensuremath{\tau}=216(7)$ ps. The reduced transition probability, $B(E2)=32(5)$ W.u., for the $9/{2}^{+}\ensuremath{\rightarrow}5/{2}^{+}$ transition agrees with that calculated within the shell model using a Hamiltonian based on the charge-dependent Bonn nucleon-nucleon interaction. In contrast, the much larger transition probability, $B(E2)=209(39)$ W.u., measured for the $11/{2}^{+}\ensuremath{\rightarrow}7/{2}^{+}$ transition has been interpreted, with the aid of configuration-constrained total Routhian surface calculations, as resulting from a slightly $\ensuremath{\gamma}$-soft rotor with an associated quadrupole deformation of ${\ensuremath{\beta}}_{2}\ensuremath{\approx}0.18$. Remarkably similar reduced $E1$ transition probabilities of $5.5(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $4.9(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ W.u. were deduced for the $11/{2}^{\ensuremath{-}}\ensuremath{\rightarrow}9/{2}^{+}$ and $11/{2}^{\ensuremath{-}}\ensuremath{\rightarrow}11/{2}^{+}$ transitions, respectively, which feed apparently dissimilar but competing structures.

The low-lying level schemes and electromagnetic transitions of ${}^{109}$Te, ${}^{109}$I, and the neighboring even-even nucleus ${}^{108}$Te are calculated within the framework of the $SD$-pair approximation of the nuclear shell model. Good agreement is obtained between the calculated results and experimental data. The favored components of low-lying bands are discussed in the collective nucleon-pair subspace. The weak-coupling picture shown in these nuclei and its relationship with residual quadrupole-quadrupole interaction between valence protons and neutrons are analyzed.

In recent experiments at the velocity filter Separator for Heavy Ion reaction Products (SHIP) (GSI, Darmstadt), an extended and improved set of $\ensuremath{\alpha}$-decay data for more than 20 of the most neutron-deficient isotopes in the region from lead to thorium was obtained. The combined analysis of this newly available $\ensuremath{\alpha}$-decay data, of which the $^{186}\mathrm{Po}$ decay is reported here, allowed us for the first time to clearly show that crossing the $Z=82$ shell to higher proton numbers strongly accelerates the $\ensuremath{\alpha}$ decay. From the experimental data, the $\ensuremath{\alpha}$-particle formation probabilities are deduced following the Universal Decay Law approach. The formation probabilities are discussed in the framework of the pairing force acting among the protons and the neutrons forming the $\ensuremath{\alpha}$ particle. A striking resemblance between the phenomenological pairing gap deduced from experimental binding energies and the formation probabilities is noted. These findings support the conjecture that both the $N=126$ and $Z=82$ shell closures strongly influence the $\ensuremath{\alpha}$-formation probability.

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 $\ensuremath{\alpha}$-decay widths from heavy nuclei.

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 ${}^{45}$Fe and ${}^{48}$Ni are reproduced by using a realistic proton-proton interaction.

Recent B(E2; 0(g.s.)(+) -> 2(1)(+)) measurements in light tin isotopes have revealed surprisingly large values relative to standard shell model predictions, generating an unexpected asymmetry in ...

The 278-keV M2 gamma decay from the vh(11/2) isomeric state in Xe-113 has been observed for the first time using the recoil-isomer tagging technique. The half-life of the isomer has been measured t ...

A single particle basis consisting of two different harmonic oscillator representations is introduced with the aim of studying microscopically {alpha}- and cluster-decay processes. A correct description of the wave functions at large distances is obtained within a minimal single particle basis. Experimental data corresponding to a large number of {alpha} decay transitions from even-even nuclei are well reproduced. {copyright} {ital 1996 The American Physical Society.}

Energies, sum rules and partial decay widths of giant resonances are calculated solving exactly the continuum RPA equations corresponding to a central Woods-Saxon potential. An approximated treatment of those quantities in terms of pole expansions of the Green function is also performed. It is found that the approximated results agree well with the exact ones. The expansions allow one to understand the microscopic structure of the resonances. Comparison with experimental data is made and a search for physically meaningful resonances is carried out.

We propose a simple method to evaluate α-transition rates to low-lying excited states in even–even nuclei. For this a realistic α-daughter double-folding interaction is approximated by a parabola in the region where the decay process takes place. This allows us to evaluate the penetration probability analytically. The main experimental features of branching ratios to excited states are reproduced by this simple approach.

A microscopic description of the $\ensuremath{\alpha}$ decay to intruder ${0}_{2}^{+}$ states of Pb isotopes in terms of proton-neutron pairing vibrations is performed. The calculated hindrance factors with respect to $\ensuremath{\alpha}$ transitions into the ground state are in good agreement with the available experimental data. Predictions for further measurements are given. Hindrance factors corresponding to the decay towards Po, Hg, and Pt isotopes are calculated within a simple model. The calculated quantities agree well with the experimental data, indicating that $\ensuremath{\alpha}$ decay is a powerful tool to precisely determine the transition from spherical to deformed shapes in the region around $Z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}82$.

The quasiparticle multistep shell model method is applied to calculate the spectra of light Sn isotopes. A simple interpretation of the main excitations is given. The calculated quantities agree reasonable well with the sparse experimental data which are available.

Lifetime measurements have been made in the neutron-deficient nucleus ${}^{109}$Te using the coincident recoil distance Doppler-shift method. The experimental $B(E2)$ values have been compared with state-of-the-art shell-model calculations using the monopole-corrected realistic charge-dependent Bonn nucleon-nucleon potential. Lifetimes in the $\ensuremath{\nu}{h}_{11/2}$ band are consistent with an interpretation based on the deformation driving properties of a single valence neutron outside of the even-even tellurium core and highlight the unexpected presence of collective behavior as the $N=50$ shell closure is approached. Lifetime measurements for the low-lying positive-parity states also appear to correlate well with shell-model calculations. In addition, a comparison with the proton-unbound nucleus ${}^{109}$I suggests that the presence of a single decoupled valence proton affects the total measured $B(E2)$ strengths in a manner that is not currently well understood.

The intraband electromagnetic transitions in ${}^{210}$Po and ${}^{210}$Pb are well described within the shell model approach. In contrast, similar transitions in ${}^{212}$Po are one order of magnitude smaller than the experimental values, suggesting the existence of an $\ensuremath{\alpha}$-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 $\ensuremath{\alpha}$-decay width in ${}^{212}$Po. We analyzed the recently measured unnatural parity states ${I}^{\ensuremath{-}}$ in ${}^{212}$Po in terms of the collective octupole excitation in ${}^{208}$Pb coupled to positive parity states in ${}^{210}$Pb. They are connected by relatively large dipole transitions to yrast positive natural parity states. We described $E1$ transitions by using the same $\ensuremath{\alpha}$-cluster component and an effective neutron dipole charge ${e}_{\ensuremath{\nu}}=\ensuremath{-}eZ/A$. $B(E2)$ values and absolute $\ensuremath{\alpha}$-decay width in ${}^{212}$Po are simultaneously described within the shell model plus a cluster component depending upon one free strength parameter.

It is shown that the proton formation probability, extracted from experimental data corresponding to one-proton radioactivity, is divided into two regions when plotted as a function of an universal parameter. This parameter is derived from a microscopic description of the decay process. In this way we explain the systematics of proton emission half-lives. At the same time the formation probability is shown to be a useful quantity to determine the deformation property of the mother nucleus., 5 pages, 5 figues, 2 tables, printer-friendly version, submitted to Phys. Rev. C

The seniority scheme has been shown to be extremely useful for the classification of nuclear states in semi-magic nuclei. The neutron-proton ($np$) correlation breaks the seniority symmetry in a major way. As a result, the corresponding wave function is a mixture of many components with different seniority quantum numbers. In this contribution we show that the $np$ interaction may favor a new kind of coupling in $N=Z$ nuclei, i.e., the so-called isoscalar spin-aligned $np$ pair mode. Shell model calculations reveal that the ground and low-lying yrast states of the $N = Z$ nuclei $^{92}$Pd and $^{96}$Cd may mainly be built upon such spin-aligned $np$ pairs each carrying the maximum angular momentum $J = 9$ allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region., Comment: 5 pages, 4 figues, Proceedings of the Nordic Conference on Nuclear Physics 2011. To appear in Physica Scripta T

We have adopted the multistep shell model in the complex energy plane to study nuclear excitations occurring in the continuum part of the spectrum. In this method one proceeds by solving the shell model equations in a successive manner. That is, in each step one constructs the building blocks to be used in future steps. We applied this formalism to analyze the unbound nuclei $^{12,13}$Li starting from the one-particle states in $^{10}$Li and two-particle states in $^{11}$Li. In the former case the excitations correspond to the motion of three particles partitioned as the product of a one-particle and two-particle systems. The ground state of $^{12}$Li is thus calculated to be an antibound (virtual) state. In the four-particle system $^{13}$Li the states can be constructed as the coupling of two correlated pairs. We found that there is no bound or antibound state in $^{13}$Li., Comment: 10 pages, 2 table, 3 figures, Proceedings of the Conference on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Series

It is shown that the set of bound states and single-pa tide esonances consisting of the outgoing solutions of the Schodinge equation can be used as a ep esentation to describe p ocesses taking place in the continuum part of nuclear spectra. This is the first thoough investigation of completeness properties using realistic nuclear wave functions.