Search

The authors present a empirical nuclear shell model interaction and use it to interpret the structure of the sd-shell nuclei.

Background: Clustering plays an important role in the structure of $^{10}\mathrm{Be}$. Exotic molecular-like configurations, such as $\ensuremath{\alpha}$:$2n$:$\ensuremath{\alpha}$, have been suggested at relatively low excitation energies.Purpose: To search for the high-spin states that may belong to the molecular-like $\ensuremath{\alpha}$:$2n$:$\ensuremath{\alpha}$ configuration in $^{10}\mathrm{Be}$.Method: Measuring excitation functions for $^{6}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}\ensuremath{\alpha}$ scattering, populating states in the excitation energy range from 4.5 MeV to 8 MeV in $^{10}\mathrm{Be}$ using a $^{6}\mathrm{He}$ rare-isotope beam and a thick helium gas target.Results: No new excited states in $^{10}\mathrm{Be}$ have been observed. Stringent limits on the possible degree of $\ensuremath{\alpha}$-clustering of the hypothetical yrast ${6}^{+}$ state have been obtained.Conclusions: The high-spin members of the $\ensuremath{\alpha}$:$2n$:$\ensuremath{\alpha}$ molecular-like rotational band configuration, that is considered to have a ${0}^{+}$ band head at 6.18 MeV, either do not exist or have small overlap with the $^{6}\mathrm{He}$(g.s.)$+\ensuremath{\alpha}$ channel.

The $^{11}$Be neutron halo nucleus appears to decay into $^{10}$Be with a rate that exceeds expectations. Neutron disappearance into dark matter, beta decay of a halo neutron, or beta-delayed proton decay have been offered as explanations. In this work we study the latter option; we carry out shell model calculations and sequential decay analysis examining the beta-delayed proton decay going through a resonance in $^{11}$B. The narrow energy window, lack of states with sufficient spectroscopic strength, overwhelming alpha decay branch, all make reconciling the observed rate with beta-delayed proton decay difficult., 8 pages, 2 figures

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory’. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections., SCOPUS: re.j, info:eu-repo/semantics/published

The first study of resonances in $^{17}\mathrm{O}+\ensuremath{\alpha}$ elastic scattering was carried out using the thick target inverse kinematics method. The data were analyzed in the framework of an R-matrix approach. Many $\ensuremath{\alpha}$-cluster states were found in the $^{21}\mathrm{Ne}$ excitation region of the 9--13 MeV excitation energy including the first observation of a broad $l=0$ state in an odd-even nucleus, which is likely the analog of the broad ${0}^{+}$ at 8 MeV in $^{20}\mathrm{Ne}$. The observed structure in $^{21}\mathrm{Ne}$ appeared to be strikingly similar to that populated in the resonant $^{16}\mathrm{O}+\ensuremath{\alpha}$ scattering in $^{20}\mathrm{Ne}$. The results are also useful for refinement of data on an $^{17}\mathrm{O}(\ensuremath{\alpha},n)$ reaction important for astrophysics.

Excited states of the neutron-rich isotopes $^{42,44}\mathrm{S}$ and $^{41,43}\mathrm{P}$ have been studied via inverse-kinematics proton scattering from a liquid hydrogen target, using the GRETINA $\ensuremath{\gamma}$-ray tracking array to extract inelastic-scattering cross sections. Deformation lengths of the ${2}_{1}^{+}$ excitations in $^{42,44}\mathrm{S}$ have been determined and, when combined with deformation lengths determined with electromagnetic probes, yield the ratio of neutron-to-proton matrix elements ${M}_{n}/{M}_{p}$ for the ${2}_{1}^{+}$ excitations in these nuclei. The present results for $^{41,43}\mathrm{P}(p,{p}^{\ensuremath{'}})$ are used to compare two shell-model interactions, SDPF-U and SDPF-MU. As in a recent study of $^{42}\mathrm{Si}$, the present results on $^{41,43}\mathrm{P}$ favor the SDPF-MU interaction.

Background: Atomic nuclei are remarkable quantum many-body systems where clustering properties develop naturally from underlying interactions between the constituent nucleons. Clustering degrees of freedom manifest themselves in multiple structure and reaction observables.Purpose: Our goal is to study nuclear clustering and its emergence in many-nucleon dynamics from nucleon-nucleon interactions. Clustering is a phenomenon that is known to emerge on the boundary between structure and reactions, therefore developing appropriate techniques that bridge the structure-reaction divide and establishing connections to observables is among our principal objectives. Showing consistency and how the new techniques can be reduced to well established other methods is an important part of this work.Methods: The configuration-interaction technique based on second quantization is used to treat the quantum many-body problem assuring that fermionic antisymmetry is fully satisfied. The use of the harmonic oscillator single-particle basis allows for the center-of-mass coordinate to be separated and prepared in a desired oscillator state for each cluster. The relative motion reaction basis channels are constructed by coupling clusters in different harmonic oscillator states with respect to their relative motion. Finally, using a resonating group method strategy we solve the generalized eigenvalue problem to obtain scattering channels. Structural clustering characteristics are discussed and the modified harmonic oscillator representation for scattering equations method is used to extract scattering observables.Results: New methods for treating clustering problems have been put forward. We demonstrate broad applicability of the developed techniques. Examples highlight connections with algebraic techniques, and the role of approximations leading to algebraic limits is assessed using realistic examples. Various types of clustering characteristics are used to study alpha clustering in light nuclei that are relevant to currently ongoing experimental efforts. We demonstrate the emergence of strongly clustered bands of states in beryllium, triple alpha channels in $^{12}\mathrm{C}$, and molecular type clustering in $^{21}\mathrm{Ne}$. Starting from nucleon-nucleon interactions without any additional assumptions scattering phase shifts for alpha-alpha scattering are determined and shown to be consistent with those observed.Conclusions: In this work we put forward a new configuration-interaction-based method that targets the physics of clustering, and further unifies nuclear structure and reactions. We provide detailed discussions and many examples highlighting features and advantages of the approach.

The analyzing powers $^{T}T_{10}\phantom{\rule{0.16em}{0ex}},^{T}T_{20}$, and $^{T}T_{30}$ for the $^{12}\mathrm{C}(^{7}\mathrm{Li},t$) reaction were measured and combined with new and previously determined angular distributions to probe the role of multistep processes through coupled channel Born approximation (CCBA) calculations employing new $\ensuremath{\alpha}$-particle spectroscopic amplitudes calculated with the phenomenological shell model in the unrestricted $psd$ space. Good descriptions of the cross-section angular distributions could be obtained except for the larger angles for the 6.05 MeV ${0}^{+}$ and 6.13 MeV ${3}^{\ensuremath{-}}$ states, while the analyzing powers were not generally described. The calculations presented demonstrate the sensitivity of the angular distributions of both the differential cross sections and the analyzing powers to various multistep routes. While the measured analyzing power $^{T}T_{30}$ is roughly zero for all states, the various CCBA calculations produced large and highly oscillatory values for this observable, showing that other multistep processes must be present beyond those taken into account in this work. Standard distorted wave Born approximation (DWBA) calculations were also carried out and these show considerable differences from the CCBA results but the description of the analyzing powers, while slightly improved, is still poor.

High-spin states in $^{39}\mathrm{Ar}$ were populated using the $^{27}\mathrm{Al}(^{14}\mathrm{C},\phantom{\rule{4pt}{0ex}}pn)$ reaction at 25.6 MeV. The de-exciting $\ensuremath{\gamma}$ rays were measured with the FSU $\ensuremath{\gamma}$ detector array along with evaporation protons in a Si $E\text{\ensuremath{-}}\mathrm{\ensuremath{\Delta}}E$ telescope. The known high-spin level scheme was extended up to over 11 MeV with a dozen new levels above the neutron decay threshold. The decay pattern appears somewhat atypical for heavy-ion fusion-evaporation reactions. The structure of $^{39}\mathrm{Ar}$ is discussed in terms of the new FSU cross-shell $spsdpf$ interaction fitted to a wide range of nuclei. This interaction has proved quite successful in accounting for the level scheme of $^{39}\mathrm{Ar}$, including the previously suggested fully aligned $\ensuremath{\pi}{f}_{7/2}\ensuremath{\bigotimes}\ensuremath{\nu}{f}_{7/2}17/{2}^{+}$ state and previously discovered analogs of the lowest states in $^{39}\mathrm{Cl}$.

Garrett et al. systematically investigated band-crossing frequencies resulting from the rotational alignment of the first pair of i13/2 neutrons (AB) in rare-earth nuclei. In that study, evidence was found for an odd-even neutron number dependence attributed to changes in the strength of neutron pairing correlations. The present paper carries out a similar investigation at higher rotational frequencies for the second pair of aligning i13/2 neutrons (BC). Again, a systematic difference in band-crossing frequencies is observed between odd-N and even-N Er, Yb, Hf, and W nuclei, but in the BC case, it is opposite to the AB neutron-number dependence. These results are discussed in terms of a reduction of neutron pairing correlations at high rotational frequencies and of the effects of Pauli blocking on the pairing field by higher-seniority configurations. Also playing a significant role are the changes in deformation with proton and neutron numbers, the changes in location of single-particle orbitals as a function of quadrupole deformation, and the position of the Fermi surface with regard to the various ω components of the neutron i13/2 shell.

The decay of unbound excited 11 Li was measured after being populated by a two-proton removal from a 13 B beam at 71 MeV/nucleon. Decay energy spectra and Jacobi plots were obtained from measurements of the momentum vectors of the 9 Li fragment and neutrons. A resonance at an excitation energy of ∼1.2 MeV was observed. The kinematics of the decay are equally well fit by a simple dineutron-like model or a phase-space model that includes final state interactions. A sequential decay model can be excluded.

A method for studying cluster spectroscopic properties of nuclear fragmentation, such as spectroscopic amplitudes, cluster form factors, and spectroscopic factors, is developed on the basis of modern precision nuclear models that take into account the mixing of large-scale shell-model configurations. Alpha-cluster channels are considered as an example. A mathematical proof of the need for taking into account the channel-wave-function renormalization generated by exchange terms of the antisymmetrization operator (Fliessbach effect) is given. Examples where this effect is confirmed by a high quality of the description of experimental data are presented. By and large, the method in question extends substantially the possibilities for studying clustering phenomena in nuclei and for improving the quality of their description.

We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have pre-exponential, exponential, and long-term power-law limiting behaviors. This result relies on complexity of the wave functions and thus is generic to many systems. In the chaotic limit modeled by the Gaussian Orthogonal Ensemble we show that the survival probability obtained analytically also fully defines the relaxation timescale of observables. This is not the case in general, using realistic nuclear shell model and the quadrupole moment as an observable we demonstrate that the relaxation time is significantly longer than defined by the survival probability of the initial state. An example of the non-chaotic limit of coherent and squeezed states provides an additional illustration., Comment: 14 pages, 16 figures

The higher-spin structure of $^{38}$Cl ($N = 21$) was investigated following the $^{26}$Mg($^{14}$C, $pn$) reaction at 30 and 37 MeV beam energies. The outgoing protons were detected in an $E- \Delta E$ Si telescope placed at 0$^\circ$ close to the target with a Ta beam stopper between the target and telescope. Multiple $\gamma$ rays were detected in time coincidence with the protons using an enhanced version of the FSU $\gamma$ detection array. The level scheme was extended up to 8420 keV with a likely spin of 10 $\hbar$. A new multishell interaction was developed guided by the experimental information. This FSU interaction was built by fitting to the energies of 270 experimental states from $^{13}$C to $^{51}$Ti. Calculations using the FSU interaction reproduce observed properties of $^{38}$Cl rather well, including the spectroscopic factors. The interaction has been successfully used to interpret the $1p1h$ and $2p2h$ configurations in some nearby nuclei as well., Comment: Published in https://doi.org/10.1103/PhysRevC.100.034308

Author(s): Lubna, RS; Tripathi, V; Tabor, SL; Tai, PL; Kravvaris, K; Bender, PC; Volya, A; Bouhelal, M; Chiara, CJ; Carpenter, MP; Janssens, RVF; Lauritsen, T; McCutchan, EA; Zhu, S; Clark, RM; Fallon, P; MacChiavelli, AO; Paschalis, S; Petri, M; Reviol, W; Sarantites, DG | Abstract: Excited states in the neutron-rich isotopes P33 and P34 were populated by the O18+O18 fusion-evaporation reaction at Elab=24 MeV. The Gammasphere array was used along with the Microball particle detector array to detect γ transitions in coincidence with the charged particles emitted from the compound nucleus S36. The use of Microball enabled the selection of the proton emission channel. It also helped in determining the exact position and energy of the emitted proton; this was later employed in kinematic Doppler corrections. 16 new transitions and 13 new states were observed in P33 and 21 γ rays and 20 energy levels were observed in P34 for the first time. The nearly 4π geometry of Gammasphere allowed the measurement of γ-ray angular distributions leading to spin assignments for many states. The experimental observations for both isotopes were interpreted with the help of shell-model calculations using the (0+1)ω PSDPF interaction. The calculations accounted for both the 0p-0h and 1p-1h states reasonably well and indicated that 2p-2h excitations might dominate the higher-spin configurations in both P33 and P34.

Recently, a new strategy that unifies the structure, clustering, and reactions aspects of the nuclear quantum many-body problem has been put forward; the configuration interaction technique combined with the resonating group method based on a harmonic oscillator basis allows one to treat the reaction and multi-clustering dynamics in a translationally invariant way and preserve Pauli principle. In this presentation we apply the developed method to study the alpha clustering in 8Be, 9Be, and 10Be from ab-inito principles. Isotopes of beryllium are classic examples of molecular type clustering structures and thus provide an ideal arena for exploring the emergence of complex dynamics from realistic nucleon-nucleon interaction.

There is strong evidence that some states in 10Be exhibit molecular like α:2n:α configuration. Based on theoretical studies it appears that the 6.179 MeV 0+ state in 10Be has a pronounced α:2n:α configuration with an α-α inter-distance of 3.55 fm [1]. This is 1.8 times more than the corresponding value for the 10Be ground state. The 2+ at 7.542 MeV in 10Be is believed to be the next member of this rotational band. The state at 10.2 MeV was identified as a 4+ member in recent experiments. The algebraic model predicts that this band should also include the 6+ and 8+ states. We performed an experiment to search for the higher spin cluster states in the excitation function for 6He+α scattering. No evidence for the new states has been observed.

We put forward a new ab initio approach that seamlessly bridges the structure, clustering, and reactions aspects of the nuclear quantum many-body problem. The configuration interaction technique combined with the resonating group method based on a harmonic oscillator basis allows us to treat the reaction and multiclustering dynamics in a translationally invariant way and preserve the Pauli principle. Our presentation includes studies of $^{8,10}\mathrm{Be}$ and an exploration of $3\ensuremath{\alpha}$ clustering in $^{12}\mathrm{C}$.

The Si31 nucleus was produced through the O18(O18, αn) fusion-evaporation reaction at Elab=24MeV. Evaporated α particles from the reaction were detected and identified in the Microball detector array for channel selection. Multiple γ-ray coincidence events were detected in Gammasphere. The energy and angle information for the α particles was used to determine the Si31 recoil kinematics on an event-by-event basis for a more accurate Doppler correction. A total of 22 new states and 52 new γ transitions were observed, including 14 from states above the neutron separation energy. The positive-parity states predicted by the shell-model calculations in the sd model space agree well with experiment. The negative-parity states were compared with shell-model calculations in the psdpf model space with some variations in the N=20 shell gap. The best agreement was found with a shell gap intermediate between that originally used for A≈20 nuclei and that previously adapted for P32,34. This variation suggests the need for a more universal cross-shell interaction.

CITATION: Long, A. M., et al. 2017. Indirect study of the stellar ³⁴ Ar(α,p) ³⁷K reaction rate through ⁴⁰Ca(p,t) ³⁸Ca reaction measurements. Physical Review C, 95(5):1-9, doi:10.1103/PhysRevC.95.055803.

We present techniques that allow for $\alpha$-cluster channels with realistic $\alpha$-particle wave functions from No Core Shell Model calculations to be constructed. We compare results of several clustering calculations with realistic $\alpha$ wave functions to those assuming a trivial $(0s)^4$ structure., Comment: 3 pages, 1 table, 11th International Conference on Clustering Aspects of Nuclear Structure and Dynamics

Low-lying excited states in $^{38,40}\mathrm{P}$ have been identified in the $\ensuremath{\beta}$ decay of ${T}_{z}=+5,\phantom{\rule{0.16em}{0ex}}+6, ^{38,40}\mathrm{Si}$. Based on the allowed nature of the Gamow-Teller (GT) decay observed, these states are assigned spin and parity of ${1}^{+}$ and are core-excited 1p1h intruder states with a parity opposite to the ground state. The occurrence of intruder states at low energies highlights the importance of pairing and quadrupole correlation energies in lowering the intruder states despite the $N=20$ shell gap. Configuration interaction shell model calculations with the state-of-art SDPF-MU effective interaction were performed to understand the structure of these 1p1h states in the even-$A$ phosphorus isotopes. States in $^{40}\mathrm{P}$ with $N=25$ were found to have very complex configurations involving all the $fp$ orbitals leading to deformed states as seen in neutron-rich nuclei with $N\ensuremath{\approx}28$. The calculated GT matrix elements for the $\ensuremath{\beta}$ decay highlight the dominance of the decay of the core neutrons rather than the valence neutrons.

Studies of nuclei far from the valley of stability are currently in the center of modern nuclear physics. For such loosely bound systems, the continuum effects are vitally important. We develop the continuum shell model based on an effective non-Hermitian Hamiltonian. This rigorous quantum-mechanical method is powerful for description of open quantum systems unifying their structure and reactions. The formalism is explained and examples of its application are given; the results are in a very good agreement with recent experiments on exotic nuclei. We show also how this approach can be successfully applied to a general problem of a signal transmission through an open quantum system.

Previous experiments observed a 4^{+} state in the N=28 nucleus ^{44}S and suggested that this state may exhibit a hindered E2-decay rate, inconsistent with being a member of the collective ground state band. We populate this state via two-proton knockout from a beam of exotic ^{46}Ar projectiles and measure its lifetime using the recoil distance method with the GRETINA γ-ray spectrometer. The result, 76(14)_{stat}(20)_{syst} ps, implies a hindered transition of B(E2;4^{+}→2_{1}^{+})=0.61(19) single-particle or Weisskopf units strength and supports the interpretation of the 4^{+} state as a K=4 isomer, the first example of a high-K isomer in a nucleus of such low mass.

Thick target inverse kinematics technique was combined with Time of Flight method to study resonance reactions induced by heavy ions at low energy, to minimize background and to identify various possible nuclear processes in extended target. The 17 O, 20 Ne spectrum, the cluster and nucleon spectroscopic factors were calculated using cluster-nucleon configuration interaction model.

The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI., Comment: 7 pages 6 figures

Reactions on certain proton-rich, radioactive nuclei have been shown to have a significant influence on X-ray bursts. We provide an overview of two recent measurements of important X-ray burst reactions using in-flight radioactive ion beams from the RESOLUT facility at the J. D. Fox Superconducting Accelerator Laboratory at Florida State University. The 17 F(d,n) 18 Ne reaction was measured, and Asymptotic Normalization Coefficients were extracted for bound states in 18 Ne that determine the direct-capture cross section dominating the 17 F(p, γ ) 18 Ne reaction rate for T≲ 0.45 GK. Unbound resonant states were also studied, and the single-particle strength for the 4.523-MeV (3 + ) state was found to be consistent with previous results. The 19 Ne(d,n) 20 Na proton transfer reaction was used to study resonances in the 19 Ne(p, γ ) 20 Na reaction. The most important 2.65-MeV state in 20 Na was observed to decay by proton emission to both the ground and first-excited states in 19 Ne, providing strong evidence for a 3 + spin assignment and indicating that proton capture on the thermally-populated first-excited state in 19 Ne is an important contributor to the 19 Ne(p, γ ) 20 Na reaction rate.

The structure of $^{29}\mathrm{Al}$ and $^{27}\mathrm{Mg}$ was investigated using the reactions $^{18}\mathrm{O}$($^{14}\mathrm{C},p2n$) and $^{18}\mathrm{O}$($^{14}\mathrm{C},\ensuremath{\alpha}\phantom{\rule{0.16em}{0ex}}n$) at 40 MeV. The charged particles were detected and identified with a $\mathrm{\ensuremath{\Delta}}E\ensuremath{-}E$ telescope in coincidence with $\ensuremath{\gamma}$ radiation detected in the Florida State University Compton suppressed $\ensuremath{\gamma}$ detector array. The level and decay schemes of both nuclei have been expanded at higher spins and excitation energies. The positive-parity states up to 3.5\char21{}4.5 MeV agree well with shell model calculations using the USDA interaction. The negative-parity states in $^{27}\mathrm{Mg}$ are reproduced relatively well by one-particle\char21{}one-hole calculations with the WBP-a interaction. Three $^{27}\mathrm{Mg}$ states unbound by 0.4\char21{}1.4 MeV to neutron decay were observed to decay radiatively. One of these states had been previously observed to $\ensuremath{\gamma}$ decay in a ($d,p\ensuremath{\gamma}$) experiment along with a surprising 16 other neutron unbound states. The competition between neutron and $\ensuremath{\gamma}$ decay in these states is discussed in terms of angular momentum barriers and spectroscopic factors.

International audience; Note from publisher: This article contains the abstract only.

The emission of γ rays from neutron-bound and neutron-unbound states in Mo95, populated in the Mo94(d,p) reaction, has been investigated. Charged particles and γ radiation were detected with arrays of annular silicon and Clover-type high-purity Germanium detectors, respectively. Utilizing p-γ and p-γ-γ coincidences, the Mo95 level scheme was greatly enhanced with 102 new transitions and 43 new states. It agrees well with shell model calculations for excitation energies below ≈2 MeV. From p-γ coincidence data, a new method for the determination of spins of discrete levels is proposed. The method exploits the suppression of high-angular momentum neutron emission from levels with high spins populated in the (d,p) reaction above the neutron separation energy. Spins for almost all Mo95 levels below 2 MeV (and for a few levels above) have been determined with this method.

The Continuum Shell Model is a powerful theoretical tool for analysis of many-body dynamics embedded in the continuum. Here we formulate the method and use an example of a realistic shell model calculation for oxygen isotopes to demonstrate the seamless transition from bound states to resonances and cross sections in continuum within the same framework. The coupled dynamics of intrinsic states and continuum is traced further to the regime of continuum dominance that implies the decay width collectivization and onset of super-radiance. The coexistence and interplay of internal collective motion, such as giant resonances, and decay are of particular interest. Schematic and realistic calculations illustrate changes in the strength distribution and the natural appearance of the so-called pygmy mode.

Excited states were investigated in $^{21}\mathrm{F}$ and $^{25}\mathrm{Na}$ using the $^{9}\mathrm{Be}(^{14}\mathrm{C},pn\ensuremath{\gamma})$ reaction at 30, 35, and 45 MeV and the $^{9}\mathrm{Be}(^{18}\mathrm{O},pn\ensuremath{\gamma})$ reaction at 35 MeV. Protons were detected and identified in an $E\ensuremath{-}\mathrm{\ensuremath{\Delta}}E$ telescope at ${0}^{\ensuremath{\circ}}$ in coincidence with one or more $\ensuremath{\gamma}$ radiations in the FSU Compton-suppressed Ge detector array. Many new levels and electromagnetic decays were observed, especially among the higher spin states. Angular distributions and mean lifetimes were measured wherever possible in both nuclei. The energy levels of the positive-parity states in the two nuclei agree rather well with shell model calculations using both the USDA and WBP interactions up to the highest spins observed of $13/2\phantom{\rule{0.28em}{0ex}}\ensuremath{\hbar}$. Both a weak coupling approximation and shell model calculations using the WBP interaction generally reproduce the negative-parity states in $^{21}\mathrm{F}$. The shell model calculations reproduce relatively well the measured $M1$ and $E2$ transitions in both nuclei, but overpredict the parity-changing $E1$ transitions in $^{21}\mathrm{F}$, the only nucleus in which negative-parity states were observed in the present experiment.

Pairing correlations in nuclei play a decisive role in determining nuclear drip lines, binding energies, and many collective properties. In this work a new configuration-space Monte Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with nonconstant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.

Experimental evidence has recently put the validity of the Porter-Thomas distribution (PTD) for partial neutron widths into question. We identify two terms in the effective Hamiltonian that violate orthogonal invariance (the basis for the PTD). Both are due to the coupling to the decay channels. We show that realistic estimates for the coupling to the neutron channel and for non-statistical gamma decays yield significant modifications of the PTD., 5 pages, 2 figures

Nuclear clustering, alpha decays, and multiparticle correlations are important components of nuclear dynamics. In this work we put forward the cluster-nucleon configuration interaction model. We use the modern configuration interaction approach with advanced realistic shell-model Hamiltonians in order to study clustering phenomena; the study is facilitated by the algebraic properties of many-nucleon configurations in the harmonic oscillator basis. Using a translationally invariant formalism we built cluster channels that satisfy the Pauli exclusion principle as well as orthogonality and normalization conditions. We formally justify the formalism and demonstrate that, within the new method, clustering strengths satisfy sum rules that are consistent with the statistical properties of nuclear reactions with composite particles. Using properly renormalized cluster form factors our approach appears to resolve long-standing problems related to absolute normalization of the alpha clustering spectroscopic factors and their behavior in $sd$-shell nuclei. Our methods are demonstrated in studies of $\ensuremath{\alpha}$ spectroscopic factors in $sd$-shell nuclei and in $^{16}\mathrm{O}$ treated in $p\ensuremath{-}sd$ shells. Comparison with experimental data supports the validity of the approach.

New $^{14}\mathrm{N}(d,p)$ angular distribution data were taken at a deuteron bombarding energy of 16 MeV to locate all narrow peaks up to 15 MeV in excitation. A new shell model calculation is able to reproduce all levels in $^{15}\mathrm{N}$ up to 11.5 MeV and is used to characterize a narrow level at 11.236 MeV and to provide a map of single particle strengths. The known levels in $^{15}\mathrm{N}$ are then used to suggest mirrors in the lesser known nucleus $^{15}\mathrm{O}$. Neutron spectroscopic factors obtained from the present work and proton spectroscopic factors previously published in a $^{14}\mathrm{N}(^{3}\mathrm{He},d)$ study were used to determine the $2{s}_{1/2}$ and $1{d}_{5/2}$ single particle energies for the $^{15}\mathrm{N}\ensuremath{-}^{15}\mathrm{O}$ mirror pairs as $^{15}\mathrm{N}\phantom{\rule{4pt}{0ex}}({2s}_{1/2})=7.64$ MeV, $^{15}\mathrm{O}\phantom{\rule{4pt}{0ex}}({2s}_{1/2})=7.11$ MeV, $^{15}\mathrm{N}\phantom{\rule{4pt}{0ex}}({1d}_{5/2})=7.26$ MeV, and $^{15}\mathrm{O}\phantom{\rule{4pt}{0ex}}({1d}_{5/2})=6.98$ MeV. These results confirm the degeneracy of these orbitals and that the $^{15}\mathrm{N}\ensuremath{-}^{15}\mathrm{O}$ nuclei are where the transition of the $2{s}_{1/2}$ orbital transitions from lying below the $1{d}_{5/2}$ to above it. The $1{d}_{3/2}$ single particle strength is estimated to be centered around 14 MeV in these nuclei.