Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Decay properties of the new isotopes 172Hg and 173Hg

The α decays of the two neutron-deficient nuclei 172Hg and 173Hg were observed for the first time using the 78Kr(96Ru,2n) and 80Kr(96Ru,3n) reactions, respectively. The reaction products were dispersed according to their mass-to-charge state ratios in the Argonne Fragment Mass Analyzer and implanted in a double-sided silicon strip detector, where their subsequent decays were studied using spatial and time correlations between implants and decays. A half-life of 250(+350-90) μs and an energy of 7350(12) keV were deduced for the α decay of 172Hg. In 173Hg the half-life was measured to be 0.93(+0.57-0.26) ms and the corresponding energy is 7211(11) keV. In addition, the half-life and energy of the α decay of 174Hg were measured more precisely. The reduced widths deduced for these Hg isotopes indicate that the observed decays correspond to unhindered Δl = 0 transitions. The α-decay Q values are compared with the values calculated using mass tables by Möller and Nix, and by Liran and Zeldes. The latter mass tables show better agreement with the data

Low-energy structure of Mn61 populated following β decay of Cr61

β decay of the Cr6137 ground state has been studied. A new half-life of 233±11 ms has been deduced, and seven delayed γ rays have been assigned to the daughter Mn6136. The low-energy level structure of Mn6136 is similar to that of the less neutron-rich Mn57,59 nuclei. The odd-A25Mn isotopes follow the systematic trend in the yrast states of the even-even, Z+1 26Fe isotopes, and not that of the Z-1 24Cr isotopes, where a possible onset of collectivity has been suggested to occur already at N=36

Ecosystem-based management for military training, biodiversity, carbon storage and climate resiliency on a complex coastal land/water-scape

The Defense Coastal/Estuarine Research Program (DCERP) was a 10-year multi-investigator project funded by the Department of Defense to improve understanding of ecosystem processes and their interactions with natural and anthropogenic stressors at the Marine Corps Base Camp Lejeune (MCBCL) located in coastal North Carolina. The project was aimed at facilitating ecosystem-based management (EBM) at the MCBCL and other coastal military installations. Because of its scope, interdisciplinary character, and duration, DCERP embodied many of the opportunities and challenges associated with EBM, including the need for explicit goals, system models, long-term perspectives, systems complexity, change inevitability, consideration of humans as ecosystem components, and program adaptability and accountability. We describe key elements of this program, its contributions to coastal EBM, and its relevance as an exemplar of EBM

Two-neutron and core-excited states in Pb 210: Tracing E3 collectivity and evidence for a new β -decaying isomer in Tl 210

Yrast and near-yrast levels up to an I=17 spin value and a 6-MeV excitation energy have been delineated in the "two-neutron" Pb210 nucleus following deep-inelastic reactions involving Pb208 targets and a number of heavy-ion beams at energies ∼25% above the Coulomb barrier. The level scheme was established on the basis of multifold prompt and delayed coincidence relationships measured with the Gammasphere array. In addition to the previously known states, many new levels were identified. For most of the strongly populated states, spin-parity assignments are proposed on the basis of angular distributions. The reinvestigation of the ν(g9/2)2, 8+ isomeric decay results in the firm identification of the low-energy E2 transitions involved in the 8+→6+→4+ cascade, and in a revised 6+ level half-life of 92(10) ns, nearly a factor of 2 longer than previously measured. Among the newly identified states figure spin I=4-10 levels associated with the νg9/2i11/2 multiplet, as well as yrast states involving νg9/2j15/2, νi11/2j15/2, and ν(j15/2)2 neutron couplings. The highest-spin excitations are understood as 1p-1h core excitations and the yrast population is found to be fragmented to the extent that levels of spin higher than I=17 could not be reached. Four E3 transitions are present in the Pb210 yrast decay; three of these involve the g9/2→j15/2 octupole component, as reflected in the 21(2) and >10 Weisskopf unit enhancements of the B(E3) rates of the first two. The fourth, 16+→13-E3 transition corresponds to the 3- core octupole excitation built on the νi11/2j15/2 state, in analogy to a similar E3 coupling to the νj15/2 level in Pb209. Shell-model calculations performed for two-neutron states and 1p-1h Pb208 core excitations are in good agreement with the data. Evidence was found for the existence of a hitherto unknown high-spin β-decaying isomer in Tl210. Shell-model calculations of the Tl210 levels suggest the possibility of a 11+ long-lived, β-decaying state, and the delayed yields observed in various reactions fit rather well with a Tl210 assignment

Analogous intruder behavior near Ni, Sn, and Pb isotopes

Near shell closures, the presence of unexpected states at low energies provides a critical test of our understanding of the atomic nucleus. New measurements for the N=42 isotones Co2769 and Cu2971, along with recent data and calculations in the Ni isotopes, establish a full set of complementary, deformed, intruder states astride the closed-shell Ni28 isotopes. Nuclei with a one-proton hole or one-proton particle adjacent to Z=28 were populated in β-decay experiments and in multinucleon transfer reactions. A β-decaying isomer, with a 750(250)-ms half-life, has been identified in Co422769. It likely has low spin and accompanies the previously established 7/2- state. Complementary data for the levels of isotonic Cu422971 support the presence of a deformed, ΔJ=1 band built on the proton intruder 7/2- level at 981 keV. These data, together with recent studies of lower-mass Co and Cu isotopes and extensive work near Ni68, support the view that intruder states based on particle-hole excitations accompany all closed proton shells with Z≥28

Doubly magic Pb 208: High-spin states, isomers, and E3 collectivity in the yrast decay

Yrast and near-yrast levels up to spin values in excess of I=30 have been delineated in the doubly magic Pb208 nucleus following deep-inelastic reactions involving Pb208 targets and, mostly, 430-MeV Ca48 and 1440-MeV Pb208 beams. The level scheme was established up to an excitation energy of 16.4 MeV, based on multifold γ-ray coincidence relationships measured with the Gammasphere array. Below the well-known, 0.5-μs 10+ isomer, ten new transitions were added to earlier work. The delineation of the higher parts of the level sequence benefited from analyses involving a number of prompt- and delayed-coincidence conditions. Three new isomeric states were established along the yrast line with Iπ=20- (10 342 keV), 23+ (11 361 keV), and 28- (13 675 keV), and respective half-lives of 22(3), 12.7(2), and 60(6) ns. Gamma transitions were also identified preceding in time the 28- isomer; however, only a few could be placed in the level scheme and no firm spin-parity quantum numbers could be proposed. In contrast, for most states below this 28- isomer, firm spin-parity values were assigned, based on total electron-conversion coefficients, deduced for low-energy (<500keV) transitions from γ-intensity balances, and on measured γ-ray angular distributions. The latter also enabled the quantitative determination of mixing ratios. The transition probabilities extracted for all isomeric transitions in Pb208 have been reviewed and discussed in terms of the intrinsic structure of the initial and final levels involved. Particular emphasis was placed on the many observed E3 transitions as they often exhibit significant enhancements in strength [of the order of tens of Weisskopf units (W.u.)] comparable to the one seen for the neutron j15/2→g9/2 E3 transition in Pb209. In this context, the enhancement of the 725-keV E3 transition (56 W.u.) associated with the decay of the highest-lying 28- isomer observed in this work remains particularly challenging to explain. Large-scale shell-model calculations were performed with two approaches, a first one where the 1, 2, and 3 particle-hole excitations do not mix with one another, and another more complex one, in which such mixing takes place. The calculated levels were compared with the data and a general agreement is observed for most of the Pb208 level scheme. At the highest spins and energies, however, the correspondence between theory and experiment is less satisfactory and the experimental yrast line appears to be more regular than the calculated one. This regularity is notable when the level energies are plotted versus the I(I+1) product and the observed, nearly linear, behavior was considered within a simple "rotational" interpretation. Within this approximate picture, the extracted moment of inertia suggests that only the 76 valence nucleons participate in the "rotation" and that the Sn132 spherical core remains inert

Novel Δj=1 Sequence in Ge 78: Possible Evidence for Triaxiality

A sequence of low-energy levels in Ge327846 has been identified with spins and parity of 2+, 3+, 4+, 5+, and 6+. Decays within this band proceed strictly through ΔJ=1 transitions, unlike similar sequences in neighboring Ge and Se nuclei. Above the 2+ level, members of this sequence do not decay into the ground-state band. Moreover, the energy staggering of this sequence has the phase that would be expected for a γ-rigid structure. The energies and branching ratios of many of the levels are described well by shell-model calculations. However, the calculated reduced transition probabilities for the ΔJ=2 in-band transitions imply that they should have been observed, in contradiction with the experiment. Within the calculations of Davydov, Filippov, and Rostovsky for rigid-triaxial rotors with γ=30°, there are sequences of higher-spin levels connected by strong ΔJ=1 transitions which decay in the same manner as those observed experimentally, yet are calculated at too high an excitation energy

Seniority, collectivity, and B(E2) enhancement in 72Ni

Gamma rays assigned to 2872Ni44 have been identified with Gammasphere in deep-inelastic reactions involving a 450-MeV 76Ge beam and a 198Pt target. Using a combination of spectra produced by double gates on the known 454-, 843-, and 1095-keV members of the ground-state cascade, a coincident line at 199 keV has been identified and is tentatively assigned as the 8+→6 + transition. These γ-ray coincidences have been observed only in prompt events, indicating an 8+ half-life below 20 ns and requiring a large B(E2) enhancement compared to that expected from a seniority scheme. This value is consistent with models showing decay to a seniority ν=4, 6+ level that is depressed by the same two-body interaction responsible for the rather low 1095-keV 21+ energy, as compared to the valence-symmetry counterpart 4494Ru50

Search for intruder states in 68Ni and 67Co

The level schemes of 68Ni and 67Co were extended following 70Zninduced deep-inelastic reactions. No evidence for a previously reported proton intruder 0+ state at 2202 keV in 68Ni was found. In 67Co, two new states at 3216 and 3415 keV have been established; additional states associated with the intruder configuration have yet to be identified