Amino­(5-{2-[amino­(iminio)meth­yl]hydrazin-1-yl}-3,5-dimethyl-4,5-dihydro-1H-pyrazol-1-yl)methaniminium dinitrate

The reaction of aqueous solutions of amino­guanidine hydrogennitrate and acetyl­acetone produces the title pyrazole salt, C7H18N8 2+·2NO3 −. The crystal structure is stabilized by a complex N—H⋯O hydrogen-bonding network. The difference in the engagement of the two nitrate anions in hydrogen bonding is reflected in the variation of the corresponding N—O bond lengths

Retrodictively Optimal Localisations in Phase Space

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalised to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a meaurement belongs to the class of generalised Husimi functions most recently discussed by Wuensche and Buzek. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vaccuum state.Comment: 11 pages, 2 figures. AMS Latex. Replaced with published versio

Generalized Husimi Functions: Analyticity and Information Content

The analytic properties of a class of generalized Husimi functions are discussed, with particular reference to the problem of state reconstruction. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vacuum state. The fact that the function is analytic means that perfectly precise knowledge of its values over any small region of phase space provides enough information to reconstruct the density matrix. If, however, one only has imprecise knowledge of its values, then the amplification of statistical errors which occurs when one attempts to carry out the continuation seriously limits the amount of information which can be extracted. To take account of this fact a distinction is made between explicate, or experimentally accessible information, and information which is only present in implicate, experimentally inaccessible form. It is shown that an explicate description of various aspects of the system can be found localised on various 2 real dimensional surfaces in complexified phase space. In particular, the continuation of the function to the purely imaginary part of complexified phase space provides an explicate description of the Wigner function.Comment: 16 pages, 2 figures, AMS-latex. Replaced with published versio

Lifetime measurement of neutron-rich even-even molybdenum isotopes

Background: In the neutron-rich A approximate to 100 mass region, rapid shape changes as a function of nucleon number as well as coexistence of prolate, oblate, and triaxial shapes are predicted by various theoretical models. Lifetime measurements of excited levels in the molybdenum isotopes allow the determination of transitional quadrupole moments, which in turn provides structural information regarding the predicted shape change. Purpose: The present paper reports on the experimental setup, the method that allowed one to measure the lifetimes of excited states in even-even molybdenum isotopes from mass A = 100 up to mass A = 108, and the results that were obtained. Method: The isotopes of interest were populated by secondary knock-out reaction of neutron-rich nuclei separated and identified by the GSI fragment separator at relativistic beam energies and detected by the sensitive PreSPEC-AGATA experimental setup. The latter included the Lund-York-Cologne calorimeter for identification, tracking, and velocity measurement of ejectiles, and AGATA, an array of position sensitive segmented HPGe detectors, used to determine the interaction positions of the gamma ray enabling a precise Doppler correction. The lifetimes were determined with a relativistic version of the Doppler-shift-attenuation method using the systematic shift of the energy after Doppler correction of a gamma-ray transition with a known energy. This relativistic Doppler-shift-attenuation method allowed the determination of mean lifetimes from 2 to 250 ps. Results: Even-even molybdenum isotopes from mass A = 100 to A = 108 were studied. The decays of the low-lying states in the ground-state band were observed. In particular, two mean lifetimes were measured for the first time: tau = 29.7(-9.1)(+11.3) ps for the 4(+) state of Mo-108 and tau = 3.2(-0.7)(+ 0.7) ps for the 6(+) state of Mo-102. Conclusions: The reduced transition strengths B(E2), calculated from lifetimes measured in this experiment, compared to beyond-mean-field calculations, indicate a gradual shape transition in the chain of molybdenum isotopes when going from A = 100 to A = 108 with a maximum reached at N = 64. The transition probabilities decrease for Mo-108 which may be related to its well-pronounced triaxial shape indicated by the calculations

Study of Isomeric States in ^{198,200,202,206}Pb and ²⁰⁶Hg Populated in Fragmentation Reactions

Isomeric states in isotopes in the vicinity of doubly-magic 208Pb were populated following reactions of a relativistic 208Pb primary beam impinging on a 9Be fragmentation target. Secondary beams of 198;200;202;206Pb and 206Hg were isotopically separated and implanted in a passive stopper positioned in the focal plane of the GSI Fragment Separator. Delayed γ rays were detected with the Advanced GAmma Tracking Array (AGATA). Decay schemes were re-evaluated and interpreted with shell-model calculations. The momentum-dependent population of isomeric states in the two-nucleon hole nuclei 206Pb/206Hg was found to differ from the population of multi neutron-hole isomeric states in 198;200;202Pb

Study of isomeric states in 198,200,202,206 Pb and 206 Hg populated in fragmentation reactions

Isomeric states in isotopes in the vicinity of doubly-magic 208 Pb were populated following reactions of a relativistic 208 Pb primary beam impinging on a 9 Be fragmentation target. Secondary beams of 198,200,202,206 Pb and 206 Hg were isotopically separated and implanted in a passive stopper positioned in the focal plane of the GSI Fragment Separator. Delayed γ rays were detected with the Advanced Gamma Tracking Array (AGATA). Decay schemes were re-evaluated and interpreted with shell-model calculations. The momentum-dependent population of isomeric states in the two-nucleon hole nuclei 206 Pb/ 206 Hg was found to differ from the population of multi neutron-hole isomeric states in 198,200,202 Pb

Quadrupole and octupole collectivity in the semi-magic nucleus 80206Hg126

The first low-energy Coulomb-excitation measurement of the radioactive, semi-magic, two proton-hole nucleus 206Hg, was performed at CERN's recently-commissioned HIE-ISOLDE facility. Two γ rays depopulating low-lying states in 206Hg were observed. From the data, a reduced transition strength B(E2;21+→01+)=4.4(6) W.u. was determined, the first such value for an N=126 nucleus south of 208Pb, which is found to be slightly lower than that predicted by shell-model calculations. In addition, a collective octupole state was identified at an excitation energy of 2705 keV, for which a reduced B(E3) transition probability of 30−13+10 W.u. was extracted. These results are crucial for understanding both quadrupole and octupole collectivity in the vicinity of the heaviest doubly-magic nucleus 208Pb, and for benchmarking a number of theoretical approaches in this key region. This is of particular importance given the paucity of data on transition strengths in this region, which could be used, in principle, to test calculations relevant to the astrophysical r-process