Moment bounds for the Smoluchowski equation and their consequences

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a \in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T]) for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass.Comment: 30 page

Low-energy Coulomb excitation of 62^{62}Fe and 62^{62}Mn following in-beam decay of 62^{62}Mn

Sub-barrier Coulomb-excitation was performed on a mixed beam of $^{62}$Mn and $^{62}$Fe, following in-trap $\beta^{-}$ decay of $^{62}$Mn at REX-ISOLDE, CERN. The trapping and charge breeding times were varied in order to alter the composition of the beam, which was measured by means of an ionisation chamber at the zero-angle position of the Miniball array. A new transition was observed at 418~keV, which has been tentatively associated to a $(2^{+},3^{+})\rightarrow1^{+}_{g.s.}$ transition. This fixes the relative positions of the $\beta$-decaying $4^{+}$ and $1^{+}$ states in $^{62}$Mn for the first time. Population of the $2^{+}_{1}$ state was observed in $^{62}$Fe and the cross-section determined by normalisation to the $^{109}$Ag target excitation, confirming the $B(E2)$ value measured in recoil-distance lifetime experiments.Comment: 9 pages, 10 figure

Coulomb excitation of 73Ga

The B(E2; Ii -> If) values for transitions in 71Ga and 73Ga were deduced from a Coulomb excitation experiment at the safe energy of 2.95 MeV/nucleon using post-accelerated beams of 71,73Ga at the REX-ISOLDE on-line isotope mass separator facility. The emitted gamma rays were detected by the MINIBALL-detector array and B(E2; Ii->If) values were obtained from the yields normalized to the known strength of the 2+ -> 0+ transition in the 120Sn target. The comparison of these new results with the data of less neutron-rich gallium isotopes shows a shift of the E2 collectivity towards lower excitation energy when adding neutrons beyond N = 40. This supports conclusions from previous studies of the gallium isotopes which indicated a structural change in this isotopical chain between N = 40 and N = 42. Combined with recent measurements from collinear laser spectroscopy showing a 1/2- spin and parity for the ground state, the extracted results revealed evidence for a 1/2-; 3/2- doublet near the ground state in 73 31Ga42 differing by at most 0.8 keV in energy

Electric quadrupole moments of the 21+_{1}^{+} states in 100,102,104^{100,102,104}Cd

Using the REX-ISOLDE facility at CERN the Coulomb excitation cross sections for the 0gs+→21+ transition in the β-unstable isotopes 100,102,104Cd have been measured for the first time. Two different targets were used, which allows for the first extraction of the static electric quadrupole moments Q(21+) in 102,104Cd. In addition to the B(E2) values in 102,104Cd, a first experimental limit for the B(E2) value in 100Cd is presented. The data was analyzed using the maximum likelihood method. The provided probability distributions impose a test for theoretical predictions of the static and dynamic moments. The data are interpreted within the shell-model using realistic matrix elements obtained from a G-matrix renormalized CD-Bonn interaction. In view of recent results for the light Sn isotopes the data are discussed in the context of a renormalization of the neutron effective charge. This study is the first to use the reorientation effect for post-accelerated short-lived radioactive isotopes to simultaneously determine the B(E2) and the Q(21+) values

Collectivity in Pb-196,Pb-198 isotopes probed in Coulomb-excitation experiments at REX-ISOLDE

The neutron-deficient Pb-196,Pb-198 isotopes have been studied in Coulomb-excitation experiments employing the Miniball gamma-ray spectrometer and radioactive ion beams from the REX-ISOLDE post-accelerator at CERN. The reduced transition probabilities of the first excited 2(+) states in Pb-196 and Pb-198 nuclei have been measured for the first time. Values of B (E2) = 18.2(-4.1)(+4.8) W. u. and B (E2) = 13.1(-3.5)(+4.9) W. u., were obtained, respectively. The experiment sheds light on the development of collectivity when moving from the regime governed by the generalised seniority scheme to a region, where intruding structures, associated with different deformed shapes, start to come down in energy and approach the spherical ground state.Peer reviewe

Coulomb excitation of 222Rn

The nature of quadrupole and octupole collectivity in 222Rn was investigated by determining the electricquadrupole (E2) and octupole (E3) matrix elements using subbarrier, multistep Coulomb excitation. The radioactive 222Rn beam, accelerated to 4.23 MeV/u, was provided by the HIE-ISOLDE facility at CERN. Data were collected in the Miniball gamma -ray spectrometer following the bombardment of two targets, 120Sn and 60Ni. Transition E2 matrix elements within the ground-state and octupole bands were measured up to 10 h over bar and the results were consistent with a constant intrinsic electric-quadrupole moment, 518(11) e fm2. The values of the intrinsic electric-octupole moment for the 0+ -> 3- and 2+ -> 5- transitions were found to be respectively -210 e fm3 and 2300+300-500 e fm3 while a smaller value, 1200+500-900 e fm3, was found for the 2+ -> 1- transition. In addition, four excited non-yrast states were identified in this work via gamma -gamma coincidences.Peer reviewe

The observation of vibrating pear-shapes in radon nuclei (vol 10, 2473, 2019)

An amendment to this paper has been published and can be accessed via a link at the top of the paper