Remarks on the self-shrinking Clifford torus

On the one hand, we prove that the Clifford torus in $\mathbb{C}^2$ is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian $F$-stable and locally area minimising under Hamiltonian variations. On the other hand, we show that the Clifford torus is rigid: it is locally unique as a self-shrinker for mean curvature flow, despite having infinitesimal deformations which do not arise from rigid motions. The proofs rely on analysing higher order phenomena: specifically, showing that the Clifford torus is not a local entropy minimiser even under Hamiltonian variations, and demonstrating that infinitesimal deformations which do not generate rigid motions are genuinely obstructed.Comment: 31 pages, v3: additional details for proof of local uniqueness of the Clifford torus as a self-shrinker provide

SU(2)² -invariant G₂ -instantons

We initiate the systematic study of G₂-instantons with SU(2)² -symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on R⁴ x S³ with its two explicitly known distinct holonomy G₂ metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We alsogive an explicit example of sequences of G₂-instantons where “bubbling” and “removable singularity” phenomena occur in the limit

Measurement of the 18Ne(a,p_0)21Na reaction cross section in the burning energy region for X-ray bursts

The 18Ne(a,p)21Na reaction provides one of the main HCNO-breakout routes into the rp-process in X-ray bursts. The 18Ne(a,p_0)21Na reaction cross section has been determined for the first time in the Gamow energy region for peak temperatures T=2GK by measuring its time-reversal reaction 21Na(p,a)18Ne in inverse kinematics. The astrophysical rate for ground-state to ground-state transitions was found to be a factor of 2 lower than Hauser-Feshbach theoretical predictions. Our reduced rate will affect the physical conditions under which breakout from the HCNO cycles occurs via the 18Ne(a,p)21Na reaction.Comment: 5 pages, 3 figures, accepted for publication on Physical Review Letter

Identification of key astrophysical resonances relevant for the Al26g(p,γ)Si27 reaction in Wolf-Rayet stars, AGB stars, and classical novae

A γ-ray spectroscopy study of Al26g+p resonant states in Si27 is presented. Excitation energies were measured with improved precision and first spin-parity assignments made for excited states in Si27 above the proton threshold. The results indicate the presence of low-lying resonances with lp=0 and lp=2 captures that could strongly influence the Al26g(p,γ)Si27 reaction rate at low stellar temperatures, found in low-mass asymptotic giant branch (AGB), intermediate-mass AGB, super AGB, and Wolf-Rayet stars

Octupole transitions in the 208Pb region

The 208Pb region is characterised by the existence of collective octupole states. Here we populated such states in 208Pb + 208Pb deep-inelastic reactions. γ-ray angular distribution measurements were used to infer the octupole character of several E3 transitions. The octupole character of the 2318 keV 17− → 14+ in 208Pb, 2485 keV 19/2 − → 13/2 + in 207Pb, 2419 keV 15/2 − → 9/2 + in 209Pb and 2465 keV 17/2 + → 11/2 − in 207Tl transitions was demonstrated for the first time. In addition, shell model calculations were performed using two different sets of two-body matrix elements. Their predictions were compared with emphasis on collective octupole states.This work is supported by the Science and Technology Facilities Council (STFC), UK, US Department of Energy, Office of Nuclear Physics, under Contract No. DEAC02-06CH11357 and DE-FG02-94ER40834, NSF grant PHY-1404442

Identification of analog states in the T=1/2 A=27 mirror system from low excitation energies to the region of hydrogen burning in the 26Alg ,m(p,γ)27Si reactions

The reactions 26Alg(p,γ)27Si and 26Alm(p,γ)27Si are important for influencing the galactic abundance of the cosmic γ-ray emitter 26Alg and for the excess abundance of 26Mg found in presolar grains, respectively. Precise excitation energies and spin assignments of states from the ground state to the region of astrophysical interest in 27Si, including the identification and pairing of key astrophysical resonances with analog states in the mirror nucleus 27Al, are reported using γ rays observed in the 12C + 16O fusion reaction. The detailed evolution of Coulomb energy differences between the states in 27Si and 27Al is explored, including the region above the astrophysical reaction thresholds

Analog E1 transitions and isospin mixing

We investigate whether isospin mixing can be determined in a model-independent way from the relative strength of E1 transitions in mirror nuclei. The specific examples considered are the A=31 and A=35 mirror pairs, where a serious discrepancy between the strengths of 7/2--->5/2+ transitions in the respective mirror nuclei has been observed. A theoretical analysis of the problem suggests that it ought to be possible to disentangle the isospin mixing in the initial and final states given sufficient information on experimental matrix elements. With this in mind, we obtain a lifetime for the relevant 7/2- state in 31S using the Doppler-shift attenuation method. We then collate the available information on matrix elements to examine the level of isospin mixing for both A=31 and A=35 mirror pairs

TSR: A storage and cooling ring for HIE-ISOLDE

It is planned to install the heavy-ion, low-energy ring TSR, currently at the Max-Planck-Institute for Nuclear Physics in Heidelberg, at the HIE-ISOLDE facility in CERN, Geneva. Such a facility will provide a capability for experiments with stored, cooled secondary beams that is rich and varied, spanning from studies of nuclear ground-state properties and reaction studies of astrophysical relevance, to investigations with highly-charged ions and pure isomeric beams. In addition to experiments performed using beams recirculating within the ring, the cooled beams can be extracted and exploited by external spectrometers for high-precision measurements. The capabilities of the ring facility as well as some physics cases will be presented, together with a brief report on the status of the project

Decay properties of 22Ne+α^{22}\mathrm{Ne} + \alpha resonances and their impact on ss-process nucleosynthesis

The astrophysical $s$-process is one of the two main processes forming elements heavier than iron. A key outstanding uncertainty surrounding $s$-process nucleosynthesis is the neutron flux generated by the ${}^{22}\mathrm{Ne}(\alpha, n){}^{25}\mathrm{Mg}$ reaction during the He-core and C-shell burning phases of massive stars. This reaction, as well as the competing ${}^{22}\mathrm{Ne}(\alpha, \gamma){}^{26}\mathrm{Mg}$ reaction, is not well constrained in the important temperature regime from ${\sim} 0.2$--$0.4$~GK, owing to uncertainties in the nuclear properties of resonances lying within the Gamow window. To address these uncertainties, we have performed a new measurement of the ${}^{22}\mathrm{Ne}({}^{6}\mathrm{Li}, d){}^{26}\mathrm{Mg}$ reaction in inverse kinematics, detecting the outgoing deuterons and ${}^{25,26}\mathrm{Mg}$ recoils in coincidence. We have established a new $n / \gamma$ decay branching ratio of $1.14(26)$ for the key $E_x = 11.32$ MeV resonance in $^{26}\mathrm{Mg}$, which results in a new $(\alpha, n)$ strength for this resonance of $42(11)~\mu$eV when combined with the well-established $(\alpha, \gamma)$ strength of this resonance. We have also determined new upper limits on the $\alpha$ partial widths of neutron-unbound resonances at $E_x = 11.112,$ $11.163$, $11.169$, and $11.171$ MeV. Monte-Carlo calculations of the stellar ${}^{22}\mathrm{Ne}(\alpha, n){}^{25}\mathrm{Mg}$ and ${}^{22}\mathrm{Ne}(\alpha, \gamma){}^{26}\mathrm{Mg}$ rates, which incorporate these results, indicate that both rates are substantially lower than previously thought in the temperature range from ${\sim} 0.2$--$0.4$~GK.Comment: 17 pages, 4 figures, accepted for publication in Phys. Lett.