Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. 7 Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a 'fragmented' condensate discussed by Nozières and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.One of the most novel aspects of the creation of Bose condensates with neutral atoms in traps is the possibility of observing a bose gas with attractive interactions (negative scattering lengths). The case of 7 Li has been studied both experimentally [1,2] and theoretically. Condensation has been predicted to be stable for a sufficiently small number of particles or sufficiently weak interactions [3,4]. The instability to collapse when these conditions are not obeyed has also been discussed by several authors [5][6][7][8][9].In this Letter we show, using two exactly soluble models, that there may be other possibilities for noncondensed states with attractive interactions. The states are the 'fragmented' condensates discussed by Nozières and Saint James [10] in the context of excitonic bose condensates. The possibility of such states emerges from the realisation [11] that it is the exchange interaction which causes bosons with repulsive interactions to condense into a single one-particle state, if there are several one-particle ground states. Conversely for attractive interactions, the exchange term is negative and may prefer 'fragmented' [10] condensation into more than one state if there is a degeneracy (or perhaps if the interactions are sufficiently strong). Kagan et al. [4] argue that trapped gases with sufficiently large negative scattering lengths are unstable to the formation of clusters using a somewhat different argument, but with the same physical origin.The two models we examine are: particles in a harmonic trap with L quanta of angular momenta with attractive interactions treated as a degenerate perturbation [12]; rotating particles in a harmonic trap interacting with harmonic interactions [13][14][15][16]. (Both of these cases have been of interest for fermions [12,14], where rotation is replaced by a magnetic field and the phenomena are related to the fractional quantum Hall effect.) Rotation is considered in both cases, partly because the non-rotating ground state, in the thermodynamic limit, is trivial in both cases (for different reasons) and partly because the response to rotation is characteristic of superfluidity in the system [17,18].Consider the two-dimensional Hamiltonianin the limit where the dimensionless coupling is weak, |η| ≪ 1, so that the contact interaction can be treated perturbatively. We will now determine the gr...

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We consider a model of N two-dimensional bosons in a harmonic potential with weak repulsive delta-function interactions. We show analytically that, for angular momentum L ≤ N , the elementary symmetric polynomials of particle coordinates measured from the center of mass are exact eigenstates with energy N (N − L/2 − 1). Extensive numerical analysis confirms that these are actually the ground states, but we are currently unable to prove this analytically. The special case L = N can be thought of as the generalisation of the usual superfluid one-vortex state to Bose-Einstein condensates in a trap.

Through ab initio approaches in nuclear theory, we may now seek to quantitatively understand the wealth of nuclear collective phenomena starting from the underlying internucleon interactions. No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, as evidenced by rotational patterns for excitation energies, electromagnetic moments, and electromagnetic transitions. In this review, NCCI calculations of 7-9Be are used to illustrate and explore ab initio rotational structure, and the resulting predictions for rotational band properties are compared with experiment. We highlight the robustness of ab initio rotational predictions across different choices for the internucleon interaction.Comment: 34 pages, 19 figures; to be published in Int. J. Mod. Phys.

We investigate an implication of the most recent observation of a second J π = 2 + state in 12 C, which was measured using the 12 C(γ,α) 8 Be (g.s.) reaction. In addition to the dissociation of 12 C to an α-particle and 8 Be in its ground state, a small fraction of events (2%) were identified as direct decays and decays to excited states in 8 Be. This allowed a limit on the direct 3α partial decay width to be determined as Γ3α < 32(4) keV. Since this 2 + state is predicted by all theoretical models to be a collective excitation of the Hoyle state, the 3α partial width of the Hoyle state is calculable from the ratio of 3α decay penetrabilities of the Hoyle and 2 + states. This was calculated using the semi-classical WKB approach and we deduce a stringent upper limit for the direct decay branching ratio of the Hoyle state of Γ 3α Γ < 5.7 × 10 −6 , over an order of magnitude lower than previously reported. This result places the direct measurement of this rare decay mode beyond current experimental capabilities.

Gamma-Beams at the HIγS facility in the USA and anticipated at the ELI-NP facility, now constructed in Romania, present unique new opportunities to advance research in nuclear astrophysics; not the least of which is resolving open questions in oxygen formation during stellar helium burning via a precise measurement of the 12 C(α, γ) reaction. Time projection chamber (TPC) detectors operating with low pressure gas (as an active target) are ideally suited for such studies. We review the progress of the current research program and plans for the future at the HIγS facility with the optical readout TPC (O-TPC) and the development of an electronic readout TPC for the ELI-NP facility (ELITPC).

Asim (2019). Extracting the spectral signature of alpha-clustering in 44,48,52Ti using the continuous wavelet transform. Physical Review C -Nuclear Physics, 100 (051302).

Background: Near-threshold α-clustered states in light nuclei have been postulated to have a structure consisting of a diffuse gas of α-particles which condense into the 0s orbital. Experimental evidence for such a dramatic phase change in the structure of the nucleus has not yet been observed. Method:To examine signatures of this α-condensation, a compound nucleus reaction using 160, 280, and 400 MeV 16 O beams impinging on a carbon target was used to investigate the 12 C( 16 O, 7α) reaction. This permits a search for near-threshold states in the α-conjugate nuclei up to 24 Mg.Results: Events up to an α-particle multiplicity of 7 were measured and the results were compared to both an Extended Hauser-Feshbach calculation and the Fermi break-up model. The measured multiplicity distribution exceeded that predicted from a sequential decay mechanism and had a better agreement with the multi-particle Fermi break-up model. Examination of how these 7α final states could be reconstructed to form 8 Be and 12 C(0 + 2 ) showed a quantitative difference in which decay modes were dominant compared to the Fermi break-up model. No new states were observed in 16 O, 20 Ne, and 24 Mg due to the effect of the N-α penetrability suppressing the total α-particle dissociation decay mode. Conclusion:The reaction mechanism for a high energy compound nucleus reaction can only be described by a hybrid of sequential decay and multi-particle breakup. Highly α-clustered states were seen which did not originate from simple binary reaction processes. Direct investigations of near-threshold states in N-α systems are inherently impeded by the Coulomb barrier prohibiting the observation of states in the N-α decay channel. No evidence of a highly clustered 15.1 MeV state in 16 O was observed from ( 28 Si , 12 C(0 + 2 )) 16 O(0 + 6 ) when reconstructing the Hoyle state from 3 α-particles. Therefore, no experimental signatures for α-condensation were observed. arXiv:1907.05471v2 [nucl-ex]